Spatiotemporal interpolation of discharge across a river network by using synthetic SWOT satellite data

Recent efforts have sought to estimate river discharge and other surface water-related quantities using spaceborne sensors, with better spatial coverage but worse temporal sampling as compared with in situ measurements. The Surface Water and Ocean Topography (SWOT) mission will provide river discharge estimates globally from space. However, questions on how to optimally use the spatially distributed but asynchronous satellite observations to generate continuous fields still exist. This paper presents a statistical model (River Kriging-RK), for estimating discharge time series in a river network in the context of the SWOT mission. RK uses discharge estimates at different locations and times to produce a continuous field using spatiotemporal kriging. A key component of RK is the space-time river discharge covariance, which was derived analytically from the diffusive wave approximation of Saint Venant's equations. The RK covariance also accounts for the loss of correlation at confluences. The model performed well in a case study on Ganges-Brahmaputra-Meghna (GBM) River system in Bangladesh using synthetic SWOT observations. The correlation model reproduced empirically derived values. RK (R-2=0.83) outperformed other kriging-based methods (R-2=0.80), as well as a simple time series linear interpolation (R-2=0.72). RK was used to combine discharge from SWOT and in situ observations, improving estimates when the latter is included (R-2=0.91). The proposed statistical concepts may eventually provide a feasible framework to estimate continuous discharge time series across a river network based on SWOT data, other altimetry missions, and/or in situ data.