1. 1Civil and Environmental Engineering, University of Washington
Quantifying the impact of model errors on river discharge retrievals through assimilation of SWOT-observed water surface elevations
Elizabeth Clark1, Konstantinos Andreadis1, and Dennis Lettenmaier1
1Civil and Environmental Engineering, University of Washington
Workshop on Microwave Remote Sensing for Land Hydrology, Oxnard, CA Oct 2009
1. Abstract
4. Precipitation Errors
SWOT 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 the 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 estimation from the assimilation of SWOT observations. The study area is a 1000 km reach of the Ohio River, where synthetic SWOT WSL observations have been generated. An ensemble representation is used for model errors in precipitation, which determines channel boundary inflows. Errors in precipitation are modeled by generating random offsets based on the spatial offset of the maximum precipitation, and generating random fields based on the error probability distribution inferred from the errors between downscaled precipitation fields from the the IPSL-CM4 Global Circulation Model and interpolated fields from in-situ stations. The relative importance of these errors in the estimation of river discharge is assessed. Finally, caveats in the methodology of the present work are identified and options for future research are discussed.
Magnitude Errors
Position Errors
CDF
Fract. GCM to interpolated precip -5 5
0.2
0.4
0.6
0.8
1.0
Fitted
Empirical
The entire precipitation field was spatially perturbed based on random x- and y-offsets derived from a normal distribution with mean of approx. 1° and standard deviation of ~2.5° for both latitude and longitude. This is based on the offset between grid cells containing maximum precipitation in IPSL-CM4 and Maurer et al. (2002) precipitation fields.
The at-cell fraction of IPSL-CM4 precipitation to the Maurer et al. (2002) interpolated ground-based precipitation was log-normally distributed with a mean of 11.56% and standard deviation of 69.93%.
“Truth” (Maurer et al., 2002)
Ensemble member
For the magnitude and spatial errors case, magnitude was perturbed first, then these values were shifted.
Precipitation
Magnitude and Spatial Errors
“Truth” (Maurer et al., 2002)
Ensemble member
2. Motivation
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 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.
“Truth” (Maurer et al., 2002)
Ensemble member
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
Ensemble member
“Truth” (Maurer et al., 2002)
Ensemble member
“Truth” (Maurer et al., 2002)
Ensemble member
“Truth” (Maurer et al.,
2002)
3. Experimental Design
Baseline Meteorological Data
Hydrologic Model
Baseline Boundary and Lateral Inflows
Hydrodynamics Model
Baseline Water Depth and Discharge
JPL SWOT Simulator
“Observed” WSL
Kalman Filter
Updated Water Depth, Discharge
Baseline Model Parameters
Perturbed Meteorological Data
Perturbed Boundary and Lateral Inflows
Perturbed Water Depth and Discharge
Open loop discharge
Hydrodynamics Model
LISFLOOD-FP (Bates and De Roo, 2000) is 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.
Open loop water depth
EnKF discharge
EnKF water depth
Ensemble Kalman Filter update performed for one overpass, across the first 352 km chainage. Observations of water surface 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.
5. Conclusions and Future Work
Model
Magnitude Errors
Spatial Errors
Spatial and Magnitude Errors
Depth RMSE (m)
Open Loop
12.5
2.2
0.92
EnKF
4.3
0.72
0.31
Discharge RMSE (m3/s)
20921
2382
1130
4742
918
466
The combined VIC-LISFLOOD system is quite sensitive to errors in the spatial distribution of precipitation over this basin.
Assimilation of SWOT measurements of water elevation into this system improves estimates of discharge commiserate with the level of model error.
Need to develop a better method for estimating errors in spatial distribution, one that de-convolves the positioning errors from the magnitude errors.
Three meteorological forcing perturbation schemes were implemented:
Magnitude errors derived from IPSL-CM4 (from IPCC 4th Assessment Report, experiment 20c3m) relative to interpolated ground data
Spatial positioning errors estimated from IPSL-CM4 relative to interpolated ground data
Both magnitude and position errors
6. References
Andreadis, K. M., E. A. Clark, D. P. Lettenmaier, and D. E. Alsdorf, 2007, Geophys. Res. Lett., 34, L10403, doi: /2007GL
Andreadis, K., D. Lettenmaier, and D. Alsdorf, ASLO Ocean Sciences Meeting, Orlando, FL, Mar
Bates, P. D., and A.P.J. De Roo, 2000, J. Hydrol., 236,
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,