ESTIMATION FOR RAINFALL-RUNOFF MODELED AS A PARTIALLY OBSERVED MARKOVPROCESS

Linear continuous time stochastic Nash cascade conceptual models for r unoff are developed. The runoff is modeled as a simple system of linea r stochastic differential equations driven by white Gaussian and marke d point process noises. In the case of d reservoirs, the outputs of th ese reservoirs form a d dimensional vector Markov process, of which on ly the dth coordinate process is observed, usually at a discrete sampl e of time points. The dth coordinate process is not Markovian. Thus ru noff is a partially observed Markov process if it is modeled using the stochastic Nash cascade model. We consider how to estimate the parame ters in such models. In principle, maximum likelihood estimation for t he complete process parameters can be carried out directly or through some form of the EM (estimation and maximization) algorithm or variati on thereof, applied to the observed process data. In this research we consider a direct approximate likelihood approach and a filtering appr oach to an algorithm of EM type, as developed in Thompson and Kaseke ( 1994). These two methods are applied to some rear life runoff data fro m a catchment in Wales, England. We also consider a special case of th e martingale estimating function approach on the runoff model in the p resence of rainfall. Finally, some simulations of the runoff process a re given based on the estimated parameters.