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

5. Data partition: The time-series data is relatively long (2000 to 2021), 70% of the data are used for model calibration (2000 to 2015), and the rest are used for testing. The number of data points was fixed in that case to ensure a fair evaluation of the proposed model through- out the most critical step (testing phase). Notably, this procedure does not affect the data partitions. For example, for daily scale 2411, which represents about 30% of the entire daily records (Table 3) 6. Normalizing the training and testing dataset based on the minimum and maximum tem- perature in the training data set using the following formula [56]: Tnormalized ¼ Ti Tmin Tmax Tmin ð21Þ Tnormalized is the normalized temperature for ith temperature record (Ti) while Tmin and Tmax are minimum and maximum and temperature data obtained from the training data set. 7. Assigning the hyperparameters of the applied models. The trial- and error- method is used for this process where each model was trained 100 times over the training dataset with dif- ferent parameters. When these models were trained several times, the best ones were selected according to the statistical criteria. According to several statistical metrics, the model which generates lowest forecasting error in the training step is selected. In addition, the performance of the model should be stable so that there is no significant difference between its performance in the training and testing phase. 8. De-normalizing the data based on the following formula: Ti ¼Tmin þ Tnoralizei Tmax Tmin ð Þ � � ð22Þ

9. Evaluating the accuracy of the models with the testing dataset. It is important to mention that all models are constructed using MATLAB software. The candidate parameters of the applied models can be illustrated below: • RF: The number of trees is selected between 20–100 while the leaf node ranges from 1–5. • GBR: the learning rate 2 [0 1] and the number of trees 2 [150,1]. In Bag fraction = 1. • SVR: Box Constraints "regularization parameter "is set between 0.7 to 1. mean the sigma ranges from 0.8452 to 0.7071. • Epsilon parameter 2 [0.6 1] and sigma. Finally, the kernel scale parameter ranges from 0.8 to 1. • DT: MaxNumSplits (maximum number of decision splits) 2 [1 8]. Tree depth controllers 2 [5 10]. • Bag fraction = 1 for assembling models that’s mean "roughly 2/3 of input data is selected for training for every tree and the remaining 1/3 is used as out-of-bag observations". In the second scenario of this work, we used the randomization method to divide the data into the training and testing phase. In this scenario, the effect of the climate would be more PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 12 / 31