Swath altimetry provides measurements of water surface elevation but not discharge key flux in surfa

1
Quantifying the impact of model errors on river
discharge retrievals through assimilation of
SWOT-observed water surface elevations Elizabeth
Clark1, Konstantinos Andreadis1, Sylvain
Biancamaria2, Michael Durand3, Delwyn Moller4,
Ernesto Rodriguez4, Doug Alsdorf3, and Dennis
Lettenmaier1 1Civil and Environmental
Engineering, University of Washington, Seattle
WA 2Laboratoire d'Etudes en Géophysique et
Océanographie Spatiales, Toulouse France 3School
of Earth Sciences, the Ohio State University,
Columbus OH 4Jet Propulsion Laboratory,
California Institute of Technology, Pasadena
CA American Geophysical Union Annual Meeting, San
Francisco, CA, December 16, 2008
H23A-0956
4. Perturb Meteorological Forcings
1. Abstract
Magnitude Errors
Position Errors
Data set Variance
The planned NASA/CNES Surface Water and Ocean
Topography (SWOT) swath satellite altimetry
mission will provide highly accurate measurements
of surface water slope (order on microradian over
reach lengths 1-10 km) and water surface level
(centimetric scale accuracy over areas order of 1
km2). Discharge would be derived through
assimilation of slope and/or elevation and other
quantities into a hydrodynamic model. Previous
studies have demonstrated the potential for such
an approach. We describe a system that includes a
hydrology (Variable Infiltration Capacity, VIC)
and hydrodynamics (LISFLOOD) model that provide
the background predictions of river discharge and
depth, which are then merged with SWOT
observations. Among the key determinants of the
accuracy of predictions resulting from such
assimilations are the model and observation
errors. The former can arise from errors in model
forcings (e.g. precipitation and channel boundary
inflows) as well as model parameters (e.g.
channel width and roughness coefficient). In this
study we make an initial attempt at quantifying
the impact of model errors on river discharge
estimates produced via the assimilation of SWOT
observations into LISFLOOD and VIC. The study
area is a 1000 km reach of the Ohio River, where
synthetic SWOT WSL observations have been
generated using the JPL instrument simulator. An
ensemble representation is used for model errors
in precipitation, hence channel boundary inflows,
and roughness. Errors in precipitation are
modeled by generating random fields based on the
spatial probability distribution of the storm
center and extent, and the error probability
distribution inferred from the errors between
downscaled precipitation fields from the ERA40
reanalysis project (ECMWF) and interpolated
fields from in-situ stations. These errors are
compared to those derived from calculating the
EOFs of ERA40 precipitation fields.
For each time step, we calculated the center of
mass of ERA40 and Maurer et al. precipitation
within the Ohio River basin. The latitudinal and
longitudinal offsets of the ERA40 center of mass
relative to that of Maurer et al. were
calculated. A normal distribution was then fitted
to offsets in each direction. From these
distributions, a latitudinal and longitudinal
offset was randomly generated for each timestep.
The Maurer et al. precipitation fields were
uniformly shifted by these random offsets to
create an ensemble of 25 possible precipitation
fields.
Magnitude errors were calculated on a monthly
basis. Maurer et al. precipitation data was
binned into 0 mm, 0-5 mm, 5-10 mm, 10-25 mm, and
greater than 25 mm days. For each bin, the
fraction of occurences of concurrent zero
precipitation days in the ERA40 data set was
calculated. For those days on which the ERA40
data set had precipitation, probability
distributions were fit for each bin. For days
when Maurer et al. had no precipitation, a gamma
distribution was fit to the ERA40 data/ When
Maurer et al. had 0-5 mm of precipitation, a
log-normal distribution was fit to the ratio of
ERA40 to Maurer et al. For each of the remaining
bins, a gamma distribution was fit to the ratio
of ERA40 to Maurer et al. Ensembles of
precipitation were generated by perturbing Maurer
et al. following these distributions.
ERA40
Maurer et al.
ERA40
ERA40
Maurer et al.
Maurer et al.
CDF of latitudinal offset
2. Background
F(x)
SWOT is the Surface Water/Ocean Topography
Mission Direct measurements of land-surface
hydrology Water surface elevation of lakes,
reservoirs, streams, wetlands Water surface
extent of of lakes, reservoirs, streams,
wetlands Some derived measurements Lake,
reservoir, wetland storage change in space and
time Changes in river discharge in space and
time Key elements KaRIN Ka-band radar
interferometer Two 60-km wide swaths One
Jason-class nadir altimeter 22-day repeat cycle,
74 or 78 degree inclination
January CDF for Maurer 0 to 5 mm ERA40 gt 0
mean0.24 deg stdev 1.33 deg
January CDF for Maurer 0 ERA40 gt 0
x
CDF of longitudinal offset
F(x)
F(x)
Top plot shows a time series of ERA40, Maurer et
al. and perturbed ensemble members of
precipitation from Jan. 1, 1995 to April 30,
1995. The lower plot shows maps of precipitation
fields for Jan. 15, 1995 with the smaller maps
showing the 25 ensemble members.
Top plot shows a time series of ERA40, Maurer et
al. and perturbed ensemble members of
precipitation from Jan. 1, 1995 to April 30,
1995. The lower plot shows maps of precipitation
fields for Jan. 15, 1995 with the smaller maps
showing the 25 ensemble members.
Top plot shows a time series of ERA40, Maurer et
al. and perturbed ensemble members of
precipitation from Jan. 1, 1995 to April 30,
1995. The lower plot shows maps of precipitation
fields for Jan. 15, 1995 with the smaller maps
showing the 25 ensemble members.
F(x)
Spatial (left) and temporal (right) mode 1 EOFs
mean0.05 deg stdev 191 deg
x
x
Gamma distribution of ERA40 precipitation shape
0.59, rate 1.71
Log-normal distribution of the ratio of ERA40 to
Maurer et al. precipitation mean(ln) 0.09,
stdev(ln) 1.83
x
5. Hydrologic Model
6. Hydrodynamics Model

