How accurately will SWOT measurements be able to characterize river

discharge?

Michael Durand, Doug Alsdorf, Paul Bates, Ernesto Rodríguez, Kostas Andreadis, Elizabeth Clark

AGU Fall MeetingDecember 17, 2008

Outline

1. Algorithms:

How will we estimate

discharge from SWOT

observations?

2. Virtual Mission:

Simulating true water depth

and discharge, and

simulating SWOT

observations

3. Discharge Accuracy:

Comparing SWOT discharge

estimates with true

discharge

The SWOT Ka-band radar interferometer

Discharge algorithms

• Method 1: Manning’s retrieval algorithm

– Similar to heritage SRTM work

– Very computationally efficient

• Method 2: Data assimilation

– Incorporates ancillary data

– Relatively more accurate, more computationally

expensive

€

Q =1

nwS

1

2z5

3

Width - observed by SWOTSlope - observed by SWOT

Roughness - estimated from ancillary data

Depth - estimated via observables, ancillary data

Algorithm to estimate depth

1. Given: SWOT observables

2. Find: Estimate depth at initial time: z1

3. Solution:

a) Assume continuity between two pixels s1 and s2

b) Rewrite for unknowns

c) Solve over-constrained problem for unknown depth

€

Qs1 ,t =Qs2 ,t

€

ws,t Ss,t δzs,t

€

βs,t =1

nsws,tSs,t

1

2 ⎛

⎝ ⎜

⎞

⎠ ⎟

3

5

Note:

Simulating true Ohio River depth and discharge

• LISFLOOD diffusion wave model (Paul Bates)

• Eleven Ohio tributaries

• USGS gages for b.c.

• Channels from Hydro1k

• Study period: 1992 - 1993

• Study area: Ohio River Basin

Model Output Model Inputs

SWOT spatiotemporal sampling and errors

€

hSWOT = htrue + N 0,1

nσ SWOT

⎛

⎝ ⎜

⎞

⎠ ⎟

Discharge and depth errors: Examples

Cumberland RiverOhio Mainstem

Kanawha River

Discharge errors: Summary

• Error metric:

– Pixelwise RMSE of

discharge timeseries,

normalized by mean Q

• Median: 11%

• 86 % of pixels have

error less than 25 %

• Outliers should be

easily identified

In Progress:

Optimally leverage available in-situ depth measurements and statistical models

Discharge monthly errors

• Temporal sampling

errors only (shown):

– Median: 14 %

• Temporal and

retrieval errors

combined:

– Median: 22%In Progress:

Estimate discharge at unobserved times using spatio-temporal correlations

More temporal sampling

Biancamaria et al., H43G, Thursday.

Discharge anomaly accuracy and depth error

€

εQQ

=5

3

εzz

€

εΔQQ

=5

3

εzz

Δz

z

⎛

⎝ ⎜

⎞

⎠ ⎟

2

3−1

Δz

z

⎛

⎝ ⎜

⎞

⎠ ⎟

5

3−1

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

Discharge Discharge Anomaly

Summary

• Instantaneous discharge errors estimated with median 11% RMSE

• Monthly discharge errors estimated with median 22% RMSE

• Discharge anomaly is less sensitive than absolute discharge to depth error

Afterword: We are also exploring data assimilation as a means of estimating SWOT discharge. See Andreadis et al., GRL, 2007 (below), and Durand et al., GRL, 2008.

Thanks and Acknowledgments

• Funding from OSU’s Climate Water Carbon program

• Funding from NASA’s Physical Oceanography and Terrestrial Hydrology programs

• Paul Bates at University of Bristol - use of LISFLOOD model