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Simulating surface water and groundwater flow dynamics in tile-drained catchments Thèse Guillaume De Schepper Doctorat interuniversitaire en Sciences de la Terre Philosophiæ doctor (Ph.D.) Québec, Canada © Guillaume De Schepper, 2015

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Page 1: Simulating surface water and groundwater fl ow dynamics in ...nitrat.dk/xpdf/phd-thesis-guillaume-de-schepper_small.pdf · Simulating surface water and groundwater fl ow dynamics

Simulating surface water and groundwaterflow dynamics in tile-drained catchments

Thèse

Guillaume De Schepper

Doctorat interuniversitaire en Sciences de la TerrePhilosophiæ doctor (Ph.D.)

Québec, Canada

© Guillaume De Schepper, 2015

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Résumé

Pratique agricole répandue dans les champs sujets à l’accumulation d’eau en surface, le

drainage souterrain améliore la productivité des cultures et réduit les risques de stagnation

d’eau. La contribution significative du drainage sur les bilans d’eau à l’échelle de bassins

versants, et sur les problèmes de contamination dus à l’épandage d’engrais et de fertilisant, a

régulièrement été soulignée. Les écoulements d’eau souterraine associés au drainage étant sou-

vent inconnus, leur représentation par modélisation numérique reste un défi majeur. Avant de

considérer le transport d’espèces chimiques ou de sédiments, il est essentiel de simuler correcte-

ment les écoulements d’eau souterraine en milieu drainé. Dans cette perspective, le modèle

HydroGeoSphere a été appliqué à deux bassins versants agricoles drainés du Danemark.

Un modèle de référence a été développé à l’échelle d’une parcelle dans le bassin versant de

Lillebæk pour tester une série de concepts de drainage dans une zone drainée de 3.5 ha. Le

but était de définir une méthode de modélisation adaptée aux réseaux de drainage complexes

à grande échelle. Les simulations ont indiqué qu’une simplification du réseau de drainage

ou que l’utilisation d’un milieu équivalent sont donc des options appropriées pour éviter les

maillages hautement discrétisés. Le calage des modèles reste cependant nécessaire.

Afin de simuler les variations saisonnières des écoulements de drainage, un modèle a ensuite

été créé à l’échelle du bassin versant de Fensholt, couvrant 6 km2 et comprenant deux réseaux

de drainage complexes. Ces derniers ont été simplifiés en gardant les drains collecteurs princi-

paux, comme suggéré par l’étude de Lillebæk. Un calage du modèle par rapport aux débits de

drainage a été réalisé : les dynamiques d’écoulement ont été correctement simulées, avec une

faible erreur de volumes cumulatifs drainés par rapport aux observations. Le cas de Fensholt a

permis de valider les conclusions des tests de Lillebæk, ces résultats ouvrant des perspectives

de modélisation du drainage lié à des questions de transport.

iii

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Abstract

Tile drainage is a common agricultural management practice in plots prone to ponding issues.

Drainage enhances crop productivity and reduces waterlogging risks. Studies over the last

few decades have highlighted the significant contribution of subsurface drainage to catchments

water balance and contamination issues related to manure or fertilizer application at the soil

surface. Groundwater flow patterns associated with drainage are often unknown and their

representation in numerical models, although powerful analysis tools, is still a major challenge.

Before considering chemical species or sediment transport, an accurate water flow simulation

is essential. The integrated fully-coupled hydrological HydroGeoSphere code was applied to

two highly tile-drained agricultural catchments of Denmark (Lillebæk and Fensholt) in the

present work.

A first model was developed at the field scale from the Lillebæk catchment. A reference

model was set and various drainage concepts and boundary conditions were tested in a 3.5

ha tile-drained area to find a suitable option in terms of model performance and computing

time for larger scale modeling of complex drainage networks. Simulations suggested that a

simplification of the geometry of the drainage network or using an equivalent-medium layer

are suitable options for avoiding highly discretized meshes, but further model calibration is

required.

A catchment scale model was subsequently built in Fensholt, covering 6 km2 and including two

complex drainage networks. The aim was to perform a year-round simulation accounting for

variations in seasonal drainage flow. Both networks were simplified with the main collecting

drains kept in the model, as suggested by the Lillebæk study. Calibration against hourly

measured drainage discharge data was performed resulting in a good model performance.

Drainage flow and flow dynamics were accurately simulated, with low cumulative error in

drainage volume. The Fensholt case validated the Lillebæk test conclusions, allowing for

further drainage modeling linked with transport issues.

v

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Contents

Résumé iii

Abstract v

Contents vi

List of Figures viii

List of Tables ix

Acknowledgments xiii

Preface xv

1 Introduction 1

1.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Drainage definition and classification . . . . . . . . . . . . . . . . . . 41.2.2 Use of tile drainage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.3 Hydrology of drained areas . . . . . . . . . . . . . . . . . . . . . . . 81.2.4 Tile drainage modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Study sites 21

2.1 Lillebæk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2 Norsminde and Fensholt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Numerical model 27

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Governing flow equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.1 Subsurface flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Surface flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.3 Drainage flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2.4 Coupling water flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2.5 Interception and evapotranspiration . . . . . . . . . . . . . . . . . . 31

3.3 Discrete drains vs. Seepage nodes . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 Steady-state simulations . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Transient simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 42

vi

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4 Simulating coupled surface and subsurface water flow in a tile-drainedagricultural catchment 45Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2.1 Study area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.2 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2.3 Conceptual model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.2.4 Reference model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.5 Test models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.1 Reference model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.2 Test models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.3.3 Computational performance . . . . . . . . . . . . . . . . . . . . . . . 78

4.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5 Seasonal variations simulation of local scale tile drainage discharge inan agricultural catchment 83Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.1 Site description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2.2 Numerical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.2.3 Model conceptualization . . . . . . . . . . . . . . . . . . . . . . . . . 925.2.4 Heterogeneous vs. homogeneous models . . . . . . . . . . . . . . . . 1005.2.5 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.3.1 Water balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.3.2 Drainage processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.3.3 Drain flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.3.4 Hydraulic heads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1185.4.1 HydroGeoSphere model performance . . . . . . . . . . . . . . . . . . 1185.4.2 Drainage conceptualization . . . . . . . . . . . . . . . . . . . . . . . 1195.4.3 Comparison of model codes (HydroGeoSphere vs. MIKE SHE) . . . 121

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6 Conclusions and perspectives 125

Bibliography 129

vii

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List of Figures

1.1 Classification of agricultural drainage system types . . . . . . . . . . . . . . . . 51.2 Conventional vs. controlled subsurface drainage systems . . . . . . . . . . . . . 91.3 Flow paths in a typical glacial till catchment of Denmark . . . . . . . . . . . . 12

2.1 Location of the Lillebæk and Fensholt catchments . . . . . . . . . . . . . . . . 222.2 Geological map of Denmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.3 Lillebæk catchment topography . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Topography in the Fensholt and Norsminde catchments . . . . . . . . . . . . . 26

3.1 Simulation domain of the Fipps et al. (1986) verification example . . . . . . . . 353.2 Verification example: vertical pressure head profiles of numerical and analytical

solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Verification example: hydraulic head distribution in the yz plane . . . . . . . . 383.4 Verification example: hydraulic head distribution in 3D . . . . . . . . . . . . . 393.5 Verification example: hydraulic head in 3D and water flow pathways . . . . . . 403.6 Verification example: discrete drain and seepage nodes hydrographs of the

transient simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1 Location of the Lillebæk catchment and modeling area . . . . . . . . . . . . . . 544.2 2D meshes used for the Lillebæk reference and test simulations . . . . . . . . . 614.3 Lillebæk reference model hydrographs . . . . . . . . . . . . . . . . . . . . . . . 684.4 Lillebæk reference model saturation distribution in the clayey till . . . . . . . . 694.5 Water table elevation in the Lillebæk reference and Test 2 model . . . . . . . . 704.6 Drainage flow hydrographs of the Lillebæk test models . . . . . . . . . . . . . . 754.7 Drainage flow hydrograph with daily precipitation applied in Lillebæk . . . . . 77

5.1 Location of the Fensholt and Norsminde catchments . . . . . . . . . . . . . . . 915.2 Fensholt 2D mesh with refined nodes highlighted . . . . . . . . . . . . . . . . . 945.3 Geological units of the Fensholt heterogeneous model . . . . . . . . . . . . . . . 955.4 Cumulative corrected precipitation, corrected potential evapotranspiration,

simulated evapotranspiration and simulated canopy interception in Fensholt . . 1035.5 Observed and simulated drainage hydrographs in Fensholt with HydroGeoSphere 1065.6 Pressure head distribution and depth to water table in AreaA and AreaB . . . 1075.7 Observed and simulated cumulative drain flow volumes in Fensholt . . . . . . . 1095.8 Hydrographs produced by HydroGeoSphere and MIKE SHE for Fensholt . . . 1135.9 Observed and simulated hydraulic head in piezometers of AreaA in Fensholt . . 1165.10 Observed and simulated hydraulic head in piezometers of AreaB in Fensholt . . 117

viii

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List of Tables

1.1 Subsurface drainage indirect effects on soils, streams or plants . . . . . . . . . . 121.2 Non exhaustive list of models suitable for tile drainage modeling . . . . . . . . 19

3.1 Verification example: pressure head values along the x = 15 m vertical profile . 373.2 Verification example: computational times and drainage volumes of the discrete

drain and seepage node simulations . . . . . . . . . . . . . . . . . . . . . . . . . 413.3 Verification example: flux rate values compared to discrete drain and seepage

nodes discharge rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1 Hydraulic properties of the Lillebæk reference model . . . . . . . . . . . . . . . 594.2 Lillebæk simulations convergence criteria . . . . . . . . . . . . . . . . . . . . . 604.3 List of Lillebæk simulations performed and their properties . . . . . . . . . . . 624.4 Hydraulic properties of the Lillebæk equivalent medium test . . . . . . . . . . . 634.5 Hydraulic properties for the Lillebæk dual-permeability test . . . . . . . . . . . 644.6 Drainage and overland flow rates, and groundwater head values in Lillebæk . . 694.7 Water balance values of the Lillebæk simulations . . . . . . . . . . . . . . . . . 714.8 Mesh specification and computational times for the Lillebæk simulations . . . . 77

5.1 Overland flow properties of the Fensholt model . . . . . . . . . . . . . . . . . . 925.2 Hydraulic properties of the hydrofacies from the Fensholt heterogeneous geo-

logical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.3 Hydraulic properties of the topsoil units from the Fensholt model . . . . . . . . 975.4 Overland flow properties of the Fensholt model . . . . . . . . . . . . . . . . . . 995.5 Performance criteria for measuring the Fensholt model efficiency . . . . . . . . 1025.6 Model performance criteria calculated over the calibration period in Fensholt . 111

ix

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Je vais par les sentiers

Par les sentiers et sur les routes,

Par delà la mer et plus loin, plus

loin encore, (...)

Devant moi s’avancent les

Souffles des Aïeux.

Birago Diop, Viatique

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Acknowledgments

My special thanks go to my supervisor, Prof. René Therrien, for giving me the opportunity

to step into the HydroGeoSphere world through this PhD work. The fulfillment of this work

was made possible thanks to his guidance and wise advice. While giving my models a trained

eye, he has kept me on track throughout my labor. And by his flexibility, he gave me room

for maneuver that has led me to interesting modeling challenges. I’m also grateful to René

for giving me the chance to present our work at various international conferences.

I would like to gratefully thank Prof. Jens Christian Refsgaard, of the Geological Survey of

Denmark and Greenland (GEUS), who has implemented and lead the NiCA Research Project,

of which this thesis is part. We have had many valuable and fruitful discussions that were

essential for the progress of my work. Our successful collaboration is due to his formidable

knowledge and input on concepts we have developed for the Lillebæk and Fensholt models. I

am also thankful to the occasion he gave me to join his friendly research team in Copenhagen

for half a year.

From the Department of Hydrology at GEUS, my gratefulness goes especially to Anne Lausten

Hansen for our Lillebæk collaboration and her helpful comments, data provided and warm

welcome when I was there. She has always had a full involvement when answering my ques-

tions. I remember my first steps in Copenhagen on a foggy Sunday morning with Anne and

Britt Stenhøj Baun Christensen, who very kindly took me on a discovery walk through the

city. I also deeply thank Xin He for his contribution, data and insightful comments during

our Fensholt collaboration. I thank Lisbeth Flindt Jørgensen who perfectly organized our

meetings in Denmark. I would also like to thank all the other members of this department

for welcoming me as one of them. I would like to underline my gratitude to Charlotte Kjær-

gaard and Bo Vangsø Iversen (Department of Agroecology, Aarhus University) for their data

provided and details given about Fensholt.

Accurate runs of my models have been ensured by high quality meshes created by means of

powerful scripts from Pierre Therrien, teaching and research coordinator at Université Laval.

He has performed a considerable amount of work in the shadow of Master and PhD students

while being available when the need was felt. He has contributed in many ways to our success

and I am thankful to him for that.

xiii

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As Pierre has played an important role for me, so have colleagues and friends from the Depart-

ment of Geology and Geological Engineering by continuously exchanging our experiences with

HydroGeoSphere and sticking together in hard modeling times. Nelly Montcoudiol (geanre),

Fabien Cochand (tu chiales), Tobias Graf (c’est l’optimal) and Jalil Hassaoui (on fait les

choses) have been the motivating core from which advice, help and support have originated,

together with lots of fun and relaxing times. Some visiting professors and researchers have

helped me with their knowledge and input; I particularly think of Prof. Philip Brunner (Uni-

versité de Neuchâtel, Switzerland), Tanguy Robert (AQUALE, Belgium), Samuel Wildemeer-

sch (SPAQuE, Belgium), Oularé Sékouba (Université Félix Houphouët-Boigny, Ivory Coast),

Christian Möck (Eawag, Switzerland) and Carlos Guevara (Leibniz Universität Hannover,

Germany). Life at the department was made pleasant by their members with whom I enjoyed

having discussions and sharing time. I especially thank my former officemates, that have not

been named yet: Elham, Debora, Antoine, Arnaud, Donald, Jia, Karl, Nicolas and Olivier.

I thank Rob McLaren (Golder Associates Ltd., ON), Young-Jin Park and Hyoun-Tae Hwang

(Aquanty Inc., ON) for their help, tips and sharing of their deep knowledge of HydroGeo-

Sphere.

I give special regards to Prof. Philippe Renard (Université de Neuchâtel) who incited me to

jump into this doctorate when finishing my masters under his supervision. His passion and

involvement for the profession made me want to carry on in the research field. I also thank

Andrea Borghi (Bundesamt für Landestopografie swisstopo, Switzerland), who completed his

PhD in Neuchâtel under the supervision of Philippe Renard. I did learn a lot from you,

especially how to keep motivated during a doctorate.

I would like to thank my family for their unwavering support since my very first day in

the geology field. After putting a mountain range between us, this time was an ocean: my

beloved Belgium is far from here, but their encouragement and strength always guided me

throughout my work. I was also blessed with support originating from relatives in France

and Switzerland. Last but not least, I deeply thank Virginie for her support and trust along

the years, dispelling any doubt about the achievement of this work regardless of the ups and

downs.

To all the friends who have crossed my path in Belgium, Switzerland, Canada, Denmark and

Serbia to get to this point: thank you.

xiv

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Preface

The work presented in this thesis was fulfilled at the Department of Geology and Geological

Engineering at Université Laval (Quebec City, Canada) under the supervision of Professor

René Therrien. It was carried out in collaboration with the Department of Hydrology at

the Geological Survey of Denmark and Greenland (GEUS) (Copenhagen, Denmark). Half a

year of external research stay was spent at the Department of Hydrology at GEUS under the

supervision of Prof. Jens Christian Refsgaard.

This work was financially supported by the Danish Strategic Research Council through the

NiCA Research Project’s Program Commission on Sustainable Energy and Environment un-

der contract No. DSF 09-067260.

The first chapter of this manuscript provides an overview of the present PhD research back-

ground, state-of-the-art knowledge of the use of drainage systems and tile drainage modeling,

and the research objectives. Following this, chapter 2 briefly describes both sites studied in

this work. In chapter 3, governing flow equations used in models developed for both study

sites are defined. In addition, a simple tile drainage verification example was run to document

the differences observed in simulated water flow from a discrete drain and from drainage sink

nodes. Chapter 4 is a research paper published in Journal of Hydrology (De Schepper et al.,

2015) entitled «Simulating coupled surface and subsurface water flow in a tile-drained agri-

cultural catchment ». In this article, various concepts were tested for describing tile drainage

in numerical models. Chapter 5 is a paper that was submitted to Water Resources Research

on October 16, 2015. Its title is «Seasonal variations simulation of local scale tile drainage

discharge in an agricultural catchment ». Here, tile drainage flow was run over a year-round

simulation with two complex drainage networks. The last chapter concludes this work, dis-

cusses perspectives and provides insight on potential future research in the field of tile drainage

modeling.

xv

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Chapter 1

Introduction

1.1 Background and motivation

Agricultural production needs have lead to widespread use of tile drainage under humid

climatic conditions over the last few decades. Tile drainage is used worldwide in agricultural

lands for reducing flooding risks, for removing unwanted excess water from the top soil, for

enhancing crop yields, for land reclamation to expand crop areas and, in some cases, for

reducing or controlling the salinity of soils (Hoffman and Durnford, 1999). Tile drains are

usually found in low permeability clayey to silty soils. Such pipes buried underground act as

shortcuts in the water cycle: water is captured, channeled and discharged to local streams in

extremely short times, compared to its natural residence time in soils. In addition, macropores

or fractures generate even faster water flow as they are preferential flow pathways. This often

comes with nutrient and pesticide transport through the soils to the drains (Šimůnek et al.,

2003). In the drains, soil particle transport occurs in addition to solute transport, which

regularly leads to clogging issues (e.g. Chapman et al., 2001).

Nutrient contamination of groundwater and surface water is a widely known threat to water

resources. The presence of such compounds in discharge waters has also been shown to lead

to significant eutrophication of surface water, accompanied by deterioration of water quality,

and what is referred to as dead zones due to algal blooms in estuaries and coastal waters

(Blann et al., 2009). This promotes algal productivity leading to depletion of oxygen in

waters (Grant and Blicher-Mathiesen, 2004), all of which causes significant changes to local

conditions. The intensification of agricultural practices in Europe since the late 1970’s goes

1

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hand in hand with an increase in nitrate concentrations in groundwater and surface water

bodies (Iversen et al., 1998). In Denmark, tile drainage is commonly used in agricultural areas

(Olesen, 2009); related nutrient contamination issues are thus of major concern (Kronvang

et al., 1996).

Particular attention is paid to these issues within the NiCA Project1, of which the present

PhD work is part. The NiCA Project focuses on nitrate reduction within geologically hetero-

geneous catchments in Denmark. The main aim of the project is to use and develop tools for

estimating nitrate reduction rates in the saturated and unsaturated zones under agricultural

crops. The starting hypothesis of the project is that a good prediction of nitrate reduction

in the soil relies on an appropriate characterization of geological heterogeneity. The setting-

up of the NiCA Project has been done in response to the Water Framework Directive of

the European Parliament and the European Council. By means of this directive, published

and adopted in December 2000, the European Commission expects the European Member

States to implement a water management strategy and to reach a good quality for their water

bodies (groundwater, surface and coastal waters). In the NiCA case, the Nitrates Directive

91/676/EEC (European Commission, 2008) is the most important one. It requires, among

others, reducing the impact of nutrient loads from agricultural crops on groundwater, surface

and coastal waters. A report published by the Geological Survey of Denmark and Greenland

(GEUS) (Ernstsen et al., 2006) presents a national scale nitrate reduction map and shows

that two-thirds of the nitrate leached from the soil surface is being reduced before reaching

the coastal waters. It is known that nitrate reduction processes may occur in the saturated

zone of clayey tills in Denmark (e.g. Hansen et al., 2008), and that these processes are af-

fected by geological heterogeneities at small scales. In addition to this nitrate reduction map,

a tool has recently been developed for estimating nitrogen risk in Danish catchments based

on nitrogen leaching and retention data (Blicher-Mathiesen et al., 2014). Even though such

tools are of prime importance, they are not precise enough to distinguish vulnerable areas

at catchment or field scales. One of the main objectives of the NiCA project is therefore to

develop methods and knowledge at smaller scales. A comprehensive description of this project

has been provided by Refsgaard et al. (2014).

Numerous studies have shown the significant impact of subsurface drainage on groundwater

1Official website: http://www.nitrat.dk

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and surface water flow patterns by mean of numerical models at the field scale to catchment

scale (e.g. Rozemeijer et al., 2010). Such studies usually present results of groundwater flow

models only (Purkey et al., 2004), coupled modeling approaches of a groundwater flow and

overland water flow model (Kim and Delleur, 1997; Maalim and Melesse, 2013; Hansen et al.,

2013), or even groundwater and drainage water flow models coupled by means of an external

module (Henine et al., 2014). Water exchange processes occur between the subsurface body,

the surface domain and drainage pipes. Yet few models have been developed with a fully

coupled scheme, having the ability of simulating tile drainage flow in a variably saturated

subsurface domain fully coupled to the surface domain, even if they are promising tools

for understanding and quantifying tile-drained catchments dynamics. In the framework of

the NiCA project, such modeling capabilities were needed and the HydroGeoSphere code

(Therrien et al., 2010) was chosen for exploring its potential in the project context.

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1.2 Literature review

1.2.1 Drainage definition and classification

Tile drainage is one of the various techniques used in agricultural drainage systems. The

intended effect of using such systems is to improve water runoff and to avoid ponding at the

land surface. Drainage systems are artificial and installed for ensuring agricultural production

needs. They can be installed at the land surface (surface drainage systems) or underground

(subsurface drainage systems) (Figure 1.1). In both cases, they consist of two main compo-

nents (Oosterbaan, 1994): a field drainage system, which aims at lowering the water table in

the field, and a main drainage system, also known as a collector system, used for conducting

water out of the field to an outlet.

Surface field drainage systems are divided into regular and checked systems, in both of which

water flow is driven by gravity. Surface regular drainage systems are generally made of ditches

or trenches used in bedded land (flat) or graded land (sloping) for drying the land surface.

Surface checked systems are used in basins and terraces having water flow control bunds that

are typically found in submerged fields (e.g. rice-growing terraces).

Subsurface field drainage systems are differentiated into conventional and controlled systems

(see Figure 1.2). Conventional drainage systems are composed of a simple drainage network

without any complementary equipment. Controlled drainage is a drainage technique in which

the network has additional equipment (pit, tank, flashboard riser, drop log, etc.) in order to

control drainage flow (Evans et al., 1991, 1995). Both systems drain water by gravity but, by

using controlled drainage, the global drainage outflow of a field may be reduced by up to 30

% in comparison to conventional drainage. In the case of controlled systems, drainage may

be performed by pumping water in a series of vertical wells.

As they are located at the surface, surface drainage systems allow for faster water flow than

subsurface drains, which have thus slower response to rainfall events (Robinson, 1990). In

either case, water is routed by collector drains to an outlet that is an open-ditch surrounding

fields or a local stream. Before reaching the outlet, collector drains direct water to disposal

drains (surface drainage systems) or to deep main drains (subsurface drains), and then to the

outlet or to disposal drains. Disposal drains act here as temporary storage drains.

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One should note here that natural drainage systems exist too, such as caves, root holes,

fractures, etc. Drains are also installed in other hydrologic environments for avoiding floods,

such as in urban areas (Maršálek and Sztruhár, 1994) or even sports fields (Adams, 1986).

Outlet

FIELD DRAINAGE

SYSTEMS

(I )NTERNAL

Graded land

Bedded land

Bunded basins

Bunded terraces

Subsurface drains(tiles, pipes, moles,ditches, channels)

Subsoiling(deep ploughing)

Subsurface drains(gravity flow with

controlledstructures)

Well drainage(pumped)

Deep main drains

Disposal drains

MAIN DRAINAGE

SYSTEMS

(E )XTERNAL

Surface drainagesystems

(by gravity)

Subsurfacedrainage systems

(by gravity orpumped)

Conventionalsystems

Deep collectorsusing pipes or ditches

(for subsurface drainage)

Shallow collectorsusing channels or ditches

(for surface drainage)

Bedded land

Regularsystems

Checkedsystems

Controlledsystems

Figure 1.1: Classification of agricultural drainage system types. Black solid lines depict theclassification in itself, while blue arrows indicate a transfer of water from one drainage networkcomponent to another. Modified from Oosterbaan (1994).

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1.2.2 Use of tile drainage

Tile drainage systems are generally found in the Northern Hemisphere, mostly in North Amer-

ica and Europe, but they are also used in other regions such as China, India or Egypt (Nijland

et al., 2005). The northern European countries usually have a large proportion of subsurface

drained agricultural lands, with the Netherlands having the highest percentage of drained

fields in the region (about 65 % of the total fields) (Robinson and Rycroft, 1999), whereas

southern European countries seem to have less than 10 to 20 % of the cropland equipped

with subsurface drainage systems. This marked difference highlights the presence of glacial

till deposits in the topmost soils of northern Europe which, combined with spatial climatic

variations (rain, temperature and evaporation distribution), cause longer waterlogging pe-

riods (Green, 1980). An exception to this statement is Hungary with 73 % of agricultural

fields that are drained (Goudie, 2013). This country is part of the Pannonian Basin that is

dominated by fine lake and deltaic deposits (Juhász et al., 1997).

