SWOT spatio-temporal errors from in-situ measurements S. Biancamaria (1), N. Mognard (1), Y. Oudin (1), M. Durand (2), E. Rodriguez (3), E. Clark (4), K. Andreadis (4), D. Alsdorf (2), D. Lettenmaier (4) ‏ (1) LEGOS, FR (2) Ohio State University, US (3) Jet Propulsion Laboratory, US (4) University of Washington, US

This study aims to address 2 questions: – What is the error due to the SWOT temporal sampling ? – How accurate can we expect discharge derived from SWOT measurements to be ? Preliminary estimates of these errors are based on in-situ measurements at stream gauges. Extend these errors from gauges to the whole rivers (for global estimates).

1. Temporal sampling

Purpose of this study Estimate the maximum errors due to the orbit temporal sampling. Hypothesis: SWOT measurements have already been converted to discharge. Focus only on errors for monthly discharge estimates.

Methodology Step 1: Estimate the « true » discharge = daily discharge from in-situ gauges (Q t ). Step 2: From daily discharge, extract the discharge at SWOT observation time. 5-day and 10-day discharge have also been extracted. Step 3: Compute the monthly mean from daily discharge (our « true » monthly mean, Qm t ) and from the subsampled discharge (Qm sub ).

Methodology Step 4: Compute the error (σ t /Q): Step 5: Compute this error for gauges around the world and classify them as a function of the river drainage area. Step 6: Fit a relationship between the maximum error and the drainage area.

Data used 201 gauges used from USGS, GRDC, ANA and HyBAM:

Data used Orbit 1: 20 day repeat period, 74° inclination and ~1000km altitude (3 day sub-cycle), Orbit 2: 22 day repeat period, 78° inclination and ~1000km altitude. Two different orbits have been considered:

Results Error vs drainage area for all the gauges: Maximum error fit (power law)‏

Results Equatorial rivers (-13°N<gauges latitude<3°N ) ‏ Tropical rivers (8°N<gauges latitude<20°N )‏ Mid-latitude rivers (33°N<gauges latitude<53°N )‏ Arctic rivers (50°N<gauges latitude<72°N )‏

Results Very similar errors between the 2 orbits. Comparison with a constant sub-sampling: - 5 day subsampling = 4 observations in 20 days day subsampling = 2 observations in 20 days. - SWOT errors closer to 10day subsampling errors. - Yet SWOT observation number in 20 days: from 2 (at the equator) to 7 and more (at high latitudes).

Results Why SWOT errors not closer to 5 day subsampling errors ? SWOT sampling - Equatorial gauges SWOT sampling - Arctic gauges Because SWOT does not have a constant time sampling: Time period not sampledVery close observations

Results summary A fit of the relationship between maximum errors and the drainage area has been computed. Importance of the SWOT temporal sampling on the monthly discharge.

2. Measurement error

Purpose of this study – Rough estimate of the discharge error (using in- situ discharge) due to measurement error. – How the study could be extended to all the rivers. Methodology – Hypothesis: Power law relationship between discharge (Q) and river depth (D): Q=c.D b. – For river depth D=h-h 0, h is the elevation measured by SWOT and h 0 is the river bed elevation.

Methodology – The error on the discharge estimates (σ Q /Q) is: where σ D is SWOT measurement error (σ D =10cm) and η is the model error (between in-situ discharge and the discharge from rating curve).

Data used Gauges from USGS, ANA,HyBAM and IWM: 64 gauges in America10 gauges in Bangladesh

Results Model error (η) vs SWOT measurement error (b.σ D /D):

Results The measurement error is low. Estimate the model error (η) is difficult: most of the discharges come from rating curve (very low error with good fit or high error because of bad fit). Hypothesis: the model error ~20% (Dingman and Sharma, 1997; Bjerklie et al., 2003).

Results Power coefficient b in the power law rating curve depends on bathymetry, difficult to interpolate between gauges. How is the discharge error sensitive to this parameter ?

Results σ Q /Q vs D and b (for η =0.2 and σ D =10cm):

Results Median value and histogram of b for the 5 rivers: 3.8Missouri 2.3All rivers 1.6Mississippi 2.5Colorado 3.2Bangladeshi 2.0Amazon Median(b) ‏ River Coherent with previous studies: Fenton (2001) and Fenton and Keller (2001) found b=2; Chester (1986) found b=2.5.

Results σ Q /Q computed for each gauge (η =0.2 and σ D =10cm): Very low value of D (<80cm)‏

Results summary The model error used here is difficult to estimate from in-situ measurement. Yet it it can be assumed that η~0.2. The coefficient b cannot be interpolated from gauge locations to the whole river. Low influence of b on SWOT error for rivers with a depth above 1.5m (for a b coefficient below 3.5). From Moody and Troutman (2002), a river depth of 1.5m ~ a river width of 90m. b=2 can be used to estimate SWOT measurement globally as it is close to the value found in this study and previous ones.

Conclusion A fit of the maximum errors due to SWOT temporal sampling has been computed for different kind of rivers. A rough estimate of the error on the instantaneous discharge from SWOT measurement can be done using η =0.2 and b=2. Then using a global river network, map of the discharge error can be computed (see the following talk from Kostas Andreadis).

Thank you for your attention!