An integrated approach to hydrologic data assimilation: interpolation, smoothing, and filtering

The hydrologic data assimilation problem can be posed in a probabilistic framework that emphasizes the need to account for uncertainty when combining different sources of information. This framework indicates where approximations need to be introduced and provides a way to compare alternative data assimilation methods. When discussing data assimilation it is useful to distinguish interpolation, smoothing, and filtering problems. Interpolation is illustrated here with an example based on multi-scale estimation of rainfall during the TOAGA-COARE field experiment. Smoothing is illustrated with a variational soil moisture estimation algorithm applied to the SGP97 field experiment. Filtering is illustrated with an ensemble Kalman filter, also applied to the SGP97 experiment. All of these data assimilation algorithms implicitly rely on linear Gaussian assumptions that can only be expected to apply in special cases. Although more general nonlinear data assimilation methods are available they are not practical for the very large problems frequently encountered in hydrology. Future research in hydrologic data assimilation will be need to focus on the issue of high dimensionality and on the need for more realistic descriptions of model and measurement error. This effort will be most successful if the modeling and data assimilation problems are approached in a coordinated way.