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

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

Furthermore, the ARIMA model requires only one input lag (ARIMA 1,1,1) for weekly predic- tion to reach its best performance. For further assessment, we compared the performance of the best models obtained from the daily prediction (SVR − M5, RT − M5, GBR − M6, QRT − M9, and RF-M1) for each month of the year. In other words, the daily temperature prediction may vary from month to month, so it is essential to investigate the performance of the applied models for each month. What supports the importance of conducting this investigation is the considerable variation in temperature during the months of the year (see Table 2). It can be observed that the Standard deviation (St.D) varies from 2.916 to 7.905. The other significant indicator is that the data length varies monthly (see Fig 6). Fig 7 shows the performance of the best models based on RMSE statistics for each month of the year. After the training process was completed, the performance of each model was assessed individually. In general, statistical metrics such as RMSE provide the model’s overall evaluation. Therefore, this figure is created to see the monthly performance of each model. It is observed that the models have faced problems in estimating the temperatures for the winter Fig 5. Input determination for ARIMA model., a) is the original data, b) after applying differencing method, c) PACF for weekly scale. https://doi.org/10.1371/journal.pone.0277079.g005 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 18 / 31

season. According to the Fig 7, the RF and SVR model provided the least amount of prediction error for almost all months, followed by the GBR model. It can be observed that the highest forecasted error is observed in January, February and December. Two reasons may efficiently explain this problem. The first reason may be associated with variability of temperature in the Fig 6. Percentage of data length used in this study. https://doi.org/10.1371/journal.pone.0277079.g006 Fig 7. The performance of proposed models in predicting the air temperature for each month. https://doi.org/10.1371/journal.pone.0277079.g007 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 19 / 31

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

For further evaluation, the residual error diagrams for both daily and weekly scales have been developed (Figs 14 and 15). The diagram acts as a performance measure for the applied models and represents the difference between the forecasted and the actual temperature values. It is observed from Figs 14 and 15 that the RF model demonstrates the least residual error in comparison to all other applied models and outmatches them in terms of prediction accuracy and performance. Lastly, the capacity of the predictive models has been investigated through the hottest months (June, July, and August). These months have the highest temperatures; thus, it is vital to see which applied AI models mimic the extreme temperature values. For that, the probabil- ity records (data points), which have lined at 95% confidence interval (mean ± standard devia- tion), have been computed; it can be seen from Fig 16 that only the RF-M1 model managed to generate more excellent performance than the comparable models. Moreover, the SVR-M5 model could not deal well with the high-temperature values in the hottest months for this study area. Fig 8. Comparison between measured daily temperatures and predicted ones through the testing phase. https://doi.org/10.1371/journal.pone.0277079.g008 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 21 / 31

3.2 Second scenario The previously described findings were obtained when data from 2000 to 2015 were utilized for training the applied models. This data counted for 70% of the total records and the rest of the measured data, which represented 30% of the entire data points, was used for testing the models. This type of data division helps to test how these models can simulate the pattern of data recorded in recent years. It is known that the world, in not a few parts of it, is facing a global warming crisis and the time series of temperatures studied in the last decade have shown a behavior and pattern which differs somewhat from what they were observed in the previous years. Accordingly, this study investigates how climate change affects the temperature records. The current records of temperature were used in both the training and testing phases. To do that, the data records are randomly divided into two phases: training (70%) and testing Fig 9. Comparison between measured weekly temperatures and predicted ones through the testing phase. https://doi.org/10.1371/journal.pone.0277079.g009 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 22 / 31

(30%). After that, the data-driven models (QRT, GBR, RF, and RF) were trained and assessed using several statistical metrics based on this data division. Furthermore, the outcomes of these models are compared with their corresponding results, which have already been dis- cussed. This technique may help observe whether there is an effect on the behavior and accu- racy of the model predictions when using recent time series data during the training process. According to the results shown in Table 10, all the predictive models’ performances are posi- tively affected using the Randomization method approach. For example, when classical data division procedure was used the RF model generates relatively higher errors (RMSE = 1.776, U = 0.063, and MAE = 1.353) and however, the prediction accuracy is slightly enhanced and the model provides lower forecasting error (RMSE = 1.697, U = 0.061, and MAE = 1.325). Overall the Randomization method has a role in improving the model capacity because it includes features related to future temperature trends in the training data used to train the sug- gested models in this work. 4. Conclusion The accuracy of the Data-Driven Models, namely RT, SVR, QRT, RF, ARIMA, and GBR, have been investigated to forecast atmospheric air temperature on different time scales (daily and weekly) using historical meteorological data. The data was collected from Cray station, located in North Dakota, USA. This region experiences a volatile continental climate throughout the

