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

Aug 5, 2026

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River water temperature prediction is essential for environmental science because it affects water quality processes and aquatic organism distribution and growth. Many low-order river datasets lack sufficient forcing observations, creating a need for modeling strategies that extract maximal information from limited inputs. This study tests five approaches—three machine learning methods (random forest, artificial neural network, support vector regression), the hybrid Air2stream model, and multiple regression—using ERA5-Land meteorological data to predict 83 rivers with 98% missing forcing data. Hyperparameters are optimized via a tree-structured Parzen estimator and synthetic training sets are improved through oversampling–undersampling. Results emphasize the critical role of optimization and indicate that all models perform best at least for one station, with the ensemble achieving RMSE and NSE ranges of about 2.75–1.00 °C and 0.56–0.48.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages30

Reading Time1 h 16 min

AccessFree to download

1 Introduction

Water temperature as a key parameter

Modeling challenges under limited forcing data

Relationship with air temperature and lag effects

Geosci. Model Dev., 16, 4083–4112, 2023 [https://doi.org/10.5194/gmd-16-4083-2023](https://doi.org/10.5194/gmd-16-4083-2023)[ ](https://doi.org/10.5194/gmd-16-4083-2023)© Author(s) 2023 . This work is distributed under the Creative Commons Attribution 4 .0 License. Modeling river water temperature with limiting forcing data: Air2stream v1.0.0, machine learning and multiple regression Manuel C. Almeida and Pedro S. Coelho MARE – Marine and Environmental Sciences Centre, ARNET – Aquatic Research Network Associate Laboratory, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal Correspondence: Manuel Almeida ([mcvta@fct.unl.pt](mcvta@fct.unl.pt)) Received: 18 August 2022 – Discussion started: 21 November 2022 Revised: 18 May 2023 – Accepted: 25 June 2023 – Published: 20 July 2023 Abstract. 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 anda 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 bethe 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 􀀎 C, respectively. The model that performed the best overall was random forest (annual mean – RMSE: 3:18 􀀆 1:06 􀀎 C; NSE: 0:52 􀀆 0:23) . With the application of the oversampling–undersampling technique, the RMSE val- ues obtained with the random forest model were reduced from 0 .00 % to 21 . 89 %(􀀖 D 8:57 %; 􀀛 D 8:21 %) and the NSE values increased from 1 . 1 % to 217 .0 %(􀀖 D 40 %;􀀛 D 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 􀀎 C with a 1 h increase in the watershed time of concentration (watershed area: 􀀖 D 106 km2 ; 􀀛 D 153) . 1 Introduction Water temperature (WT) is recognized as a key parameter in aquatic systems due to its inﬂuence on water quality (e.g., chemical reaction rate, oxygen solubility), as well as the distribution and growth rate of aquatic organisms (e.g., primary production; ﬁsh growth and habitat) (Smith, 1972; Webb et al., 2003; Caissie, 2006) . As such, the accurate prediction and assessment of river WT are crucial parts of many Earth science applications. The thermal dynamics in riv

FAQs

Why is predicting river water temperature important?

River water temperature strongly influences water quality processes (e.g., chemical reaction rates and oxygen solubility) and affects the distribution and growth of aquatic organisms, making accurate prediction crucial for many Earth science applications.

How does the study address missing or scarce forcing data?

The models are forced with ERA5-Land meteorological datasets and evaluated across 83 rivers with 98% missing forcing data. Synthetic training datasets are generated using oversampling–undersampling to improve learning under data scarcity.

Which modeling approach performed best overall?

Random forest achieved the best overall performance, with the lowest reported error metrics among the evaluated methods, and results indicate that hyperparameter optimization is vital for practical modeling when predictors and observations are limited.

Aug 5, 2026

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