Evaluating North Sea Water Level Monitoring Network Considering Uncertain Information Theory Quantities

Information-theory provides, among others, conceptual methods to quantify the amount of information contained in a random variable, as well as methods to quantify the amount of information contained and shared among two or more variables. Although these concepts have been successfully applied in Hydrology and other fields, the valuation of these quantities is sensible to different parameters used to estimate the probabilities that underline the entropy concept. Typical examples are the bin size of histograms used to compute probabilities and the Kendall correlation coefficient used to estimate copula entropy. The selection of these parameters has subsequent effects on other Information Theory quantities such as Joint Entropy and Total Correlation, which are commonly used in optimization procedures for monitoring networks. The present research aims at introducing a method to take into consideration the uncertainty coming from these parameters in the evaluation of the North Sea’s water level network. The main idea is to represent entropy of random variables through their probability distribution, instead of considering entropy as a deterministic value. The method considers solving multiple scenarios of Multi-Objective Optimization in which, for a given set of stations, information content (Joint Entropy) is maximized and redundancy (Total Correlation) is minimized. These scenarios are generated with parameter sampling methods such as the Latin Hypercube. Results include probabilistic analysis of the chosen parameters on the resulting family of Pareto fronts, providing additional criteria on the selection of the final set of monitoring points and the elimination of redundant/non-informative points. Data used was the raw data available from the Dutch Ministry of Infrastructure and Environment. The resulting water level monitoring network will be compared to the one obtained by other methods that will be described in a report currently under preparation, which will be publicly available soon in the Deltares websit