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The integration of these hydraulic geometry relationships with widths and spectral

reflectances extracted from high-resolution World-View 2 (WV2) remotely-sensedimagery are explored for retrieving water depths and scaling up to larger rivers in

catchments across the entire ablation zone. Combined with automated WV2extraction of supraglacial streams (Yang and Smith, in press), this will allow for

large-scale mapping of supraglacial hydrology across the Greenland Ice Sheet.

Vena W. Chu 1, Laure nce C . Smi th 1, A sa K . R e n n e r m a l m 2, R i ch a r d R . F o r s t e r 3, Colin J . Gleason 1, L inco ln H . P i t che r 1, Samiah E . Mous ta fa 2,

B r a n d o n T . O ve r s t r e e t 4 , Carl J . Leglei ter 4 , A lbe r to E . Behar 5, Marco Tedesco 6, Kang Yang 1,7

D a ta a n d m e t h o d s2

This study provides a first assessment of supraglacial streamhydraulic relationships and preliminary findings integrating those

relationships with remotely-sensed imagery. While hydraulicgeometry relationships are traditionally evaluated for down-

stream reaches of the same stream catchment, results show thathydraulic relationships across a variety of cross-sections and

catchments yield a universal hydraulic geometry for Greenland

Ice Sheet supraglacial streams. Velocity is typically theparameter with the highest rate of change with discharge in other

supraglacial environments, driven by both steep slopes andrelatively low resistance from smooth stream beds (Brykala

1999; Knighton 1981; Marston 1983), but here discharge iscontrolled almost equally by width and depth variations, with very

little contribution from velocities. While the strong relationship

between width and depth over larger scales may help constrainwater flux measurements, preliminary results show that empirical

models relating depth to spectral reflectance ratios can mapdepths from satellite imagery. Future work will assess our ability

to estimating ablation zone meltwater fluxes at other ice sheetlocations using high-resolution WV2 satellite imagery.

Conc lus ion7

This work was supported by the NASACryospheric Scien ces Program grant NNX11AQ38G, man-

aged by Dr. Thomas P. Wagner. The WorldView imagery was provided by Paul Morin and Claire

Porter from the Polar Geospatial Center at the University of Minnesota. We thank Kangerlussuaq

International Science Support (KISS) for providing logistical support for field work.

A c k n o w l e d g m e n t s

R e f e r e n c e sBrykala D (1999). “Hydraulic geometry of a supraglacial stream on the Waldemar Glacier

(Spitsbergen) in the summer.” Polish Polar Studies 51–64.

Colgan W, Steffen K, McLamb WS, et al. (2011). “An increase in crevasse extent, West Greenland:

Hydrologic implications.” Geophysical Research Letters 38:1–7.

Leopold LB, Maddock TJ (1953). “The hydraulic geometry of stream channels and some

physiographic implications.” U S Geological Survey Professional Paper 252:1–57.

Knighton AD (1981). “Channel form and flow characteristics of supraglacial streams, Austre

Okstindbreen, Norway.” Arctic and Alpine Research 13:295–306.

Marston RA(1983). “Supraglacia l stream dynamics on the Juneau lcefield.” Annals of the

Association of American Geographers 73:597–608.

Yang K, Smith LC (in press). “Supraglacial streams on the Greenland Ice Sheet delineated from

combined spectral-shape information in high resolution satellite imagery. IEEE Geoscience and

Remote Sensing Letters.

Fig. 2. Locations of stream measurements in southwest Greenland over the period of July 20 - August 20 in summer of 2012 along a 75 km transect. Each site is labeled with the elevation and number of cross-sectional hydraulic mea-surements. Two highly sampled sites at 500 m and 875 m also provide measurements of ablation rate , stream water and temperature data, and meteorological variables. Rivers are extracted from World-View 2 imagery from July 18-23,2012 coincident with the field campaign.

Fig. 3. Ice Camp meteorological measurements of temperature and upward/downward shortwave radiation. Aheavilyovercast day on July 22, 2012 dampened to diurnal temperature variation and muted the shortwave radiation.

C43C-0618

Increasing surface melting on the Greenland ice sheet and rising sea level haveheightened the need for understanding the complex pathways transporting

meltwater from the ice sheet surface to the ice edge and the ocean. Supraglacialstreams are abundant throughout the ablation zone, transporting large volumes of

meltwater into moulins and crevasses (Colgan et al., 2011), yet these streamsremain poorly studied. Here we present a study of supraglacial stream hydraulics

and geometry in the ablation zone of western Greenland during summer 2012. Wemeasured various parameters including flow width, depth, velocity, and water

surface slope at different elevations and stream network types in a 75 km transect

spanning 500 m to 1480 m in elevation. This transect includes two highly sampledcatchments, one at 500 m (”Ice Edge”) and one at 875 m elevation (”Ice Camp”),

and 6 other day trip sites, yielding a total of 78 cross-sections.

