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

winter season (St. D range from 2.916 to 7.905) which leads to a considerable effect on the model performance. The second significant reason is that the training data doesn’t have large number of negative extreme values which limits the training efficiency of the model in this scenario. In terms of the total number of days, February is the shortest month. It can be observed from Fig 7 that the number of data records used in this month constitutes only 7.74% of the total data, which is undoubtedly the lowest percentage of data used in this study. Therefore, the models do not have enough training to simulate that period of the year in which the tem- perature changes significantly within a short period. Furthermore, the RF provides better effi- ciency in predicting the temperatures measured in February. The model presents less variance in comparison to the other models. A further noticeable observation related to daily tempera- ture prediction is the fact that all the models except the QRT model require fewer input lags to reach their optimum performance (RF − M1, SVR − M5, RT − M5, GBR − M6), while the QRT model requires more input lags (nine lags) to achieve the optimum performance (QRT − M9). The performance of the proposed models during the testing phase is also assessed using scatter diagrams (see Figs 8 and 9), histograms (see Figs 10 and 11), and box plots (see Figs 12 and 13). Figs 8 and 9 represent the scatter plot between the observed and predicted tempera- tures for daily and weekly prediction. The plots examine the cause-effect relationship between

the predicted and the observed temperatures and check the degree of association between these two variables in terms of coefficient of determination (R2). For daily prediction, the RF model yielded the best prediction performance in terms of R2 � 0.983, while the other models provided slightly similar performance in terms of R2. Additionally, for all data samples, there is considerably less diversion with the ideal line for the RF model compared to the other mod- els. For weekly prediction, the RF model still demonstrated a robust prediction performance with a significantly higher R2 values (R2 � 0.964) compared to the other models. At the same time, the RF model showed the least diversion with the ideal line for all data samples compared to the other models. Figs 10 and 11 show the histogram plots for the forecasting error in the case of both hori- zons (i.e., daily and weekly) during the testing phase. The plot visually interprets the error dis- tribution by showing the number of error values within a specified range and includes the Gaussian kernel density function to check the error normality. From Figs 10 and 11, it can be inferred that the RF model performs better than the other models in terms of mean error and standard deviation for daily temperature and weekly predictions and provides an error distri- bution similar to the normal distribution. Moreover, box plots are also constructed to depict the distribution and skewness of forecasting error values by displaying quartiles and averages.

The plots display the values in a standardized manner using a five-number summary (i.e., min- imum, first quartile, median, third quartile, and maximum) and present more visual informa- tion regarding the effectiveness of each model separately. The figures help to better understand the characteristics of forecasting errors generated by the applied models. For daily scale, all models provide the same outlier values, slightly less for the RF − M1 model (see Fig 12a). The quantile of the measured errors is provided in Fig 12b. Accordingly, the RF − M1 model gener- ates a lower interquartile range (IQR = 3.93) than the other models, indicating the efficiency of predicting the daily temperature. For the weekly time scale, the RF − M1 model shows the best performance because its median and mean values are very close to zero compared to other models (Fig 13a). Besides, the generated outliers are fewer than those reported in other models. The most important note can be observed in Fig 13b which shows that the RF-M1 model gen- erates significantly fewer outliers (IQR = 2.554) in comparison to the other models whose IQR ranges from 4.738 to 5.353. PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 20 / 31