Besides its application to arable land, tile drainage is also used in peatlands found in northern

Europe and North America (Baldock et al., 1984; Hillman, 1992). By lowering the water table,

subsurface drainage enhances soil aeration in peat soils, which is essential for the forestry

industry in boreal regions of Fennoscandian and North-American countries (Rothwell et al.,

1996). Extraction of peat is another application linked with peatlands drainage. Tile drainage

is also commonly associated with irrigation systems for proper water management in arid and

semi-arid regions (e.g. Mohanty et al., 1998). In such regions, where high evapotranspiration

rates are observed, controlled drainage is preferred to conventional drainage so that the water

table level is kept at a desired level allowing sufficient soil moisture content for plant uptake

in the root zone (Ayars et al., 2006). Another purpose of subsurface drainage in arid areas is

to control the salinity of soils (Skaggs et al., 1994). As evapotranspiration is high, residual

salt precipitates at the soil surface or in the root zone. Infiltrating water through the soil

surface and leaching through the root zone may thus dissolve salt and transport it in drainage

pipes, resulting in contamination of surface water (Tedeschi et al., 2001).

In North America, it is estimated that about 43 million ha of land in the United States,

mostly in the Corn Belt region (Zucker and Brown, 1998), and 8 million ha in Canada are

tile-drained (Skaggs et al., 1994; Madramootoo et al., 2007). Tile drainage is a common

practice in forested peatlands in Alberta (Rothwell et al., 1996) and in Ontario (Payandeh,

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1973) to ensure tree growth. Subsurface drainage is also encountered in agricultural fields

of eastern Canadian provinces (Madramootoo et al., 2007), mainly in Ontario (Whiteley and

Ghate, 1979; Irwin and Bryant, 1986) and Québec (Natho-Jina et al., 1987; Simard et al.,

1995; Elmi et al., 2004).

In some cases, tile drainage likely induces enhanced migration of certain chemical species

and contamination of downstream water bodies such as streams, lakes and marine waters.

Nutrient and pesticide transport can lead to freshwater and coastal water contamination,

threatening local ecosystems (Blann et al., 2009). Serious eutrophication and hypoxia issues

have been reported worldwide, for example, in the Gulf of Mexico (Rabalais et al., 2001),

the Baltic Sea (Larsson et al., 1985), the North Sea (Howarth et al., 1996), coastal waters of

Southern Japan (Suzuki, 2001) and the Black Sea (Mee, 1992). Other environmental issues

have also been reported such as trout spawning beds filling with sediments or drying waterfowl

habitat in Ontario (Irwin and Bryant, 1986) and even bacterial contamination (Escherichia

coli) of surface water bodies due to manure application in tile-drained areas (Stratton et al.,

2004).

In Denmark, about 50 % of agricultural lands are tile-drained (Olesen, 2009). Irrigation

systems, likely combined with subsurface drainage systems, are present in 17 % of the Danish

agricultural lands and they are only used temporarily (effective irrigation is less than 17 %)

(Baldock et al., 2000).

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1.2.3 Hydrology of drained areas

Surface drainage systems, as defined in Figure 1.1, are installed in flat areas where high

precipitation rates are observed in combination with a low infiltration capacity of soils, leading

to water ponding at the surface. When shallow water tables are observed, subsurface drainage

systems are typically installed in low hydraulic conductivity soils (Oosterbaan, 1994). If

needed, both drainage systems may work simultaneously as a preventive measure when high

waterlogging risks are encountered.

When considering the water cycle in an agricultural environment, tile drainage may not be

the first component that comes to mind. Precipitation, evapotranspiration, stream flow,

runoff and groundwater flow are usually the main components considered (Gordon et al.,

2008). Irrigation may be another key part of the hydrologic cycle in some cases (Tedeschi

et al., 2001), but it often goes hand in hand with subsurface drainage. An appropriate balance

between irrigation and drainage is needed to control water transfer from the land surface to the

drains. Limited drainage induces high watertables and soil salinization. On the other hand,

too intense drainage can critically lower the water table and may result in salt dissolution and

mobilization in drainage waters. Drainage flow salinity is therefore likely proportional to the

water table depth: the deeper the water table, the higher the salinity of the water discharged

by drains (Christen and Skehan, 2001).

According to common practice, tile drainage pipes are usually buried from 1 to 2 m below the

soil surface and the horizontal spacing is about 20 to 50 m between each pipe (Burton, 2010).

These values may vary depending on specific local conditions such as hydraulic properties of

soils or precipitation rates (Brooks and Corey, 1964b; Randall and Goss, 2008).

Water management systems such as tile drains have an impact on water flow and water

quality at the field scale, but impacts may also be significant at the catchment scale (Carlier

et al., 2007). At the field scale, tile drainage flow is affected by horizontal drain spacing,

the shape of the drainage network and the soil properties. At the catchment scale, drainage

flow is influenced by the spatial disposition of the fields within the catchment, and therefore

by the spatial arrangement of the entire collecting network, as well as the drainage capacity

of the network (Robinson and Rycroft, 1999). As defined by Yue (2010), drainage flow can

be separated in two parts: a lateral flow component, for which water flows to pipes and

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Water table

Controlstructure

CONVENTIONAL DRAINAGE

CONTROLLED DRAINAGE

Drainageoutlet

Drainageoutlet

Water table

Figure 1.2: Conventional versus controlled subsurface drainage systems, and their associatedconceptual flow paths. Modified from Zucker and Brown (1998).

originates from the surrounding media, and the actual drainage flow in the drains. Lateral

flow intensity determines the drainage network efficiency, and it depends on several factors,

namely soil hydraulic conductivity, drain diameter, perforation frequency along the pipes, etc.

When tile drains are found in clay-dominated soils (>35 %), additional drainage structures

may be created by digging subsurface channels with a ripper blade combined to a cylindrical

foot and an expander (Filipović et al., 2014). This is called mole drainage. It helps maintain

a low water table when tile drainage systems action is not sufficient and it allows greater

lateral flow to tile drains. While creating mole drains, ripper blades induce the formation

of vertical cracks in which preferential water flow occurs towards the underlying mole drains

(Leeds-Harrison et al., 1982). Tile and mole drains are non conductive under unsaturated

conditions because positive pressure must occur before water can start flowing into them

(Stormont and Zhou, 2005).

As pointed out here, tile drainage avoids water storage in soils and discharges water to local

streams, acting as a shortcut in the hydrologic cycle. A non-exhaustive insight of indirect

effects related to subsurface drainage is listed in Table 1.1 (Schothorst, 1978; Konyha et al.,

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1992; Oosterbaan, 1994; Uusitalo et al., 2001; Rudy, 2004; Blann et al., 2009).

Despite their widespread use, tile drainage systems can’t be designed based on established

rules. Designing such networks is highly dependent on local factors such as soil structure,

topography and crop rotation (Sheler, 2013). As drainage systems usually discharge in local

streams, tile-drained areas likely induce higher flow peaks in downstream surface waters during

heavy rainfall events (Wiskow and van der Ploeg, 2003). However, as mentioned in Table 1.1, it

appears from the literature that both reductions and increases of downstream peak discharge

in surface waters are observed in tile-drained areas. This issue has been documented and

discussed for decades (Robinson and Rycroft, 1999). In general, low permeability drained soils

seem to have a positive effect by reducing downstream peak discharge (Robinson, 1990; Skaggs

et al., 1994). On the other hand, more permeable drained soils tend to increase downstream

peak discharge leading in some cases to flooding events (Robinson, 1990; Wiskow and van

der Ploeg, 2003). Robinson and Rycroft (1999) add a shade to this statement by remarking

that, in areas where shallow water table levels are found, peak discharge rates appear to

be decreased compared to the initial water table, prior to the drainage network installation.

During drainage, higher water storage capacity of soils is gained and therefore water infiltrates

and runoff decreases. Whereas with a deep initial water table level, tile drainage shortcuts

the infiltrating water after a rainfall event and discharges water in local streams resulting in

increased surface water peaks intensity. Both increases and decreases in discharge peaks have

been observed in agricultural catchments as well as in forest peatlands (Mustonen and Seuna,

1971; Heikurainen et al., 1978; Christen and Skehan, 2001; Holden et al., 2004; Deasy et al.,

2009).

The extension of tile-drained areas is known to be proportional to drainage flow rates; the

larger the drainage network, the higher the drainage flow rate (King et al., 2014). Yet, this

observation may be site-specific and the authors mention that detailed comprehension of all

the hydrological processes that occur in tile-drained areas is still a major knowledge gap.

Water flow patterns in a typical Danish tile-drained catchment are shown in Figure 1.3. A

part of the infiltrating water is drained and exported to surface water bodies with a very

short residence time in the underground due to fast turbulent flow in the drainage pipes. The

remaining water recharges local, regional or deep aquifers by following natural flow pathways

and discharges in surface or coastal waters. Nitrate transport is often associated with these

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water flow patterns. It is transported from the soil surface or the root zone to the drains and

aquifers. When reaching the drains, nitrate is usually transported as a conservative chemical

species favored by oxic conditions, as shown by the oxidized zone. A reduced zone is found

deeper, usually in the saturated zone. Denitrification occurs when reaching the saturated

zone, that is delimited by the redox interface (Hansen, 2006); nitrate is transported and

reduced as it becomes a reactive chemical species (Hansen, 2014). Nitrate reduction results in

nitrogen loss from the system through gas mainly under its N2 forms (Korom, 1992; Appelo

and Postma, 2005). When discharged in stream waters, unreduced nitrate causes severe

contamination issues (e.g. Blann et al., 2009).

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Table 1.1: Subsurface drainage indirect effects on soils, streams or plants.

Positive effects Negative effects

Increased aeration of the soil Increased risks of droughtReduction of downstream peak discharge ∗ Increase of downstream peak discharge ∗

Stabilized soil structure Soil subsidence in peat soilsHigher availability of nitrogen in the soil Decomposition of organic matterHigher crop production Erosion of soilsBetter workability of the soil Acidification of potential acid sulphate soilsEarlier planting dates Surface water loading with sedimentsDecrease of chemical species in soils Downstream surface water contaminationChemical species are typically nitrate, phosphorous, salt, some pesticides, etc.

∗ Reduction or increase of downstream peak discharge rates depend on local hydrologic conditions. See discussion

above.

Figure 1.3: Flow paths in a typical glacial till catchment of Denmark and associated redoxinterface. Modified from Hinsby et al. (2008).

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1.2.4 Tile drainage modeling

Several numerical models have been developed to simulate hydrological processes related to

subsurface drainage. They have been used to demonstrate that tile drainage networks have

a key impact on groundwater and surface water flow as well as chemical species transport

and erosion (Gärdenäs et al., 2006; Kiesel et al., 2010; Rozemeijer et al., 2010; Warsta et al.,

2013). Numerical models have also demonstrated reliable predictive abilities when used in

conjunction with in situ monitoring systems (Tim, 1996). Representing discrete tile drains

in a model requires information on the location and depth of the individual drains that

constitute the drainage network, but which is often unavailable. Discretizing complex drainage

networks may also lead to extremely dense computational meshes causing potentially very long

simulation times. As a result, the representation of complex tile drainage networks in models

is often simplified and drains are simulated as high conductivity layers (e.g. Carluer and de

Marsily, 2004; Rozemeijer et al., 2010), open cylinders with a seepage face boundary condition

(e.g. Lin et al., 1997; Akay et al., 2008), or represented as nodal sinks (e.g. Gärdenäs et al.,

2006) for which subsurface water fluxes are estimated from mass balance equations (Purkey

et al., 2004). The simplification is also considered by authors (e.g. Morrison, 2014) because

drainage networks are rarely mapped in detail and information on location, spacing, diameter

and orientation of drains is lacking.

Alongside Richards’ equation, which is commonly solved by models for describing variably-

saturated subsurface water flow (see Table 1.2), subsurface drainage water flow has usually

been simulated using three different spacing formulas under steady-state conditions:

– the Hooghoudt equation that characterizes steady flow in regular parallel tile networks

with constant recharge in flat lands (Hooghoudt, 1940);

– the Kirkham equation developed for calculating drainage flow in a ponding context

(Kirkham, 1949);

– the Ernst equation used in drained layered profiles (Ernst, 1956).

The Hooghoudt formula considers radial water flow under and towards the drains, and hori-

zontal water flow above these. The Ernst equation takes radial flow into account above and

below the drains as total flow. By combining both expressions, a generalized form of the

Hooghoudt equation has been developed so that both radial and horizontal flow to drains

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are calculated (van Beers, 1976). The generalized Hooghoudt equation is referred to in the

literature as shown in Table 1.2.

When transient drainage water flow is considered, the Boussinesq equations (Boussinesq, 1872)

may be applied but its inherent non-linearity makes it difficult to solve. Even when these

equations are linearized (van Schilfgaarde, 1963), their use is restricted to analytical solutions.

More recently a powerful analytical solution was developed for calculating transient flow to a

single drain (Cooke et al., 2000). Yet, numerical solutions are usually preferred. Fipps et al.

(1986) were amongst the first authors to consider subsurface drains as boundary conditions

represented in a 2D numerical solution. Based on this study, MacQuarrie and Sudicky (1996)

developed a one-dimensional drainage flow equation for drains in three-dimensional variably

saturated models. Nowadays, one-, two- and three-dimensional numerical codes are available

with a wide variety of applications for tile drainage simulations.

One-dimensional models

Depending on the specific simulation needs for a given tile drainage application, models have

focused on simulating hydrological processes at different scales and dimensions. For example,

comprehensive one-dimensional models such as SWAP (Kroes et al., 2008), formerly known

as SWATR (Feddes et al., 1978), or DRAINMOD (Skaggs, 1978) have been widely used for

simulating vertical water flow and solute transport through the saturated and unsaturated

zones. SWAP represents tile drains as nodal sinks while DRAINMOD solves the Kirkham’s

or Hooghoudt’s equations for 1D drains (Youssef et al., 2005). DRAINMOD can simulate

nutrient dynamics in drained soils in relation to local agricultural and climatic conditions.

Sheler (2013) provides detailed information and comparison of these codes. Other models

have integrated the tile drainage algorithms from DRAINMOD into other groundwater flow

models. For example, the ADAPT model (Warld et al., 1988) couples the root-zone model

GLEAMS (Leonard et al., 1987) to DRAINMOD. Ale et al. (2013) document the performance

of both ADAPT and DRAINMOD. In another example, the DRAIN-WARF model (Dayyani

et al., 2010) links DRAINMOD to the shallow groundwater flow model WARMF (Chen et al.,

2001) and uses a distributed parameters approach for simulating freezing and thawing in

tile-drained environments. Other examples of 1D models include SaltMod, which simulates

salinity variation in soil moisture, groundwater and drainage water (Oosterbaan, 2002), and

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ANSWERS, which simulates water flow in the unsaturated zone only at the field scale with

the Brooks-Corey model (Brooks and Corey, 1964a) accounting for soil erosion (Beasley et al.,

1980).

Two-dimensional models

Models have been developed for two-dimensional simulations, such as MHYDAS-DRAIN

(Tiemeyer et al., 2007), a two-dimensional spatially distributed model for simulating field

scale water flow in drained lowlands. Tile drains are defined by their depth, slope, diameter

and spacing and where drainage water flow is assumed to originate from the soil matrix and

macropores. At a larger scale, AnnAGNPS (Binger and Theurer, 2001) solves Hooghoudt’s

equation for tile drains in 2D agricultural watersheds. The model is mainly applied to eval-

uate water quality related to crop rotation. SIDRA is another deterministic model that

simulates water fluxes through the saturated zone by solving Boussinesq’s equation (Lesaffre

and Zimmer, 1988). It can incorporate subsurface drains as discrete drains at the bottom of

a conductive layer that is located at the boundary with a low permeability unit. SIDRA can

compute drainage flow rates and hydraulic heads at mid-distance between two parallel drains.

PESTDRAIN (Branger et al., 2009) has been later developed by coupling SIDRA to the un-

saturated and surface flow model SIRUP (Kao et al., 1998) and to the pesticides transport

model SILASOL. Another example of a 2D model that simulates unsaturated and saturated

water flow is ANTHROPOG (Carluer and de Marsily, 2004), which represents drains as a

high-permeability porous medium.

When creating catchment scale models, it may be relevant to work with the representative

elementary watershed concept, which is included in the physically-based semi-distributed

THREW model (Tian et al., 2008, 2006). A storage-discharge relation regulates tile drainage

flow in drains as drainage flow rate values are proportional to the height of the water table

above the drains (Li et al., 2010). The physically-based, semi-distributed and process-oriented

SWAT model (Arnold et al., 1998) uses a method similar to the representative elementary

watershed concept of THREW by dividing the simulation domain in hydrologic response units

to simulate water flow, solute transport and sediment transport in agricultural catchments,

accounting for crop use rotation. Du et al. (2005) improved SWAT with respect to the

simulation of tile drainage water flow by including a simple tile flow equation to the original

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SWAT model.

Another approach for simulating subsurface drainage is to assume that drained plots are

interconnected by filled pipes for which the Richards’ equation is solved, which is used in the

2D physically-based catchment model CATFLOW (Maurer, 1997; Klaus and Zehe, 2011).

Three-dimensional models

A smaller number of three-dimensional models have been developed to simulate tile drainage.

The finite-difference flow model MODFLOW represents drains as individual sinks that are

active when the water table is higher than the elevation of the drain (McDonald and Har-

baugh, 1988). The volumetric flow rate out of the subsurface into the drain is computed

with Darcy’s law and requires that the conductance of the drain is specified. The FLUSH

model was developed for simulating 3D hydrological processes in tile-drained clayey fields

(Warsta et al., 2013). FLUSH treats macropores and drains as local sinks, with macropores

being coupled to tile drains and the soil matrix. Furthermore, FLUSH considers additional

cracks created in a clayey matrix resulting from decreased matrix water saturation produced

by drainage. Subsurface drains are defined in FLUSH as water sinks and cannot represent

a source of water. In contrast, the HYDRUS model allows drains located in the saturated

zone to represent pressure head sinks as well as sink/source terms when the surrounding

matrix becomes unsaturated (Šimůnek et al., 2006). HYDRUS simulates 2D or 3D water

flow and solute transport in variably-saturated porous media and can also represent a system

consisting of macropores and porous matrix with a dual-permeability approach (Akay et al.,

2008). In the 3D integrated catchment model MIKE-SHE/MIKE 11 (Refsgaard and Storm,

1995) tile drainage is also accounted for as a sink where drainage is generated when the wa-

ter table is above the drain level. The drainage water is then routed either downhill or to

the nearest stream. The original version of MIKE-SHE/MIKE 11 coupled groundwater flow,

surface water flow, unsaturated flow and evapotranspiration. A macropore option was added

by Christiansen et al. (2004).

Few models have a limited application to arid tile-drained areas where salinity is to be taken

into account as they have been developed only for simulating density-dependent groundwater

flow and transport. SUTRA (Voss and Provost, 2010) is one of those models. It treats drains

only as sink nodes in a subsurface domain governed by the Darcy equation. In FEMWATER

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(Lin et al., 1997), Richards’ equation is solved for groundwater flow with drains being given

a seepage boundary condition. In both codes, overland flow is not considered.

All the models mentioned in the previous paragraphs are listed in Table 1.2. This is a non

exhaustive list; models that are commonly used for simulating tile-drained environments were

considered, but some others may be suitable for similar aims. HydroGeoSphere is added for

comparison purposes to the other models, details about the model and governing equations

are given in chapter 3.

Tile drainage modeling with HydroGeoSphere

The first authors to simulate tile drainage were MacQuarrie and Sudicky (1996), using

FRAC3DVS (Therrien and Sudicky, 1996) from which HydroGeoSphere originated. They

have contributed to the implementation of tile drainage in the code by developing a one-

dimensional flow equation for drains in three-dimensional variably saturated media that is

equivalent to an open channel flow equation. Subsurface drains were superimposed onto the

porous medium by using a common node coupling approach in a theoretical model having a

single pipe.

Rozemeijer et al. (2010) created a field scale model with a few parallel drains discharging in

an open ditch, accounting for subsurface, surface and tile drainage water flow. The authors

emphasized the action of drains at an experimental area of their study area, by including

discrete pipes. However, when simulating water flow for the whole field, drainage water

flow was represented as a high conductivity layer, which is defined as an equivalent medium

(Carlier et al., 2007).

Yue (2010) developed a tile drainage module that removes the pressure continuity assumption

between subsurface and drain common nodes. In this approach, the Preissman slot method

(Cunge and Wegner, 1964) was used for modeling 1D free surface or pressurized transient flow

in the drains. A flux boundary condition was applied at the outlet by a hypothetical diffusive

wave flow between the drain outlet and adjacent water. As a result, water flux exchange

between a drain outlet and the surface domain was made workable. In addition, resistance

adjustment factors were introduced for lateral flow exchange between the soil and the pipes

to get rid of the mesh size effects along drains.

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Modeling of drainage water flow accompanied by solute transport was studied by Frey et al.

(2012) in a two-dimensional model simulating liquid manure transport to a single drain in a

macroporous silt loam soil. This study showed the importance of including a dual-permeability

medium when considering fast transport through soils with macropores for accurate simulation

results.

Spatial scale of tile drainage models

The models listed in Table 1.2 cover a wide range of applications, depending on the modelers’

interest in the description of specific physical processes. Since most were developed for field

or crop-scale applications, drainage dynamics are usually well represented at those scales in

the literature (e.g. Warsta et al., 2013; Kroes et al., 2008). At larger scales (subcatchment

to catchment scale), drainage is generally simplified (e.g. Hansen et al., 2013; Carluer and de

Marsily, 2004). Modeling subsurface drainage effects on groundwater flow and surface water

flow dynamics at the catchment scale is still a major challenge. Catchment scale modeling is

essential to investigate the entire water cycle in catchments dominated by tile drainage flow.

Yet, no guideline states the best tile drainage modeling approach to account for detailed

physical processes at large scale while avoiding too dense mesh. Modelers must often choose

a balance between the level of discretization of model meshes and the associated simulation

time. Hansen et al. (2013) are one of the few authors that mention scaling issues regarding

tile drainage modeling. In their study, groundwater flow dynamics simulated at the scale

of drainage networks produced results that were not precise enough for small-scale model

calibration purposes. Nevertheless, these authors did not define a minimum representative

scale at which accurate drainage flow results could be expected. It is believed that such issues

are site specific and can rarely be defined with a general rule.

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Table 1.2: Non exhaustive list of models suitable for tile drainage modeling. Each model isgiven its dimension (Dim.) and scale (F = field, C = catchment) application. Surface, Sub-surface and Drain domains show governing equations (plain text) or waterbalance parameters(in italics).

Model Dim. Scale Overland Subsurface Drain Reference

AnnAGNPS 2D C Curve number∗ Darcy Hooghoudt Binger and Theurer (2001)ANSWERS 1D F - Brooks-Corey Hooghoudt Bouraoui et al. (1997)CATFLOW 2D F Saint-Venant Richards Richards Maurer (1997)DRAINMOD 1D F - Richards Hooghoudt/Kirkham Skaggs (1978)FEMWATER 3D F - Richards Seepage Lin et al. (1997)FLUSH 3D F Saint-Venant Richards Sink Warsta et al. (2013)HydroGeoSphere 3D Any Saint-Venant Richards Hazen-Williams Therrien et al. (2010)HYDRUS 3D Any - Richards Sink/Source Šimůnek et al. (2006)MHYDAS-DRAIN 2D F Hortonian flow Reservoir Hooghoudt Tiemeyer et al. (2007)MIKE SHE/MIKE 11 3D Any Saint-Venant Richards Sink Refsgaard and Storm (1995)MODFLOW 3D Any - Darcy Sink McDonald and Harbaugh (1988)PESTDRAIN 2D F Reservoir Boussinesq Boussinesq Branger et al. (2009)SaltMod 1D F Waterbalance equation for the three domains Oosterbaan (2002)SUTRA 3D Any - Darcy Sink Voss and Provost (2010)SWAP 1D F Reservoir Richards Hooghoudt Kroes et al. (2008)SWAT 2D C Curve number∗ Storage Sink Arnold et al. (1998)

∗ The curve number values for surface runoff are calculated based on Soil Conservation Service curves developedby the U.S. Department of Agriculture (1972).

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1.3 Research objectives

This research was undertaken to extend knowledge and understanding of water dynamics in

heterogeneous clayey till soils under tile drainage conditions. A field-scale model that couples

subsurface water flow to surface and drainage water flow was developed for the Lillebæk

catchment. A coupled surface and subsurface flow model of the Fensholt subcatchment was

also built. Drainage flow was not coupled to the subsurface in this model; discrete drains

were rather represented by seepage nodes to eliminate numerical issues.

Specific objectives for application to the Lillebæk area were to test various concepts for simu-

lating field scale drainage water flow, and to highlight the best suited concepts for field scale

or larger scale modeling in terms of simulation time, mesh refinement and degree of precision

in the processes described.

In the Fensholt case, one of the objectives was to use and validate suggested options high-

lighted in Lillebæk for accurate drainage flow modeling at large scale. A simplified version of

two drainage network were therefore included in a catchment scale model. Instead of focusing

on a short-term precipitation event, such as in the Lillebæk case, investigating drainage re-

sponse to seasonal climate variations was selected. Another objective was to compare results

from a model run of Fensholt by means of HydroGeoSphere with results from a larger scale

model developed with MIKE SHE.

