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.

Insights from an Evaluation of Nitrate Load Estimation Methods in the Midwestern United States

“…The study used three normalized indicator methods to evaluate the performance of the model [25][26][27][28][29][30]. The three indicators were calculated using the same dataset.…”

Comparison of Long Short-Term Memory and Weighted Regressions on Time, Discharge, and Season Models for Nitrate-N Load Estimation

“…The daily discharge and nitrate-N concentration data were applied for load estimation. The daily discharge data were obtained from USGS [28], and the daily nitrate-N concentration data [4] were obtained from the Water Quality Laboratory of the National Center for Water Quality Research at Heidelberg University [29]. The variables used for load estimation were transformed for normality and standardized.…”

“…The models based on the LSTM and WRTDS approaches were validated using two measures, the relative root mean squared error (rRMSE) and the mean percentage error (MPE). These statistical indices are commonly used for the evaluation of estimates derived from models [1,3,4,36]. The two measures can be computed as follows:…”

“…These specific characteristics may limit the applicability of the LSTM approach. Therefore, the model may be improved using a combination of relevant features of the nitrate-N concentration and discharge based on canonical correlation analysis [4]. Several studies have been conducted to evaluate the effects of hydrological and biogeochemical processes on the relationship between nitrate-N concentration and discharge [44][45][46][47].…”

“…River basins in the Midwestern United States have encountered difficulties with regard to water resource management because of nutrient enrichment and water pollutants derived from crop production using fertilizers and pesticides [3]. Specifically, rivers and streams in the state of Ohio are affected by the presence of high levels of nutrients, and they have been monitored for a long time period to estimate nitrate-N loads, in order to obtain an accurate assessment of water quality [4]. Notably, nonpoint sources aggravating streams and rivers contributed an average of 79% of the total nitrate-N load in the Ohio River Basin, which should be reduced [5].…”