I n t r o d u c t i o n1

6Department of Earth and Atmospheric Sciences, The City College of New York, 160 Convent Ave., New York City, NY, 100317Department of Geographic Information Science, Nanjing University, 210093, China

Fig. 1. a) Surface velocity measured using a portable velocity meter and near-surface velocity mea-sured using a mechanical flowmeter. b) ADCP tethered to a cross-sectional cable for measuring depthand velocity. c) Water surface slope measurement using an automatic level and leveling rod.

M et eo ro lo g ic al m ea su re m en ts

Univer sa l hydrau l i c geomet r y and sca l ing r e l a t ionsh ips5Fie ld loca t ions3

H yd r a u lic ge o m e t r y o f G r e e n l a n d I c e S h e e t s u p r a gla c ia l s t r e a m s :

F ie ld m e a s u r e m e n t s fr o m 2 0 12

4Department of Geography, University of Wyoming, 1000 E. University Ave., Laramie, WY, 820715Jet Propulsion Laboratory, Pasadena, CA

2Department of Geography, Rutgers, The State University of New Jersey, 54 Joyce Kilmer Avenue, Piscataway, New Jersey 088543Department of Geography, University of Utah, 260 S. Central Campus Dr., Salt Lake City, UT 84112

1UCLA Department of Geography, 1255 Bunche Hall, Los Angeles, CA 90095 ([email protected])

I ce Cam p c l im a t i c and hydr au l i c

d i u r n a l v a r i a ti o n s

4

H y d ra u li c g eo m et ry

• Stream hydraulics and geometries at cross-sections were measured along a

75 km transect and at two highly sampled catchments using different methodsfor different stream scales.

• Discharge (Q): calculated by the velocity-area method

• Width (w ): leveling rod and helicopter-aided cable cross-sections

• Mean depth (d ): depth probe and Acoustic Doppler Current Profiler (ADCP)

• Mean velocity (v ): surface velocity using a FloWav Phaser portable velocity

meter for streams < 8 m wide, with ADCP used for larger streams.

• Cross-section area ( A)

• Wetted perimeter (P )

• Width/depth ratio (F ): F = w/d

• Water surface slope (S ): automatic level and leveling rod at the water surface

• Hydraulic radius (R): R = A/P

• Froude number (Fr ): , where Fr > 1 describes supercritical flow

• Manning’s resistance coefficient (n):• Meteorological station (Onset HOBO) for climatic variables measuring

temperature, wind speed/direction, shortwave radiation (↑↓), and precipitation.• Diurnal water levels and water/air temperature from Solinst pressure

transducers.

• World-View 2 high-resolution satellite imagery over the field locations provideremotely-sensed maps of stream networks

Fr

Fig. 6. (Left image) The relationship between width and average depth shows a strong correlation, providing thepossibility for extracting depths from remotely-sensed widths. (Right image) Width is is also strongly correlatedwith hydraulic radius, a component of Manning’s n. The empirically-derived Manning’s n represents surface rough-ness and sinuosity and can be used to calculate velocity using hydraulic radius and slope.

The highly sampled ”Ice Camp” site at 875m elevation from July 19 - 24, 2012 contains 23

cross-section measurements of hydraulics and geometries, ablation rate, meteteorologicalstation variables, and diurnal stream water level and water temperature. Ablation rate in Ice

Camp for the four days is an average of 5.09 cm/day . Water levels are highly driven by air temperatures, and water temperatures remain at 0°C until the last day when it drops to below

zero.

