Evaluation of Nitrate Load Estimations Using Neural Networks and Canonical Correlation Analysis with K-Fold Cross-Validation

Abstract

The present work aimed to examine the feasibility of using artificial neural network (ANN) based models to obtain accurate estimates of nitrate loads in river basins, which is an important parameter for water quality management. Both Single ANN (SANN) and Ensemble ANN (EANN) models were used to obtain the load estimations for five river basins in the Midwest United States. These basins included the Cuyahoga, Raisin, Sandusky, Muskingum, and Vermilion basins in Michigan and Ohio. Further, canonical correlation analysis (CCA) was applied to the ANN models to improve the performance. The k-fold cross-validation method was then utilized to evaluate the proposed models based on two statistical indices, namely, the rRMSE and rBAIS, and the estimates were compared for four different k values (k = 3, 5, 7, and 10). According to the results, the EANN model seemed to produce better load estimations than the SANN model, and the CCA based EANN model tended to produce the best estimates among all of the proposed models in this study. The box plot data for the rRMSE index were also investigated, and the plot results indicated that increasing values of k tended to generate better estimates. Thus, the use of k = 10 is recommended for load estimations since this value was associated with better performances and less biased estimates.