Calibration and Prediction Problems in Catchment Scale Hydrology

Statistical models in environmental applications are making increasing use of the scientific knowledge represented in systems of partial differential equations describing the evolution of environmental processes over time. I will discuss the use of such a model to estimate/predict soil moisture fields under current/future climatic conditions. We use a catchment-level hydrology model to describe the evolution of catchment-averaged state variables over time. This model, called BetaSPM, is similar to the "saturation path" models described by Kavetski et al. (2003), but it parameterizes fluxes in a particularly interpretable way, using quantile constraints imposed on Beta distribution functions. We model soil moisture observations using a stochastic redistribution of total water according to local topographic variables. I will discuss how we probabilistically calibrate the model, and how we account for uncertainties in the model parameters when making predictions.