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Chapter 2

Study sites

Two study areas have been investigated in Denmark: the 4.7 km2 Lillebæk catchment and

the 6 km2 Fensholt catchment that is located in the larger Norsminde catchment (100 km2).

Within these catchments, land use is dominated by agriculture (Figure 2.1, grain crops) and

agricultural plots are commonly tile-drained, which implies that stream discharge is dominated

by drainage discharge. Both catchments are found in glacial landscapes originating from the

Weichsel and Saale glaciations (Houmark-Nielsen and Kjær, 2003). Highly heterogeneous

clayey to silty till geological materials are found in the shallow subsurface (Knutsson, 2008)

(Figure 2.2). Sand lenses of various extension and sand layers of glaciofluvial origin may

be included in the till units or found deeper. In Denmark, these sandy units, together with

glaciofluvial gravel units, represent at least 50 % of the groundwater resources (Kelstrup et al.,

1982). They are connected to the surrounding clayey till layers which are usually fractured

allowing preferential water flow (Fredericia, 1990; Klint and Gravesen, 1999; Nilsson et al.,

2003). As aquitards show high bulk hydraulic conductivities, they are therefore of prime

importance when considering aquifer recharge. At the national scale, groundwater recharge is

known to vary from 15 - 60 mm year−1 in eastern Denmark to 170 - 193 mm year−1 in western

Denmark (Jacobsen, 1995). Groundwater recharge is tied to the yearly average precipitation

variation that is on average from less than 600 mm in eastern Denmark to 900 mm in western

Denmark (Kronvang et al., 1993).

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Sweden

Germany 0 100 200

Stream

Agriculture

Catchment boundary

Lilleb k model areaæ

Urban/Settlement

Road

Forest

Grass

Wetland

Peatland

Lake

Sea

Mining

Industrial area

Technical area

Graveyard

Sports facilities

Recreation area

Horticulture

Polyculture

Sand

Salt marsh

Legend

0.0 2.5

Norsminde

Fensholt0.0 0.5 2.01.0

km

0.0 1.0km

Lillebæk0.5

km

km

N

1.25

Figure 2.1: Location of the Lillebæk catchment and the Fensholt catchment, that is includedin the Norsminde catchment, with associated land use maps from Nielsen et al. (2000).

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0 25

Bornholm

Post-glacial eolian sand

Post-glacial freshwater peat

Legend

50 100 km

Post-glacial marine sand and clay

Glacial melt water sand and gravel

Glacial melt water clay

Sandy till and gravel

Clayey till

Outwash plains

Marsh

Beach ridges

Older marine deposits

Pre-Quaternary

Lakes

Norsminde

Lillebæk

Figure 2.2: Geological map of Denmark (Schack Pedersen, 2011), with the Lillebæk andNorsminde catchments locations highlighted.

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2.1 Lillebæk

The Lillebæk catchment is located on the southeastern shore of Fyn island. The topography

in Lillebæk gently slopes toward the southeast and varies from 50 to 60 meters above mean

sea level (mamsl) to a few meters above sea level along the coast (Figure 2.3). A tile-drained

plot was chosen in this catchment to build a model that covers 3.5 ha comprising an irregular

drainage network made of 5 main collecting drains and 15 secondary drains. The Lillebæk

catchment has to date been well characterized (Hansen, 2010) as it is part of the Danish

Agricultural Watershed Monitoring Program LOOP, established in 1989 as part of the Danish

aquatic environment action plan (Grant et al., 2007). In the context of the LOOP-program,

the Lillebæk catchment has been monitored in detail for several years to investigate nitrate

issues at the catchment scale (Rasmussen, 1996).

Elevation[mamsl]

93

0

0 250 500 1000 m

Model area

N

Figure 2.3: Lillebæk catchment topography and highlighted model area (red line).

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2.2 Norsminde and Fensholt

The Norsminde catchment is located on the east coast of Jutland. This catchment shows high

topographical variations from about 100 mamsl in the western part to low elevations in the

eastern part; the western part being characterized by hilly terrains while the eastern part is

dominated by low-lands, divided by a Wechselian glacial melt water valley (Figure 2.4). The

catchment outlet is the Normsinde Fjord, a 2 km2 estuary located northeast of the catchment,

in which the catchment surface waters discharge through the Odder and Rævs rivers. The

area of interest for our model is the Fensholt subcatchment, located in the western hilly

land. This area is highly tile-drained with well mapped drains. Two complex and dense tile

drainage networks, covering 34 ha and 28 ha, respectively made of 199 and 95 drain pipes,

were targeted for our model.

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Elevation[mamsl]

173

0

0 1.25 2.5 5km

Fensholt

NorsmindeFjord

N

Figure 2.4: Topography in the Norsminde catchment, with the Fensholt subcatchment high-lighted.

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Chapter 3

Numerical model

3.1 Introduction

HydroGeoSphere is a fully integrated, physically-based three-dimensional numerical model

able to simulate subsurface, surface and drainage water flow, solute and heat transport (Ther-

rien et al., 2010). A brief overview of the governing flow equations is presented here. Hy-

droGeoSphere is the numerical model of choice for the tile-drainage studies of the Lillebæk

and Norsminde catchments. The reader is referred to Therrien et al. (2010) and Brunner and

Simmons (2012) for a comprehensive model description.

3.2 Governing flow equations

In HydroGeoSphere, water flow is described in three-dimensional subsurface porous media,

two-dimensional water flow is considered at the surface and in fractures, and one-dimensional

flow occurs in features such as wells and drain pipes. Coupling water flow in such domains,

by taking complex physical processes into account (such as variably-saturated flow, evapo-

transpiration or runoff), requires solving non-linear equations.

3.2.1 Subsurface flow

HydroGeoSphere applies a modified form of Richards’ equation to describe subsurface flow

driven by gravity and capillary forces in porous media. Water flow in discrete fractures or

dual continua can be simulated and are fully coupled to the subsurface porous media by a

27

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volumetric fluid exchange rate factor. The general form of Richards’ equation for 3D transient

subsurface water flow in a variably-saturated porous medium is given by:

− ∇ · (wmq) +∑

Γext ±Q = wm∂

∂t(θsSw) (3.1)

where wm is the volumetric fraction of the total porosity occupied by the porous medium [-],

Γext is an exchange flux term between the subsurface domain and another domain (i.e. surface

or drain) [LT−1], Q is the volumetric flow rate per unit volume of the medium representing

external sources and sinks [LT−1], θs is the saturated water content [-], Sw is the water

saturation [-].

The Darcy flux q [LT−1] is:

q = −K · kr∇ (ψ + z) (3.2)

where K is the hydraulic conductivity tensor [LT−1], kr is the relative permeability of the

medium [-], ψ is the pressure head [L] and z is the elevation [L].

In equation (3.1), the storage term on the right-hand side is defined as the sum of a com-

pressibility effect term in the saturated zone and a saturation change term in the unsaturated

zone (Cooley, 1971; Neuman, 1973). It gives then:

∂t(θsSw) ≈ SwSS

∂h

∂t+ θs

∂Sw

∂t(3.3)

where SS is the specific storage coefficient [-].

Under variably-saturated conditions in the subsurface domain, the unsaturated zone can

be characterized in HydroGeoSphere by the van Genuchten (1980) or Brooks and Corey

(1964a) models for identifying relations between head, saturation and relative permeability.

Subsurface and surface flow are described using non-linear equations that are discretized with

the control volume finite element method and linearized by means of the Newton-Raphson

iterative method (Huyakorn and Pinder, 1983).

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3.2.2 Surface flow

Surface flow is solved by a 2D diffusion wave approximation of the Saint-Venant equations

for unsteady surface water flow (Barré de Saint-Venant, 1871). This diffusion wave equation

originates from the simplification of two-dimensional Saint-Venant mass balance equations and

a momentum equation for the x-direction and y-direction respectively. The general diffusion

wave equation for surface water flow is:

− ∇ · (doqo) − doΓo ±Qo =∂φoho

∂t(3.4)

where do is the depth of flow [L], Γo is an exchange flux term [LT−1], Qo is a volumetric

flow rate per unit area representing external sources and sinks [LT−1], ho is the water surface

elevation [L], φo is the surface flow domain porosity [-] and qo is the surface water flow flux

given by Manning’s equation:

qo = −d

2/3o

nΦ1/2· kro∇ (do + zo) (3.5)

where n is the Manning roughness coefficient [TL−1/3], Φ is the surface water gradient [-],

kro is a relative permeability factor [-] and zo is the elevation [L].

3.2.3 Drainage flow

The general water flow along one-dimensional features, such as tile drains, is described as

follows:

Q1D = −C ·Af · (RH)p ·

[

∂hp

∂s

]q

(3.6)

where C is a proportionality constant [-], Af is the area of flow in a pipe [L2], RH is the

hydraulic radius [L] (calculated by dividing the area of flow and the wetted perimeter of the

pipe), hp is the hydraulic head in the pipe [L], s is the distance along the pipe’s axis [L], p

and q are exponent factors.

When considering tile drainage, the Hazen-Williams empirical equation (Williams and Hazen,

1905) is used for describing water flow depending on head loss along pipes due to friction of

29

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water flowing in them:

Q1D = −k · CHW ·Af · (RH)0.63 ·

[

∂hp

∂s

]0.54

(3.7)

where k is a unit conversion factor (0.849 m0.37/s) and CHW is the Hazen-Williams roughness

coefficient [-].

3.2.4 Coupling water flow

As shown in equations (3.1) and (3.4), water exchange terms are involved for expressing

exchanges between model domains (i.e. subsurface, surface and drains). Those terms can

be determined by two different approaches: the dual node approach and the common node

approach. The dual node approach is based on a Darcy flux transfer between two domains

separated by a thin porous medium holder of the water exchange. The common node approach

assumes hydraulic head continuity between two domains, corresponding to a superposition

principle (Therrien and Sudicky, 1996). In our case, the dual node approach is chosen for

coupling of subsurface and surface flows. Coupling of groundwater flow and tile drainage flow

also uses a dual node approach, as does the flow coupling for a porous medium with a second

continuum.

Governing equations for coupled groundwater (pm) and surface water flow (olf) are:

Γpm→olf = − (kr)exch(pm,olf)Kexch(pm,olf)(ho − h)

lexch(pm,olf)(3.8)

∂dv

∂t= −∇̄ · doq̄o +Q∂ (x̄ − x̄o) + Γpm→olf (3.9)

where dv is the volume depth [L], x̄ − x̄o is the node position [L], (kr)exch, Kexch and lexch are

the relative permeability, saturated hydraulic conductivity and the coupling length for fluid

exchange.

Coupled groundwater (pm) and drainage water flow (d) is expressed by:

Γd→pm = −2πrdKexch(pm,d)(hd − h)lexch(pm,d)

(3.10)

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∂s

(

k · CHW ·Af · (RH)0.63 ·

[

∂hd

∂s

]0.54)

+Qdδ (s− sc) + Γd→pm = πr2dSsp

∂hd

∂t(3.11)

where rd is the drain radius [L]. Equation 3.10 accounts for pressurization in drainage pipes

that induces leakage of water to the surrounding porous medium.

3.2.5 Interception and evapotranspiration

When applying a potential evapotranspiration boundary condition at the surface of a model,

HydroGeoSphere simulates interception by vegetation or buildings and actual evapotranspi-

ration by plants.

Interception is a storage factor that is proportional to the type of land cover (vegetation

or buildings) and, when vegetation is considered, its seasonal development stage. Rain is

intercepted and stored, where latter mentioned water becomes available for depletion by

evaporation. The interception varies from 0 to SMaxint , which is defined as the maximum

interception storage capacity [L] and calculated as follows (Kristensen and Jensen, 1975):

SMaxint = cint · LAI (3.12)

where cint is the canopy storage parameter [L] and LAI is the leaf area index [-].

Evapotransporation is considered as a combination of transpiration by plants and evaporation.

Transpiration (Tp) is calculated based on the model developed by Kristensen and Jensen

(1975):

Tp = f1 (LAI) · f2 (θ) ·RDF · (Ep − Ecan) (3.13)

where f1 (LAI) is a function of leaf area index [-] , f2 (θ) is a function of moisture content

(θ) [-], RDF is a root distribution function [-], Ep is the reference evapotranspiration [L] and

Ecan is the evaporation by vegetation [L].

The first three dimensionless factors of equation (3.13) are defined by the following equations:

f1 (LAI) = max {0,min [1, (C2 + C1LAI)]} (3.14)

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where C1 and C2 are fitting parameters [-].

f2 (θ) =

0 for 0 ≤ θ ≤ θwp

1 −[

θfc−θθfc−θwp

]C3

for θwp ≤ θ ≤ θfc

1 for θfc ≤ θ ≤ θo

1 −[

θan−θθan−θo

]C3

for θo ≤ θ ≤ θan

0 for θan ≤ θ

(3.15)

where θwp is the moisture content at the wilting point [-], θfc is the moisture content at field

capacity [-], θo is the moisture content at the oxic limit [-] and θan is the moisture content at

the anoxic limit [-].

RDF =

∫ z′

2

z′

1

rF (z′) dz′

∫ Lr

0 rF (z′) dz′

(3.16)

where rF (z′) is a root extraction function [L3 T−1], z′ is the depth coordinate from the soil

surface [L] and Lr is the effective root length [L].

Evaporation (Es) occurs at the soil surface and along a prescribed depth (Bsoil) in the sub-

surface domain. It is calculated with the following formulation:

Es = α∗ · (Ep − Ecan) · [1 − f1 (LAI)] · EDF (Bsoil) (3.17)

where EDF is an evaporation distribution function limiting evaporation from the soil surface

to the Bsoil depth, and α∗ is a wetness factor [-] calculated as follows:

α∗ =

θ−θe2

θe1−θe2for θe2 ≤ θ ≤ θe1

1 for θ > θe1

0 for θ < θe2

(3.18)

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3.3 Discrete drains vs. Seepage nodes

From the preliminary models created in Lillebæk and Fensholt, it appeared that the Hazen-

Williams drainage equation (equation 3.7) may induce some numerical issues. In hummocky

terrains of Fensholt, results showed an undesired increased drainage effect, which didn’t show

up in the gently sloping Lillebæk case. Hydraulic gradients simulated within the pipes of a

drainage network are smaller than those calculated in the surrounding porous media. Hy-

draulic heads therefore show very little variations along the pipes, whereas the hydraulic head

for each node in the discrete drains should be equal to its elevation. A zero pressure head

value would therefore be calculated, which is physically closer to what is generally observed

in tile drainage systems: drainage occurs when the groundwater table rises above the drain

elevation with water flowing from saturated soils into the drains (Warsta et al., 2013).

An alternative option to model drainage flow had to be investigated. The two-dimensional

steady-state flow example created by Fipps et al. (1986) and numerically tested with Hydro-

GeoSphere by MacQuarrie and Sudicky (1996) in a three-dimensional configuration was used

here. Note here that MacQuarrie and Sudicky (1996) used a one-dimensional drainage flow

equation that differs slightly from the Hazen-Williams equation. The drainage formulation in

HydroGeoSphere was recently modified so that the actual Hazen-Williams equation is solved.

A 3D benchmark model of sandy loam domain having a hydraulic conductivity of 1.5 × 10−5

m s−1 was built to verify the simulation approach. The domain ranges from 0 to 30 m in the x

and y direction, covering an area of 900 m2, and from 0 to 3 m in the z direction (Figure 3.1).

The top boundary of the domain is assigned a 3 m prescribed head boundary condition, while

the lateral and bottom boundaries are impermeable.

Two set-ups were then tested. First, a single discrete drain (diameter = 0.0216 m) was

implemented in the model, located at x = 15 m, z = 2 m and ranges in the y direction from y

= 1 m to y = 29 m. A critical depth boundary condition was applied at the outlet of the drain

(x = 15 m, y = 1 m and z = 2 m) allowing free drainage. This set-up couples the drain to the

subsurface domain with a dual-node approach and solves the Hazen-Williams equation. A

second set-up was considered by replacing the drain segments by nodes being given a seepage

boundary condition. This is physically suitable for drainage simulation purposes as seepage

nodes are given a zero pressure head condition when the water table rises above the nodes’

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elevation (Therrien et al., 2010), allowing free drainage to occur by acting as sink nodes. On

the other hand, if the water table drops below the seepage nodes elevation, a no-flow boundary

condition is applied to these nodes and drainage stops.

Regarding the spatial dicretization of the model domain, a nodal spacing of 0.5 m was set in

the x direction, 1.0 m in the y direction and 0.2 m in the z direction. Following MacQuarrie

and Sudicky (1996) model set-up, the grid was refined in the y direction between y = 14 m

to y = 16 m with decreasing nodal spacing from y = 14 m to 15 m (minimum nodal spacing

= 0.05 m) and increasing nodal spacing from y = 15 m to 16 m. In the z direction, nodal

spacing decreases from z = 1.8 m to z = 2.0 m (minimum nodal spacing = 0.05 m) and

increases from z = 2.0 m to z = 2.2 m. In total, the model has 53 878 nodes and 49 140

elements. Simulations were run for a period of 100 000 sec, which corresponds to 27 h 46 min

40 sec.

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3.3.1 Steady-state simulations

Conventional drainage under steady-state flow conditions was simulated in both set-ups. The

numerical results were compared to the drainage analytical solution developed by Kirkham

(1949). In Figure 3.2, the vertical profile displayed at x = 22 m shows the same results from

the discrete drain and seepage cases, and they coincide with the analytical solution. At x =

15 m, the seepage drainage simulation shows pressure head values, in the near vicinity of the

drain, that are closer to the analytical solution than the discrete drain values. This behavior

was seen along the entire profile as well (Table 3.1).

x = 0 m 15 m 30 m

z = 0 m

3 m

2 m

Imp

erm

ea

ble

bo

un

da

ry

Drain(r = 0.0108 m)

Prescribed head boundary (H = 3 m)

K = 1.5 E-5 m/s

Figure 3.1: Simulation domain of the Fipps et al. (1986) example used as a verificationexample. The domain ranges in the y direction from 0 to 30 m. Modified from MacQuarrieand Sudicky (1996).

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Pressure head [m]

Ele

vation a

bove d

atu

m [m

]

3.0

0.0

0.5

1.0

1.5

2.0

2.5

0.0-0.5 0.5 1.0 1.5 2.0 2.5 3.0

Analytical (x = 22 m)

Analytical (x = 15 m)

Numerical (x = 22 m)

Numerical, discrete drain (x = 15 m)

Numerical, seepage (x = 15 m)

Figure 3.2: Numerical and analytical solutions for pressure head along vertical profiles at x= 15 m and x = 22 m. The discrete drain and seepage node set-ups are displayed. At x = 22m, seepage and discrete drain numerical solutions coincide; they are displayed under a singlejoint vertical profile. Modified from MacQuarrie and Sudicky (1996).

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Table 3.1: Pressure head values along the x = 15 m vertical profile for the discrete drain andseepage node numerical solutions, compared to the Kirkham (1949) analytical solution.

Elevation [m]Pressure head [m]

Analytical Seepage nodes Discrete drain

3.00 0.000 0.000 0.0002.95 0.030 0.030 0.0312.75 0.149 0.150 0.1562.55 0.259 0.260 0.2722.35 0.342 0.348 0.3662.15 0.316 0.372 0.4012.05 0.181 0.260 0.3022.00 ∼0.01 0.000 0.0611.95 0.285 0.337 0.3801.89 0.464 0.538 0.5731.82 0.678 0.696 0.7261.73 0.837 0.846 0.8721.63 0.997 1.000 1.0231.50 1.152 1.166 1.1861.35 1.326 1.350 1.3681.17 1.535 1.558 1.5740.97 1.767 1.780 1.7950.77 1.997 1.996 2.0100.57 2.203 2.207 2.2200.37 2.409 2.414 2.4260.17 2.615 2.618 2.6300.00 2.795 2.794 2.806

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Cross-sections in the yz plane at x = 15 m (Figure 3.3) show groundwater heads above and

below the drain in the discrete drain model (Figure 3.3a) and in the seepage nodes model

(Figure 3.3b). Both profiles look similar although slight differences can be seen. The seepage

nodes profile is perfectly symmetric in the y direction, with a hydraulic head value of 2.0 m

at the drain elevation (thin dark blue line from y = 1 m to 29 m), where the pressure head

is equal to 0.0 m. On the other hand, the discrete drain profile is asymmetric due to a small

hydraulic head gradient along the drain from its upstream end (y = 29 m) to its outlet (y

= 1 m). A zero pressure head is calculated at the outlet of the drain but positive values are

simulated in the upstream part, inducing the asymmetry seen below the drain in the hydraulic

head distribution.

2.0 3.02.2 2.82.5

Hydraulic head [m]

a)

b)

Figure 3.3: Hydraulic head distribution in the yz plane at x = 15 m in the discrete drain (a)and the seepage nodes model (b) models.

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Figure 3.4 shows the hydraulic head distribution in the 3D domain for the discrete drain

(Figure 3.4a) and seepage nodes (Figure 3.4b) cases. Lateral hydraulic head values appear

to be equivalent in both cases. The symmetry differences observed in Figure 3.3 are also

seen here along the cross-sections at y = 4 m, 13 m and 22 m (Figure 3.4a). Nevertheless,

the lateral drainage flow patterns, as defined by Yue (2010), exposed in 2D vertical sections

in Figure 3.5 with the associated hydraulic head distribution, appear to be similar in both

simulations.

2.0 3.02.2 2.82.5

Hydraulic head [m]

a)

b)

Discrete drain

Seepage nodes

Figure 3.4: Hydraulic head distribution in the 3D domain for the discrete drain (a) and theseepage nodes examples (b). Three cross-sections are displayed at y = 4 m, 13 m and 22 m.

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a)

b)

2.0 3.02.2 2.82.5

Hydraulic head [m]

Discrete drain

Seepage nodes

Figure 3.5: Hydraulic head distribution in the 3D domain for the discrete drain (a) and theseepage nodes examples (b), with associated water flow pathways.

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In terms of computational performances, both simulations were run in serial mode using a

3.70 Gb RAM computer with 1 CPU core at 2.60 GHz. The discrete drain simulation ran

in 2 h 31 min and the seepage nodes simulation in 37 min (Table 3.2). About 77 300 m3

of water was drained during the both simulations, thereby validating the use of the seepage

nodes option as a drainage boundary condition.

With this verification example, the seepage drainage option appears to be suitable for simu-

lating lateral drainage water flow, i.e. water flow in the porous medium towards the drains.

However, for this simulation option, the physical properties of the pipe were not specified

and pipe flow and drainage routing, with potential pressurized flow, were not considered.

Drainage flow was mainly driven by the resistance from the porous medium here.

Table 3.2: Computational times and drainage volumes of the discrete drain and seepagenode steady-state and transient simulations. All simulations were run using a 3.70 Gb RAMcomputer with 1 CPU core at 2.60 GHz.

Discrete drain Seepage nodes

Computational timeSteady-state 2 h 31 min 37 minTransient state 3 d 21 h 19 min 11 h 13 min

Drainage volumeSteady-state 77 300 m3 77 302 m3

Transient state 47 322 m3 47 331 m3

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3.3.2 Transient simulations

The seepage drainage option test was also conducted with a transient simulation. The model

set-up was quite similar to the steady-state test, except the top boundary condition that was

modified. A time-varying flux was applied at the top nodes during a period of 100 000 s, as

shown in Table 3.3. The initial flux value applied (8.59 × 10−4 m s−1) is equivalent to the

flux induced by the steady-state case prescribed head boundary condition.

In Figure 3.6, the discrete drain and seepage nodes options show similar response to varying

flux: both drainage discharge hydrographs are superimposed. Yet, Table 3.3 shows discharge

rates for both set-ups with the seepage nodes option having a little time-lag (of about 150

s) in response to varying flux values, while the discrete drain option doesn’t show any time-

lag. This difference is not noticeable in Figure 3.6 and it doesn’t affect the total drainage

volume, as seen in Table 3.2 (discrete drain = 47 322 m3, seepage nodes = 47 331 m3), since

the discrete drain and seepage nodes options roughly drain the same amount of water during

the simulation. The seepage nodes time-lag issue is therefore believed to be numerical rather

than conceptual and doesn’t affect the drainage results significantly.

Computational times were much longer than the steady-state simulations, with 3 d 21 h 19

min for the discrete drain case and 11 h 13 min for the seepage nodes case (Table 3.2).

Table 3.3: Flux rate values applied at the Fipps et al. (1986) domain during transient sim-ulations compared to discrete drain and seepage nodes discharge rates. Positive flux valuesreveal water entering the simulation domain while negative discharge values indicate waterleaving the domain.

Time [s] Flux [m s−1] Discrete drain [m3 s−1] Seepage nodes [m3 s−1]

0 8.59 × 10−4 −7.73 × 10−1 −7.73 × 10−1

12 500 8.59 × 10−4 −7.73 × 10−1 −7.73 × 10−1

25 000 4.29 × 10−4 −3.86 × 10−1 −3.87 × 10−1

37 500 4.29 × 10−4 −3.86 × 10−1 −3.86 × 10−1

50 000 2.15 × 10−4 −1.93 × 10−1 −1.99 × 10−1

62 500 2.15 × 10−4 −1.93 × 10−1 −1.93 × 10−1

75 000 4.29 × 10−4 −3.86 × 10−1 −3.79 × 10−1

87 500 4.29 × 10−4 −3.86 × 10−1 −3.86 × 10−1

90 000 8.59 × 10−4 −7.73 × 10−1 −7.64 × 10−1

100 000 8.59 × 10−4 −7.73 × 10−1 −7.73 × 10−1

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Flu

x in [m

/s]

0.0

-0.2

0.0

-0.4

-0.6

-0.8

-1.0

0.0 2.0 x 104

4.0 x 104

6.0 x 104

8.0 x 104

1.0 x 105

Dra

inage d

ischarg

e [m

³/s]

2.0 x 10-4

4.0 x 10-4

6.0 x 10-4

8.0 x 10-4

1.0 x 10-3

Time [s]

Flux in

Discrete drain

Seepage nodes

Figure 3.6: Discrete drain and seepage nodes hydrographs (drainage discharge) of the Fippset al. (1986) case in a transient simulation, compared to the time-varying flux boundarycondition applied at the top of the simulation domain (flux in).

