Variational assimilation of streamflow into operational distributed hydrologic models: effect of spatiotemporal adjustment scale

Abstract. State updating of distributed rainfall-runoff models via streamflow assimilation is subject to overfitting because large dimensionality of the state space of the model may render the assimilation problem seriously under-determined. To examine the issue in the context of operational hydrology, we carry out a set of real-world experiments in which streamflow data is assimilated into gridded Sacramento Soil Moisture Accounting (SAC-SMA) and kinematic-wave routing models of the US National Weather Service (NWS) Research Distributed Hydrologic Model (RDHM) with the variational data assimilation technique. Study basins include four basins in Oklahoma and five basins in Texas. To assess the sensitivity of data assimilation performance to dimensionality reduction in the control vector, we used nine different spatiotemporal adjustment scales, where state variables are adjusted in a lumped, semi-distributed, or distributed fashion and biases in precipitation and potential evaporation (PE) are adjusted hourly, 6-hourly, or kept time-invariant. For each adjustment scale, three different streamflow assimilation scenarios are explored, where streamflow observations at basin interior points, at the basin outlet, or at both interior points and the outlet are assimilated. The streamflow assimilation experiments with nine different basins show that the optimum spatiotemporal adjustment scale varies from one basin to another and may be different for streamflow analysis and prediction in all of the three streamflow assimilation scenarios. The most preferred adjustment scale for seven out of nine basins is found to be the distributed, hourly scale, despite the fact that several independent validation results at this adjustment scale indicated the occurrence of overfitting. Basins with highly correlated interior and outlet flows tend to be less sensitive to the adjustment scale and could benefit more from streamflow assimilation. In comparison to outlet flow assimilation, interior flow assimilation at any adjustment scale produces streamflow predictions with a spatial correlation structure more consistent with that of streamflow observations. We also describe diagnosing the complexity of the assimilation problem using the spatial correlation information associated with the streamflow process, and discuss the effect of timing errors in a simulated hydrograph on the performance of the data assimilation procedure.