Application of Markov chain model in streamflow forecasting : a thesis submitted in partial fulfilment of the requirements for the degree of Master of Science in Geography at Massey University

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Massey University
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This thesis presents an approach to streamflow forecasting based on a Markov chain model to estimate conditioned probabilities that a one time-step ahead streamflow forecast will be within a certain streamflow range. In this application a set of "states of flow" defined over streamflow ranges (intervals) forms a finite state space of a Markov chain. Flood forecasting is made by focusing on a preselected state of flow as a flood state. A multi-objective (two criteria) function for the quantification of the model performance is introduced. Specifically designed for a flood forecasting and warning system the two criteria are the probability of issuing a false alarm and the probability of failing to forecast a flood event. The goal is to minimize both criteria simultaneously together with a preference of accepting more false alarms than misses. The model has two options of making a forecast: (1) a Threshold Forecast (ThF) approach in which a forecast is based on the probability of making a one-step transition from any state into the flood state; (2) the Most Probable Event (MPE) forecast approach selects the state of flow where the next streamflow is most likely to occur. Forecasts being probabilistic, there are several options for deciding on when it is appropriate to issue a flood warning in the probabilistic framework. A search for the appropriate probability p0 is made on interval [0,1] through evaluation of the objective function at each p0, using data sets from three North Island catchments ( Akitio River, Makakahi River and Kiwitea Stream). The model applying the option of threshold forecasts performed generally well depending on the relative costs assigned to false alarms and misses. The model performed better on the Akitio River which has strongly fluctuating streamflows than on the Makakahi River and Kiwitea Stream which have relatively modest variations in flows. When the Model applied the option of the most probable event forecasts did not perform well as the probabilities of false alarms were found to be too high for the model to be accepted. The outcome of this study suggests a simple short-term flood forecasting procedure especially for rivers with strongly fluctuating flows.
Stream measurements, Mathematical models, Hydrological forecasting, Markov processes, Streamflow