Tiknohov regularization as a tool for assimilating soil moisture data in distributed hydrological models

Discharge, water table depth, and soil moisture content have been observed at a high spatial and temporal resolution in a 44 ha catchment in Costa Rica over a period of 5 months. On the basis of the observations in the first 3 months (period A), two distinct soil moisture models are identified and calibrated: a linear stochastic time-varying state-space model, and a geo-statistical model. Both models are defined at various spatial and temporal resolutions. For the subsequent period of 2 months (period B), four different ways to predict the soil moisture dynamics in the catchment are compared: (1) the application of the dynamic models in open-loop form; (2) a re-calibration of the dynamic models with soil moisture data in period B, and subsequent prediction in open-loop form; (3) prediction with the geostatistical models, using the soil moisture data in period B; (4) prediction by combining the outcomes of (1) and (3) via generalized cross-validation. The last method, which is a form of data assimilation, compares favourably with the three alternatives. Over a range of resolutions, the predictions by data assimilation have overall uncertainties that are approximately half that of the other prediction methods and have a favourable error structure (i.e. close to Gaussian) over space as well as time. In addition, data assimilation gives optimal predictions at finer resolutions compared with the other methods. Compared with prediction with the models in open-loop form, both re-calibration with soil moisture observations and data assimilation result in enhanced discharge predictions, whereas the prediction of ground water depths is not improved.