-2

0

2

4

6

8

5

10

15

20

25

30

7/20/201217:00

7/21/201205:00

7/21/201217:00

7/22/201205:00

7/22/201217:00

7/23/201205:00

7/23/201217:00

7/24/201205:00

T e m p e r a

t u r e

( C )

W a

t e r

l e v e

l ( c m

)

Waterlevel (cm)

WaterTemperature(°C)

Air Temperature(°C)

S t r e a m l e v e l s a n d t e m p e r a t u r e

0

200

400

600

800

-2

-1

0

1

2

3

4

7/20 7/21 7/22 7/23 7/24 R a

d i a n

t e n e r g y

f l u x

( W m - 2

)

T e m p e r a

t u r e

( C )

Temperature,°C

Upwardshortwaveradiation, W/m²

Downwardshortwave radiation, W/m²

Cloudy

w = 3.260Q 0.516

R²= 0.883, n = 780.1

1

10

100

0.001 0.01 0.1 1 10 100

W i d t h ( m )

d = 0.331Q 0.498

R²= 0.897, n = 780.01

0.1

1

10

0.001 0.01 0.1 1 10 100

A v g d e p t h ( m )

v = 0.927Q -0.014

R²= 0.003, n = 780.1

1

10

0.001 0.01 0.1 1 10 100

A v g s u r f a c e v e l o c i t y

( m s - 1 )

Discharge (m3s-1)

m = -0.014

f = 0.498

b = 0.516

In teg ra t ion wi th r emote ly - sensed

Wor ld -View 2 im agery6

Fig. 4. Ice Camp meteorological measurements of temperature and upward/downward shortwave radiation. Aheavilyovercast day on July 22, 2012 dampened to diurnal temperature variation and muted the shortwave radiation.

Combining 78 cross-sections from a 75km transect spanning various streamtypes and catchments yields a universalhydraulic geometry for Greenland IceSheet supraglacial streams. Width anddepth show high and very similar b and f exponents, while velocity shows a near-zero m exponent, indicating that dis-charge is predominantely driven byvariations in width and depth. Withvelocity less important and averaging ~1m/s, the three variables controlling dich-arge may possibly be simplified to justtwo, width and depth.

a) b) c)

a)

b)

Legend

!( Daysites

!. Ice camps

Rivers

10km

“Ice Edge”500m elev31 cross-sections

“Ice Camp”875m elev20 cross-sections

1080m elev

2 cross-sections

1070m elev7 cross-sections


1293m elev

4 cross-sections

1410m elev

1 cross-sections



R = 0.075w + 0.013R²= 0.880, n = 78

0

0.5

1

1.5

2

0 5 10 15 20 25

H y

d r a u

l i c r a

d i u s

( m )

Width (m)

d = 0.010w + 0.010R²= 0.866, n = 78

0

0.5

1

1.5

2

0 5 10 15 20 25

A v g

d e p

t h ( m )

Width (m)

P ar am et er U ni ts Mi n Me an M ax

Discharge(Q ) m3s-1 0 .0 06 3 .7 49 2 8. 78 2

Width(w ) m 0.20 4.62 19.06

Avgdepth(d ) m 0.03 0.48 1.95

Avgsurfacevelocity (v ) ms-1 0.24 1.08 2.60

Cross-sectionalarea( A ) m2 0 .0 08 5 .7 56 2 9. 00 0

Wetted perimeter (P ) m 0.21 6.01 31.14

Width/DepthRatio(F ) 1.3 11.2 42.2

Hydraulicradius( R ) m 0.024 0.363 1.627

Froudenumber (Fr ) 0.055 0.892 3.116

Manning'sresistancecoeficient( n ) 0.009 0.136 1.278

Water surfaceslope (S ) 0.001 0.032 0.088

In te g ra ti on w it h re m ot e s en si n g

WV2 extraction of stream networks provides remotely-sensed widths and

spectral reflectances, two opportunities for retrieving water depth. While thewidth and depth relationship may help constrain depth estimates, an empiri-

cal model relating reflectance ratios of WV2 green (R545) and green (R605)

bands developed from field measurements provides a more direct method.

Fig. 4. WV2 imagery from July 18, 2012 showing (a) the extracted water mask, and (b) retrieved

water depths from application of the empirical model:d = -0.936+ 3.09ln(R545 /R605 )

Table 1. All measured parameters for the 78 cross-sections.

Fig. 5. Power functions relating discharge with width, average depth, andaverage surface velocity for the 78 cross-sections.

Hydraulic geometry describes an empirical model where changes in width,w , depth,d , and velocity, v at cross-sections are power functions of discharge, Q ( Leopold and

Maddock, 1953):w = aQ

b ; d = cQ

f ; v = kQ

m, where ack = b+f+m = 1

Science questions : What are the relationships between supraglacial stream hydrau-

lics and geometries, and are they scaleable to larger rivers? Is there a universalhydraulic geometry for Greenland Ice Sheet supraglacial streams?

Science questions : Can remotely-sensed widths and reflectances mapped from

high-resolution satellite imagery retrieve water depths? Can we assess and

constrain water flux using these empirical hydraulic geometry relationships?