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

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

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

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.

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)

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?

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

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

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

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.

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

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

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)

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

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

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.