Optimization of water level monitoring network in polder systems using information theory

A method for siting water level monitors based on information theory measurements is presented. The first measurement is joint entropy, which evaluates the amount of information content that a monitoring set is able to collect, and the second measurement is total correlation, which evaluates the level of dependency or redundancy among monitors in the set. In order to find the most convenient set of places to put monitors from a large number of potential sites, a multiobjective optimization problem is posed under two different considerations: (1) taking into account the costs of placing new monitors and (2) considering the cost of placing monitors too close to hydraulic structures. In both cases, the joint entropy of the set is maximized and its total correlation is minimized. The costs are considered in terms of information theory units, for which additional terms affecting the objective functions are introduced. The proposed method is applied in a case study of the Delfland region, Netherlands. Results show that total correlation is an effective way to measure multivariate independency and that it must be combined with joint entropy to get results that cover a significant proportion of the total information content of the system. The maximization of joint entropy gives results that cover between 82% and 85% of the total information content.