year. 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. Several input groups were Fig 10. The histogram and Gaussian kernel density function for daily temperature prediction during the testing phase. https://doi.org/10.1371/journal.pone.0277079.g010 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 23 / 31

examined with different times of lags. The daily scale showed that the RF technique provided more accurate outcomes than the comparable models. Moreover, the advanced analysis of forecasting error exhibited that the performance of the models was significantly affected by data variability, consistency, and extreme temperature val- ues. As January, February and December had higher variability of temperature data values, the effect on the model performance was greater for these months. In addition to this, the forecast- ing errors observed for these months were higher than other months due to the fact that the average temperature observed for these months fell below the overall average temperatures observed for the entire dataset. The models performed very well for the weekly time scale, but the RF, modeling technique provided more accurate results compared to other models. In general, the accuracy of daily Fig 11. The histogram and Gaussian kernel density function for weekly temperature prediction during the testing phase. https://doi.org/10.1371/journal.pone.0277079.g011 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 24 / 31

Fig 13. a) Boxplot of the forecasting error in weekly temperature prediction for all proposed models. b) Quantile percent of the forecasting error. https://doi.org/10.1371/journal.pone.0277079.g013 Fig 14. Daily residual: testing phase. a) GBR-M6, b) RT-M5. c)SVR-M5. d)QRT-M9. e) RF-M1. https://doi.org/10.1371/journal.pone.0277079.g014 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 26 / 31

Fig 15. Weekly residual: testing phase. a) GBR-M16, b) RT-M16, c) SVR-M16, and e) are RF-M10. https://doi.org/10.1371/journal.pone.0277079.g015 Fig 16. The probability of the data falling at the confidence level of 95% (μ±2σ). μ is the average, and σ is the standard deviation. https://doi.org/10.1371/journal.pone.0277079.g016 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 27 / 31

• Applying a Bio-inspirited algorithm to select the optimal hyperparameters of SVR • Studying to what extent the size of the data used to train the performed models affects the accuracy of predictions. This task can be accomplished using different training and testing rations. Acknowledgments The authors would like to thank the anonymous reviewers for their constructive comments, which significantly improved this research. Author Contributions Conceptualization: Adil Masood. Data curation: Mohammed Majeed Hameed. Formal analysis: Faidhalrahman Khaleel, Mohammed Abdulhakim AlSaadi, Mohammed Majeed Hameed. Funding acquisition: Mohammed Abdulhakim AlSaadi. Investigation: Mohamed Khalid Alomar, Siti Fatin Mohd Razali. Methodology: Faidhalrahman Khaleel, Adil Masood, Siti Fatin Mohd Razali. Project administration: Siti Fatin Mohd Razali, Mohammed Abdulhakim AlSaadi. Resources: Siti Fatin Mohd Razali. Software: Mohammed Majeed Hameed. Supervision: Nadhir Al-Ansari. Validation: Faidhalrahman Khaleel. Visualization: Mohammed Majeed Hameed. Writing – original draft: Adil Masood, Mohammed Majeed Hameed. Writing – review & editing: Mohamed Khalid Alomar, Faidhalrahman Khaleel, Mustafa M. Aljumaily. References 1. Woolf S. H. and Aron L., ’US. Health in International Perspective: Shorter Lives, Poorer Health’, U.S. Heal. Int. Perspect. Shorter Lives, Poorer Heal., pp. 1–394, 2013, https://doi.org/10.17226/13497 PMID: 24006554 Table 10. Comparison of the performance of the models when two different data division methods are applied. without randomization Randomization method

Model RMSE R U MAE RMSE R U MAE QRT-M9 3.691 0.961 0.13 2.835 3.659 0.962 0.130 2.828 GBR-M6 3.612 0.963 0.128 2.791 3.598 0.965 0.129 2.795 RT-M5 3.67 0.962 0.13 2.831 3.655 0.962 0.131 2.849 SVR-M5 3.592 0.964 0.127 2.745 3.582 0.963 0.129 2.760 RF-M1 1.776 0.991 0.063 1.353 1.697 0.992 0.061 1.325 https://doi.org/10.1371/journal.pone.0277079.t010 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 28 / 31

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