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Chapter 4

Simulating coupled surface and

subsurface water flow in a

tile-drained agricultural catchment

Simulation des écoulements couplés de surface et souterrains dans un bassin

versant agricole drainé

G. De Schepper, R. Therrien

Department of Geology and Geological Engineering, Université Laval

Quebec City, Canada

J. C. Refsgaard, A. L. Hansen

Department of Hydrology, Geological Survey of Denmark and Greenland

Copenhagen, Denmark

Reference:

G. De Schepper, R. Therrien, J. C. Refsgaard, and A. L. Hansen (2015). Simulating coupled

surface and subsurface water flow in a tile-drained agricultural catchment. J. Hydrol., 521,

374 – 388. doi:10.1016/j.jhydrol.2014.12.035

© 2014 Elsevier B.V.

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Abstract

The impact of shallow tile drainage networks on groundwater flow patterns, and associated

transport of chemical species or sediment particles, needs to be quantified to evaluate the

effects of agricultural management on water resources. A current challenge is to represent

tile drainage networks in numerical models at the scale of a catchment for which accurate

simulation and reproduction of subsurface drainage water dynamics are essential. This study

investigates the applicability of various tile drainage modeling concepts by comparing their

results to a reference model. The models were set up for a 3.5 hectare regularly monitored

tile-drained area located in the clayey till Lillebæk catchment in Denmark, where the main

input of water to the streams originates from subsurface drainage. Several simulations helped

identify the most efficient way of modeling tile-drained areas using the integrated surface

water and groundwater HydroGeoSphere code, which also simulates one-dimensional water

flow in tile drains. The aim was also to provide insight on the design of larger scale models

of complex tile drainage systems, for which computational time can become very large. A

reference model that simulated coupled surface flow, groundwater flow and flow in tile drains

was set up and showed a rapid response in drain outflow when precipitation is applied. A series

of additional simulations were performed to test the influence of flow boundary conditions,

temporal resolution of precipitation data, conceptual representations of clay tills and drains,

as well as spatial discretization of the mesh. For larger scale models, the simulations suggest

that a simplification of the geometry of the drainage network is a suitable option for avoiding

highly discretized meshes. Representing the drainage network by a high-conductivity porous

medium layer reproduces outflow simulated by the reference model. This approach greatly

reduces the mesh complexity and simulation time and thus represents an alternative to a

discrete representation of drains at the field scale, but specifying the hydraulic properties of

the layer requires calibration against observed drain discharge.

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Résumé

L’impact des réseaux de drainage agricole sur les écoulements souterrains, associés au trans-

port d’espèces chimiques ou de particules sédimentaires, doit être quantifié pour évaluer les

effets de la gestion agricole sur les ressources en eau. La représentation des réseaux de

drainage souterrain dans les modèles numériques à l’échelle d’un bassin versant reste essentielle

pour simuler correctement les dynamiques d’écoulement de drainage. Cette étude examine

l’applicabilité de divers concepts de modélisation de drainage en comparant leurs résultats à

un modèle de référence. Les modèles ont été construits sur base d’une parcelle drainée de 3.5

hectare régulièrement contrôlée située dans le bassin versant de Lillebæk (Danemark), dont

le sous-sol est majoritairement constitué de till argileux et où les cours d’eau sont majori-

tairement alimentés par les eaux de drainage. Plusieurs simulations ont permis d’identifier la

manière la plus efficace de modéliser des parcelles drainées à l’aide du code HydroGeoSphere

intégrant écoulements de surface et écoulements souterrains, et capable aussi de simuler les

écoulements de drainage unidimensionnels. Le but était aussi de donner un aperçu de la

conception de modèles à plus grande échelle de systèmes de drainage complexes, pour lesquels

les temps de calcul peuvent devenir très importants. Un modèle de référence qui simule les

écoulements couplés de surface, souterrains et de drainage a été créé et a montré une réponse

rapide du drainage lorsque des précipitations ont été imposées. Une série de simulations ad-

ditionnelles ont été réalisées pour tester l’influence des conditions aux limites d’écoulement,

de la résolution temporelle des données de précipitation, de la représentation conceptuelle des

tills argileux et des drains, tout comme la discrétisation du maillage. Pour les modèles à plus

grande échelle, les simulations suggèrent qu’une simplification de la géométrie du réseau de

drainage est une option pertinente pour éviter les maillages trop fins. Représenter le réseau de

drainage par une couche à haute conductivité hydraulique reproduit correctement les débits

de drainage du modèle de référence. Cette approche réduit considérablement la complexité

du maillage et le temps de simulation, et elle représente donc une alternative à une représen-

tation discrète de drains à l’échelle d’un champ, mais un calage du modèle par rapport aux

débits de drainage observés est nécessaire.

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4.1 Introduction

Subsurface drainage is a common agricultural practice in humid climates and is designed

to lower the water table to prevent waterlogging and flooding and to maintain agricultural

crop productivity. In addition, drainage systems are used for land reclamation to expand crop

areas. Such systems, added with control structures, are also found in semi-arid to arid regions

where they are used to reduce or control the salinity of the root zone and soils by maintaining

a shallow water table depth (Hoffman and Durnford, 1999; Ayars et al., 2006). Tile drainage

networks are typically installed in low hydraulic conductivity soils, such as clays or silty clays.

Macropores or fractures located in these soils are preferential flow pathways that can generate

fast water flow and advection-dominant solute transport to the drains (Šimůnek et al., 2003).

While overland flow decreases during drainage, nutrients, pesticides and even soil particles

are transported through the tile drains. Nutrient transport leads to surface and coastal water

contamination, eutrophication and hypoxia issues, threatening local ecosystems (Blann et al.,

2009).

As stated by Warsta et al. (2013), proper nutrient transport quantification relies on water

movement quantification. When considering water balance at the crop or catchment scale,

field data collection is needed for quantifying rainfall, drainage flow or stream flow. However,

field data typically only gives information on the amount of water that flows at a drainage

system outlet, while the physical processes controlling water flow upstream of the outlet are

difficult to measure, even if it has been demonstrated that drainage water flow intensity is

tied to the area of land that is actually drained (King et al., 2014). Precise water flow/routing

separation could be measured, for example, by adding flowmeters at each contributing pipe

of the network, but that would imply arduous equipment installation and excessive costs. In

addition, it would disturb farmers work when plowing fields and thus disturb the object of the

study. Numerical models are therefore considered as necessary tools to characterize drainage

water flow in and around the entire drainage network, including their interactions with the

surrounding porous media.

Several numerical models have been developed to simulate hydrological processes related to

the drainage of clayey soils. These models have demonstrated that tile drainage networks have

a key impact on groundwater and surface water flow as well as on chemical species transport

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and erosion (Gärdenäs et al., 2006; Kiesel et al., 2010; Rozemeijer et al., 2010; Warsta et al.,

2013). Numerical models have also demonstrated reliable predictive abilities when used in

conjunction with in situ monitoring systems (Tim, 1996). Representing discrete tile drains

in a model requires information on the location and depth of the individual drains that

constitute the drainage network, which is often unavailable. Discretizing complex drainage

networks may also lead to extremely dense computational meshes and potentially very long

simulation times. As a result, the representation of complex tile drain networks in models

is often simplified and drains are simulated as high conductivity layers (e.g. Carluer and de

Marsily, 2004; Rozemeijer et al., 2010), open cylinders with a seepage face boundary condition

(e.g. Akay et al., 2008), or represented as nodal sinks (e.g. Gärdenäs et al., 2006) for which

subsurface water fluxes are estimated from mass balance equations (Purkey et al., 2004).

Depending on the specific simulation needs for a given tile drainage application, models have

focused on simulating hydrological processes at different scales. For example, comprehensive

one-dimensional models such as SWAP (Kroes and van Dam, 2003) or DRAINMOD (Skaggs,

1978) have been widely used for simulating vertical water flow and solute transport through

the saturated and unsaturated zones. Few models have been developed for two-dimensional

simulations, such as MHYDAS-DRAIN (Tiemeyer et al., 2007), a two-dimensional spatially

distributed model for simulating field-scale water flow in drained lowlands, where tile drains

are defined by their depth, slope, diameter and spacing and where drainage water flow is

assumed to originate from the soil matrix and macropores. At a larger scale, AnnAGNPS

(Binger and Theurer, 2001), which is an annualized version of the single-event agricultural

model AGNPS, solves Hooghoudt’s equation for tile drains in 2D agricultural watersheds.

The model is mainly applied to evaluate water quality related to crop rotation. SIDRA is

another deterministic model that simulates water fluxes through the saturated zone by solving

Boussinesq’s equation (Lesaffre and Zimmer, 1988). SIDRA can incorporate subsurface drains

as discrete drains at the bottom of a conductive layer that is located at the boundary with

a low permeability unit, and can compute drainage flow rates and hydraulic heads at mid-

distance between two parallel drains. PESTDRAIN (Branger et al., 2009) was later developed

by coupling SIDRA to the unsaturated and surface flow model SIRUP (Kao et al., 1998) and

to the pesticide transport model SILASOL. Another example of a 2D model that simulates

unsaturated and saturated water flow is ANTHROPOG (Carluer and de Marsily, 2004),

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which represents drains as a high-permeability porous medium.When creating catchment scale

models, the representative elementary watershed concept is used in the physically-based, semi-

distributed and process-oriented SWAT model (Arnold et al., 1998) by dividing the simulation

domain in hydrologic response units to simulate water flow, solute transport and sediment

transport in agricultural catchments. Du et al. (2005) improved SWAT with respect to the

simulation of tile drainage water flow by including a simple tile flow equation to the original

SWAT model.

A number of three-dimensional models have been developed to simulate tile drainage. The

finite-difference flow model MODFLOW represents drains as individual sinks that are ac-

tive when the water table is higher than the elevation of the drain (McDonald and Harbaugh,

1988). The volumetric flow rate out of the subsurface into the drain is computed with Darcy’s

law and requires that the conductance of the drain be specified. The FLUSH model was de-

veloped for simulating 3D hydrological processes in drained clay soils (Warsta et al., 2013).

FLUSH treats macropores and drains as local sinks, with macropores being coupled to tile

drains and the soil matrix. Furthermore, FLUSH considers additional cracks created in a

clayey matrix resulting from decreased matrix water saturation produced by drainage. Sub-

surface drains are defined in FLUSH as water sinks and cannot represent a source of water.

In contrast, the HYDRUS model allows drains located in the saturated zone to represent

pressure head sinks as well as sink/source terms when the surrounding matrix becomes un-

saturated (Šimůnek et al., 2006). In the 3D integrated catchment model MIKE-SHE/MIKE

11 (Refsgaard and Storm, 1995) tile drainage is also accounted for as a sink where drainage

is generated when the water table is above the drain level. The drainage water is then

routed either downhill or to the nearest stream. Another approach for simulating subsurface

drainage is to assume that drained plots are interconnected by pipes, which is used in the 3D

physically-based catchment model CATFLOW (Klaus and Zehe, 2011; Maurer, 1997).

MacQuarrie and Sudicky (1996) simulated 3D variably-saturated flow in a porous medium

coupled with one-dimensional channel flow into tile drains. They represent tile drains with

one-dimensional finite elements that are superimposed onto three-dimensional elements rep-

resenting the subsurface. Continuity of fluid pressure is assumed for nodes that belong to

both one-dimensional tile drain elements and three-dimensional subsurface elements, which

allows for water exchange between the drains and the surface. Drains can therefore act as

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either sources or sinks in the model. MacQuarrie and Sudicky (1996) used an earlier version of

the coupled surface and subsurface HydroGeoSphere model (Therrien et al., 2010) that only

simulated subsurface flow. The same approach described in MacQuarrie and Sudicky (1996)

to couple one-dimensional flow into tile drains to three-dimensional subsurface flow is used in

HydroGeoSphere, which can further couple tile drain and subsurface flow to two-dimensional

surface flow. Rozemeijer et al. (2010) used HydroGeoSphere for coupled surface and subsur-

face flow simulations but represented drains as equivalent-medium high conductivity layers in

a 3D model to test an experimental tile drainage network in a Dutch agricultural subcatch-

ment. Yue (2010) extended the approach developed by MacQuarrie and Sudicky (1996) to

simulate tile drains in HydroGeoSphere by removing the assumption of pressure continuity

at common drain and subsurface nodes, introducing resistance along the drain to compute

lateral flow, using the Preissmann slot method to combine free surface and pressurized flow

and allow for a flux boundary condition at the drain outlet.

In this study, results from various models were compared to identify an appropriate combi-

nation of model properties, with respect to simulation time, process description and mesh

refinement, to determine the most efficient model set-up to accurately simulate tile drainage.

We have applied the HydroGeoSphere model (Therrien et al., 2010) to simulate coupled

surface and subsurface flow in a tile-drained plot in the agricultural Lillebæk catchment in

Denmark. Previous work on the Lillebæk catchment has highlighted the significant impact of

tile drainage on surface water flow (Kronvang et al., 2003; Hansen et al., 2013). That work

suggests that a coupled surface and subsurface flow modeling approach that can also account

for flow into a complex tile drain network, such as provided by HydroGeoSphere, would be

well-suited for the catchment. To our knowledge, such a modeling approach has not been

documented before.

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4.2 Methods

4.2.1 Study area

The study area is a tile-drained agricultural plot of the Lillebæk catchment, which is located

on the island of Fyn in Denmark (Figure 4.1). The catchment is dominated by agricultural

land and its surface elevation varies between a maximum of 50 to 60 mamsl (meters above

mean sea level) to sea level elevation along the coast. Groundwater levels, stream discharge,

drainage discharge and nutrient fluxes in the catchment are regularly monitored within the

Danish Agricultural Watershed Monitoring Program LOOP, established in 1989 as part of

the Danish Action Plan for the Environment (Grant et al., 2007).

The regional landscape and near-surface geology have been shaped by several ice advances

and retreats associated with the Weichsel and the Saale glaciations (Houmark-Nielsen and

Kjær, 2003). Horizontal to subhorizontal Quaternary glacial and interglacial deposits lay

unconformably on Paleogene limestones (Danian) and marls (Selandian), which dip gently

towards the southwest (Gravesen and Nyegaard, 1989). The total thickness of the Quaternary

deposits varies between 30 m and 60 m. They consist of an upper clayey till from the

Weichsel glaciation that overlies a sand unit, which in turn overlies a clayey till from the

Saale glaciation. The upper till provides confinement for the sand unit, which is the regional

aquifer. The upper till also contains complex fracture and macro-pore networks that can

create vertical preferential water flow and mass transport pathways between the surface and

the underlying sand (Rasmussen, 1996; Klint and Gravesen, 1999; Klint, 2001; Nilsson et al.,

2001). Fractures and macropores form a well-connected network and they have been shown

to be hydraulically active along their total vertical extent (Nilsson et al., 2003). In addition

to vertical fractures and macropores, the tills at the site also contain horizontal sand lenses.

Depending on their extent, these lenses may be interconnected, for example through vertical

fractures, which can lead to fast water flow and contaminant transport (Kessler et al., 2012).

The average precipitation recorded in the Lillebæk catchment from 1990 to 2004 was about

839 mm/year (Hansen et al., 2013). The years 1996 and 2003 have been among the driest

for that period, with an average precipitation of 600 mm/year, while 1994 was the wettest

year with an annual precipitation of about 1100 mm/year. It is estimated that a third of the

yearly precipitation infiltrates into the soil and the recharge for the regional sandy aquifer is

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estimated at 150 mm/year (Grant et al., 2000).

Most agricultural soils are tile drained in the catchment and, as a result, surface water flow

is highly influenced by drainage flow. Tile drainage discharge has been regularly measured

at the outlet of the drainage network in Lillebæk. Water flowing in the drains discharges

into a collector well and water fluxes are measured with a 30◦ Thompson weir combined to

a water pressure transducer and a datalogger (Hedeselskabet, 1989). Manual water levels in

the collector are regularly monitored to validate these measurements. The drainage discharge

is continuously monitored but only daily discharge rates are recorded and available.

Sweden

Germany 0 50 100 200km

Copenhagen

Lillebæk

Lillebæk catchment Stream

Model area Piped stream

32 m

7 m

Urban/Settlement

Road

Agriculture

Grass

Natural grassland

Forest

Peatbog

Inland marsh

Surface water

Sea

Land use

a) b)

c)

Figure 4.1: Location of the Lillebæk catchment (55◦ 7’ N, 10◦ 44’ E) (a), shown with localland use and surface streams (b). The model area located within the catchment is highlightedin red, with the drainage network illustrated (c).

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4.2.2 Numerical model

Coupled 2D surface and 3D subsurface flow at the study site, along with 1D flow in individual

tile drains, was simulated with HydroGeoSphere, which is a fully-integrated three-dimensional

surface/subsurface water flow, solute and heat transport model (Therrien et al., 2010; Brunner

and Simmons, 2012). The governing equation for three-dimensional variably-saturated flow

in the subsurface is the following form of Richards’ equation:

∇ · krK · ∇h+Qδ (x− x0) +∑

Γext =∂

∂t(θsSw) (4.1)

where kr is the relative permeability of the porous medium, K is the hydraulic conductivity

tensor [L T−1], h is the hydraulic head [L], Q is source or sink term that represents an external

volumetric applied per unit volume [L3 T−1 L−3] at location x0, θs is the saturated water

content and Sw is the porous medium volumetric saturation. In equation 4.1, the term Γext

represents volumetric fluid exchange per unit volume [L3 T−1 L−3] with either the surface

flow domain or the tile drains.

Depth-integrated surface water flow is described by the following diffusion wave approxima-

tion:

∇ · (doKo) · ∇h0 +Qoδ (x− x0) + Γodo =∂dv

∂t(4.2)

where ∇ is the two-dimensional gradient operator, do is the depth of surface water flow [L],

Ko is a surface conductance that can be described, for example, with Manning’s formula, Qo

is a source or sink term that represents an external volumetric exchange term applied per

unit volume [L3 T−1 L−3] at location x0, and dv is the equivalent volume depth of water [L]

for depth of flow do in the presence of microtopography and surface obstructions. The term

Γo represents volumetric fluid exchange per unit volume [L3 T−1 L−3] with the subsurface

domain. This exchange is described by a first-order fluid flux term that depends on the

subsurface hydraulic head and depth of flow.

Fluid flow in tile drains can be represented with one-dimensional line elements where flow

along the element axis (s) is described by the following equation:

−∂

∂s(Q1D) +Qwδ (s− sp) +Af Γ1D =

∂t(Af ) (4.3)

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where Q1D is the volumetric water flux along the drain [L T−3] defined as Q1D = Afq1D

, where q1D is the linear velocity [L T−1] averaged over cross-section Af [L2], and Qw is

the volumetric flow rate in and out of the tile drain at location s = sp. The term Γ1D

represents the volumetric fluid exchange per unit volume [L3 T−1 L−3] with the subsurface

domain. Similarly, for the fluid exchange between the surface and subsurface, that exchange

is described by a first-order fluid flux term that depends on subsurface hydraulic head and

depth of flow in the tile drains.

Equation 4.3 represents the general form used in HydroGeoSphere to represent flow along one-

dimensional features such as wells, surface channels, pipes or tile drains. The volumetric flow

rate along these one-dimensional elements is represented by the following general equation:

Q1D = −C ·Af · (RH)p ·

[

∂hw

∂s

]q

(4.4)

where C is a proportionality constant, RH is the hydraulic radius and p and q are exponents.

For the tile drain simulations presented here, parameters were chosen such that equation 4.4

corresponded to the Hazen-Williams empirical equation for pipe flow.

All governing flow equations in HydroGeoSphere are discretized with the control volume finite

element method and the iterative Newton-Raphson method is used to solve the resulting

systems of discretized non-linear equations. Further details of the governing equations and

solution methodology are presented in Therrien et al. (2010).

4.2.3 Conceptual model

The exact location of most drains in the Lillebæk catchment is unknown but five small tile

drain sectors have been mapped and monitored as part of the LOOP program (Grant et al.,

2007). One such sector was selected for this study. The sector, which covers 3.5 ha, contains a

drainage network of irregular shape consisting of 5 main drains and 15 secondary drains with

a diameter of 0.1 m (Figure 4.1). A conceptual model for water flow was defined for this sector

to support the numerical simulations of coupled 2D surface and 3D subsurface flow along with

one-dimensional flow in the tile drain network. The conceptual model, described below, served

as the reference model for a series of simulations designed to investigate different conceptual

and numerical representations of the tile drainage network, as well as different boundary

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conditions. These other simulations, which represent variations of the reference model, are

also described in this section.

The lateral boundaries of the sector considered in the conceptual model, and highlighted

in Figure 4.1, are assumed to correspond to the area of influence of the drainage network.

Although Hansen et al. (2013) indicate that there is likely lateral flow in the regional sand

aquifer across these lateral boundaries, they are assumed here to be no-flow boundaries for

the conceptual model. The impact of lateral flow in the sand aquifer was assessed in one of

the simulations described below. The top of the domain corresponds to ground surface while

the bottom corresponds to the bottom of the sand aquifer, which overlies the lower clay till.

The bottom boundary is assumed to be a no-flow boundary. The geological units considered

in the model are the top soil, the upper clay till unit, and the sand aquifer. The upper clay till

is further divided into two sub-units, the A/B horizon and the C horizon, according to their

distinct hydraulic properties. There are no surface water bodies on the domain considered

and any water flow occurring at ground surface is assumed to exit at the point of lowest

ground surface elevation.

To assess the impact of the tile drainage network on surface and subsurface flow dynamics,

precipitation over a 4 day period, from 25 February 2002 to 1 March 2002, was considered.

Daily precipitation data for this period for the Lillebæk station were provided by the Danish

Meteorological Institute (DMI). However, we preferred to use hourly precipitation data to

provide a finer temporal resolution of the drain response to the rainfall input. In the absence of

hourly data at the Lillebæk station, we used temporal precipitation patterns from the nearby

Årslev weather station to infer hourly precipitation at Lillebæk, assuming that the hourly

precipitation pattern was similar at both locations. The Årslev station is located about 25 km

north-west of the Lillebæk catchment and records hourly precipitation. For the 4 day period,

the hourly precipitation at the Årslev station was calculated as a percentage of the total daily

precipitation. This hourly percentage was then applied to the recorded daily precipitation

at Lillebæk to provide discrete hourly values, which represents precipitation input at ground

surface for the model. The period considered is in winter and evapotranspiration is therefore

equal to zero.

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4.2.4 Reference model

The model area for the study site, shown in Figure 4.1c, was first discretized horizontally

with a triangular finite element mesh using the method described in Käser et al. (2014). This

method allows to automatically refine the mesh in areas with larger surface topography gra-

dients, compared to flat areas, which is better suited for surface flow simulations. Automatic

refinement is also possible near linear features such as tile drains or rivers. For the study site,

the 2D triangular mesh was refined along the drains and the lateral boundaries of the model,

as illustrated in Figure 4.2a. The length of the 1D elements representing tile drains was equal

to 2 m. The resulting triangular mesh, which represents the domain where the surface water

flow equation is solved, contains 5370 nodes and 10 383 elements. The hydraulic properties

of the surface flow domain are taken from (Hansen et al., 2013) and are assumed uniform

(Table 4.1). A critical depth boundary condition is applied at the lowest elevation of the

surface domain to allow outflow of surface water.

The 2D triangular mesh was duplicated in the third dimension, from ground surface down to

the bottom of the sandy aquifer to form 3D triangular prism elements. A total of 10 layers

of 3D elements with variable thicknesses were thus generated to discretize the top soil and

the two sub-units that form the upper clayey till, while the sandy aquifer was discretized

with one layer of elements. The 3D mesh thus contained 64 440 nodes and 114 213 triangular

prism elements. The nodes at the top of the mesh represent ground surface, which gently

slopes towards the southeast with elevations ranging from 29 to 23 mamsl. The elevation of

the nodes at the top of the mesh was interpolated from a digital elevation model that has

a grid size of 1.6 m. The thickness of the top soil was assumed to be uniform and equal

to 0.2 m while the thicknesses of the two upper till units were assumed equal to 2.0 m and

0.8 m for the A/B and C horizons, respectively (Table 4.1). The elevation of the top and

bottom boundaries of the sandy aquifer were interpolated from a geological model set up for

the Lillebæk catchment by Hansen (2010) on a 50 m grid. The resulting total thickness of

the sandy layer in the model varies between 30 m and 35 m.

The hydraulic properties of the four different geological units are shown in Table 4.1. Each

unit is assumed to be homogeneous with hydraulic conductivity and specific storage values

taken from Hansen et al. (2013) and also based on infiltration tests (Nilsson et al., 2001). A

vertical to horizontal anisotropy ratio of 10 is assumed for the hydraulic conductivity of the

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Table 4.1: Hydraulic properties of the reference model for the subsurface units, surface flowdomain and tile drains.

