Evaluating North Sea water level monitoring network considering uncertain information theory quantities

Although Information Theory concepts have been successfully applied in hydrology and other fields to quantify the amount of information contained in singular variables and shared by multiple variables, the valuation of these quantities is sensible to different parameters. In particular, the bin size of histograms and the Pearson correlation coefficient to estimate probabilistic measures such as Joint Entropy and Total Correlation are of interest when evaluating a monitoring network. This work extends the ensemble entropy method developed by the authors to take into consideration the uncertainty coming from these parameters in the assessment of the North Sea’s water level network for large number of sensors. 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 information content (Joint Entropy) of a set of stations is maximized and redundancy (Total Correlation) is minimized. These scenarios are generated with parameter sampling methods such as the Latin Hypercube. Results include probabilistic Pareto fronts generated by parameter sampling, which provided additional criteria on the selection of the final set of monitoring points and the elimination of redundant/noninformative points.