1. 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 Meeting December 17, 2008

2. 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

3. 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 Width - observed by SWOT Slope - observed by SWOT Roughness - estimated from ancillary data Depth - estimated via observables, ancillary data

4. Algorithm to estimate depth 1.Given: SWOT observables 2.Find: Estimate depth at initial time: z 1 3.Solution: a)Assume continuity between two pixels s 1 and s 2 b)Rewrite for unknowns c)Solve over-constrained problem for unknown depth Note:

5. 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

6. SWOT spatiotemporal sampling and errors

7. Discharge and depth errors: Examples Cumberland River Ohio Mainstem Kanawha River

8. 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

9. 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.

10. Discharge anomaly accuracy and depth error DischargeDischarge Anomaly

11. 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.

12. 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