Domain Unit Parameter Value

Subsurface

Top soil

Horizontal hydraulic conductivity Kh [m s−1] 2.2 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 2.2 × 10−5

Specific storage Ss [-] 1.0 × 10−3

Thickness [m] 0.2

Clayey till(A/B hori-zons)

Horizontal hydraulic conductivity Kh [m s−1] 3.8 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 3.8 × 10−5

Specific storage Ss [-] 1.0 × 10−3

Thickness [m] 2.0

Clayey till(C horizon)

Horizontal hydraulic conductivity Kh [m s−1] 3.8 × 10−8

Vertical hydraulic conductivity Kv [m s−1] 1.9 × 10−8

Specific storage Ss [-] 1.0 × 10−3

Thickness [m] 0.8

Sandy aquifer

Horizontal hydraulic conductivity Kh [m s−1] 4.6 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 4.6 × 10−7

Specific storage Ss [-] 2.0 × 10−3

Thickness [m] 30 to 35

SurfaceManning roughness coefficient [m1/3 s−1] 10Rill storage height [m] 1.0 × 10−3

Obstruction storage height [m] 1.0 × 10−3

Tile drains Diameter [m] 0.1

top soil and clay tills to account for the presence of macropores and vertical fractures (Nilsson

et al., 2003). The unsaturated hydraulic properties of the top soil and clayey till units were

described with the van Genuchten functions (van Genuchten, 1980), with a residual saturation

equal to 0.164 and van Genuchten parameters α and β equal to 2.3 m−1 and 1.26, respectively.

These values were obtained with the ROSETTA pedotransfer model (Schaap et al., 2001) by

calibrating van Genuchten’s curves based on grain size analysis on soil samples from the

Lillebæk catchment. The calibration process and the van Genuchten parameter values were

given by Hansen et al. (2014).

When constructing the 3D mesh, one layer of nodes was located at a depth of 1 m below

ground surface, which is the assumed depth of the tile drains for the study site. Nodes

belonging to that layer, and whose position corresponds to that of the network shown in

Figure 4.1c, were selected to construct the drainage network with one-dimensional elements.

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The trace of the network is visible when inspecting the mesh shown in Figure 4.2a, which

has been refined close to the drains. The tile drains, which were represented in the model by

discrete 1D linear elements, were assumed to have a diameter of 0.1 m (Table 4.1). A critical

depth boundary condition is applied at the outlet of the drainage network to allow water to

flow out of the simulation domain.

For all simulations described below, hourly precipitation for the 4 day period described pre-

viously was applied at the top of the surface domain. A challenge in coupled surface and

subsurface flow simulations is to specify initial conditions that are in equilibrium with the

prescribed boundary condition before precipitation is applied (Ajami et al., 2014). To define

the initial conditions, a preliminary simulation was conducted where the model domain was

initially fully saturated and then allowed to drain, without precipitation, for a sufficiently

long period (100 years in this case) to reach steady-state flow conditions for the prescribed

boundary conditions, excluding precipitations. The simulations were then started for the 4

day period and the model was run for another 3 month period without any rainfall to analyze

the response of the drains to the 4 day period and to let the model reach quasi steady-state

again. Very low convergence criteria were specified for the Newton-Raphson iterations to keep

the mass balance error as low as possible (Table 4.2). Adaptive time stepping was used for

adjusting time steps according to the variation in saturation during each simulation (Therrien

et al., 2010).

Table 4.2: Convergence criteria for the Newton-Raphson iteration and the flow matrix solver.

Criterion Value

Newton-Raphson absolute convergence criterion [m] 1.0 × 10−20

Newton-Raphson residual convergence criterion [-] 5.0 × 10−7

Iterative flow matrix solver convergence criterion [m] 1.0 × 10−13

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4.2.5 Test models

A series of test models, based on the reference model, were developed to investigate the

impact of some of the assumptions of the conceptual model. This section describes the test

models, which are also listed in Table 4.3. For some of these test models, parameters were

adjusted during the simulations to reproduce the model output from the reference model.

These adjustments are commented below.

100 m

(a) (b) (c)

(d) (e) (f)

Figure 4.2: a) 2D triangular mesh created to discretize the domain shown in Figure 4.1c andused for the reference model and tests 1 -4, b) coaser mesh, with 5 m discretization for tiledrains, used for test 5, c) finer mesh, with 1 m discretization for tile drains, used for test 6,d) mesh for a simplified network (test 7), e) mesh used for the simulation with a drainagelayer (test 2) where the drainage network is shown but was not discretized, f) location of theoutflow boundary nodes of the drainage layer for test 2.

Test 1

The first test was set up by modifying the drainage boundary condition at the drainage

network outlet, where a prescribed hydraulic head was specified instead of a channel critical

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Table 4.3: Tests performed on the reference model (Ref.) illustrating the type of represen-tation for the drains (Drain type), the boundary condition at the drain outlet (Drains BC),the lateral flow boundary condition along the aquifer layer (Lateral BC), the time interval forprecipitation (Precip.) and the conceptual model for the subsurface (Porous media).

Test n◦ Drain type Drains BCLateral BC(aquifer)

Precip. Porous media

Ref. discrete channel no flow hourly single

1 discrete fixed head no flow hourly single

2 equivalentmedium

- no flow hourly single

3 discrete channel fixed head hourly single4 discrete channel no flow hourly dual5 discrete channel no flow hourly single6 discrete channel no flow hourly single7 discrete channel no flow hourly single8 discrete channel no flow daily single

depth boundary condition. The prescribed hydraulic head was equal to the elevation of the

drain at the outlet, which is a boundary condition often used to represent drains. For example,

in MODFLOW, a high prescribed value for the drain conductance will produce a hydraulic

head at the drain cell equal to the drain elevation. This situation corresponds to a very

efficient drain that always maintains the water table lower or equal to its elevation. The goal

of this first test was thus to compare results for both types of boundary conditions and to

observe potential differences in water outflow values.

Test 2

For this test, the discrete drainage network was not discretized with one-dimensional elements

but rather represented as an equivalent porous medium by introducing a high hydraulic

conductivity layer having a thickness of 0.1 m, which corresponds to the drains diameter.

This layer is assumed to be present over the whole simulation domain. Including such a

conceptual drainage layer greatly simplifies the mesh since individual drains are no longer

discretized (Figure 4.2e). The layer was given properties of a typical sand to gravel material

(Table 4.4). Hydraulic conductivities were initially defined with an anisotropy factor of 10

in the horizontal direction, but were subsequently modified for reproducing the simulated

drainage discharge from the reference model. Values shown in Table 4.4 are the adjusted

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ones.

To simulate outflow from the drainage layer, all nodes belonging to that layer that are located

at the downstream boundary of the domain were assigned prescribed hydraulic heads equal

to their elevation. Those nodes are shown in Figure 4.2f. Other types of boundaries were

tested for these nodes, such as a seepage face, but the prescribed heads were best suited here.

Table 4.4: Hydraulic properties of the equivalent porous medium layer used to represent thedrainage network (Test 2).

Parameter Value Reference

Horizontal hydraulic conductivity Kh [m s−1] 1.0 × 10−2 Assumed, manually adjustedVertical hydraulic conductivity Kv [m s−1] 1.0 × 10−5 Assumed, manually adjustedSpecific storage Ss [-] 1.0 × 10−5 AssumedResidual saturation Sr [-] 0.045 Carsel and Parrish (1988)van Genuchten parameter α [m−1] 1.45 Carsel and Parrish (1988)van Genuchten parameter n [-] 2.68 Carsel and Parrish (1988)

Test 3

For this simulation, the lateral boundaries of the domain were modified to account for regional

flow in the sandy aquifer. The no-flow lateral boundaries in the sandy aquifer were thus

changed to prescribed hydraulic heads, with values taken from the model developed by Hansen

et al. (2013). These hydraulic heads were assumed to remain constant during the simulated

4 day-precipitation event.

Test 4

Nutrient transport is a current issue in the Lillebæk catchment and future work will likely

focus on nutrient transport modelling. In this case, a dual continuum approach might be more

appropriate than a single continuum approach to account for transport and preferential water

flow in fractured and macropore bearing clayey tills (Rosenbom et al., 2009). Although a

discrete fracture modeling approach is the most efficient way of simulating water flux through

fractured clayey till aquitards (Jørgensen et al., 2004), there is no data on fracture length,

spacing, density and orientation for our study area. Efficiency of a dual-permeability model

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using HydroGeoSphere and its ability to accurately simulate nutrient transport in macrop-

orous soils has been demonstrated by Frey et al. (2012). We have consequently decided to

apply a similar conceptual model here.

Macropores have been observed in the A horizon of the upper clay till in Lillebæk, as well as

in the top soil, while the B horizon mostly contains fractures (Nilsson et al., 2003). Both hori-

zons were therefore defined as dual-permeability media for this simulation, with one medium

representing the clay matrix and another medium representing either the system of macrop-

ores for horizon A and the top soil or fractures for horizon B (Table 4.5). Properties of the

interface between the matrix and both the macropores and fractured media, which control

fluid exchange between the media, are assumed to be similar to those of the clay matrix,

which is the approach used by Gerke and van Genuchten (1993). Volume fractions for the

dual-permeability medium were assumed equal to 55 % for the matrix and 45 % for the macro-

pores and fractures. Although the actual volume fractions of matrix and macropores/fractures

are unknown; it is likely that the volume fraction for macropores and fractures is lower than

the value assumed here. Furthermore, those volume fractions were selected to also fit the

drainage outflow hydrograph simulated with the reference model.

Table 4.5: Hydraulic properties for the dual-permeability simulation (Test 4).

Medium Parameter Value Reference

Matrix(A/B hori-zons)

Hydraulic conductivity K [m s−1] 7.0 × 10−9 Nilsson et al. (2003)Specific storage Ss [-] 1.0 × 10−3 AssumedResidual saturation Sr [-] 0.10 Estimated from Yates et al. (1992)van Genuchten parameter α [m−1] 1.5 Estimated from Yates et al. (1992)van Genuchten parameter n [-] 1.25 Estimated from Yates et al. (1992)

Macropores(A horizon)

Horizontal hydraulic conductivity Kh [m s−1] 1.0 × 10−5 Estimated from Nilsson et al. (2003)Vertical hydraulic conductivity Kv [m s−1] 1.0 × 10−3 AssumedSpecific storage Ss [-] 1.0 × 10−3 AssumedResidual saturation Sr [-] 0.01 Rosenbom et al. (2009)van Genuchten parameter α [m−1] 10 Gerke and van Genuchten (1993)van Genuchten parameter n [-] 2.0 Gerke and van Genuchten (1993)

Fractures(B horizon)

Horizontal hydraulic conductivity Kh [m s−1] 3.8 × 10−7 Estimated from Hansen et al. (2013)Vertical hydraulic conductivity Kv [m s−1] 3.8 × 10−5 Estimated from Hansen et al. (2013)Specific storage Ss [-] 1.0 × 10−3 AssumedResidual saturation Sr [-] 0.01 Rosenbom et al. (2009)van Genuchten parameter α [m−1] 4.687 Rosenbom et al. (2009)van Genuchten parameter n [-] 2.297 Rosenbom et al. (2009)

Matrix volume fraction [-] 0.55 Assumed, manually adjusted

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Tests 5, 6 and 7

The representation of discrete drains in a numerical model can greatly increase the number of

nodes, as illustrated by the mesh in Figure 4.2a, and thus increase simulation times. Models

developed for catchments larger than that considered here can potentially lead to extremely

large meshes and make simulation impractical. It is therefore useful to investigate the impact

of the level of discretization of drains on flow dynamics, which was done here for Tests 5

to 7. The reference model had 2 m elements along discrete drains. For Test 5, a coarser

mesh was created with 5 m elements along drain segments (Figure 4.2b) while a finer mesh

was created for Test 6 with 1 m elements along drain segments (Figure 4.2c). For another

simulation, Test 7, the drainage network was simplified by retaining only the 5 main drains,

which reduces the number of nodes (Figure 4.2d). This last simulation aimed at assessing the

effective contribution of the main drains to the total water outflow.

Test 8

This simulation aimed at comparing the impact of using the original daily precipitation data

as opposed to the hourly precipitation data used in the reference model. The simulated

drainage outflow rates were also compared to the measured daily outflow rates to evaluate

the representativeness of this model. Since this model was not calibrated, this comparison

remains qualitative. However, the total volume of water flowing through the drains could be

evaluated for both the reference model and this Test 8 model to assess any differences in the

amount of water stored in the subsurface following precipitation.

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4.3 Results

In this section, results from the reference model are first presented followed by a comparison

of simulated hydrographs and water balance between the reference model and the various test

models.

4.3.1 Reference model

The applied precipitation for the 4-day period shows three main peaks within the first 24 hours

(Figure 4.3). The highest precipitation intensity of 7.9 mm h−1 corresponds to the second

peak. The simulated drainage discharge shows that the drainage system quickly responds

to precipitation, with drainage flow peaks reached 50 to 60 minutes after precipitation peak

values are applied to the model surface (Figure 4.3).

The generated overland flow hydrograph also contains three peaks but their intensities vary

more than that of the drainage system. The first peak in overland flow only seems to be

influenced by the second half of the first precipitation peak, meaning that during the first half

of the peak all the water is infiltrating and either flowing through the unsaturated zone to the

drains or recharging the aquifer. The second overland flow peak has a maximum water flow

rate value that is almost twice as high as the drainage peak value (Table 4.6). For this specific

period in the simulation, the drainage water flow capacity may thus be exceeded inducing

pipe pressurization issues in some pipes of the drainage network.

The overland flow values for the third peak are lower than that of drainage flow. Secondary

precipitation peaks after day 86 (after 2 days of simulation) produce drainage flow but don’t

lead to generation of overland flow, as shown in Figure 4.3. This figure also shows that the

recession for drainage is slower than for overland flow, with drainage flow rates gradually

decreasing to zero over a few days after the rainfall event, whereas overland flow rates show

an abrupt decrease to zero. At the outlet of the drainage network, the hydraulic head is 17

cm higher at the second peak than it is initially before the first peak (Table 4.6).

As a full simulation including evapotranspiration is outside the scope of the present study

and, as hourly observed discharge data are not available, we aim at simulating plausible

hydrographs that reflect the hydrological regime and allow realistic studies of numerical issues

related to alternative model conceptualizations rather than matching the observed hydrograph

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perfectly. Furthermore, the flows and water balance of such a small catchment are to a large

extent governed by boundary fluxes that are unknown. Therefore we have not attempted

to calibrate our model against observed discharge. Figure 4.3 shows that the simulated

discharges are somewhat higher than the observed ones, and analyses of the total water flows

during the four day period reveal that the model simulates about 50 % more runoff than

observed, indicating that the model dynamics are slightly more flashy than the observations.

But altogether, the pattern of response is reasonable and the simulated hydrographs reflect

the observations sufficiently well to serve the purpose of our study.

The total water balance for the simulation period is displayed in Table 4.7. The total water

outflow is higher than precipitation and the amount of water stored in the porous medium

therefore decreases as the simulation progresses. All precipitation water is thus flowing out

through the drains or at the soil surface while, before the start of precipitation, no water orig-

inating from precipitation is flowing through the drains. Because the initial head distribution

corresponds to a quasi steady-state, the outflow at the drain outlet during the transient sim-

ulation is not exactly equal to zero but its value is very small compared to the magnitude of

precipitation. This background outflow was also observed for most of the test models, except

for tests 3 and 4 for which no background outflow is observed. Outflow from the drains cor-

responds to 78.7 % of the total water outflow for the model. Outflowing water also originates

from the soil matrix.

The saturation distribution in the glacial clayey till unit, shown in Figure 4.4 where the sandy

aquifer layer has been masked, shows that tile drainage leads to a quick drop in saturations

during and after the precipitation event. The impact of drainage is clearly seen in the down-

stream part of the model, which is almost fully saturated during the event (first and second

peaks). Low saturations are observed around the drains in an otherwise saturated surrounding

environment. The upstream part shows lower saturation values than the downstream part,

however in the part of the model having no drains a high saturation lens distinctly appears

at the first peak and persists to the end of the event. The steady-state snapshot taken before

the event shows that the water table is initially below the drainage system. The water table

rises at the end of the event (day 89) but remains mostly below the drains.

The initial baseflow value, which is very close to 0 m3 s−1 and corresponds to a pseudo steady-

state, is reached again shortly after the event.

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Figure 4.3: Hydrographs of drainage discharge at the network outlet and overland flow at thesurface outlet and applied hourly precipitation at ground surface for the 4-day simulation.Observed daily drainage flow data results are also presented.

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Table 4.6: For each model, computed maximum drainage (Qmax drains) and overland(Qmax surface) flow rates at second peak, and computed hydraulic heads at the outlet ofthe drainage network just before the rainfall event (Hout init) and for the second peak(Hout peak).

Test Qmax drains [m3 s−1] Qmax surface [m3 s−1] Hout init [m] Hout peak [m]

Ref. 2.30 × 10−2 4.41 × 10−2 22.63 22.80

1 2.39 × 10−2 4.31 × 10−2 22.63 22.632 2.23 × 10−2 4.64 × 10−2 22.63 22.803 2.27 × 10−2 4.18 × 10−2 20.83 22.804 1.79 × 10−2 5.08 × 10−2 22.63 22.715 2.47 × 10−2 4.25 × 10−2 22.63 22.816 2.22 × 10−2 4.47 × 10−2 22.63 22.807 1.30 × 10−2 5.50 × 10−2 22.63 22.748 7.63 × 10−3 2.63 × 10−3 22.63 22.71

Figure 4.4: Saturation distribution in the clayey till for steady-state conditions (before theprecipitation event), at the time of the first precipitation peak, at the time of the second peakand at the end of the 4-day simulation. The black lines across the sections show the drainagenetwork.

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a) b)

c) d)

Figure 4.5: Water table elevation (WT), expressed in mamsl, of the reference (a) and test 2(b) models at peak 2 (day 85.3). Water table elevation after the three main peaks, displayedat day 86, is also shown for the reference (c) and Test 2 (d) models. The black lines arethe pipes constituting the drainage network. Coordinates are ETRS 89 / UTM Zone 32 Ncoordinates.

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Table 4.7: Global water balance for each model illustrating the total precipitation amount (Ptot), the total water outflow amount (Vout),the total drainage outflow (Vdrains), the total overland outflow (Vsurface), the corresponding storage to/from the matrix (Stor.) andthe total water mass balance. Positive Stor. values reveal water storage in the porous medium while negative values show water releasedby the porous medium.

Test Ptot [mm] Vout [mm]Vdrains [mm] Vsurface [mm]

Stor. [mm]Mass balance

Amount [mm] % of Vout Amount [mm] % of Vout Amount [mm] Error [%]

Ref. 41.4 42.8 33.7 78.7 9.1 21.3 −0.8 −0.6 0.1

1 41.4 44.5 35.6 80.0 8.9 20.0 −2.1 −1.0 0.32 41.4 45.1 37.4 82.9 7.7 17.1 −2.4 −1.3 0.33 41.4 24.1 16.4 68.0 7.7 32.0 0.0a 0.0 0.04 41.4 31.5 23.9 75.9 7.6 24.1 9.5 0.4 0.015 41.4 42.5 33.3 78.4 9.2 21.6 0.4 −0.7 0.46 41.4 42.3 33.7 79.7 8.6 20.3 0.2 −0.7 0.37 41.4 42.2 27.3 64.7 14.9 35.3 −0.1 −0.7 0.38 41.4 40.3 35.8 88.8 4.5 11.2 1.6 −0.5 0.8

aThe storage value for Test 3 doesn’t account for the outflow induced by the prescribed head aquifer boundary condition.

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4.3.2 Test models

Test 1: drainage fixed head boundary condition

Modifying the boundary condition at the outlet of the drainage network produces a hydro-

graph similar to the reference hydrograph (Figure 4.6a). Compared to the reference model,

the second peak is slightly higher (+4 %) while the first and third ones are close to the

reference. Recession after the peaks is identical to that of the reference model. While the

highest peak for drainage is slightly higher than that of the reference model, the maximum

simulated overland flow rate is lower (−2 %, see Table 4.6) and the total overland outflow is

slightly lower than the reference (−2 %, see Table 4.7). In addition, this first test produces

an increase in the total volume of water drained compared to the reference model (+5 %)

and the soil matrix contribution (storage) is higher (+162 %). The total mass balance error

is a bit higher than that of the reference model (+0.2 %). Finally, because of the fixed head

boundary condition, no hydraulic head changes are observed at the outlet of the drainage

network from the beginning of the rainfall event and the second peak (Table 4.6).

Test 2: equivalent medium as drainage layer

The model (Test 2) that represents the drainage network as a single drainage layer, using an

equivalent porous medium approach, reproduced almost exactly the outflow hydrograph of

the reference model. Since the hydrograph for Test 2 cannot be distinguished from that of

the reference model, it is not shown in Figure 4.6. From a conceptual perspective, the outflow

hydrograph is not for a single location, such as the outlet of the drainage network as is the

case for the reference model, but a series of nodes that correspond to the outlet of the drainage

layer (as shown in Figure 4.2f). That outlet corresponds to a vertical face having a thickness

of 0.1 m and a length slightly larger than 100 m where hydraulic heads are prescribed, which

explains why no change in hydraulic head is seen (Table 4.6). Although the total outflow is

similar to that of the reference model, the equivalent porous medium model produces spatial

distributions of hydraulic head and saturation that are different from those produced by

the reference model. However, when looking at Figure 4.5, it appears that the water table

elevation calculated by the Test 2 model (Figure 4.5b and Figure 4.5d) doesn’t show extreme

differences from the reference model water table elevation (Figure 4.5a and Figure 4.5c). The

highest peak intensity for drainage is slightly lower than that of the reference model (−3 %),

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but the maximum overland flow rate at peak 2 is higher than for the reference (+5 %, see

Table 4.6). This model produces more intense overland flow peaks but the overall amount of

surface water is lower than for the reference (−15 %, see Table 4.7). This test also produces

water storage unlike the reference (+200 %) and the total mass balance error is a bit higher

than the reference model (+0.2 %).

Test 3: aquifer layer prescribed head boundary condition

Compared to the reference model, the drainage outflow caused by the first precipitation peak

during day 84 is delayed and lower, while the drainage outflow for the other two precipitation

peaks at day 85 is similar. The model also produces faster drainage recession, with outflow

rates becoming zero after the first precipitation and third precipitation peaks. Furthermore,

outflow drainage remains equal to zero after day 86 since the water table remains below the

location of the drains for that period.

The sum of drainage and overland outflow for this model is much lower than that of the

reference (−44 %, see Table 4.7). The model also produces less drainage outflow and surface

outflow (−51 % and −15 % respectively). A feature of this model is that there is no change

in the amount of water stored in the matrix (storage = 0 mm). The total mass balance

error is also somewhat higher than the reference (+0.2 %). Finally, the second precipitation

peak produces higher overland flow rate than drain outflow (Table 4.6), suggesting pipe

pressurization, and the initial groundwater head at the outlet is much lower than the reference

(about 1.60 m lower), while the peak head value is the same.

The lateral boundaries for the underlying sandy aquifer were assumed to be no-flow boundaries

for the reference model, although there is evidence of horizontal water flow in the sandy aquifer

across these boundaries (Hansen et al., 2013). For the Lillebæk catchment, observed lateral

inflow into the sandy aquifer should ideally be included in the model, since it influences

the drainage outflow. However, assigning the inflow boundary for the Lillebæk model, or

for similar catchment models, is a challenge since lateral flow rates in aquifers are generally

unknown. Specifying a constant head as was done here remains an approximation since it

assumes that other boundary conditions, such as rainfall, do not affect the hydraulic heads

at the aquifer boundary.

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Test 4: clayey till dual permeability medium

The dual-permeability model produces lower peaks for drainage outflow compared to the

reference model (Figure 4.6a). Peaks appear less smooth than the other cases. Even if dual

media are taken into account here, this model shows a similar peak time lag simulated of 57

min than the reference case (Figure 4.6a). Since lower peaks are observed on the hydrograph,

the maximum drainage outflow value (−22 %) and the hydraulic head at the outlet at peak

2 (9 cm lower, see Table 4.6) and the total drainage outflow volume (−29 %, see Table 4.7)

are much lower than for the reference model. The total volume of overland flow for this

simulation is lower than for the reference model and the maximum overland flow rate is

higher. Less overland flow is generated and drainage is less effective. This model shows a

significant increase in the water stored for the total simulation period, meaning that some

part of the total water flowing through the model is stored in the soil matrix. It is also the

model with the lowest mass balance error.

Tests 5, 6 and 7: mesh refinement and simplification influences

Simulations for models 5 and 6 produced similar drainage hydrographs at the outlet of the

network (Figure 4.6b). The simulation with the coarser mesh (Test 5) produces peaks that

are slightly larger than those produced by the reference model (+7 %). Test 6 shows a second

peak that is slightly lower than that of the reference model (−3 %). The mass balance shows

that the total outflow for the coarser mesh model is slightly lower than for the reference model

(−0.7 %, see Table 4.7), but the mass balance error is higher (+0.3 %). A lower contribution

of drainage and a slightly higher contribution of overland flow are observed (−1 % and +1 %

respectively). For the finer mesh (test 6), the water balance for drain outflow is similar to the

reference model but overland flow is smaller (−5 %). In both cases, storage values are positive

and the total error is higher (+ +0.2 %, see Table 4.7). The main difference caused by the

different levels of discretization used for Tests 5 and 6 is thus lower overland flow produced

by the finer mesh. Additionally, the overland outflow peak for test 6 is higher than for the

reference model while it is lower for Test 5 (+1 % and −4 % respectively, see Table 4.6).

