SWOT spatio-temporal errors from in-situ measurements

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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

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• 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).

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1. Temporal sampling
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Purpose of the temporal sampling 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.

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Methodology (1/2)

• Step 1 Estimate the  true  discharge daily
  discharge from in-situ gauges (Qt).
• 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, Qmt) and
  from the subsampled discharge (Qmsub).

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Methodology (2/2)

• Step 4  Compute the error (st/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.

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Gauges data used

• 201 gauges used from USGS, GRDC, ANA and HyBAM

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SWOT orbit data used

• Two different orbits have been considered

• 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.

Histogram of the SWOT observations for the 201
gaugesr
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Error vs drainage area for the 201 gauges
Maximum error fit (power law)?
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Error vs drainage area for the 201 gauges

• Very similar errors between the 2 orbits.
• Comparison with a constant sub-sampling

• 5 day subsampling 4 observations in 20 days.
• 10 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).

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SWOT temporal sampling

• Why SWOT errors not closer to 5 day subsampling
  errors ?

• Because SWOT does not have a constant time
  sampling

SWOT sampling - Equatorial gauges
SWOT sampling - Arctic gauges
Time period not sampled
Very close observations
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Results summary

• Using more than 200 gauges and 2 different SWOT
  orbits
• 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.

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2. Measurement error
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• 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 (1/2)
• Hypothesis Power law relationship between
  discharge (Q) and river depth (D) Qc.Db.
• For river depth Dh-h0, h is the elevation
  measured by SWOT and h0 is the river bed
  elevation.

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• Methodology (2/2)
• The error on the discharge estimates (sQ/Q) is
• where sD is SWOT measurement error (sD10cm) and
  ? is the model error (between in-situ discharge
  and the discharge from rating curve).

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Gauges data used

• Gauges from USGS, ANA,HyBAM and IWM

64 gauges in America
10 gauges in Bangladesh
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Model error (?) vs SWOT measurement error
(b.sD/D)
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Model error (?) vs SWOT measurement error

• The SWOT measurement error is low.
• Estimate the model error (?) 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).

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Sensitivity to the b coefficient

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

with Qc.Db
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Sensitivity to the b coefficient

• sQ/Q vs D and b (for ? 0.2 and sD10cm)

30
1.5m
with Qc.Db
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Sensitivity to the b coefficient

• Median value and histogram of b for the 5 rivers

Coherent with previous studies Fenton (2001) and
Fenton and Keller (2001) found b2 Chester
(1986) found b2.5.
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Sensitivity to the b coefficient

• sQ/Q computed for each gauge (? 0.2 and sD10cm)

Very low value of D (lt80cm)?
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Results summary

• Using more then 70 gauges with both discharge and
  water elevation.
• The model error (? ) can be assumed 20.
• Low influence of b on SWOT error for rivers with
  a depth above 1.5m (for a b coefficient below 3).
• b2 can be used to estimate SWOT measurement
  globally as it is close to the value found in
  this study and previous ones.

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Conclusions

• Importance of the SWOT temporal sampling on the
  computation of monthly discharge.
• SWOT spatio-temporal errors have been computed
  from the in situ networks for different satellite
  orbits.
• General hydrological parameters have been derived
  from these analysis.
• These parameters will be used to generate
  discharge error maps for a global river network,
  (see the following talk from Kostas Andreadis).

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Thank you for your attention!
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Results

• Equatorial rivers
• (-13Nltgauges latitudelt3N )?

• Tropical rivers
• (8Nltgauges latitudelt20N )?

• Mid-latitude rivers
• (33Nltgauges latitudelt53N )?

• Arctic rivers
• (50Nltgauges latitudelt72N )?