1. Assimilation of Remotely-Sensed Surface Water Observations into a Raster-based Hydraulics Model
Elizabeth Clark1, Paul Bates2, Matthew Wilson3, Delwyn Moller4, Ernesto Rodriguez4, Dennis Lettenmaier1, Doug Alsdorf5
University of Washington
University of Bristol
University of Exeter in Cornwall
Jet Propulsion Laboratory
Ohio State University

2. Purpose Globally, discharge measurements are sparse and non-continuous
Knowledge of global discharge aids in:
Closing the global water balance
Transboundary water management
Prediction of biogeochemical fluxes
Estimation of freshwater fluxes to the Arctic
Satellite altimetry is able to estimate water level of rivers, reservoirs, lakes, and wetlands
We would like to extract discharge from water level
Also note that gauges have difficulties with measuring discharge on braided rivers

3. Water Elevation Retrieval
Ka-band SAR (synthetic aperture radar) with two 50 km swaths
Uses low incidence angle (<4o) to increase the brightness signal of water relative to land
Produces heights and co-registered imagery
IS IT POSSIBLE TO OBTAIN DISCHARGE FROM WATER LEVEL?
Incidence angle < 4 deg
Image from Ernesto Rodriguez
Also see Doug Alsdorf’s talk tomorrow at 11:55 am Lido Room

4. Heritage: Estimation of Streamflow from Water Level
Stage-discharge relationships derived for several locations in Congo River basin (Coe and Birkett, 2004)
Regression models, generally based on Manning’s equation (Bjerklie et al., 2003)
2004)Satellite radar altimetry has been applied to monitor changes in surface water height for large wetlands, rivers, and floodplains (e.g. Birkett, 1998; Birkett et al., 2002; Rosenqvist and Birkett, 2002). Birkett et al. (2002) note that discharge cannot be derived directly from satellite measurements of stage; however, stage-discharge relationships for TOPEX/POSEIDON measurements have been obtained from ground measurements of discharge at several locations in the Congo river basin (Coe and Birkett, 2004).
Bjerklie et al. (2003) compare observed discharge to discharge predicted from five regression models, each generally based on Manning's equation; the accuracy of these predictions varies with the magnitude of discharge.

5. Heritage: Hydrologic Data Assimilation
Soil moisture (e.g. Margulis et al., 2002; Crow and Wood, 2003; Reichle et al., 2002)
Snow water equivalent (Andreadis et al., in review; Durand and Margulis, 2004)

6. Context: Virtual Mission
Conceptual Design
Truth model:
Hydrologic model to generate lateral inflows and boundary conditions
Hydrodynamic model to generate ‘true’ stage
Measurements:
Instrument simulator to add measurement error
Inversion problem:
Now can we estimate the ‘true’ inflows from the synthetic measurements?

7. Context: Virtual Mission
Hydrologic
Model (VIC)
Spatial and
Temporal Resolution
Tradeoffs
Lateral inflows and boundary conditions
Simulated Streamflow
Simulated
Interferometric
Altimeter Swaths
Measurement Error
Simulated Surface
Water Extent and
Elevation
Hydraulics
Model
(LISFLOOD-
FP)
NASA/JPL
Instrument
Simulator
“Truth”
Back Calculation
of Discharge
(Data Assimilation)
Inversion

8. Study Domain Ohio River flood during 1996
14 km hydrologic model resolution
270 m DEM for hydraulics model
50 m simulated satellite sampling resolution

9. Model Inputs
Discharge (lateral inflows and boundary conditions) generated by VIC model

10. LISFLOOD-FP
1-D finite difference solutions of the full St. Venant equations
2-D finite difference and finite element diffusion wave representation of floodplain flow
Qij=AijRij2/3Sij1/2/n,
i= upstream cell
j= downstream cell
n varies (channel vs. floodplain)
Seeks to balance computational cost and modelling accuracy. Calculates Q and elevation. Initial conditions (elevation of water in each pixel, channel width, etc.) Boundary conditions: lateral inflows and upstream flows.

11. Simulated Truth Water depth and discharge from 1995-1998
20 s time step
Output for every ~11 hours
Oct 28-Dec 17

12. Observations Generated by JPL Instrument Simulator 39.2oN, 81.7oW
Observed
“True”
Error
Generated by JPL Instrument Simulator
80.6 km
38.5oN, 82.3oW
If trying to calculate channel slope, these are potentially very important errors.
Water elevation (m)
Error (m)
Frequency
34.9 to 35.1
GHz
Mean Error cm
Repeat Cycle 16
Days
Std. Dev. Error
10-15

13. Data Assimilation: Ensemble Kalman Filter
Boundary condition (BC) and lateral inflow (LI) ensemble members represent propagation through VIC model of input errors from:
Precipitation (Nijssen and Lettenmaier, 2003)
Temperature (Andreadis, 2004)
LISFLOOD-FP propagates error from these BCs and LIs
Observations synthesized to minimize model errors versus normally-distributed measurement errors
Water level and discharge (states) updated
Precipitation :log-normal distribution, 25% relative error, spatially correlated Gaussian random fields
Temperature: perturbed using spatially correlated Gaussian random fields (Andreadis, 2004)

14. Prospects for Data Assimilation
Schematic of Ensemble Kalman Filter
Filter incorporates available measurements to minimize error
MEASUREMENTS
Swaths of remotely-sensed water elevation with known error distribution
Perturbed INPUTS
Simulated discharge from VIC
Manning’s n
STATE
Water depth
Spatially distributed discharge
UPDATED STATE
Water depth
Spatially distributed discharge
Kalman Filter Analysis Step
Error is introduced into model
Model propagates error
Measurement operator converts forecast state to measurement. Kalman gain matrix converts back to state.
2-D System Model Lisflood-FP
OUTPUTS
Estimated water depth
Estimated discharge
Associated error distributions

15. What will we learn from this exercise?
Feasibility of recovering discharge with little to no in-situ data
Evaluation of trade-offs between acceptable error and spatial resolution
Will elevation recovery work for streams of different sizes?
How fast does the ability to recover discharge degrade with spatial resolution?
Sensors and satellites 2x10 vs. 2x20

16. Conclusions
Satellites have a great potential for measuring the stage of inland waters.
The use of data assimilation has been effective in other hydrologic applications and will likely play a role streamflow estimation.
Results of this exercise will show the extent to which discharge can be recovered from surface water elevations.