Although the maximum drainage flow rates are observed for different mesh refinements, the

hydraulic heads at the outlet remain similar (Table 4.6).

The simulation for a simplified drainage network (Test 7) results in a lower drainage outflow

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Figure 4.6: Outflow hydrographs of the drainage network for a) the reference model and tests1, 3 and 4 and b) the reference model and models with refined meshes along the drains (5 to7). Precipitation is also plotted for comparison purpose.

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(−19 %), as illustrated by the lower intensity of the peaks in the hydrograph (Figure 4.6b) and

a higher contribution to overland flow than for the reference model (+64 %, see Table 4.7).

The water released by the matrix storage is also lower for this case (storage = −0.1 mm). The

maximum water flow rate variations calculated by the model for drainage and overland flow

are emphasized as the drainage value is lower than the reference (−43 %) and the overland

flow is higher (+25 %). Lower drainage flow rates imply a lower hydraulic head at the outlet

of the network during the rainfall event (6 cm lower) while the initial head is equal to the

reference model initial head value.

Test 8: daily precipitation

The daily precipitation time series, shown in Figure 4.7, has only one main peak. When daily

precipitation is applied, the simulated drainage curve shows a distinct response of drains to

the infiltrating rain and even shows a tendency to reach plateaus for each daily precipitation

value (Figure 4.7). The simulated drainage discharge rates are higher than the observed ones,

but the temporal trend for both drainage curves is similar and shows a distinct response to

rainfall. Comparison of Figure 4.3 and Figure 4.6 shows that the maximum discharge rates at

the outlet of the network are smaller than those computed for the reference model, although

the total volumetric outflow is similar. Those lower discharge rates, which can be viewed as

mean rates for a 24-hour period, are also associated with a smaller difference in hydraulic

head at the network outlet (9 cm difference), even though the initial value is the same as in

the reference model. The water mass balance for this test shows a slightly lower water amount

exported with 88.8 % flowing out through the drains while water is stored in the matrix (1.6

mm). The total mass balance error is the highest of all models (0.8 %).

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Figure 4.7: Calculated and observed drainage discharge hydrographs and daily precipitationvalues applied to the model. Precipitation values originate from data measured daily at 6 am,this explains the short time-lag for the precipitation curve.

Table 4.8: Mesh specification and computational times for the reference and test models.Each simulation was run using a 3.39 Gb RAM computer with 8 CPU cores at 3.40 GHz.

Test Description Nodes Elements Computing time Time steps

Ref. Critical depth drainage 64 440 114 213 2 h 40 min 206

1 Prescribed head drainage 64 440 114 213 1 h 12 min 2752 Equivalent medium 21 564 35 618 15 min 5293 Aquifer prescribed head 64 440 114 213 1 h 37 min 5294 Clay till dual-permeability 64 440 114 213 13 h 35 min 66745 Coarse mesh 30 012 51 095 21 min 4356 Fine mesh 139 020 250 888 6 h 2 min 4497 Simplified network 47 112 82 445 50 min 3508 Daily precipitation 64 440 114 213 50 min 518

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4.3.3 Computational performance

All simulations were run using a 3.39 Gb RAM computer with 8 CPU cores at 3.40 GHz

and with the parallelized version of HydroGeoSphere (Hwang, 2012; Hwang et al., 2014).

One of the objectives of testing different models was to investigate computational aspects,

in particular the simulation time and the number of time steps required for the simulation.

Both results are found in Table 4.8 for the various models. The total number of time steps

required for the simulation varies because a variable time stepping option was used in Hydro-

GeoSphere. As a result, the number of time steps, and the time step size, required to reach a

similar convergence criteria for the Newton-Raphson iteration can vary from one simulation

to another.

The reference model and the Tests 1, 3, 4 and 8 had the same mesh but the total simulation

time varied. Specifying a prescribed hydraulic head boundary at the drainage outlet for the

first test reduced the simulation time by more than half compared to the reference model.

The equivalent medium drainage layer model (test 2) had the mesh with the fewer elements

and nodes and was the fastest model. Changing the aquifer lateral boundary conditions from

no flow to prescribed head (test 3) also speeds up the simulation compared to the reference

model but more time steps are taken by the model. On the other hand, the dual-permeability

model (test 4) greatly increased the total simulation time, which was 13 h 35 min, as well as

required a much larger number of time steps for the simulation.

Models 5 to 7 used meshes that were different from that of the reference model, which influ-

enced the total simulation time, in addition to the variations made to the model compared

to the reference model. A coarser mesh along the drains (test 5) reduced by more than half

the number of nodes and elements and decreased the total simulation by a factor of 10. The

finer mesh had the opposite effect, with a longer simulation time. A simpler drainage network

(test 7) also shortened the total time needed for a model run as the model has fewer elements.

Finally, applying daily precipitation data (test 8) also greatly reduced the total simulation

time compared to the reference model, even if more time steps were taken by the model.

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4.4 Discussion and conclusions

The simulations presented here suggest that, in the context of tile drainage, a fully coupled

subsurface, surface and drainage model allows for a more realistic representation of the flow

dynamics.

However, simulation time and data availability remain major challenges. For example, if

drains are only partially mapped within a catchment and their location, orientation, and

length are unknown, using an equivalent medium layer for representing drainage remains a

valid option. Creating an equivalent medium layer is also appropriate to avoid dense meshes

and therefore exceedingly long simulation times. A similar drain representation has been

successfully applied in real cases (e.g. Rozemeijer et al., 2010) and provides considerable

advantages in simplifying the model mesh and avoiding internal boundary conditions. Carlier

et al. (2007) have developed a method for calculating equivalent medium parameters based

on the drainage network geometry. They have applied it at the field scale on a drainage

network made of parallel pipes located at regular intervals. Defining the equivalent layer

properties with this method did not seem feasible in our case as the drainage network is

irregular and most of the drains do not show a parallel pattern. The equivalent medium

hydraulic parameters were therefore defined by modifying the model properties to reproduce

the reference model drainage outflow values. On the other hand, such a model ideally requires

calibration against drainage observation data to reproduce the water budget at the field or

catchment scale.

Using HydroGeoSphere, Frey et al. (2012) have shown that a dual-permeability representation

of the subsurface is required to simulate nutrient transport in low-permeability macroporous

soils. Tile drainage is commonly used in agricultural environments, where transport of chem-

ical species or even sediment particles is often a key modeling issue. The conceptual model

to represent that tile-drained material, for example an equivalent porous medium or a dual-

permeability medium, should therefore be carefully chosen.

The temporal resolution of precipitation data applied in the model can significantly affect

flow dynamics. Using hourly datasets instead of daily datasets produced more pronounced

drainage peaks, suggesting that a higher rainfall frequency should be used when possible.

Although a coupled surface, subsurface and tile drain flow model is suggested as the preferred

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one, the various models tested here also show the influence of other model parameters on

drainage outflow, such as choice of boundary conditions and mesh size. Even though we have

been focusing on the subsurface drainage network in the clayey till unit, setting lateral fixed

head boundary conditions to the underlying sandy aquifer layer improves the drainage sim-

ulation. Depending on the need of further transport simulations, using a dual-permeability

representation of the low-permeability clayey till may be required for better representation

of matrix diffusion and advective transport through macropores. When constructing larger

scale models, simplifying the drainage network also simplifies the mesh and reduces simula-

tion times, but model calibration against observation data is needed to adequately represent

drainage.

As pointed out by Koch et al. (2013), proper flow modeling of tile drained areas should include

discrete tile drainage systems. At field scale, our simulations showed that discrete pipes are

the most relevant concept to be chosen for modeling proper drainage flow dynamics. However,

a representation of the whole drainage network in a model may lead to very long and perhaps

impractical simulation times. Simplifying the drainage network, as tested here by taking into

account the main collecting pipes of the network, represents an alternative for fast computing

times.

When performing simulations at larger scales, one would need to include various drainage

areas made of numerous pipes in a model. The need of modeling drainage flow originating

from such areas may be restrained by highly discretized meshes. In such a case, the network

simplification option is a suitable option for simulating drainage flow. In addition to reducing

simulation time, it allows modelers to avoid creating dense and complex meshes. Another rec-

ommended concept to avoid dense meshes is to represent drainage networks by an equivalent

high-conductivity porous medium layer, as adopted by Rozemeijer et al. (2010). Nevertheless,

with both options, calibration is needed against observed drainage flow rate data to ensure

proper calculations of water volumes involved in drainage.

Even if no transport simulation was performed here, it is believed that the most relevant

concept to envisage, in terms of appropriate physical processes simulated, is creating a dual

permeability model with discrete drains so that preferential flow and transport pathways are

taken into account.

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In any case, the heterogeneity of tile-drained clayey tills can greatly influence groundwater

flow dynamics as well as tile drainage. We are currently developing a larger scale model to

simulate seasonal variations in tile drainage outflow, where heterogeneities of the clayey tills

will be represented in greater detail, as investigated in the NiCA research project (Refsgaard

et al., 2014), which this study is part of. This project focuses on nitrate reduction within

geologically heterogeneous agricultural catchments. In the light of this project framework,

more realistic simulated water flow patterns in heterogeneous tile-drained field are required,

which is the cornerstone of potential nutrient transport modeling through subsurface drained

soils. Although each case is unique, we would argue that some of the key conclusions are

generic and apply to many tile drained areas, namely that a simplified mesh may be adequate

for simulating the flow dynamics at the drain outlet, while a detailed mesh and probably a

dual permeability concept are recommended for detailed studies of contaminant transport.

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Chapter 5

Seasonal variations simulation of

local scale tile drainage discharge in

an agricultural catchment

Modélisation des variations saisonnières du drainage souterrain dans un bassin

versant agricole

G. De Schepper, R. Therrien

Department of Geology and Geological Engineering, Université Laval

Quebec City, Canada

J. C. Refsgaard, X. He

Department of Hydrology, Geological Survey of Denmark and Greenland

Copenhagen, Denmark

C. Kjærgaard, B. V. Iversen

Department of Agroecology, University of Aarhus

Aarhus, Denmark

Submitted to Water Resources Research, October 16, 2015.

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Abstract

Seasonal variations of tile drainage discharge were simulated in the 6 km2 Fensholt catchment,

Denmark, with the coupled surface and subsurface HydroGeoSphere model. The catchment

subsurface is represented in the model by 3 m of topsoil and clay, underlain by a hetero-

geneous distribution of sand and clay units. Two subsurface drainage networks were repre-

sented as nodal sinks. A stochastic distribution of the heterogeneous units was generated and

their hydraulic properties were adjusted to reproduce drainage discharge for one of the two

drainage networks and validated with drainage discharge for the other. Simulation results

were compared to those of another model for which the heterogeneous sand and clay units

were replaced by a homogeneous unit, whose hydraulic conductivity was the mean value of the

heterogeneous model. With the homogeneous model, drainage dynamics were well simulated

but drainage discharge was less accurate than the heterogeneous model. Results were also

compared to those a larger scale model created with the MIKE SHE code, built with the

same heterogeneous model. HydroGeoSphere and MIKE SHE generated drainage discharge

that was significantly different, with better simulated groundwater dynamics data produced

by HydroGeoSphere. Nodal sinks in HydroGeoSphere reproduced drain flow peaks more ac-

curately. Calibration against drainage discharge data suggests that drain flow is controlled

primarily by geological heterogeneities included in the model and, to a lesser extent, by the

nature of the soil units located between the drains and the ground surface.

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Résumé

Les variations saisonnières du drainage agricole ont été simulées dans le bassin versant de

Fensholt (6 km2) au Danemark, à l’aide du modèle hydrologique couplé de surface et subsur-

face HydroGeoSphere. Le modèle de subsurface de Fensholt est représenté par 3 m de terre

arable et d’argile sous lesquels une distribution hétérogène d’unités de sable et d’argile est

présente. Deux réseaux de drainage ont été représentés par des pertes nodales alignées. Un

modèle stochastique des unités hétérogènes a été utilisé et leurs propriétés hydrauliques ont

été calées pour reproduire les débits de drainage de l’un des réseaux de drainage et valider

les écoulements observés dans le second. Les résultats de simulation ont été comparés à ceux

d’un autre modèle pour lequel les unités hétérogènes de sable et d’argile ont été remplacées

par une unité homogène, dont la conductivité hydraulique a la valeur moyenne des unités

hétérogènes. Les dynamiques d’écoulement de drainage ont été correctement simulées avec

le modèle homogène, mais les débits de drainage étaient moins précis que ceux du modèle

hétérogène. Les résultats ont aussi été comparés à ceux d’un modèle créé à plus grande

échelle avec MIKE SHE, construit sur base de la même distribution stochastique. Hydro-

GeoSphere et MIKE SHE ont généré des débits de drainage sensiblement différents, avec des

dynamiques d’écoulement souterrain mieux simulées par HydroGeoSphere. Les pertes nodales

d’HydroGeoSphere ont reproduit les pics de drainage plus précisément. Le calage des résul-

tats par rapport aux données de débit de drainage indiquent que les écoulements de drainage

sont contrôlés principalement par les hétérogénéités géologiques inclues dans le modèle, et,

dans une moindre mesure, par la nature des unités de sol situées entre les drains et la surface

du sol.

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5.1 Introduction

Tile drainage influences surface water and groundwater flow patterns at the field and catch-

ment scales and can also contribute to nutrient transport to surface water (Stenberg et al.,

2012). The impact of tile drainage on water resources has been quantified for temperate

climates, where subsurface drainage of fine-textured soils is common for agricultural lands

(Schilling et al., 2012), as well as for arid and semi-arid climates where tile drainage is gen-

erally associated with irrigation (Ayars et al., 2006). For example, King et al. (2014) showed

that 45 % of the total discharge at the outlet of a catchment in Ohio, USA, for example,

originated from tile drainage. Tile drainage varied temporally during a year, with drainage

occurring on average 75 % of the time and full pipe flow occurring for only 2 to 4 days. Larger

drained areas have shown higher drainage water volumes throughout the year. Increases in

baseflow at catchment outlets have also been reported in tile-drained catchments (Schilling

and Libra, 2003).

Some numerical models have been specifically developed for drainage simulations (e.g. Kroes

and van Dam, 2003; Tiemeyer et al., 2007), while others include drainage as one compo-

nent of the entire hydrologic cycle (e.g. Refsgaard and Storm, 1995; Šimůnek et al., 2006).

Drainage has mostly been simulated for time scales ranging from a few weeks (Boivin et al.,

2006), a few days (Rozemeijer et al., 2010; De Schepper et al., 2015) to a few hours (Frey

et al., 2012). Among the simulations that have focused on seasonal variations over one or

more years, such as those observed by King et al. (2014), most were with 1D models, such

as DRAIN-WARMF (Dayyani et al., 2010) and ANSWERS (Bouraoui et al., 1997), or 2D

models, such as SWAT (Du et al., 2005; Koch et al., 2013), M-2D (Abbaspour et al., 2001),

MHYDAS-DRAIN (Tiemeyer et al., 2007) and THREW (Li et al., 2010). These 1D and 2D

models generally produced good correlation between yearly simulated and observed drainage

discharge. Although 3D models are considered more accurate than 2D or 1D models to sim-

ulate groundwater flow and tile drainage dynamics (Koch et al., 2013; Moriasi et al., 2009),

they are not as widely used. In one example, unsaturated soil properties were estimated at the

catchment scale by 3D inverse modeling with the MODHMS model (Vrugt et al., 2004). Al-

though the uncertainty associated to calibrated parameters was large, the simulated drainage

discharge was close to the observed discharge. Warsta et al. (2013) have developed the FLUSH

model to simulate coupled 2D overland flow, 3D subsurface flow and subsurface transport of

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sediments, including erosion, with drains represented as local sinks. With the model, Warsta

et al. (2013) reproduced drainage discharge and seasonal variations in overland flow at the

field scale.

The objective of the present study was to simulate local scale seasonal variations of subsur-

face drainage discharge in an agricultural catchment, located in Fensholt, Denmark. Field

investigations have showed that tile drainage is a significant component of streamflow in the

catchment (Nilsson, 2013) and that it can also contribute to rapid transport of nutrients,

including nitrates, to streams. Tile drainage dynamics must be quantified to establish reg-

ulations for nitrogen applications that minimize nitrate release to groundwater and surface

water (Refsgaard et al., 2014). The HydroGeoSphere model (Therrien et al., 2010) has been

used here to simulate fully coupled 3D subsurface flow, 2D overland flow and drainage flow

in 1D linear drain elements. Although simulations focused on the catchment scale, individ-

ual drainage was represented explicitly in the model to simulation the impact of drainage

networks on local scale groundwater flow. The novelty of the work presented here is the

simulation of the seasonal variability of tile drainage discharge with a fully-coupled surface

water and groundwater flow model.

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5.2 Materials and methods

5.2.1 Site description

The Fensholt catchment covers an area of 6 km2 located within the larger Norsminde catch-

ment (100 km2), about 15 km south of the city of Aarhus on the east coast of Jutland,

Denmark (Figure 5.1). The average annual precipitation in the Norsminde catchment for the

1990-2013 period is 870 mm, with annual values that ranged from a maximum value of 925

mm in 2012 to a minimum of 700 mm in 2013.

Surface elevation in the Norsminde catchment varies from more than 100 meters above mean

sea level (mamsl) in the western part to sea level in the eastern part. The western part,

where the Fensholt catchment is located, is characterized by hilly terrains and the eastern

part is dominated by lowlands. Agricultural land covers 78.3 % of the catchment. Forests

cover 9.7 % of the territory, urban areas and roads cover 6.9 %, and wetlands and peatlands

cover the remaining 5.1 %. The catchment outlet is the Norsminde Fjord, a 2 km2 estuary

located to the northeast. The main stream in the Fensholt catchment is the Stampemølle

Bæk (Figure 5.1), which flows from west to east and discharges in the Odder River. A few

tributaries are present along the main stream.

The Norsminde catchment is located in the Norwegian-Danish Basin structural unit that was

formed during Permian rift tectonics and reactivated later during the Miocene (Japsen et al.,

2007; Rasmussen et al., 2010). In the Fensholt catchment, Miocene deposits are located on

top of Paleogene fine-grained marine marls and clays. The only Miocene deposits in the

region are Early Miocene marine clay and deltaic to coastal-plain sand, whose total thickness

is 40 m (Rasmussen et al., 2010). Middle and Upper Miocene were eroded following a late

Neogene exhumation (Japsen et al., 2007). The resulting hiatus is followed by heterogeneous

Quaternary clayey and sandy glacial deposits. These Quaternary deposits mainly consist

of a clay matrix that surrounds sand lenses of variable extent. The clayey deposits are of

glaciolacustrine origin and show clay to clayey till facies, whereas sandy units are glaciofluvial

(He et al., 2014). In the Fensholt catchment, the thickness of the Quaternary glacial sequence

varies from up to 30 m on hilltops to about 15 m along the Stampemølle Bæk.

In the area, Quaternary sand lenses form local aquifers while the Miocene sand and gravel

deltaic deposits correspond to regional aquifers (Knutsson, 2008). Hydraulic head data and

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stream flow monitoring at the stream discharge station (SD, Figure 5.1c) show that a local

sandy aquifer recharges the Stampemølle Bæk (Nilsson, 2013).

The Fensholt catchment is heavily tile-drained, as indicated by the available mapped tile

drainage networks (Figure 5.1c). We focused on two complex and dense tile drainage networks

(Drainage areas A and B). Drainage area A (AreaA) covers 34 ha and contains 199 pipes.

Drainage area B (AreaB) contains 95 pipes and covers 28 ha. The outlets of both networks

(Figure 5.1c, StA and StB) discharge into a tributary of the Stampemølle Bæk, whose flow is

dominated by tile drainage. Drainage discharge is monitored on an hourly basis at drainage

stations StA and StB, as part of a larger monitoring project1, with bidirectional battery-

operated electromagnetic flowmeters connected to both drainage networks outlets: stainless

steel electrodes measure water flow with a ±0.5 mm s−1 accuracy (Windgassen, 2006). A

comparison of data from the catchment stream discharge station (SD) with that from the

drainage stations suggests that about 74 % of the Fensholt catchment discharge originates

from tile drains. Shallow piezometers (Figure 5.1c, Pz1 to Pz8), which are 2 m deep, have

been installed in the drainage areas to regularly monitor groundwater levels.

5.2.2 Numerical model

The HydroGeoSphere model (Therrien et al., 2010) simulates fully-coupled variably-saturated

subsurface flow, overland flow and drainage flow. Richards’ equation is used to describe three-

dimensional variably-saturated flow in the subsurface and 2D surface flow is represented by

the diffusion wave approximation. The model uses the control volume finite element method

for discretizing the governing flow equations and the Newton-Raphson iteration method is

applied to solve the discretized non-linear equations. HydroGeoSphere uses the model de-

veloped by Kristensen and Jensen (1975) for calculating actual evapotranspiration based on

potential evapotranspiration. Details on governing equations and their implementation in

HydroGeoSphere are given by (Therrien et al., 2010). The model capabilities are discussed in

the comprehensive review by Brunner and Simmons (2012) and specific developments related

to tile drainage modeling have been documented by De Schepper et al. (2015).

1IDRÆN Project: www.idraen.dk

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Sweden

Germany 0 50 100 200km

CopenhagenNorsminde

Stream

5km

2.50

m0 750 1500

Drain pipe

Drainage catchment

Stream discharge station

Drainage station

Elevation(mamsl)

175

0

N

Norsminde

Fensholt

Drainage area B

Drainage area A

StB

StA

SD

Aarhus

NorsmindeFjord

Odder Rive

r

Stampemølle Bæk

Figure 5.1: Location of (a) the Norsminde catchment in Denmark (55◦ 58’ N, 10◦ 8’ E), (b) the Fensholt catchment within the Norsmindecatchment, (c) a zoom-in on the Fensholt catchment showing topography (1.6 m digital elevation model), mapped drainage networks,drainage discharge measurement stations (StA and StB) with their respective drainage areas and stream discharge station on theStampemølle Bæk stream at the outlet of the catchment (SD). Eight observation piezometers are located in the two drainage areas (Pz1to Pz8).

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5.2.3 Model conceptualization

Surface domain

To represent the surface flow domain, the surface of the catchment was discretized with the

automated 2D triangular mesh construction method documented by Käser et al. (2014). The

mesh was refined along the drains and streams by specifying a mean inter-nodal distance of

25 m (Figure 5.2). The mesh was also refined in areas where the surface slope is greater

than 9 %. The edges forming the triangular elements range from 6 m long. The refined 2D

triangular mesh contained 5843 nodes and 11 431 triangular elements.

The elevation of each node in the 2D mesh was interpolated from a digital elevation model with

a 1.6 m grid size. Overland flow properties representative of agricultural land were assigned

to the surface of the model (Table 5.1), with Manning roughness coefficients assumed to be

isotropic. The coupling length included in the term describing first-order water exchange flux

between surface and subsurface was assumed uniform and equal to that used by Goderniaux

et al. (2009). Rill storage and obstruction storage height values were taken from Cochand

(2014).

Table 5.1: Overland flow properties applied to the surface domain (agricultural land).

Parameter Value Source

Manning roughness coefficient n [m1/3 s−1] 3.0 × 10−1 Li et al. (2008)Rill storage height Hd [m] 5.0 × 10−3 Cochand (2014)Obstruction storage height Ho [m] 3.0 × 10−2 Cochand (2014)Coupling length Lc [m] 1.0 × 10−2 Goderniaux et al. (2009)

Subsurface domain

To generate the 3D mesh for the subsurface domain, the 2D mesh was replicated in the third

dimension from the ground surface down to a depth of 20 m. A total of 18 layers of 3D

triangular prism elements were generated (Figure 5.3a) and the total number of nodes and

elements in the 3D mesh were 111 017 and 205 758, respectively. The first 3 meters below

ground surface were discretized with 9 layers of variable thicknesses to represent the top soil,

a clayey till unit and both drainage networks, with a finer discretization close to the drain

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depth (Figure 5.3c). The 9 remaining layers extend from 3 m to 20 m below ground surface

and have a thickness of 2 m, except for a 1 m layer located between depths of 3 m and 4 m.

These layers correspond to Miocene sand and clay and Quaternary sand and clay. He et al.

(2014) further divides the Quaternary sequence into two groups: glacial sand and clay, and

tectonic sand and clay of glaciotectonic origin.

A spatially-variable distribution of the Miocene and Quaternary sand and clay units was used

here, based on the work of He et al. (2014). They generated 10 stochastic realizations of

their spatial distribution for the entire Norsminde catchment on a 20 × 20 × 2 m grid. Those

realizations were conditioned with borehole observations and airborne geophysical data. Each

realization was then used as input for 10 different hydrological models. From hydrological

validation tests, He et al. (2014) identified the realization that performed best, which we

selected here to assign subsurface properties between depths of 3 m and 20 m (Figure 5.3).

That best realization is referred here as the ’heterogeneous geological model’. The distribution

of geological units in the model is illustrated on Figure 5.3. The hydraulic properties of the

sand and clay units below a depth of 3 m were given by He et al. (2015) and are shown in

Table 5.2 as initial values.

