Groundwater Level Prediction Using Dynamic Bayesian Networks Based on Sensitivity Analysis (Case Study: Birjand Plain)

The aquifers are about four percent of the water on the earth, but they are considered as the best and most accessible source of fresh water. In recent years, they have been faced with severe water withdrawal, therefore some plains was considered as forbidden plains that it means the water withdrawal from these aquifers is unauthorized. At some point, plains have been faced with land subsidence that showed the severity of the disaster. Given such a critical situation in aquifers, management of groundwater resources in the form of tools such as monitoring the level of the aquifers is essential. One of the plains in Iran that has a critical groundwater resource is Birjand plain which requires management measures to be protected from future water resources crisis. Prediction of groundwater level in future periods is a useful tool to enforce management measures before a crisis occurs. Thus, in this study, groundwater level was predicted in Birjand aquifer taking 10 monthly forecasting scenarios in a period of 5 years and in both crisp (continues) and clustering approaches using probabilistic Dynamic Bayesian Networks (DBNs). Nowadays, various tools are used to predict the aquifer level including mathematical models, artificial neural network, neuro-fuzzy, Bayesian networks, and time series and so on. In recent years, due to the flexible and simple structure, Bayesian networks have been used for predictions of different parameters, especially in forecasting of hydrological parameters. Bayesian network as a modern forecasting probabilistic method shows probabilistic relationships between a set of variables by graphical model. It represents the dependence structure among several factors, that affecting on each other, and is based on Bayesian theory. Dynamic Bayesian Networks have been extended from Bayesian Networks which are created for two first, as the cycle of dependency detector over the time, quite similar to Markov model; second, as the fixed process which is repeated in fixed-time interval. Another feature of Dynamic Bayesian network is their willingness to approximately structured changing. In this study, the input data (predictor parameters) of the model includes: temperature, rain, evaporation, monthly aquifer recharge in each Thiessen Polygon (Recharge), monthly withdrawals of groundwater in each aquifer Thiessen Polygon (discharge), groundwater levels in the current month and the groundwater level in the next month (predicted parameter). The first step in modeling by the dynamic Bayesian network is determining the dependent and independent data for calibration and validation. Model calibration data in both crisp and clustering approach include a 12-year period (1998 to 2009) and data validation include 5-year period (2010 to 2014), in monthly time step. Depending on the type of input data, both crisp and clustering approach was used. In the crisp approach, the probability functions were used and the predicted data were obtained by using the training data. In the clustering approach, by assigning each of the numbers to the right cluster, the modeling was done. A cluster is collection of objects that their relative distance to each other is low and relative to other members is high. In the first approach by using crisp data and NPC training structure in confidence level of 5%, the training was applied. In the second approach, the Silhouette index was calculated by using MATLAB software and by using the validation Silhouette index, and then, the number of clusters was determined. Finally, the clustering was performed by using k average method. Then, training was done in the second approach, using clustered data and NPC training structure in confidence level of 5%. Considering 10 different scenarios to predict groundwater level in the next month, the uncertainty of predicted parameters in both crisp and clustering approach were assessed. In fact, using these scenarios, sensitivity analysis was performed to check the accuracy of the model with respect to the existence or absence of different predictor parameters. In addition, the uncertainty of the model output is evaluated using dynamic Bayesian network probabilistic analysis. The results of the selected scenario in crisp approach showed the high prediction accuracy of Bayesian networks. For example, in piezometers 4 and 9, the coefficient of determination was estimated about 0.98. According to the results, crisp dynamic Bayesian networks approach predicted hydrograph aquifer more accurate than clustering approach. Due to the low efficiency of clustering approach in predicting groundwater hydrograph, to obtain the accuracy of 10 scenarios predictions in this approach, instead of coefficient of determination (R^2) and root-mean-square error (RMSE), the percentage of correct predicted clusters was determined. According to the results, the clustering approach predicts clusters with high accuracy for different piezometers. The scenario 6 had the best prediction which all predictor parameters except evaporation were used for the prediction. In this scenario, R^2 and RMSE were showed good accuracy as 0.9946 and 0.1275, respectively. The other scenarios had also the accuracy in their predictions very close to scenario 6, except scenario 9 which the groundwater levels were not used as input. Thus, in the crisp approach, the groundwater levels have a substantial impact on the accuracy of the prediction. Generally, in crisp approach, all predictor scenarios have acceptable accuracy of over than 90% except scenario 9. In clustering approach, by examining the accuracy of the scenarios in predicting clusters, most scenarios were accurate except scenario 9. Dynamic Bayesian Network model in clustering approach correctly predicted clusters but, unlike the crisp approach in predicting hydrograph, it was not able to present acceptable results. The results showed the ability of the proposed model in planning and management of groundwater resources, reducing the risk of aquifer level declining by applying short term management scenarios and predict its effects on rehabilitation. Moreover, this model can be used in the similar plains for aquifer management.