A spatiotemporal Bayesian maximum entropy-based methodology for dealing with sparse data in revising groundwater quality monitoring networks: the Tehran region experience

Data inadequacy is a common problem in designing or updating groundwater monitoring systems. The developed methodologies for the optimal design of groundwater monitoring systems usually assume that there is a complete set of data obtained from existing monitoring wells and provide a revised configuration for the system by analyzing the current data. These methodologies are not usually applicable when the current groundwater quantity and quality data are highly sparse. In this paper, a new simulation–optimization approach based on Bayesian maximum entropy theory (BME) is proposed for revising spatial and temporal monitoring frequencies in a sparsely monitored aquifer. The BME is used to simulate the spatial and spatiotemporal variations of groundwater indicators, incorporating the space/time uncertainties due to insufficient data. Comparing the obtained estimations with observations, the best BME model was selected to be linked with an optimization model. The main goal of optimization was to find out the spatial and temporal sampling characteristics of the monitoring stations using the concepts of Entropy theory and a groundwater vulnerability index. The results show the BME estimations are less biased and more accurate than Ordinary Kriging in both spatial and spatiotemporal analysis. The improvements in the BME estimates are mostly related to incorporating hard (accurate) and soft (uncertain) data in the estimation process. The applicability and efficiency of the proposed methodology have been evaluated by applying it to the Tehran aquifer in Iran which is suffering from high groundwater table fluctuations and nitrate pollution. Based on the results, in addition to the existing monitoring wells, seven new monitoring stations have been proposed. Few stations which potentially can be removed or combined with other stations have been identified and a monthly sampling frequency has been suggested.