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Meeting challenges on the calibrationof the global hydrological model
WGHM with GRACE data input
S. WerthA. Güntnerwith input from R. Schmidt and J. Kusche
Introduction
S: Water storage changeP: PrecipitationE: EvaporationR: Runoff
ΔS = P - R - E
Terrestrial water balance
Time-Variable Gravity and Surface Mass Processes: Validation, Processing and First Application of New Satellite Gravity Data (TIVAGAM)
2
• Conceptual waterbalance model
• 0.5° spatial resolution
• Daily time-step
• Climate forcing data from CRU, GPCC, ECMWF
• Human water use accounted for
• Calibration for river dischargeat 1200 stations worldwide
ΔS = ΔScanop + ΔSsnow + ΔSsoil + ΔSgw + ΔSlakes + ΔSwetl + ΔSriver
The WaterGAP Global Hydrology Model (WGHM)
Total continental storage change:
3
Correspondence between GRACE and WGHM
Aim: Improve WGHM model results by a new calibration with GRACE data.
mm w.eq.
Mean maximum annual storage change (Gaussian filtering, 500 km)
GRACE
WGHM
4
Work plan for model calibration:
1) Analyze model propertiesa) Identification sensitive parametersb) Model uncertaintyc) Calibration test runs
2) Select adequate GRACE data and filter tools
3) Perform multi-objective model calibration
5
Work plan for model calibration:
1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs
2) Select adequate GRACE data and filter tools
3) Perform multi-objective model calibration
5
1c) Single-objective calibration
WGHM Monte-Carlo run
Standard WGHM
WGHM single-objective, one-parameter calibration
Ob
1.0 0.5 0.0 -0.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
Nash-Sutcliffe coefficient for water storage change
Nas
h-S
utcl
iffe
coef
ficie
nt
for
river
dis
char
ge
6
perfect model
simulation
Calibration approach
current parameter
sets
Evaluationof error
stop ?
Parameter-
variation
parameter set
ranking
Optimalsolution
yes
no
initial parameter
sets
Model simulation
GRACE total
storage variation
RunoffMeasureme
ntdata
7
0
err
or
dis
charg
e
Pareto
Frontier
0
single model simulation
error total storage change
0
Work plan for model calibration:
1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs
2) Select adequate GRACE data and filter tools
3) Perform multi-objective model calibration
8
2) GRACE filter tool evaluation
worldwide 22 largest WGHM river basins
Filter type Parameter Source
Gaussian filter (GF) filter width Jekeli, 1981
Optimized for basin shape (OF) max. satellite error Swenson and Wahr, 2002
Optimized for exp. signal model (MF) correlation length, signal variance Swenson and Wahr, 2002
GRACE signal-noise-ratio optimized (SF) factor of formal errors Seo et al, 2005
Correlation Error Filter (CEF) filter window properties Swenson and Wahr, 2006
Decorrelation Filter (DDK) covariance matrix parameter Kusche, 2007
9
2) GRACE filter tool evaluation: Amazon
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
wN
SK
500 1000 1500
filterwidth (km)
5101520
max. Satellite error (mm)
DDK decorrelated
w =10, n =30a e
w=30, n =30
a
e
w=20, n =30
a
ew =10, n =30
a
e
w =20, n =30a e
w =30, n =30a e
GFCEF decorrelated
OFCEF decorrelated
0
w =30, n =30
a
e
w =20, n =30a
e
w =10, n =30a
e
SFCEF decorrelated
5 10 15 20
error factor
50
100
150
2004006008001000
corrlation length (km)
= 250 mmσs
w =30, n =30a e
w =20, n =30a e
w =10, n =30a e 20
MFCEF decorrelated
Gaussian filter (GF)
Optimized for basin shape (OF)
Optimized for exp. signal model (MF)
GRACE signal-noise-ratio optimized (SF)
Correlation Error Filter (CEF)
Decorrelation Filter (DDK)10
2) GRACE filter tool evaluation: Lena
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
wN
SK
500 1000 1500
filterwidth (km)
5101520
max. Satellite error (mm)
w=10, n
=30
a
e
w=30, n
=30
a
e
w=20, n =30
a
e
w =30, n =30a e
w =20, n =30
a
ew =10, n =30a
e
GFCEF decorrelated
OFCEF decorrelated
DDK decorrelated
SFCEF decorrelated
0 5 10 15 20
error factor
w =20, n =30a e
w =10, n =30a e
w =30, n =30a e
MFCEF decorrelated
2004006008001000
corrlation length (km)
w =30, n =30a e
50
250= 300 mm
200
150
100
20
Gaussian filter (GF)
Optimized for basin shape (OF)
Optimized for exp. signal model (MF)
GRACE signal-noise-ratio optimized (SF)
Correlation Error Filter (CEF)
Decorrelation Filter (DDK)11
2) GRACE filter tool evaluation
Basin WGHM GLDAS
Amazon OF, MF OF,MF
Ganges MF MF
Mississippi
GF DDK
Volga SF SF
Yukon OF, CEFMF
MFOptimal filter for 5 basin examples
ParameterParameter
ValuewNS
C
rg [km] 200 0.75
εmax [mm] 13 0.78
error factor 0.4 0.77
σs [mm], cl [km]
250, 200 0.78
wa, we, na, ne 30, 3, 2, 30 0.63
a, p 1014, 4 0.74Amazon wNSC values and filter parameter for different filter types
Filter
Gaussian filter (GF)
Optimized for basin shape (OF)
Optimized for exp. signal model (MF)
GRACE signal-noise-ratio optimized (SF)
Correlation Error Filter (CEF)
Decorrelation Filter (DDK)
12
Work plan for model calibration:
1) Analyze model properties1) Identification sensitive parameters2) Model uncertainty3) Calibration test runs
2) Select adequate GRACE data and filter tools
3) Perform multi-objective model calibration
13
Work plan for model calibration:
3) Calibration Realization
Implementation of Multi-objective calibration algorithms into WGHM:
DDS Dynamically Dimension Search► single-objective calibration algorithm extended for mutli-objective problems
NSGA-II Non-dominated Sorting Genetic Algorithm► evolutionary multi objective calibration algorithm
14
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