Directly above the geological units assigned according to the He et al. (2014) model, a clayey

till unit was specified over the entire model area between depths of 3.0 m and 1.5 m. Three

soil horizons were then specified between a depth of 1.5 m and ground surface. The C horizon

is assumed located between depths of 1.5 m and 0.7 m, the B horizon is assumed to be from

0.7 m and 0.3 m and the A horizon is the uppermost layer, from an assumed depth of 0.3

m to ground surface. The hydraulic properties of each unit located between ground surface

and a depth of 3 m are listed in Table 5.3. The van Genuchten functions (van Genuchten,

1980) were used to describe the unsaturated hydraulic properties of all units in the first three

meters.

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Drainage area

Drain nodes

Stream nodes

m0 750

Topography nodes

375

N

AreaB

AreaA

Figure 5.2: 2D mesh with refined nodes highlighted for both drainage areas, rivers and to-pography areas where the surface slope is greater than 9 %.

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A

A’a)

Glacial sand

Glacial clay

Tectonic sand

Tectonic clay

Miocene sand

Miocene clay

C horizon (-0.7 to -1.5 m)

B horizon (-0.3 to -0.7 m)

A horizon (0.0 to -0.3 m)c)

Geological units

Stochastic model

Soil

b)

Clayey till (-1.5 to -3.0 m)

A’A

Vertical exaggeration: x 10

3 m

17 m

Figure 5.3: (a) Geological units in the heterogeneous model, (b) vertical cross-section through the model, (c), a zoom on this section inthe zone where drainage areas of interest are located. The vertical exaggeration for all figures is 10 x.

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Table 5.2: Hydraulic properties of the hydrofacies located below a depth of 3 m and definedfollowing the heterogeneous geological model of He et al. (2014). Initial values were thosefrom He et al. (2015) and calibrated values were obtained manually.

Hydrofacies Parameter Initial value Calibrated value

Glacialsand

Horizontal hydraulic conductivity Kh [m s−1] 4.17 × 10−4 2.0 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 4.17 × 10−5 2.0 × 10−7

Specific storage Ss [-] 5.0 × 10−5 -

Glacial clayHorizontal hydraulic conductivity Kh [m s−1] 2.54 × 10−8 1.0 × 10−8

Vertical hydraulic conductivity Kv [m s−1] 2.54 × 10−9 1.0 × 10−9

Specific storage Ss [-] 5.0 × 10−5 -

Tectonicsand

Horizontal hydraulic conductivity Kh [m s−1] 7.2 × 10−6 2.0 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 7.2 × 10−7 2.0 × 10−7

Specific storage Ss [-] 5.0 × 10−5 -

Tectonicclay

Horizontal hydraulic conductivity Kh [m s−1] 4.6 × 10−7 1.0 × 10−8

Vertical hydraulic conductivity Kv [m s−1] 4.6 × 10−8 1.0 × 10−9

Specific storage Ss [-] 5.0 × 10−5 -

Miocenesand

Horizontal hydraulic conductivity Kh [m s−1] 3.3 × 10−4 2.0 × 10−6

Vertical hydraulic conductivity Kv [m s−1] 3.3 × 10−5 2.0 × 10−7

Specific storage Ss [-] 5.0 × 10−5 -

Mioceneclay

Horizontal hydraulic conductivity Kh [m s−1] 5.4 × 10−8 1.0 × 10−8

Vertical hydraulic conductivity Kv [m s−1] 5.4 × 10−9 1.0 × 10−9

Specific storage Ss [-] 5.0 × 10−5 -

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Table 5.3: Hydraulic properties of the topsoil units (A, B and C horizons) and clayey till unit.Initial values were taken from the associated literature sources.

Unit Parameter Initial value Calibrated value Source

A horizon

Horizontal hydraulic conductivity Kh [m s−1] 8.9 × 10−8 1.0 × 10−5 He et al. (2015)Vertical hydraulic conductivity Kv [m s−1] 8.9 × 10−9 1.0 × 10−6 He et al. (2015)Specific storage Ss [-] 1.0 × 10−5 - He et al. (2015)Residual saturation Sr [-] 0.083 - Iversen et al. (2011)van Genuchten parameter α [m−1] 0.52 - Iversen et al. (2011)van Genuchten parameter n [-] 1.51 - Iversen et al. (2011)Thickness [m] 0.3 - -

B horizon

Horizontal hydraulic conductivity Kh [m s−1] 8.9 × 10−8 1.0 × 10−5 He et al. (2015)Vertical hydraulic conductivity Kv [m s−1] 8.9 × 10−9 1.0 × 10−6 He et al. (2015)Specific storage Ss [-] 1.0 × 10−5 - He et al. (2015)Residual saturation Sr [-] 0.078 - Iversen et al. (2011)van Genuchten parameter α [m−1] 0.80 - Iversen et al. (2011)van Genuchten parameter n [-] 1.45 - Iversen et al. (2011)Thickness [m] 0.4 - -

C horizon

Horizontal hydraulic conductivity Kh [m s−1] 8.9 × 10−8 4.0 × 10−6 He et al. (2015)Vertical hydraulic conductivity Kv [m s−1] 8.9 × 10−9 4.0 × 10−7 He et al. (2015)Specific storage Ss [-] 1.0 × 10−5 - He et al. (2015)Residual saturation Sr [-] 0.099 - Iversen et al. (2011)van Genuchten parameter α [m−1] 0.98 - Iversen et al. (2011)van Genuchten parameter n [-] 1.41 - Iversen et al. (2011)Thickness [m] 0.8 - -

Clayey till

Horizontal hydraulic conductivity Kh [m s−1] 8.9 × 10−8 1.0 × 10−6 He et al. (2015)Vertical hydraulic conductivity Kv [m s−1] 8.9 × 10−9 1.0 × 10−7 He et al. (2015)Specific storage Ss [-] 1.0 × 10−5 - He et al. (2015)Residual saturation Sr [-] 0.099 - Iversen et al. (2011)van Genuchten parameter α [m−1] 0.98 - Iversen et al. (2011)van Genuchten parameter n [-] 1.41 - Iversen et al. (2011)Thickness [m] 1.5 - -

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Tile drains

Two tile drainage networks, areas A and B (Figure 5.1c), were included in the model. The

number of drains in each network was however reduced to decrease simulation times. The

network in area A was thus represented with 14 drains while 8 drains were retained for area

B (Figure 5.2). Although the geometry of the drainage network was simplified, the main

drainage paths were represented in the model. De Schepper et al. (2015) show that, if the

main drainage paths are retained in a model, the drainage network can be simplified for

large-scale simulations, providing that the model is calibrated.

Although tile drains can be discretized with 1D line elements and fluid flow along drains can

be simulated in HydroGeoSphere, drain were represented here as seepage nodes to reduce

computational times. The seepage nodes were located 1 m below ground surface and their

spatial distribution was specified to represent the drainage network (Figure 5.2). Drainage

area A was discretized with 203 seepage nodes, while drainage area B contained 86 nodes

(Figure 5.2).

With the seepage node option, the pressure head at a seepage node is set to zero during a time

step if there is fluid flow from the subsurface to the drain, and a no flow boundary is assigned

in the opposite case, when the pressure head at a seepage node is negative. Drainage therefore

occurs only when the water table rises above the drain node elevation. The drainage water

is not routed to the stream but it is summed up during simulation to compare to observed

drainage. A simulation of the verification example presented in MacQuarrie and Sudicky

(1996) shows that the seepage node representation of drains provides results similar to those

for a model where drains are represented as 1D line elements.

Climate data

The period selected for the simulations is from July July 23, 2012 to July 24, 2013. Pre-

cipitations for this period were extracted from 10 km grid raster datasets provided by the

Danish Meteorological Institute (DMI), and were applied at the surface domain as a daily flux

boundary condition during the first 96 days. From day 97 until day 366, daily precipitations

were disaggregated into hourly precipitations according to rainfall measurements at a weather

station located south of Fensholt, in the Norsminde catchment. Corrections were applied to

the raw rainfall measurements following recommendations from Stisen et al. (2012).

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The daily potential evapotranspiration (PET) was estimated from reference evapotranspira-

tion data calculated on a 20 × 20 km with the Makkink equation for the Denmark landmass

(Scharling, 1999). Compared to PET calculated with the Penman-Monteith equation, the

Makkink equation overestimates evapotranspiration for western Denmark, compared to the

eastern Denmark reference (Detlefsen and Plauborg, 2001). A correction factor of 0.95 was

therefore applied to PET to account for this overestimation (Refsgaard et al., 2011; Stisen

et al., 2012). The resulting potential evapotranspiration was applied to surface domain of the

model.

To calculate actual evapotranspiration, agricultural land evapotranspiration properties, which

are predominantly winter wheat, were assigned to the top layer elements (Table 5.4). Root

depth (Lr) values are taken from Børgesen et al. (2013). Evaporation depths were estimated

based on recommendations for Danish soils given by Kristensen and Jensen (1975). The

transpiration fitting parameters (C1, C2 and C3) and the canopy interception (cint) were

defined based on Li et al. (2008). Measured soil moisture values at pF 4.2 and pF 2 were used

for defining the wilting point (θwp) and field capacity (θfc) limiting saturations respectively

(Børgesen and Schaap, 2005). Leaf Area Index values were adapted from Børgesen et al.

(2013) and varied seasonally.

Table 5.4: Evapotranspiration properties applied to the surface layer (winter wheat). LeafArea Index values are linearly interpolated between the periods shown here.

Parameter Value Source

Root depth Lr [m] 1.6 Refsgaard et al. (2011)Evaporation depth Le [m] 0.2 Default valueTranspiration fitting parameter C1 [-] 0.31 Kristensen and Jensen (1975)Transpiration fitting parameter C2 [-] 0.15 Kristensen and Jensen (1975)Transpiration fitting parameter C3 [-] 5.9 Kristensen and Jensen (1975)Wilting point θwp [-] 0.18 Iversen et al. (2011)Field capacity θfc [-] 0.69 Iversen et al. (2011)Leaf Area Index (from 01/11 to 10/04 [-] 1.0 Børgesen et al. (2013)Leaf Area Index (from 30/04 to 09/06 [-] 5.0 Børgesen et al. (2013)Leaf Area Index (from 23/07 to 17/07 [-] 0.0 Børgesen et al. (2013)Canopy interception cint [mm] 0.05 Default value

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Boundary conditions

A critical depth boundary condition was assigned to the surface domain at the outlet of

the Fensholt catchment (see SD, Figure 5.1c). The lateral boundaries were assumed to be

groundwater divides, corresponding to no-flow boundaries.

De Schepper et al. (2015) have showed that, for similar shallow systems that are not bounded

by a low-permeability geological unit, deeper flow should be accounted for. In the Fensholt

model, the bottom boundary was set at 20 m below ground surface and does not correspond

to a low-permeability boundary. The regional MIKE SHE model developed for the Norsminde

catchment for the 2000-2003 period (He et al., 2015) suggests that there is a downward flow

component in Fensholt at that depth, with little annual variation. A downward flux value

of 0.11 mm d−1 was applied at the bottom boundary of the model, which corresponds to the

average value simulated by He et al. (2015).

Simulation parameters

For the iterative solution of the non-linear flow equations, the Newton-Raphson absolute and

residual convergence criteria were set to 1.0 × 10−4 m and 1.0 × 10−4, respectively. A maxi-

mum variation of 0.05 in saturation between successive timesteps was used for the adaptive

time stepping strategy used in HydroGeoSphere (Therrien et al., 2010). In addition, time

steps were limited to a maximum of 1 hour. The model was run with the parallelized version

of the code (Hwang, 2012; Hwang et al., 2014) on a 3.39 Gb RAM computer with 4 CPU

cores at 3.40 GHz.

5.2.4 Heterogeneous vs. homogeneous models

The results presented here are for various versions of the numerical model. The first version

corresponds to the initial heterogeneous model for which the distribution of sand and clay

between depths of 3 m and 20 m was generated stochastically and their hydraulic conduc-

tivities were calibrated against stream discharge for the entire Norsminde catchment by He

et al. (2015). A second version corresponds to the same heterogeneous spatial distribution

of sand and clay but for which the hydraulic conductivities were modified to reproduce the

drainage discharge at Fensholt. This second version is the calibrated heterogeneous model.

In addition to the two heterogeneous models, results from a third model are presented, where

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the heterogeneous distribution of sand and clay is replaced with a homogeneous unit whose

properties are those of the clayey till horizon (Table 5.3, calibrated values).

The equations solved by coupled surface and subsurface flow models are non-linear. Direct

steady-state solutions are not possible and transient simulations are therefore required. Since

initial conditions are usually unknown, a model spin-up is necessary to ensure that they don’t

impact the simulation results. Each model (initial heterogeneous, calibrated heterogeneous

and homogeneous) was therefore first run with fully saturated initial conditions during an

entire year by applying precipitation and evapotranspiration datasets. The resulting hydraulic

head distribution was then used as initial hydraulic heads for the targeted yearly simulations.

5.2.5 Calibration

The heterogeneous model was calibrated manually by trial and error to reproduce observa-

tions for drainage area A. The hydraulic conductivities of all geological units were modified,

using a single value for all sand units and another value for all clay units, while keeping the

vertical anisotropy factor, Kv / Kh equal to 0.1 (Table 5.2). Hydraulic properties of A, B, C

horizons and the upper till layer were also adjusted, while initial values were used for all the

other parameters (Table 5.3). During calibration, simulated drainage water fluxes were most

sensitive to the hydraulic conductivity of the C horizon and the clayey till units (Table 5.3).

The first 96 days of simulation were not considered for calibration as only daily precipitation

data were applied to the model before day 96, while hourly drainage discharge measurements

were available. From day 97 until the end of the simulation, hourly precipitation data were

applied, which was appropriate for calibration.

Three performance criteria were calculated for the calibrated heterogeneous, initial hetero-

geneous and homogeneous models (Table 5.5). The coefficient of determination r2 was first

calculated, which estimates the correlation of observed and simulated data points. Another

common criterion is the Nash-Sutcliffe efficiency coefficient NSE (Nash and Sutcliffe, 1970),

which evaluates the model performance against the mean of the observed values if it was used

for prediction. Even if r2 and NSE are widely used, they are known to be very sensitive

to higher values as they are calculated from squared values of differences between observed

and simulated data points (Krause et al., 2005). They were therefore calculated based on

weekly-averaged drainage discharge values. Finally, a cumulative volumetric error factor was

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calculated based on cumulative drainage volumes over the entire simulated year, as seen in

Figure 5.4.

The model was calibrated for drainage area A by focusing on matching simulated and observed

graphical plots, as advised by Bennett et al. (2013) for flashy systems, and on the related

total volumetric error. Drainage measurements in area B were not used for calibration and

hence served as a proxy basin validation test (Klemeš, 1986) showing the model reliability

areas for which it has not been calibrated (blind test).

Table 5.5: Performance criteria for measuring the Fensholt model efficiency, where n is thenumber of data points, QO and QS are observed and simulated drainage flow values, QO

and QS are observed and simulated mean drainage flow values, VO and VS are observed andsimulated drainage volumes.

Criterion name Formula Range

Coefficient of determination r2

∑n

i=1(QO,i−QO)(QS,i−QS)

∑n

i=1(QO,i−QO)2

∑n

i=1(QS,i−QS)2

2

(0, 1)

Nash-Sutcliffe coefficient NSE 1 −

∑n

i=1(QO,i−QS,i)

2

∑n

i=1(QO,i−QO)2 (-∞, 1)

Volumetric Error V E∑n

i=1VS,i−

∑n

i=1VO,i

∑n

i=1VO,i

(-∞, ∞)

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PET

SET

Fall

Figure 5.4: Cumulative corrected precipitation (Precipitation), corrected potential evapotran-spiration (PET), simulated evapotranspiration (SET) and simulated canopy interception overthe simulated year with the calibrated heterogeneous model (23/07/2012 - 24/07/2013).

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5.3 Results

Results from the model calibration (AreaA) and model validation (AreaB) are presented here.

The calibrated heterogeneous model results are compared with results from the Norsminde

catchment model developed with MIKE SHE by He et al. (2015).

5.3.1 Water balance

The same precipitation and evapotranspiration datasets were applied to each of the models,

heterogeneous and homogeneous, for the simulated period (23/7/2012 to 24/7/2013). Cumu-

lative corrected precipitation, corrected potential evapotranspiration and simulated evapo-

transpiration are shown in Figure 5.4. In addition, this figure shows the cumulative simulated

canopy interception amount that is part of the simulated evapotranspiration. The total pre-

cipitation amount (715 mm) reflects a dry simulation period compared to the annual average.

Figure 5.4 shows that the first two months (end of summer) were wet, with about 150 mm of

rainfall, while the second half of winter and beginning of spring were exceptionally dry, with

very little rainfall. A major rainfall event occurred in the spring, around day 305, with about

50 of precipitation in a very short time. The last simulated month (beginning of summer

2013) was also dry. Both PET and SET curves show that evapotranspiration was mainly

effective during spring and summer.

5.3.2 Drainage processes

The simulated hydrographs with the heterogeneous calibrated model for the entire year and

for periods with major peak flow (Figure 5.5), from days 96 to 230, provided a good match

with observations, except that peak intensities for AreaB were about one third lower than for

AreaA. This difference is probably due to the difference in density of drains, and by extension

of drain nodes, in both drainage areas (Figure 5.2) since a simplified drainage network induces

lower drainage discharge values (De Schepper et al., 2015). The drain node difference in both

networks was reflected during the simulation with more effective drainage for AreaA than for

AreaB (Figure 5.6).

Also shown in Figure 5.6 are 2D snapshots of the depth to water table in the area of interest

before and during a rainfall event in late fall at days 143 and 147 (zoom-in in Figure 5.5). In

addition, a 3D close-up view of AreaA is displayed with cross-sections showing pressure head

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distributions in the soil units (from 0.0 to 3.0 m depth). The depth to water table color scale

highlights that the water table was below the drain depths (1.0 m) before the drainage peak.

The water table between drains was lower for AreaA than for AreaB. Pressure heads were

generally negative along drains in AreaA before the peak. At day 147, drain nodes were still

active, even if it was not easily seen in the 2D depth to water table plot, with lower pressure

head values in their vicinity. The water table was not lowered below the drain depth, while

drainage peaks were matching and correctly simulated as seen in Figure 5.5. Yet, some peaks

were simulated before day 147 due to applied precipitation data deviation.

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Figure 5.5: Observed and simulated drainage flow for drainage areas A and B for the initial and calibrated HydroGeoSphere models andfor the homogeneous model for the one-year simulation (23/7/2012 to 24/7/2013). Observed data were measured at drainage stationsStA and StB. A zoom-in on the period of interest highlighted in Figure 5.6 is shown on the right-hand side.

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Pz1

Pz2

Pz3

Pz4

Pz5

Pz6

Pz7Pz8

0.0

Depth towater table [m]

AreaA

AreaB

95

91

87

87

83

79

75

71

67

97

87

83

79

75

71

67

83

87

71

75 79

83

Elevation in mamsl

-0.5

-1.0

-1.5

-2.0

-2.5

-3.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Pressurehead [m]

Pressure head

a) day 143

b) day 147

Depth to water table

c) day 143

d) day 147

Fensholt catchment Drainage areas

Drain nodes

Figure 5.6: (a, b) Pressure head distribution along vertical cross-sections in DrainA for thecalibrated heterogeneous model (0.0 to 3.0 m depth), (c, d) depth to water table for bothAreaA and AreaB. Targeted output times were selected before a drainage peak (a, c - day143) and at maximum peak flow (b, d - day 147). At the top, the topography is displayed inFensholt and in the area of interest with piezometer locations.

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5.3.3 Drain flow

Initial heterogeneous model

For the initial heterogeneous model, no drainage peak flows are simulated for both drainage

areas although various flashy peaks were observed during the simulation period (Figure 5.5).

In AreaA, the simulated low flow is slightly overestimated compared to observed data during

fall and winter (from day 85 to 230), while it is underestimated for the same period in AreaB.

In the spring, little drainage flow was produced around day 265 while flow was greater during

the major rainfall event at day 304 in AreaA (Figure 5.7). During the same rainfall event,

drainage discharge also occurred in AreaB, but it was less intense than for AreaA at the same

period. No significant drainage flow was simulated before day 60 in AreaA and day 85 in

AreaB.

As no peaks were simulated with the initial heterogeneous model, the cumulative drainage

curves (Figure 5.7) reveal a markedly lower total drainage volume, expressed in mm, in both

drainage areas compared to the observed discharge volume. The yearly simulated drainage

discharge volumes of AreaA and AreaB amounted to 155 mm and 114 mm, respectively, while

measured values were 265 mm and 308 mm, which demonstrates a major water deficit in the

simulation.

The water deficit highlighted in the total amount of drained water is clearly seen in the

volumetric error (V E) values that were −41 % for AreaA and −63 % for AreaB (Table 5.6).

The coefficient of determination (r2) for AreaA was 0.70 and 0.63 for AreaB. The Nash-

Sutcliffe coefficient (NSE) was 0.49 for AreaA and 0.14 for AreaB. Thus the coefficients

demonstrated a poorer performance of the model for drainage area B than for drainage area

A.

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Figure 5.7: Observed and simulated cumulative drain flow equivalent height, expressed inmm, for drainage areas A and B. Simulated curves are displayed for the initial and calibratedheterogeneous models, the homogeneous model, and for the MIKE SHE model.

Calibrated heterogeneous model

The heterogeneous calibrated model hydrograph of AreaA showed several flashy peaks that

coincide with the observed drainage trend (Figure 5.5). Simulated peaks are generally higher

than the observed peaks. Drainage discharge in dry periods was adequately simulated, with

decreasing drainage values after peaks that are closer to the observed values than the initial

heterogeneous model results. Nevertheless, simulated drainage discharge during drawdown

periods was slightly higher than what was measured in Fensholt between days 130 and 210.

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The simulated drain flow peaks are more frequent and greater than those observed. In ad-

dition, little drainage was simulated around day 330 during a short rainfall event. In total,

about 42 peaks were simulated, while 29 were observed. The simulated cumulative drainage

curve is closely corresponding to the observed one (Figure 5.7), with a total amount of 275

mm of simulated drainage discharge. The associated volumetric error is 4 % (Table 5.6).

In drainage area B (Figure 5.5), no significant drainage was simulated before day 80. After-

wards, drainage peaks were simulated with the same frequency as in AreaA but they were

less intense, while low flow was still accurately simulated. Simulated drainage flowrates lower

than the measured rates induced a total cumulative drain flow amount of 245 mm for AreaB

(Figure 5.7), which is much lower than the observed value (308 mm). The volumetric error

is consequently much higher than in AreaA (−20 %).

In addition to the volumetric error, the NSE was also larger for AreaA (0.84) than for

AreaB (0.73), and they were the highest of all models (Table 5.6). The r2 criterion showed

similar values for both drainage areas (0.77 for AreaB against 0.84 for AreaA). These criteria

suggest better performance of the model in AreaA compared to AreaB, confirming the good

calibration against AreaA drainage discharge.

The annual drainage discharge from AreaA and AreaB, expressed as precipitation fractions,

were close to observed values. The field data showed drainage discharge recovery values from

precipitation of 37 % in AreaA and 43 % in AreaB. The associated simulated values for the

calibrated heterogeneous model were 38 % and 34 %, respectively.

Homogeneous model

The homogeneous model produced the highest drainage peaks of all models for AreaA (Fig-

ure 5.5). The model simulated most peaks that were observed, but they were flashier than

what was observed. Nevertheless, the first peaks right after day 60 and the peaks between days

250 and 300 were very low, compared to the calibrated model simulation results. The homo-

geneous hydraulic conductivity values were higher than that for the calibrated heterogeneous

clay units and slightly lower than that of the sand units. In addition, hydraulic conductivity

values were lower than the calibrated A, B and C horizon. These lower hydraulic conductivity

values made the water table drop faster during dry periods due to drainage, with simulated

low flow in between peaks that is lower than observed low flow and lower than low flow of the

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other models.

Similarly to the heterogeneous calibrated model, no significant drainage discharge was sim-

ulated before day 80 for AreaB, where simulated drainage was generally lower compared to

AreaA. However, in contrast to drainage area A, some peaks were simulated between days

250 and 300. Surprisingly, a series of significant drainage peaks were simulated around day

330, while they were of minor importance in AreaA. As AreaB is located further upstream

compared to AreaA, one would expect a similar trend in AreaA between days 325 and 345,

but this was not the case. This last group of peaks allowed the homogeneous model to have

total drainage discharge volumes that very closely resembled field measurements (Figure 5.7),

with a simulation of 312 mm compared to the measured 308 mm in AreaB. The similar curve

for AreaA showed a larger difference between simulated and observed total drainage discharge

(297 mm and 265 mm, respectively). The volumetric error was therefore 1 % in AreaB and

12 % in AreaA. The r2 criterion was equal to 0.81 for AreaA and 0.73 for AreaB and the

computed NSE is 0.78 for AreaA and 0.72 for AreaB.

Table 5.6: Model performance criteria calculated over the calibration period (from day 96 to366, i.e. 28/10/2012 to 24/07/2013) based on weekly averaged discharge values.

