The Application of the Entropy and Empirical Basin Kriging for the Optimization and Spatial Interpolation of Groundwater Monitoring Network (Case Study: Silakhor Plain)

Groundwater monitoring has an important role in water resource management. Groundwater monitoring network can provide groundwater levels, but sometimes this information is too much and not useful. Optimum water management requires sufficient information on the quantitative and qualitative features of the aquifer. Assessing and anticipating the level of groundwater through specific models helps to predict groundwater resources. In recent years, with the demonstration of the capabilities of smart models in modeling time series, these models have been enhanced in groundwater modeling. The optimization of the monitoring network is a process for having the best combination of existing stations, adding new stations, or redefining a monitoring network based on the predetermined goals.

The present study aimed to develop an optimal network monitoring model with two goals of maximum entropy value at monitoring stations and minimizing the costs of monitoring the groundwater level network. In this study, data from 29 stations in the current monitoring network were used to optimize the groundwater monitoring network in Silakhor plain located in Lorestan Province. Firstly, using the entropy method, the amount of entropy in each of the 29 stations of the monitoring network was determined. Then, the amount of the entropy matching for each station was compared with the amount of entropy of the time series of rainfall, in order to determine the optimal station water supply through the available network. Finally, the prediction of the location of data using the Empirical Bayesian Kriging (EBK) method in the ArcGIS software was carried out and evaluated by the results of four models of the K-Bessel Detrended, K-Bessel, Exponential Detrended and Whittle Detrended.

The time series of rainfall is directly related to the feeding of aquifers. In fact, the amount of precipitation entropy and its variations at different times affect the amount and variation of entropy of groundwater level at the same time. If the entropy value obtained from the station is not consistent with the season's entropy variations in rainfall, it is said that the station is able to scare water based on the uncertainties of the rainy season and aquifer feeding. The results of the research showed that the entropy variations for eleven stations of the existing stations were similar to the entropy variations of the rainy season, and also the entropy of this station was higher than the other stations. The results obtained from the first step indicated a network with 11 stations out of 29 available stations. The RMSE value of this network was 0.75 m. At this point, by reducing 62% of the network station, peak network costs and RMSE value were optimized. The comparison of the optimal network and the existing network showed that the optimal network could reduce cost of monitoring stations and had a similar zoning in Silahkor plain rather than existing monitoring network. Data interpolation was modeled in ArcGIS software and in the Geostatical Analysts section by the EBK method. The absoluteness of the estimation in interpolation and location is one of the main features of the EBK model. In this sense, the value of the estimate of the quantity at the sampling points was equal to the measured value and the estimate of variance was zero. The EBK model uses four semi-   modifications to interpolate the groundwater level. The least square standardized error between the actual and estimated values ​​in the EBK method was K-Bessel Detrended with a half-value of 0.99. In addition, the EBK method with the K-Bessel Detrended half-change was based on the average mean power of error (20.87) and the highest correlation coefficient (0.82) was the best interpolation method. The EBK methods were respectively ranked in the Whittle Detrended, K-Bessel and Exponential Detrended models.

Considering that the implementation of water resources monitoring programs is costly and requires time, a method for optimizing the existing network is necessary. The results of the research were suited to the adequacy of the network with 11 stations of 29 monitoring stations for the Silakhor plain aquifer. The optimized monitoring network, in comparison with the existing observation network, was able to reduce the number of stations in the monitoring network by 62% and improve the spatial distribution of stations. In addition, investigating the predictive results of the groundwater level and comparing it with the actual level in the aquifer area indicated the accuracy of the EBK method. In addition, the comparison of the aquifer zoning using a network with 29 monitoring stations with the network with 11 monitoring stations showed the level of groundwater level with an acceptable estimate, which indicated that the precision of the entropy criterion was in the selection and optimization of the monitoring stations.