Ensemble-based assimilation of discharge into rainfall-runoff models: A comparison of approaches to mapping observational information to state space

摘要

The optimization of hydrologic models using the ensemble Kalman filter has received increasing attention during the last decade. The application of this algorithm is straightforward when the relationship between the state variables and the observations is linear, in other words, when the observations can be directly mapped onto the state space. However, when this relationship is nonlinear, a number of methods can be derived in order to perform this transfer. Up till now, it has not been demonstrated which of these methods is recommended for discharge assimilation with the ensemble Kalman filter. The objective of this paper is to analyze these methods for conceptual rainfall-runoff models in a small-scale catchment. The study has been performed in the Bellebeek catchment (86.36 km~2) in Belgium, using two time series models and one conceptual rainfall-runoff model. A first analysis of the algorithms has been performed using the one time step ahead discharge predictions. The results indicate that linearization of the storage-discharge relationship (the observation system) should be avoided if discharge data are assimilated using the ensemble Kalman filter. Further, assimilating discharge data into conceptual rainfall-runoff models for small catchments does not work well when a unit hydrograph is used for runoff routing. This can be explained by the stronger impact of the model error (caused by errors in the forcings, model structure, and parameters), accumulated over the duration of the unit hydrograph, as compared to the impact of erroneous initial conditions. A second analysis using longer lead times has led to the conclusion that, for the type of catchment and model used in this study, the accuracy of the meteorological forcings is more important than an accurate estimation of the model initial conditions through data assimilation.