Entropy principles in the prediction of water quality values at discontinued monitoring stations

Study examines issues associated with the design and operation of water quality monitoring networks where one or more monitoring stations have been discontinued. A methodology has been developed for prediction of these water quality values at discontinued stations in Queensland.. This study examines an issue associated with the design and operation of water quality monitoring networks, namely, the situation, where, because of reductions in the budget allocated to water quality monitoring, or because the budget allocated to water quality monitoring is not increasing at the same rate at which the cost of operation of the network is increasing, or the need for a monitoring station is more acute in another location, one or more existing monitoring stations have to be discontinued. The particular question addressed in relation to this scenario is the development of an improved metho-dology for the prediction of water quality values at the discontinued stations. The methodology proposed for the improved prediction of these water quality is derived from the information theory interpretation of the entropy principle, as formulated in terms of the Principle of Maximum Entropy (POME) and the Minimum Discrimination Information (MDI). The methodology itself is a nonlinear optimisation model in which an entropy function of the form Pi ln Pi where Pi represents the probability of event xi, is maximised subject to a series of constraints on the form and statistics of the probability function from which the Pi values are derived. An important feature of the probability distribution predictions provided by the model is that they are the 'most likely' distributions and therefore are un-biased, being affected only by the information which the user chooses to include in the constraints imposed on the optimisation, and on the historical values of the probability distributions which are incorporated into the non-linear objective function. The approach is demonstrated by application to a series of water quality monitoring networks in Queensland, Australia. The model was evaluated on the basis of these cases in a verification step involving a comparison of the accuracy of the predictions provided by the entropy technique with the accuracy of the predictions available from a traditional regression based approach. The predictions from the entropy based approach were on average more accurate then those obtained from the regression approach 61% of the time. The performance of the approach in terms of the accuracy of its predictions, the unbiased nature of those predictions, and the fact that it requires the same type and amount of data as traditional regression techniques, indicates that the technique represents a significant advance in the prediction of water quality values at dis-continued water quality monitoring stations.