Data-driven models for atmospheric air temperature forecasting at a continental climate region

RT − M16, SVR − M16). It is observed that any increase in the number of lags beyond a value of seven imparts a negative effect on the model performance. At the same time, the GBR model requires five lags (same as the daily prediction) to reach its optimum accuracy (GBR − M14). Overall, QRT, RF, RT, and SVR models better predict daily temperature than weekly during the training phase. On the other hand, the GBR model better predicts the weekly temperature. Based on the training phase, all models perform very well in predicting the daily and weekly temperature. However, the assessment of the model performances based on the testing dataset is also crucial. For the training phase, the models are provided with complete data (input and targets), which may result in overfitting. Thus, excluding the models’ performances in the test- ing phase may provide users with misleading results. It is known that in the testing phase mod- els received only input features and thus the forecasting accuracy would be more reliable than in the training phase [46, 59]. During the testing phase, the performance of the proposed models was assessed firstly by comparing the performance with each other and secondly by comparing the performance with the ARIMA model as a benchmark model. Table 6 shows the performance of the proposed models during the testing phase for daily temperature prediction. For daily forecast, the RF model provides the best performance, with RMSE ranging from 1.776 to 3.765, R ranging from 0.960 to 0.991, U ranging from 0.063 to 0.133, and MAE ranging from 1.353 to 2.898 fol-

lowed by the SVR model with RMSE ranging from 3.5915 to 3.6599, R ranging from 0.9621 to 0.9635, U ranging from 0.1265 to 0.1288, and MAE ranging from 2.7451 to 2.7902. Moreover, the RF model requires only one input lag (RF − M1) to reach the best accuracy, while the SVR model requires five input lags. On the other hand, despite the RT and QRT models showing the best performance during the training phase, they came last during the testing phase as they have a tendency to overfit during the training phase. For further assessment, the ARIMA model was implemented for daily and weekly predic- tions using two different scenarios. The first one, the ARIMA used for the prediction of tem- perature using a raw data set. However, the second one, data preprocessing, is used to improve the capacity of ARIMA. At that stage, the differencing method is used to remove seasonality. It is possible to utilize that method to get rid of the temporal reliance, also known as the series dependence on time. The best prediction results are used as a benchmark to validate the AI models. Itis important to mention that the time series data became smoother after the applica- tion of differencing transformation technique (see Fig 4a and 4b). Considering the PACF Table 6. The performance of the proposed models for daily temperature prediction: Testing phase. Models GBR QRT RT SVR RF� RMSE R U MAE RMSE R U MAE RMSE R U MAE RMSE R U MAE RMSE R U MAE M1 3.697 0.961 0.131 2.84 4.015 0.954 0.141 3.07 3.978 0.955 0.14 3.055 3.66 0.962 0.129 2.79 1.776 0.991 0.063 1.353

M2 3.654 0.962 0.129 2.808 3.808 0.959 0.134 2.913 3.748 0.96 0.132 2.883 3.616 0.963 0.127 2.77 3.765 0.960 0.133 2.898 M3 3.639 0.963 0.129 2.807 3.735 0.96 0.132 2.866 3.725 0.961 0.132 2.872 3.606 0.963 0.127 2.758 3.740 0.960 0.132 2.884 M4 3.634 0.963 0.129 2.795 3.744 0.96 0.132 2.866 3.693 0.961 0.131 2.849 3.602 0.963 0.127 2.75 3.687 0.961 0.130 2.841 M5 3.623 0.963 0.128 2.794 3.701 0.961 0.13 2.839 3.67 0.962 0.13 2.831 3.592 0.964 0.127 2.745 3.678 0.962 0.130 2.836 M6 3.612 0.963 0.128 2.791 3.697 0.961 0.13 2.851 3.691 0.961 0.131 2.848 3.593 0.963 0.127 2.747 3.686 0.962 0.130 2.841 M7 3.617 0.963 0.128 2.791 3.714 0.961 0.131 2.842 3.68 0.962 0.13 2.855 3.593 0.963 0.127 2.755 3.696 0.961 0.131 2.850 M8 3.714 0.963 0.134 2.917 3.727 0.961 0.131 2.843 3.684 0.962 0.13 2.838 3.593 0.963 0.127 2.752 3.690 0.961 0.131 2.849 M9 3.633 0.963 0.129 2.813 3.691 0.961 0.13 2.835 3.692 0.961 0.131 2.857 3.595 0.963 0.127 2.758 3.720 0.961 0.132 2.872 � Symbol is the hyperparameter for the best model are number of trees = 4, and leaf node = 6. https://doi.org/10.1371/journal.pone.0277079.t006 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 15 / 31