Prospects for river discharge estimation through assimilation of remotely sensed altimetry: The WatER satellite mission Kostas Andreadis UW Land Surface Hydrology Group Seminar 14 June 2006

Summary ● Water Elevation Recovery (WatER) proposed satellite mission ● Motivation and scope of this study ● Methodology and experimental design ● Results and Problems ● Future work

Importance of water measurements ● Poor knowledge of spatial and temporal dynamics of surface water discharge and storage globally ● In-situ measurements not sufficient  Inadequate global coverage  Essentially provide an 1-D view of flow dynamics, especially in basins with extensive floodplains and wetlands  Still valuable, but do not answer key science questions

What measurements do we need? Fundamentally different from in-situ measurements ● Water surface elevation (h) ● Temporal changes in water surface (∂h/∂t) ● Water surface slope (∂h/∂x) ● Inundated area Spaceborne measurements can be a viable option for providing this type of measurements on a global scale

Current spaceborne approaches ● Area : visible band (MODIS, Landsat) and SAR imagery ● Elevation : profiling altimetry (TOPEX) and imaging (SRTM) methods ● ∂h/∂t : repeat altimeter measurements or SAR ● ∂h/∂x : derived from elevation SRTM or altimeter measurements ● Discharge : several methods, mostly problematic

Problems with existing sensors ● Poor spatial resolution (GRACE and all profiling altimeters) ● Conventional radar and lidar altimeters are nadir viewing, missing water bodies between orbital tracks ● Poor temporal resolution associated with SRTM and repeat-pass SAR ● Canopy and cloud cover problems for optical sensors

Required spatial and temporal sampling resolutions ● In summary, an interferometric altimeter (120 Km swath) covers nearly all global rivers and lakes ● Whereas, a profiling instrument would miss ~30% of rivers and ~70% of lakes (16-day cycle)

WatER instrumentation ● Two Ka-band antennae ● 200 MHz bandwidth ● Spatial resolution m ● Overpass frequency ~7 days (mid- latitudes) Ka-band Radar Interferometer (KaRIN)

What about discharge? ● Impractical to measure discharge from space ● LeFavour and Alsdorf (2005) used Manning's equation to estimate discharge from SRTM data ● Data assimilation of remotely sensed hydraulic measurements (h, ∂h/∂t, ∂h/∂x) into a hydrodynamics model, to indirectly estimate discharge

Scope of this study ● Create a baseline simulation of discharge and water surface elevation ● Generate synthetic WatER measurements using an instrument simulator ● Assimilate those into a hydrodynamic model and compare with the baseline simulation ● Proof-of-concept application

● Ohio River basin ● Small upstream reach ● Reach length ~50 km Study domain Clark (2006)

Experimental design

Hydrodynamic model ● 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 ● Assumes rectangular, wide channel ● Requires high resolution topographic data ● Overbank flow modeled using Manning's equation ● Spatially uniform or variable Manning's coefficient

Ensemble Kalman filter ● Monte Carlo approach to the traditional Kalman filter ● Ensemble representation of error covariances ● State vector containing water depth and discharge, but only former directly observable ● Discharge updated based on developed covariances with water depth

Baseline and Open-loop simulations ● Spatial resolution of 270 m, and 20 sec temporal resolution ● Baseline or “truth” simulation ● Nominal precipitation forcing VIC to provide lateral inflows and upstream boundary conditions ● Open-loop simulation ● Perturbed precipitation forcing VIC to provide lateral inflows and upstream boundary conditions, and perturbed initial depths

Satellite measurement simulation ● NASA JPL instrument simulator ● Provides “virtual” observations from LISFLOOD-FP water stage ● 50 m spatial resolution ● ~8 day overpass frequency ● Essentially Virtual_obs=Truth+Error 22 April 1995

Measurement errors ● Spatially uncorrelated ● Normally distributed, N(0, 20 cm) ● Standard deviation of 20 cm for the aggregated pixel scale (270 m) Goteti et al. (submitted)

Problems... ● Using the standard EnKF algorithm, neither depth or discharge seemed to get updated correctly

Problems... ● When the state dimension (or number of observations) is much larger than the ensemble size, the problem becomes rank deficient ● Solution with pseudo-inverse and several approximations can lead to instabilities ● But, if we assume that the observation errors are uncorrelated, we can solve the KF equation sequentially (in batches) ● Rank increases, and results should be the same as if we had solved for the entire state matrix

Water Depth Update ● Spatial snapshot (24 May 1995) of water depth simulations (shown as WSL) TruthOpen loopFilter

Discharge Update ● Spatial snapshot of discharge simulations right after an assimilation step (24 May 1995) TruthOpen loop Filter

Water depth and discharge time series ● Time series at a specific point ● Water depth (left) and discharge (x-direction) (right)

Spatially averaged RMSE time series of water depth ● Dashed lines show times of updates ● Results from one representative ensemble member

Spatial maps of time-averaged RMSE Open loopFilter ● Largest impact on the floodplain ● Assimilation had relatively smaller effect on water depth in the channel

Sensitivity to measurement error ● N(0,0.2) gave best overall results ● But other errors (s=0.1 and s=0.3) gave equally good results RMSE (m) 6-hr Timestep 20 cm 10 cm 30 cm

Conclusions ● Using a sequential EnKF, water depth gets updated properly ● But discharge still has problems, producing implausible values ● Measurement error assumptions do not affect filter performance (at least for water depth recovery)

Future Work ● Avoid using a pseudo-inverse and revert to the “standard” seqEnKF ● Perhaps, use Manning's equation as the observation operator for model discharge ● Explore model errors in other parameters (e.g. Manning's n, channel width) ● Application on a more topographically complex basin

Questions?