• Swath altimetry provides measurements of water
  surface elevation but not discharge (key flux in
  surface water balance)?
• SWOT data will be spatially and temporally
  discontinuous
• Data assimilation offers potential to merge
  information from SWOT with discharge predictions
  from river hydrodynamics models
• Previous work has addressed errors in the
  magnitude of satellite derived-precipitation
  estimates (Andreadis et al., 2007) and hydraulic
  parameter estimation from assimilation (Andreadis
  et al., 2008)
• Precipitation fields in precipitation forecasts
  (such as ERA40), GCMs, satellite-derived data,
  and interpolated ground data products also
  contain errors in the spatial distribution across
  a landscape.
• This study seeks to understand the effects of
  these spatial errors.

A hydrologic model simulates the lateral and
upstream boundary inflows that feed into
LISFLOOD. VIC itself cannot simulate the dynamics
that translate discharge into water
elevationswhich are the direct SWOT measurements.
In this study, LISFLOOD acts as a sort of
transfer function between water elevation
(observation) and discharge (end product).
Hydrologic Model

• Variable Infiltration Capacity model (Liang et
  al., 1994) to provide the lateral and upstream
  boundary inflows.
• Has been applied successfully in numerous river
  basins including the Ohio River.

EOF
EOF
Truth (Maurer et al., 2002)
Ensemble member
Magnitude Only
3. Experimental Design
The figures at right show LISFLOOD-simulated
ensemble mean values for flow (top) and depth
(bottom) along the channel chainage on Feb. 1,
1995.
Position Only
7.Data Assimilation
Figures at right show discharge time series at
the basin outflow point as modeled by VIC for
true Maurer et al. forcings and for perturbed
precipitation ensembles.
Ensemble Kalman Filter update performed for one
overpass, across the first 352 km chainage.
elevation assumed to have normally distributed
errors with zero mean and 20 cm standard
deviation. The channel topography is assumed to
be true and unchanging in time.
Time series of upstream inflows to LISFLOOD study
domain as generated by VIC from true and
perturbed precipitation.
EOF
8. Summary and Conclusions
EOF
8. References
Andreadis, K. M., E. A. Clark, D. P. Lettenmaier,
and D. E. Alsdorf, 2007, Geophys. Res. Lett., 34,
L10403, doi10.1029/2007GL029721. Andreadis, K.,
D. Lettenmaier, and D. Alsdorf, ASLO Ocean
Sciences Meeting, Orlando, FL, Mar. 2008. Bates,
P. D., and A.P.J. De Roo, 2000, J. Hydrol., 236,
54-77. Liang, X., D. P. Lettenmaier, E. F. Wood,
and S. J. Burges, 1994, J. Geophys. Res., 99(D7),
14,415-14,428. Maurer, E.P., A.W. Wood, J.C.
Adam, D.P. Lettenmaier, and B. Nijssen, 2002, J.
Climate 15, 3237-3251.
Data assimilation requires knowledge of model
errors that is not readily available. In land
surface models, one of the most important and
most readily quantifiable sources of error is in
the estimation of precipitation forcings
(interpolation techniques, human error in
measurement, gage undercatch, etc.). In this
study, we assumed that an interpolated
ground-based data set from Maurer et al. (2002)
was close to the truth and then calculated the
differences in spatial positioning and
precipitation intensity between this and the
ERA40 reanalysis product. We also compare these
errors to the statistical variation of
precipitation within the ERA40 data set. The
errors in magnitude created a larger discrepancy
between true and open loop (no assimilation)
water surface levels and discharge than those in
spatial positioning and of within data set
variance (EOF). After running through the
Ensemble Kalman Filter, these errors were all
reduced to comparable levels.

• Three meteorological forcing perturbation schemes
  were implemented
• Magnitude errors derived from ERA40 relative to
  interpolated ground data
• Spatial positioning errors estimated from ERA40
  relative to interpolated ground data
• Both magnitude and position errors

9. Acknowledgments
Special thanks to Nathalie Voisin for extracting
ERA40 precipitation fields over Ohio and to Paul
Bates and Mark Trigg for advice on the
implementation of LISFLOOD.