The challenge for SWOT is how to perform the inverse problem of characterizing bathymetry and river flow given SWOT water surface elevation (WSE) measurements. This task falls at the intersection of two disciplines, engineering open channel hydraulics and fluvial geomorphology. In hydraulic formulations the physical form of the channel combined with conservation of mass and momentum dictate a complex spatiotemporal response of WSE to spatial changes in river bathymetry (i.e. changes in bed slope and cross-section) and temporal changes of flow propagating downstream. DA strategies offer a numerical approach to solving the inverse problem and estimating river depth. Prior bathymetry is estimated using the best-available information, then refined by conditioning upon SWOT observations.
Here, we first present synthetic SWOT observations of water elevations over the Rio Grande river at several different flow levels. Second, we present a simple Bayesian approach to estimate river bathymetry. Prior estimates of bathymetry are generated based on a simple depth estimate, multiplied by random errors with an exponential autocorrelation function. We then implement a Monte Carlo Markov Chain algorithm to estimate river bathymetry, using the SWOT observations. We explore the total chain length necessary to converge, compare results to estimation approaches based on the Kalman filter, and examine the sensitivity to SWOT observation errors.