A Bayesian Markov Model of the flood forecast process

Abstract

A flood forecast process with a discrete time index k is defined as {i(k), h(k)}, where i denotes the current flood level and h denotes the forecasted flood crest. It is a finite, random duration process with the actual flood crest hh being its terminal state: {hh | i(k) h(k)}. This process is modeled as a two‐branch Markov chain. Nonstationary transition probability functions are obtained from a Bayesian information processor which can be imbedded in a dynamic programing algorithm that solves an ensuing Markovian decision problem. The lead time and the processing time of the forecasts are represented by their certainty equivalents. The structure of the model is motivated by an analysis of historical flood forecast records. Methods of estimation of the prior probability and likelihood functions are described. The model is intended primarily as a component of a decision methodology for determining the economic value of and the optimal decisions in response to riverine flood forecasts.