CriterionIdealvalue

Initial Calibrated Homogeneous MIKE SHEAreaA AreaB AreaA AreaB AreaA AreaB AreaA AreaB

r2 [-] 1 0.70 0.63 0.84 0.77 0.81 0.73 0.89 0.79NSE [-] 1 0.49 0.14 0.84 0.73 0.78 0.72 0.79 0.54V E [%] 0 −41 −63 4 −20 12 1 −37 −52

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MIKE SHE model

The MIKE SHE model of Norsminde was calibrated for the 2000 to 2003 period (He et al.,

2015), while our simulations are for the 23/7/2012 to 24/7/2013 period. In MIKE SHE, a

uniform horizontal mesh size equal to 100 × 100 m was used. In terms of drainage conceptu-

alization, both models treated drain flow the same way: drainage sinks were active as soon as

the water table rose higher than the drain elevation. But, in MIKE SHE, drainage sink con-

ditions were applied at all cells, because the distance between the drain pipes is less than the

grid size. The HydroGeoSphere model, which has a spatial resolution finer than the drainage

network, represented drainpipe locations at some of the HydroGeoSphere nodes, while the

other nodes were able so simulate the water table between drain pipes. Another main differ-

ence between both models is the output data frequency: HydroGeoSphere had hourly results

and MIKE SHE had daily. The hydrofacies properties of the MIKE SHE model were the same

as the initial heterogeneous model was created in HydroGeoSphere and are listed in Table 5.2

and Table 5.3 (initial values).

Figure 5.8 shows the observed and simulated drain flow hydrographs for AreaA and AreaB for

the calibrated HydroGeoSphere heterogeneous model and the MIKE SHE model. Similarly

to the HydroGeoSphere initial heterogeneous model, the MIKE SHE model produces low

drain flow values but the main peak dynamics were correctly calculated. In addition, faster

drawdown and lower drainage discharge during dry periods were simulated. Both MIKE SHE

hydrographs looked almost similar aside from the first substantial drainage values that were

calculated earlier for AreaA (day 61) than for AreaB (day 82). The last day of significant

drainage was day 222 for both areas. None of the peaks observed and simulated by Hy-

droGeoSphere after day 222 were reproduced by MIKE SHE. In AreaB, prior to and after

the fall/winter drainage period, zero drain flow values were simulated. In AreaA, a mini-

mum value of 1.0 × 10−2 mm d−1 was observed outside of the drainage period. The series of

drainage peaks observed between days 60 and 82, represented a challenge to both models, as

they were neither simulated by HydroGeoSphere nor by MIKE SHE, probably due to climate

data uncertainty since the same precipitation data were applied to both models.

As for the initial heterogeneous model, the MIKE SHE model results induced a major water

deficit in the total cumulative drained water amount, with V E values of −37 % for AreaA

and −52 % for AreaB. High r2 values were calculated (0.89 in AreaA and 0.79 in AreaB), but

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they were not validated by NSE calculations (0.79 and 0.54, respectively), though expressing

good performance in AreaA results.

Figure 5.8: Observed and simulated drainage flow in drainage areas A and B from 23/7/2012to 24/7/2013, with HydroGeoSphere data from the calibrated heterogeneous model and MIKESHE data from the Norsminde catchment scale model developed by He et al. (2015).

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5.3.4 Hydraulic heads

Figure 5.9 and Figure 5.10 show hydraulic heads simulated with the MIKE SHE and calibrated

HydroGeoSphere models for piezometers Pz1 to Pz9 results, along with measured values.

During the dry season (e.g. day 32) hydraulic heads for some piezometers were below the

elevation of the drains, while hydraulics heads were mostly above the drain elevations for all

piezometers during the wet season.

Beyond dry periods, simulated hydraulic heads by HydroGeoSphere tend to reach maximum

constant values in all piezometers, highlighting that drainage limits the rise of the water

table. In AreaA (Figure 5.9), simulated hydraulic heads for Pz4 are about 0.5 m lower than

the observed heads during the period of active drainage (from day 61 to 225). Before and after

this period, Pz4 was mostly dry with occasional flashy water table rises. The simulated water

table at Pz2 is lower than the drain elevation and much lower than most of the observations,

except the one at day 137 that matched the simulated hydrograph. The active drainage

period for Pz2 was from day 82 to 218. For Pz3, the active period was from day 61 to 218,

with some short dry periods in between. In the spring, some rapid water table rises were

observed, similar to Pz4. The Pz1 active drainage period was quite sporadic, with numerous

dry periods, probably because Pz1 is located in the most upstream part of the drainage area.

Plots showing the depth to the water table (Figure 5.6) illustrate hydraulic head variations

in AreaA. Pz1 was the only dry piezometer at day 143 with the water table being lower than

−1.5 m and it was about −0.8 m at day 147. During this period, the water table at Pz2 and

Pz4 was slightly lower than the drain depth. At Pz3, the water table was located between

0.5 and 0.75 m below ground surface.

The simulated head values in AreaB were mostly higher than drain elevations when piezome-

ters were not dry (Figure 5.10). In addition, simulated heads were generally higher than

the observed ones, with few observed data points matching the simulated curves. Pz5 had

a shallow water table during fall and winter. In Pz6, high hydraulic head values were sim-

ulated until day 227. The wet period was slightly shorter in Pz7, where it lasted until day

218, but a few hydraulic head losses were simulated. A fast water table rise was simulated

at day 263, matching the last observation point, which was also simulated in Pz8. Pz8 had

the longest period of high simulated hydraulic heads, from day 82 to 230. Simulated values

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higher than ground surface might have produced overland flow at the surface, but no water

accumulation was noticed after inspection of the model surface domain. As Pz8 is located in

the most downstream part of AreaB, it suggests insufficient drainage in the upstream part

and an oversimplification of the drainage network in the model. Including more drains in the

network, with more drainage nodes in AreaB, would probably lead to lower hydraulic head

values in Pz8 and in the other piezometers.

The MIKE SHE results in AreaA showed simulated hydraulic heads that were above drain

elevations in Pz2 to Pz4, and even above the soil surface in Pz2. In Pz1, they were close to

the observed data and to the HydroGeoSphere results. Similar trends were simulated during

fall and winter in Pz1 to Pz3, while Pz4 had registered a shorter and higher hydraulic head

rising period from day 90 to 200. It was similarly simulated in AreaB at Pz5, Pz7 and Pz8

from day 60 to 200. Hydraulic head values in Pz5 to Pz7 were below the drain elevation

during the entire simulation and were even lower than the bottom of piezometers Pz5 and

Pz6. Simulated heads were close to observed ones only for Pz8.

The major difference between HydroGeoSphere and MIKE SHE results relates to for flow

dynamics, with HydroGeoSphere producing relatively flashy changes in hydraulic heads while

MIKE SHE produced slowly varying hydraulic heads. This difference may be due to i) the

differences between the 3D Richards’ equation in HydroGeoSphere and the 1D Richards’

equation coupled with groundwater flow in MIKE SHE, ii) differences in spatial discretiza-

tion, and iii) drainage conceptualization differences in the codes. Nodes in HydroGeoSphere,

along with finer mesh discretization, probably allowed for finer drainage flow simulation and

enhanced lateral drainage flow, as seen with better peak flow simulated in HydroGeoSphere.

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Figure 5.9: Observed and simulated hydraulic heads in piezometers of drainage area A (Pz1 toPz4) for the one-year simulation (23/07/2012 - 24/07/2013). The dashed data line was takenfrom the calibrated heterogeneous model in HydroGeoSphere. The solid line was from a MIKESHE simulation for the Norsminde catchment, after He et al. (2015). The HydroGeoSpheredata were plotted when the water table had risen above the elevation of the piezometerbottom. Ground surface and drain elevations are also presented.

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Figure 5.10: Observed and simulated hydraulic head in piezometers of drainage area B (Pz5 toPz8) for the one-year simulation (23/07/2012 - 24/07/2013). The dashed data line was takenfrom the calibrated heterogeneous model in HydroGeoSphere. The solid line was from a MIKESHE simulation for the Norsminde catchment, after He et al. (2015). The HydroGeoSpheredata were plotted only when the water table had risen above the elevation of the piezometerbottom. Ground surface and drain elevations are also presented.

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5.4 Discussion

5.4.1 HydroGeoSphere model performance

The heterogeneous model was calibrated manually against drainage discharge in AreaA by

only varying the hydraulic conductivity values. The flow dynamics for AreaA were correctly

simulated and the total volumetric error was 4 %. However, the model could not be validated

with AreaB observations since the total volumetric error was larger, equal to 20 %, and the

simulated drainage peaks were about one third of the observed drain flow peak intensity from

AreaA, for which more drains were retained in the simplified network representation. Denser

drainage networks usually drain significantly more water (Henine et al., 2014; De Schepper

et al., 2015). As a result, the water table simulated in AreaB was generally shallower than in

AreaA.

The simulated water table in piezometers for both drainage areas was above the bottom of

the piezometer filter primarily in the fall and winter. In the spring, simulated water table

was lower than the filter bottom of the piezometers except for some rapid rises. Observed

hydraulic heads varied over time but simulated hydraulic heads showed less variability. In

the models presented here, only matrix flow was simulated in the porous media towards

the drains, although field evidence shows the presence of macropores and fractures in the

topsoil and clayey matrix. Sand lenses, macropores and fractures have been shown to be

major preferential water flow pathways for near surface deposits in Danish soils (Jørgensen

et al., 2004; Kessler et al., 2012). A more detailed representation of these heterogeneities

in the model could have improved the reproduction of the temporal variability of observed

hydraulic heads. However, adding them would require extensively refined meshes and would

greatly increase simulation times (Blessent et al., 2009).

Drainage discharge observations from catchments in North America showed rapid response

to precipitation during wet periods, in winter, and very little or no drainage discharge during

summer (Eastman et al., 2010; Williams et al., 2015). This trend was also highlighted in the

calibrated heterogeneous model of Fensholt. For AreaA, few drain flow peaks were simulated

before day 60 (late-summer) while significant drainage response was simulated in fall and win-

ter. The simulated temporal drainage pattern was similar to that observed. In AreaB, a few

low-intensity peak flows were measured in late-summer, but none was simulated. Simulated

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drainage for this drainage area is consistent with observations from Williams et al. (2015), but

the field data expressed rapid drainage response also before day 60. A heavy rainfall event in

late-spring (day 304) was clearly registered in both observed and simulated hydrographs. It

appeared after a long dry period, but the intensity of the event resulted in a fast water table

rise and consecutively significant drainage occurred.

The heterogeneous calibrated model had the highest performance criteria of all models, espe-

cially in the drainage area of interest (AreaA). The NSE coefficient for drainage discharge in

AreaA was 0.84, indicating good model performance in that area. By calibrating their model

against cumulative monthly and daily drainage discharge, Green et al. (2006) obtained 0.9 and

0.5 NSE values. Yet, in Fensholt, the NSE coefficient was 0.73 in AreaB. Drainage calibration

was mostly sensitive to the clayey till and C horizon units, which were assumed homogeneous

over the entire model area, with a vertical anisotropy factor equal to 0.1. Drainage flow

appears to be governed by the entire hydrogeological system, suggesting that a good repre-

sentation of drainage is not possible without an appropriate conceptualization of surrounding

and lower porous media properties. Finer peak flow calculations and better performance cri-

teria were reported for the heterogeneous calibrated model compared to the heterogeneous

initial model.

The NSE coefficient of 0.73 obtained for AreaB is slightly less than for the calibrated AreaA.

But the AreaB validation test reflects the performance that can be expected for areas that have

not been calibrated, and as such the result is very encouraging. On this basis we can expect

the model to have predictive capabilities for the remaining part of the Fensholt catchment.

5.4.2 Drainage conceptualization

No discrete drains were therefore in our model since they were rather represented as sink

nodes aligned along the actual drains. Lateral flow was only simulated towards drain nodes,

as defined by Yue (2010). Even though HydroGeoSphere provides an integrated drainage

module coupled to the subsurface domain, with pipe flow and drainage routing capabilities,

they were not included in the simulations. In addition, the physical characteristics of drainage

pipes were not accounted for, such as pipe diameter, drain resistance factors or progressive

clogging of pipes. Even if drains have a resistance factor that varies with drain clogging (van

der Velde et al., 2010), the resistance from the surrounding porous medium drives drainage

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flow (Yue, 2010), as illustrated by the initial and calibrated heterogeneous models.

While some authors regularly observed pipe pressurization (Henine et al., 2014), others ob-

served that full pipe flow occurred for only 2 to 5 days during a year (King et al., 2014). Both

studies considered conventional drainage networks, without any drain flow control structure.

Causes of pressurized flow are numerous. They are either of internal origin (obstruction due

to soil erosion) or of external origin: modified drainage design (additional drains added to

a network), channeling surface flow through tile drains or flooding at land surface where a

drainage outlet is located. King et al. (2014) observed both actual full pipeflow at the outlet

from upstream drains and from flooding due to heavy rainfall events. Henine et al. (2014) sim-

ulated such conditions and demonstrated that pressurization leads to head loss along drains

and backflow from pipes to the surrounding porous medium.

In Fensholt, satisfactory results were obtained with the calibrated heterogeneous model in

terms of drainage discharge compared to field measurements. The seepage boundary condition

applied at drain nodes had no drainage design limitation (i.e. pipe diameter) accounting for

full pipe flow and backflow. Hydraulic head values higher than the soil surface simulated close

to the outlet of Drain B (in Pz8) may create surface runoff. Simplifying a network artificially

increases drain spacing, which enhances surface runoff as less water is conducted through

subsurface drains.

Instead of using drainage sink nodes, if discrete drains were implemented in the model and

coupled to the subsurface domain while solving the Hazen-Williams equation, simulation

times would have increased because smaller time-steps are generally required to solve pipe

flow. Coupling pipes to the surrounding porous media would have allowed water routed in

the drains to flow back from the pipes to the porous media. Water would have been exported

from the model when reaching drainage networks outlets only (StA and StB), with water

being routed in the drains before the outlet allowing for water exchanges along the pipes.

With the sink nodes option, water leaves the simulation domain as soon as it reaches the

drains.

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5.4.3 Comparison of model codes (HydroGeoSphere vs. MIKE SHE)

The MIKE SHE model covered the entire Norsminde catchment with 2D rectangular elements

whose lateral size was 100 m. The HydroGeoSphere model focused on the smaller-scale Fen-

sholt catchment and represented ground surface with triangular prism elements whose edges

varied in length from 6 to 150 m. Both models used the same geological structure and hy-

draulic properties but produced very different results. The spatial scale and discretization

level used in integrated hydrological models were previously demonstrated to influence simu-

lation results (Blöschl and Sivapalan, 1995; Blessent et al., 2009). In MIKE SHE, Refsgaard

(1997) and Vázquez et al. (2002) highlighted the dependency of effective hydraulic parameters

on grid resolution. Refsgaard (1997) also stated that changing a model’s spatial scale and

grid resolution requires that calibration should be repeated to ensure appropriate hydraulic

properties. Similar conclusions were reached with HydroGeoSphere (Sciuto and Diekkrüger,

2010).

These authors indicated also that results were less sensitive to upscaling hydraulic parameters

in a model compared to changing the spatial scale. This lower sensitivity was validated by

our homogeneous model, whose results were closer to those of the calibrated heterogeneous

model than its initial version. The hydraulic conductivity of the clayey till in the calibrated

homogeneous model was higher than that of the topsoil units and the heterogeneous clay units,

and they were equivalent to that of the heterogeneous sand units. The volumetric error for the

homogeneous error was small, 1 % for AreaB and 12 % for AreaA. Nevertheless, AreaB had a

series of peaks in late-spring that were neither simulated in AreaA nor observed (Figure 5.5,

around day 330) but that were counted in the total volumetric error. This was probably

due to missing local heterogeneous units that were present in the heterogeneous model. The

NSE of the homogeneous model showed a good performance in AreaA (0.78), while being

0.79 in the MIKE SHE model. Both models had similar performances in terms of drainage

discharge, suggesting that heterogeneous parameterization of the geology in HydroGeoSphere

was needed, especially as both drainage networks of interest were conceptually simplified (De

Schepper et al., 2015). Even by keeping all the actual pipes in the model, the simulated drain

flow would have resulted in a similar hydrograph trend; the hydraulic conductivities were

limiting factors in peak flow.

In addition, evaluating model performance based on volumetric error, NSE or r2 was demon-

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strated here not to be sufficient. A good volumetric error may conceal average NSE or

r2 coefficient values, and vice versa. It is therefore essential to combine several criteria for

assessing model performance.

Along with spatial discretization differences, transferring parameters calibrated with a given

code to another (i.e. from MIKE SHE to HydroGeoSphere) may have had an impact on re-

sults. Both solved similar equations in the surface and subsurface domains and treated drains

as sinks. However, drains in HydroGeoSphere were conceptualized as sink nodes, which is

physically closer to reality than drainage sinks applied at elements in MIKE SHE. Further-

more, the MIKE SHE model was calibrated against stream discharge. Drainage discharge in

AreaA was targeted in the calibration process with HydroGeoSphere. The drain node ap-

proach in HydroGeoSphere assumes that water entering the drains leaves the domain without

being discharged in the subsurface domain or at the land surface, which is generally observed

in the field. In MIKE SHE, drained water was routed downhill and was locally contributed

to stream discharge. Calibration against stream discharge was thus not feasible with Hy-

droGeoSphere. It might be relevant to consider this issue since Hansen et al. (2013) stated

that combining catchment discharge calibration with drainage discharge calibration should

allow for better simulated results. The same authors warned about scaling issues leading

to low simulation performance due to drainage areas being too small with respect to larger

heterogeneous geological bodies in their MIKE SHE model. In Fensholt, the drain flow cali-

bration performed correctly with HydroGeoSphere, but it was hardly conceivable to define a

rule assessing the tile drainage network scale under which geological heterogeneities had little

impact on drain flow calibration.

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5.5 Conclusion

A 6 km2 fully coupled saturated-unsaturated-overland flow model was developed to simulate

local scale seasonal tile drainage discharge over a one-year period with the numerical model

HydroGeoSphere. Seepage nodes were specified as sinks for simulating tile drainage, which

gave satisfactory results in terms of drain flow and lateral groundwater flow dynamics towards

drains. With the existing version of the code, seepage nodes represent an alternative to

representing tile drains with 1D line elements, which is prone to convergence difficulties in

hilly terrains. The model, which was based on a heterogeneous geological conceptualization of

the glacial till area, was calibrated against hourly drainage discharge data for a 34 ha drainage

area. Subsequently, it was validated against drainage data from another 28 ha drainage area

as well as observed groundwater head data from the two subareas. The model performed well

against the independent validation data suggesting a sufficient predictive capability for areas

where it was not calibrated.

The hydraulic properties of the subsurface plays a major role in determining groundwater

dynamics related to lateral drain flow and the volume of water that was actually captured by

the drains. Calibration of hydraulic parameters for geological units (sediment facies) was of

prime importance in improving the simulation of drainage discharge.

The HydroGeoSphere results were compared to results produced with a larger scale MIKE

SHE model. Both models used the same climate data as well as the same conceptualization

of geology, soil and vegetation. Drainage was also conceptualized as sinks in both models,

but HydroGeoSphere used triangular elements with side lengths of 6 m in the drain areas and

drain nodes were only assigned at the location of the main pipes allowing to resolve the change

of ground water table between drain pipes, whereas the large scale MIKE SHE model with a

discretization of 100 × 100 m contained drains in all elements and was not able to resolve the

dynamics around the individual drain pipes. This conceptual difference, together with a full

3D Richards’ equation in HydroGeoSphere compared to a coupled 1D unsaturated and 3D

saturated flow description in MIKE SHE, lead to a better description of the flow dynamics

around the drains produced by HydroGeoSphere.

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Chapter 6

Conclusions and perspectives

This PhD research aimed at simulating tile drainage water flow and associated shallow ground-

water flow dynamics for complex irregular subsurface drainage networks at various spatial

scales (from plot to catchment) and for different time scales (from a rainfall event to an entire

year). Simulating drainage flow in subsurface networks with fully-coupled 3D groundwater

flow, surface water flow and drain flow models under variably saturated conditions is a major

challenge. Depending on the desired degree of accuracy for simulated physical drainage pro-

cesses, the representation of complex drainage networks or their simplification shows slightly

different simulated drain flow dynamics in between actual drains. Including discrete 1D lin-

ear pipes provides accurate results but may lead to extremely long computational times.

Upscaling from plot-scale to catchment-scale requires simplified drainage networks to main-

tain reasonable simulation times while ensuring accurate simulated drain flow dynamics, but

the balance between these two is difficult to define and is site-specific.

A field-scale model was built in the Lillebæk catchment. Various drainage modeling concepts

were tested to investigate the most efficient way, in terms of data handling and model runtime,

to simulate small scale tile drainage in a fully coupled subsurface, surface and drainage model.

The degree of mesh refinement and temporal resolution of rainfall data applied to a model

were also tested and were shown to significantly influence the model computing time and

drain flow dynamics. Accounting for drainage in models requires that discrete drains be

considered but may result in very dense meshes. A promising alternative to keep discrete

drains and decrease the computational burden by using coarser meshes was to simplify the

drainage network so that the main collecting pipes are represented in the model.

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This simplification approach was selected to create a larger scale model of the Fensholt sub-

catchment including two complex drainage networks. Seepage nodes were applied as sinks for

simulating tile drainage to overcome numerical issues that may occur with the current Hydro-

GeoSphere verson in hilly terrains. Even if the Hazen-Williams equation was consequently

not solved in drains, good results from the seepage nodes were reported in terms of drain

flow dynamics and associated groundwater flow. The model was calibrated against discharge

data from a 34 ha drainage area (AreaA) and was validated with data from another 28 ha

drainage area (AreaB). The simulations suggested that calibrating a model against data from

a specific area is sufficient so that uncalibrated areas elsewhere within the same catchment

give satisfactory results, demonstrating promising predictive capabilities of the model.

Warsta (2011) and Yue (2010) both recommended the development of sophisticated mesh

generation tools that are suitable for tile drainage modeling purposes. In the present work, the

Triangle mesh generator (Shewchuk, 1996) was used with a mesh refinement and relaxation

algorithm based on Python scripts created by Therrien (2012) that respects the Delaunay

criteria (Delaunay, 1934). This mesh creation and refinement method was documented by

Käser et al. (2014), and was exclusively applied to the Lillebæk and Fensholt cases. This

mesh generator was powerful enough to create meshes with varying degrees of refinement for

simulations at the field or catchment scale with appropriate mesh refinement along drains and

with .

In both catchments investigated, the models allowed for a realistic physical representation

of drainage dynamics linked with shallow groundwater flow and overland flow. They were

demonstrated to be powerful tools on which subsequent reliable analysis could be expected.

Even though several studies were conducted recently to quantify tile drainage water flow with

on-field measurements (e.g. King et al., 2014) or numerical models (e.g. Rozemeijer et al.,

2010), properly reproducing and quantifying groundwater flow patterns associated with tile

drainage remains a major challenge.

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Perspectives for future research on tile drainage modeling include:

1. Further development of the drainage module in HydroGeoSphere is needed to solve the

Hazen-Williams equation for drainage modeling in sloping terrains. The results of this

work suffered numerical issues, but they were not severe. Since the model was able

to converge, it is believed that the equation needs testing to tune one of the equation

terms and correctly generate drain flow with zero pressure head values calculated along

drainage pipes.

2. Once the updated form of the drainage equation is up and running, adding an exchange

term ensuring coupling between a drainage network outlet and a discharge node at the

surface domain should be considered. Having such a feature would allow for a better

physical representation of drainage and stream discharge. In the present state of the

model, drainage water is removed from the model, whereas it should contribute to

stream flow or supply filtering wetlands at the surface (e.g. Kovačić et al., 2000).

3. Further physically-based improvements of the code could be done by developing progres-

sive clogging of pipes related to tile drainage. Clogging is a common physical process

observed in clayey tile-drained fields due to soil erosion and sediment transport (Turtola

et al., 2007; Øygarden et al., 1997). In addition to obstructing drains, sediment loading

leads to temporal variations of pipe entrance resistance (van der Velde et al., 2010).

Pressurized flow is then favored (Henine et al., 2014), inducing head loss and leakage

along the drains while water is routed downstream. For now, drains are assumed to be

fully effective when tile drainage is active in HydroGeoSphere, each pipe being empty

and partially filled with water.

4. In Fensholt, manual calibration of the model with few adjusted parameters showed good

performance regarding simulated and observed drainage discharge. Nevertheless, it is

believed that an automatic calibration approach with tools such as PEST (Doherty,

2005) would produce more accurate results. Using PEST would probably help facilitate

calibration of models with data from multiple drainage networks. The choice of manual

vs. automatic calibration is determined by computational performance of numerical

models as automatic calibrations might be more time-consuming. Future improvements

in computational power will likely improve inverse modeling applications.

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5. After calibration, a validation period is usually chosen for testing a model’s predictive

capabilities (Refsgaard, 1997). Focusing on a specific season or short-term period may

not be sufficient for this purpose. As mentioned by Williams et al. (2015) and King

et al. (2014), tile drainage discharge is highly dependent on climate conditions. A

validation period could then be run with longer than one year time series, as was done

with the Norsminde model of He et al. (2015). Avoiding biased predictions is a major

challenge for solute transport modeling, especially when tile drainage models are used

for decision-making linked to agricultural management of fertilizer application.

6. Finally, the next step to consider is simulating solute transport for investigating, among

others, nitrate contamination issues. Since this type of contamination is diffuse, simpli-

fying drainage networks in models, such as in the Fensholt case, is not believed to be

appropriate for nitrate transport simulations since a part of nitrate would not be trans-

ported through missing drains. Including discrete drains in models should therefore be

considered for ensuring accurate mass transport.

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