Groundwater Quality Modeling with a Small Data Set.

Seventeen groundwater quality variables collected during an 8-year period (2006 to 2013) in Andimeshk, Iran, were used to implement an artificial neural network (NN) with the purpose of constructing a water quality index (WQI). The method leading to the WQI avoids instabilities and overparameterization, two problems common when working with relatively small data sets. The groundwater quality variables used to construct the WQI were selected based on principal component analysis (PCA) by which the number of variables were decreased to six. To fulfill the goals of this study, the performance of three methods (1) bootstrap aggregation with early stopping; (2) noise injection; and (3) ensemble averaging with early stopping was compared. The criteria used for performance analysis was based on mean squared error (MSE) and coefficient of determination (R(2) ) of the test data set and the correlation coefficients between WQI targets and NN predictions. This study confirmed the importance of PCA for variable selection and dimensionality reduction to reduce the risk of overfitting. Ensemble averaging with early stopping proved to be the best performed method. Owing to its high coefficient of determination (R(2)  = 0.80) and correlation coefficient (r=0.91), we recommended ensemble averaging with early stopping as an accurate NN modeling procedure for water quality prediction in similar studies.