Using the Ensemble Kalman Filter Recursively to Update Soil Moisture Estimates in a Conceptually-Based Distributed Hydrologic Model

The Ensemble Kalman Filter (EnKF) has been widely used to update unobservable states from observations of different variables or observations of the same variable at different locations. This study harnesses both aspects in a two step process in which 1) conceptual soil water storages are updated via collocated soil moisture observations and 2) conceptual soil water storages at locations without observations are updated according to their relationship to “observable” pixels from step 1 and the corresponding innovations. The National Weather Service's Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) and its conceptually-based Sacramento Heat Transfer with enhanced EvapoTranspiration (SAC-HTET) submodel for rainfall-runoff generation is used in this study. SAC-HTET includes a scheme to transform conceptual storages to physically meaningful soil layers. During the first phase of assimilation, this transformation scheme serves as the observation equation in the EnKF when updating conceptual model storages of pixels collocated with in situ observations. It is seen from this first step that at “observable” pixel locations, the ensemble members collapse and become underdispersive under certain conditions (particularly during the dry season), rendering subsequent observations virtually unused in rest of the EnKF process. Identifying this behavior provides useful knowledge on when resampling/covariance inflation may or may not be necessary. In the second phase of assimilation, the spatial spreading of the innovation at observed pixels to the remaining pixels is examined. Again the EnKF is used, except soil moisture observations are traded for the updated conceptual states at the observed locations. Various weighting schemes for the innovations are explored with the intention of reflecting the relationship between observed and non-observed pixels.