Modeling river water temperature with limiting forcing data: Air2stream v1.0.0, machine learning and multiple regression

The prediction of river water temperature is of key importance in the field of environmental science. Water temperature datasets for low-order rivers are often in short supply, leaving environmental modelers with the challenge of extracting as much information as possible from existing datasets. Therefore, identifying a suitable modeling solution for the prediction of river water temperature with a large scarcity of forcing datasets is of great importance. In this study, five models, forced with the meteorological datasets obtained from the fifth-generation atmospheric reanalysis, ERA5-Land, are used to predict the water temperature of 83 rivers (with 98% missing data): three machine learning algorithms (random forest, artificial neural network and support vector regression), the hybrid Air2stream model with all available parameterizations and a multiple regression. The machine learning hyperparameters were optimized with a tree-structured Parzen estimator, and an oversampling-undersampling technique was used to generate synthetic training datasets. In general terms, the results of the study demonstrate the vital importance of hyperparameter optimization and suggest that, from a practical modeling perspective, when the number of predictor variables and observed river water temperature values are limited, the application of all the models considered in this study is crucial. Basically, all the models tested proved to be the best for at least one station. The root mean square error (RMSE) and the Nash-Sutcliffe efficiency (NSE) values obtained for the ensemble of all model results were 2:75 +/- 1:00 and 0:56 +/- 0:48 degrees C, respectively. The model that performed the best overall was random forest (annual mean - RMSE: 3:18 +/- 1:06 degrees C; NSE: 0:52 +/- 0:23). With the application of the oversampling-undersampling technique, the RMSE values obtained with the random forest model were reduced from 0.00% to 21.89% (mu = 8 :57 %; sigma = 8 :21 %) and the NSE values increased from 1.1% to 217.0% (mu = 40 %; sigma = 63 %). These results suggest that the solution proposed has the potential to significantly improve the modeling of water temperature in rivers with machine learning methods, as well as providing increased scope for its application to larger training datasets and the prediction of other types of dependent variables. The results also revealed the existence of a logarithmic correlation among the RMSE between the observed and predicted river water temperature and the watershed time of concentration. The RMSE increases by an average of 0.1 degrees C with a 1 h increase in the watershed time of concentration (watershed area: mu = 106 km(2); sigma = 153).