Bayesian recursive parameter estimation for hydrologic models

The uncertainty in a given hydrologic prediction is the compound effect of the parameter, data, and structural uncertainties associated with the under lying model. In general, therefore, the confidence in a hydrologic predicti on can be improved by reducing the uncertainty associated with the paramete r estimates. However, the classical approach to doing this via model calibr ation typically requires that, considerable amounts of data be collected an d assimilated before the model can be used. This limitation becomes immedia tely apparent when hydrologic predictions must be generated for a previousl y ungauged watershed that has only recently been instrumented. This paper p resents the framework for a Bayesian recursive estimation approach to hydro logic prediction that can be used for simultaneous parameter estimation and prediction in an operational setting. The prediction is described in terms of the probabilities associated with different output values. The uncertai nty associated with the parameter estimates is updated (reduced) recursivel y, resulting in smaller prediction uncertainties as measurement data are su ccessively assimilated. The effectiveness and efficiency of the method are illustrated in the context of two models: a simple unit hydrograph model an d the more complex Sacramento soil moisture accounting model, using data fr om the Leaf River basin in Mississippi.