1. Prospects for river discharge and depth estimation through assimilation of swath-altimetry into a raster-based hydraulics model Konstantinos Andreadis 1, Elizabeth Clark 2, Dennis Lettenmaier 1, and Douglas Alsdorf 3 1. Department of Civil and Environmental Engineering, Box 352700, University of Washington, Seattle, WA 98195 2. Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305 3. School of Earth Sciences, Ohio State University, Columbus, OH 43210-1308 Satellite Observations of the Global Water Cycle Workshop, 7-9 March 2007, Irvine, CA ABSTRACT New methods of measuring surface water elevations from space have the potential to revolutionize the type, frequency, and spatial scale of observations that are available globally. One complication is that satellite altimeters can measure surface water elevation directly with high accuracy, but streamflow of river discharge is not amenable to direct measurement. The most effective use of satellite-based methods for this purpose may be through data assimilation. Hydrology and river hydraulics models can be used to model surface water profiles, then adjusted as satellite altimetry observations become available, and subsequently fed forward to estimate discharge. We describe our use of a synthetic data assimilation framework to evaluate the potential for such a strategy. Simulated surface water elevation profiles for a reach of the Ohio River were ingested by the Jet Propulsion Laboratory Instrument Simulator to represent satellite swath measurements of surface water altimetry fields with errors representative of those that would be inherent in observations from a dual-sensor Ka-band wide swath altimeter that is being considered jointly by U.S. And European agencies. We used the Ensemble Kalman filter, with a raster-based river hydraulics model, LISFLOOD-FP, as its dynamical core, to assimilate the synthetic observations. The filter was able to recover water depth and discharge successfully from a corrupted LISFLOOD-FP simulation by assimilation of the synthetic water surface observations. A simple autoregressive error model was used to correct boundary inflows, and which increased the persistence of the assimilation's benefits in time. In addition, the sensitivity of water depth and discharge estimation errors with assumed observation errors and assimilation frequency (i.e. satellite overpass frequency) was examined. Results showed modest sensitivity to the observation error magnitude within the range explored (which was dictated by plausible instrument performance); while as expected the shorter update frequency simulation gave the best overall results. Motivation 1 Hydrology Model 3 Experimental Design Humans use 54% of accessible global runoff for withdrawals, consumption, and instream flow needs. Estimates of river discharge globally are highly uncertain due to limitations of in-situ observations, especially in the developing world and in sparsely populated high latitude regions. Recent advances in satellite technology, particularly the development of synthetic aperture radar, have the potential to produce accurate estimates of surface water storage in complex systems such as wetlands. Although these estimates would be valuable in their own right, for many scientific and practical applications, spatially and temporally continuous estimates of discharge are required, which satellites cannot produce. Hydrodynamic models can simulate spatially and temporally continuous discharge, but they are susceptible to errors in forcing data and other error sources, and work best if they are periodically re-initialized with observations. Data assimilation provides a framework to merge satellite observations and hydrodynamic model predictions to estimate river discharge in a way that accounts for both model and observation errors. 2 7 Water Surface Elevation Results 6 Sensitivity Analysis 8 Baseline Meteorological Data Hydrologic Model Perturbed Meteorological Data Baseline Boundary and Lateral Inflows Perturbed Boundary and Lateral Inflows Hydrodynamics Model Baseline Water Depth and Discharge JPL WatER Simulator Perturbed Water Depth and Discharge “Observed” WSL Kalman Filter Updated Water Depth and Discharge The basis for our evaluation is a proposed joint European-U.S. satellite mission, WatER (Water Elevation Recovery) that produces spatial fields of surface water elevation rather than transects ~8 day overpass frequency Spatially uncorrelated, normally distributed errors, N(0,20 cm) We use an identical twin experiment, in which observations are synthetically generated using a “parent” model which is corrupted by noise, and then assimilated into a dynamical core which uses the same parent model (identical twin). TRUTH: hydrology model produces “error-free” lateral and boundary inflows, which are fed into the hydrodynamics model to simulate the baseline water depth and discharge. OPEN-LOOP: Precipitation is perturbed with log-normal errors, and artificial bias is introduced to upstream boundary inflow to produce “wrong” boundary inflow and “corrupted” water depth and discharge FILTER: Same boundary and lateral inflows as the open-loop simulation, but assimilating synthetically generated water surface elevation observations Study area is a 50 km reach in the Ohio River, near Martin's Ferry, OH Simulations were performed for April 1 to June 23 1995 (84 days) The hydrology model used is the Variable Infiltration Capacity (VIC) model The hydrodynamics model used is the LISFLOOD-FP The data assimilation technique used is the Ensemble Kalman Filter (EnKF) Discharge (lateral and boundary inflows generated by VIC Solves energy and water balance over a gridded domain Routing scheme to produce steamflow from runoff and baseflow 3-hourly timestep at ~17 km spatial resolution Forced with precipitation and air temperature “Corrupted” boundary discharge generated by perturbing precipitation with log-normally distributed errors (25% relative error) Hydrodynamics Model 4 LISFLOOD-FP, a raster-based inundation model Based on a 1-D kinematic wave equation representation of channel flow, and 2-D flood spreading model for floodplain flow Over-bank flow calculated from Manning’s equation No exchange of momentum between channel and floodplain 20 s temporal and 270 m spatial resolution Ensemble Kalman Filtering 5 Initial State Forecast Analysis Member 1 Member 2 Observation Time t1t1 t2t2 t3t3 Monte Carlo approach to the traditional Kalman Filter Widely used in hydrology Represents model and observation uncertainty through an ensemble of model states Square root low rank implementation (avoids measurement perturbation) Channel Discharge Results Spatial snapshots of WSL for the different simulations (28 April 1995, 06:00) Satellite coverage is limited by the orbits used in the simulator Water Surface Elevation RMSE Discharge along the channel on 13 April 1995 for the different simulations Filter retrieves “true” discharge using only water depth information Observations are available every 8 days Upstream boundary inflows dominate simulated discharge Persistence of WSL and discharge update not adequate for the period between observations Simple AR(1) model of upstream boundary inflow errors with upstream discharge as an exogenous variable Error model used to correct boundary inflows Discharge time series at the channel downstream edge Time series of channel discharge RMSE Combination of filter updates and boundary inflow correction, which is based on the updated discharge at each observation time Nominal observation (assimilation) frequency is ~8 days Performed additional simulations with satellite overpass frequencies of 16 and 32 days Effect of assimilation lost by ~16 days 8 day overpass gives the best results Nominal observation error spatially aggregated becomes N(0,5 cm) Contrary to a synthetic experiment, true observation errors might not be known exactly Sensitivity of results to different assumed observation errors: (1) perfect observations and (2) N(0,25cm)