A weakly-constrained data assimilation approach to address rainfall runoff model structural inadequacy in streamflow prediction

This paper presents a simple yet effective weakly-constrained (WC) data assimilation (DA) approach for hydrologic models which accounts for model structural inadequacies associated with rainfall-runoff transformation processes. Compared to the strongly-constrained (SC) DA, WC DA adjusts the control variables less while producing similarly or more accurate analysis. Hence the adjusted model states are dynamically more consistent with those of the base model. The inadequacy of a rainfall-runoff model was modeled as an additive error to runoff components prior to routing and penalized in the objective function. Two example modeling applications, distributed and lumped, were carried out to investigate the effects of the WC DA approach on DA results. For distributed modeling, the distributed Sacramento Soil Moisture Accounting (SAC-SMA) model was applied to the TIFM7 Basin in Missouri, USA For lumped modeling, the lumped SAC-SMA model was applied to nineteen basins in Texas. In both cases, the variational DA (VAR) technique was used to assimilate discharge data at the basin outlet. For distributed SAC-SMA, spatially homogeneous error modeling yielded updated states that are spatially much more similar to the a priori states, as quantified by Earth Mover's Distance (EMD), than spatially heterogeneous error modeling by up to,10 times. DA experiments using both lumped and distributed SAC-SMA modeling indicated that assimilating outlet flow using the WC approach generally produce smaller mean absolute difference as well as higher correlation between the a priori and the updated states than the SC approach, while producing similar or smaller root mean square error of streamflow analysis and prediction. Large differences were found in both lumped and distributed modeling cases between the updated and the a priori lower zone tension and primary free water contents for both WC and SC approaches, indicating possible model structural deficiency in describing low flows or evapotranspiration processes for the catchments studied. Also presented are the findings from this study and key issues relevant to WC DA approaches using hydrologic models. (C) 2016 Elsevier B.V. All rights reserved.