Comparison of long short-term memory and weighted regressions on time, discharge, and season models for Nitrate-N Load estimation

The long short-term memory (LSTM) model has been widely used for a broad range of applications entailing the estimation of variables in different fields to improve water quality management in rivers. The main objectives of this study are (1) to develop a novel LSTM-based model for the estimation of nitrate-N loads, which adversely affect water resources, and (2) to evaluate the performance of the model by comparing it with that of Monte Carlo sub-sampling and the weighted regressions on time discharge and season (WRTDS) model. We evaluated the model performance using various numbers of hidden layers, ranging from one to four, in the LSTM model to determine the appropriate number of hidden layers; furthermore, we applied the sampling frequencies of 6, 12, and 24 to assess their impact. Seven polluted river basins in the United States were used for analysis, and the relative root mean squared error (rRMSE) and the mean percentage error (MPE) metrics were applied for the validation of the model estimates. The proposed model achieved accurate nitrate-N load estimates using three to four hidden layers, and improved model performance was observed when the sampling frequency was increased. The differences among the results obtained using the LSTM model were examined based on a binning technique via a log-log plot of nitrate-N concentration against discharge. The binning analysis showed that the slope obtained from the average rates of discharge and low discharge values apparently influenced the estimates. Furthermore, box plot analyses of the statistical indices such as rRMSE and MPE demonstrate that the LSTM model seems to exhibit better performance than the WRTDS model. The results of the examination demonstrate that the LSTM model may be a good alternative with regard to estimating nitrate-N loads for the control of water quality constituents.