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

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 hydrologic forecasting, we carried out a set of real-world experiments in which streamflow data is assimilated into the gridded Sacramento Soil Moisture Accounting (SAC-SMA) and kinematic-wave routing models of the US National Weather Service (NWS) Research Distributed Hydrologic Model (RDHM) via variational data assimilation (DA). The nine study basins include four in Oklahoma and five in Texas. To assess the sensitivity of the performance of DA to the dimensionality of the control vector, we used nine different spatiotemporal adjustment scales, with which the state variables are adjusted in a lumped, semi-distributed, or distributed fashion and biases in precipitation and PE are adjusted at hourly or 6-hourly scale, or at the scale of the fast response of the basin. For each adjustment scale, three different assimilation scenarios were carried out in which streamflow observations are assumed to be available at basin interior points only, at the basin outlet only, or at all locations. The results for the nine basins show that the optimum spatiotemporal adjustment scale varies from basin to basin and between streamflow analysis and prediction for all three streamflow assimilation scenarios. The most preferred adjustment scale for seven out of the nine basins is found to be distributed and hourly. It was found that basins with highly correlated flows between interior and outlet locations tend to be less sensitive to the adjustment scale and could benefit more from streamflow assimilation. In comparison with outlet flow assimilation, interior flow assimilation produced streamflow predictions whose spatial correlation structure is more consistent with that of observed flow for all adjustment scales. We also describe diagnosing the complexity of the assimilation problem using spatial correlation of streamflow and discuss the effect of timing errors in hydrograph simulation on the performance of the DA procedure.