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

QRT − M16) and increasing the lags beyond seven tends to reduce the models’ performance. Overall, the proposed models performed slightly better in predicting the daily temperatures than the weekly ones. On the other hand, the performance of the ARIMA model for weekly temperature predic- tion is presented in Table 9. Notably, the differencing method smoothens the time series data by removing a seasonal signal from a series (see Fig 5a and 5b). According to Fig 5c, based on PACF, three lags (1, 2, and 3 weeks) have been considered for the model development. As shown in Table 9, the performance of the ARIMA model is significantly lower than the RF model, and the latter has been able to increase the prediction accuracy by 5.36% in terms of R and reduce the prediction error by 48%, 47%, and 48% in terms of RMSE, U, and MAE. Table 7. The performance of the ARIMA model for daily temperature prediction: Testing phase. Without removing With removing Model RMSE R U MAE RMSE R U MAE ARIMA (2,1,1) 21.868 -0.053 0.596 17.418 3.727 0.961 0.13 2.828 ARIMA (2,2,1) 169.046 -0.034 0.903 142.136 205.266 0.115 0.949 156.224 ARIMA (2,1,2) 21.489 -0.053 0.594 17.034 3.738 0.961 0.129 2.825 ARIMA (3,1,1) 21.526 -0.053 0.594 17.073 3.727 0.961 0.129 2.826 ARIMA (3,1,2) 21.493 -0.053 0.594 17.038 3.726 0.961 0.129 2.825 ARIMA (4,1,2) 21.714 -0.053 0.595 17.261 3.786 0.961 0.13 2.859 ARIMA (4,1,1) 21.361 -0.053 0.593 16.91 3.786 0.961 0.13 2.859 https://doi.org/10.1371/journal.pone.0277079.t007

Table 8. The performance of the proposed models for weekly 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 M10 4.693 0.932 0.172 3.62 4.922 0.925 0.179 3.795 4.796 0.929 0.175 3.721 4.54 0.936 0.167 3.465 2.478 0.982 0.091 1.874 M11 4.611 0.934 0.17 3.556 4.703 0.932 0.172 3.632 4.615 0.934 0.169 3.561 4.51 0.937 0.166 3.476 4.580 0.935 0.168 3.516 M12 4.575 0.935 0.168 3.475 4.73 0.931 0.174 3.628 4.654 0.933 0.172 3.588 4.5 0.938 0.166 3.463 4.665 0.933 0.173 3.614 M13 4.618 0.934 0.17 3.5 4.649 0.933 0.17 3.556 4.605 0.934 0.17 3.576 4.461 0.939 0.164 3.44 4.597 0.935 0.169 3.564 M14 4.557 0.936 0.167 3.513 4.653 0.933 0.171 3.564 4.585 0.935 0.17 3.525 4.416 0.94 0.162 3.404 4.562 0.936 0.169 3.525 M15 4.443 0.94 0.165 3.494 4.487 0.938 0.165 3.404 4.441 0.939 0.165 3.406 4.365 0.941 0.161 3.348 4.492 0.938 0.167 3.506 M16 4.423 0.941 0.165 3.472 4.423 0.94 0.163 3.382 4.247 0.945 0.157 3.291 4.286 0.944 0.158 3.283 4.358 0.941 0.161 3.349 M17 4.582 0.941 0.174 3.707 4.552 0.936 0.168 3.521 4.297 0.943 0.160 3.262 4.613 0.934 0.169 3.495 4.293 0.943 0.159 3.305 � Symbol is the hyperparameter for the best model are number of trees = 50, and leaf node = 5. https://doi.org/10.1371/journal.pone.0277079.t008 Table 9. The performance of the ARIMA model for weekly temperature prediction: Testing phase. Without removing With removing Model RMSE R U MAE RMSE R U MAE

ARIMA (1,1,1) 16.566 -0.058 0.567 12.983 4.77 0.932 0.172 3.622 ARIMA (1,1,2) 16.144 -0.058 0.565 12.711 4.797 0.932 0.171 3.657 ARIMA (2,1,1) 16.506 -0.058 0.567 12.94 4.84 0.932 0.172 3.701 ARIMA (2,2,1) 196.082 -0.061 0.917 171.482 38.946 0.488 0.763 31.783 ARIMA (2,1,2) 21.698 -0.047 0.596 17.36 4.797 0.932 0.171 3.657 ARIMA (3,1,1) 18.169 -0.086 0.573 14.07 4.847 0.932 0.172 3.708 ARIMA (3,1,2) 22.362 -0.042 0.602 18.035 4.794 0.932 0.171 3.652 https://doi.org/10.1371/journal.pone.0277079.t009 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 17 / 31