A Bayesian analysis scheme for estimating river depth using SWOT measurements [INVITED]

The Surface Water and Ocean Topography (SWOT) satellite is a swath-mapping radar interferometer that will provide water elevations over inland water bodies and over the ocean. One of the SWOT terrestrial hydrology motivating science questions is, "What is the temporal and spatial distribution in the world's terrestrial surface water storage change and discharge?" SWOT represents a fundamentally new approach to characterizing fluvial processes, especially river discharge. However, because SWOT will observe water surface elevations, but not river bathymetric elevations, the cross-sectional flow area will only be observed above the lowest observed river depth. The remaining, unknown river depth thus presents a major risk to SWOT's capability to produce accurate river discharge estimates. The so-called SWOT hydrology "virtual mission" (VM) has explored several approaches to depth estimation, including ensemble-based data assimilation (DA) strategies. Simplistic treatment of river depth spatial variability has been a key limitation of existing VM work; put simply, geomorphology matters.

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.