Efficient method for optimal placing of water quality monitoring stations for an ungauged basin

A core problem in monitoring water quality of a river basin is identifying an optimal positioning of a limited number of water-sampling sites. Various optimality criteria have been suggested for this selection process in earlier studies. However, the search for sets of sampling sites that satisfy such criteria poses a challenging optimization problem, especially for a large basin. Here, we show that for particular types of objective functions, the optimization procedure can be dramatically simplified via an analogy with the formulation of Shannon entropy. On this basis, we propose an efficient algorithm that can easily determine the optimal location of water quality sampling sites in a river network. The proposed algorithm can be used standalone or in conjunction with a heuristic optimization algorithm such as a genetic algorithm. For the latter, the proposed algorithm filters only competitive candidates and makes a contribution to reducing the problem size significantly. The superior performance of the proposed method is demonstrated via its application to actual river networks examined in earlier studies, in which the proposed method determines more optimal solutions in a shorter computation time. The idea presented in this study can also be applied to other problems in which the objective function can be formulated in a similar functional form.