The bio-chemical and physical characteristics of a river are directly affected by water temperature, which thereby affects the overall health of aquatic ecosystems. It is a complex problem to accurately estimate water temperature. Modelling of river water temperature is usually based on a suitable mathematical model and field measurements of various atmospheric factors. In this article, the air–water temperature relationship of the Missouri River is investigated by developing three different machine learning models (Artificial Neural Network (ANN), Gaussian Process Regression (GPR), and Bootstrap Aggregated Decision Trees (BA-DT)). Standard models (linear regression, non-linear regression, and stochastic models) are also developed and compared to machine learning models. Analyzing the three standard models, the stochastic model clearly outperforms the standard linear model and nonlinear model. All the three machine learning models have comparable results and outperform the stochastic model, with GPR having slightly better results for stations No. 2 and 3, while BA-DT has slightly better results for station No. 1. The machine learning models are very effective tools which can be used for the prediction of daily river temperature.
In this study, different versions of feedforward neural network (FFNN), Gaussian process regression (GPR), and decision tree (DT) models were developed to estimate daily river water temperature using air temperature (Ta), flow discharge (Q), and the day of year (DOY) as predictors. The proposed models were assessed using observed data from eight river stations, and modelling results were compared with the air2stream model. Model performances were evaluated using four indicators in this study: the coefficient of correlation (R), the Willmott index of agreement (d), the root mean squared error (RMSE), and the mean absolute error (MAE). Results indicated that the three machine learning models had similar performance when only Ta was used as the predictor. When the day of year was included as model input, the performances of the three machine learning models dramatically improved. Including flow discharge instead of day of year, as an additional predictor, provided a lower gain in model accuracy, thereby showing the relatively minor role of flow discharge in river water temperature prediction. However, an increase in the relative importance of flow discharge was noticed for stations with high altitude catchments (Rhône, Dischmabach and Cedar) which are influenced by cold water releases from hydropower or snow melting, suggesting the dependence of the role of flow discharge on the hydrological characteristics of such rivers. The air2stream model outperformed the three machine learning models for most of the studied rivers except for the cases where including flow discharge as a predictor provided the highest benefits. The DT model outperformed the FFNN and GPR models in the calibration phase, however in the validation phase, its performance slightly decreased. In general, the FFNN model performed slightly better than GPR model. In summary, the overall modelling results showed that the three machine learning models performed well for river water temperature modelling.
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