Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real-time assimilation of streamflow data into operational hydrologic models

Abstract

Various data assimilation (DA) methods have been used and are being explored for use in operational streamflow forecasting. For ensemble forecasting, ensemble Kalman filter (EnKF) is an appealing candidate for familiarity and relative simplicity. EnKF, however, is optimal in the second-order sense, only if the observation equation is linear. As such, without an iterative approach, EnKF may not be appropriate for assimilating streamflow data for updating soil moisture states due to the strong nonlinear relationships between the two. Maximum likelihood ensemble filter (MLEF), on the other hand, is not subject to the above limitation. Being an ensemble extension of variational assimilation (VAR), MLEF also offers a strong connection with the traditional single-valued forecast process through the control, or the maximum likelihood, solution. In this work, we apply MLEF and EnKF as a fixed lag smoother to the Sacramento (SAC) soil moisture accounting model and unit hydrograph (UH) for assimilation of streamflow, mean areal precipitation (MAP) and potential evaporation (MAPE) data for updating soil moisture states. For comparative evaluation, three experiments were carried out. Comparison between homoscedastic vs. heteroscedastic modeling of selected statistical parameters for DA indicates that heteroscedastic modeling does not improve over homoscedastic modeling, and that homoscedastic error modeling with sensitivity analysis may suffice for application of MLEF for soil moisture updating using streamflow data. Comparative evaluation with respect to the model errors associated with soil moisture dynamics, the ensemble size and the number of streamflow observations assimilated per cycle showed that, in general, MLEF outperformed EnKF under varying conditions of observation and model errors, and ensemble size, and that MLEF performed well with an ensemble size as small as 5 while EnKF required a much larger ensemble size to perform closely to MLEF. Also, MLEF was not very sensitive to the uncertainty parameters and performed reasonably well over relatively wide ranges of parameter settings, an attribute desirable for operational applications where accurate estimation of such parameters is often difficult.