how accurately will swot measurements be able to characterize river discharge? michael durand, doug...
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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
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.