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

obvious on the performance of the AI models. Accordingly, the models in this scenario will be trained using some recent records. 2.8 Statistical metrics Different statistical metrics assess the best model accuracy in daily and weekly temperature forecasting. Furthermore, it is vital to recognize the most efficient model with the least fore- casted error. Four statistical measures can be adopted to examine the forecasting accuracy of the suggested modeling approaches, such as root mean square error (RMSE), correlation coef- ficient (R), Thiels’ U-statistics (U), and mean absolute error (MAE). The mathematical expres- sions of these measures are presented below [57, 58]. RMSE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N X N i¼1 ðAi PiÞ2 s ð23Þ MAE ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N X N i¼1 jAi Pij s ð24Þ U ¼ PN i¼1 ðAi PiÞ2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN i¼1 Ai2 q þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN i¼1 Pi2 q ð25Þ R ¼ PN i¼1 Ai A ð Þ Ai P ð Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN i¼1 ðAi A Þ2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPN i¼1 ðPi P Þ2 q ð26Þ Where, Ai, and Pi are the actual and forecasting temperature for ith observation. While A−, and P− are the mean of actual and predicted value, and N is the total number of observations. The

stated statistical parameters have been used frequently in the literature for model comparison, and their estimation can be achieved directly from the observed and predicted values. Based on the results of these statistical measures, the model presenting the lowest value of forecasting error and the highest value of R (close to one) is selected as the best model for predicting the air temperature for short- and mid-term forecasting. 3. Result and discussion 3.1 First scenario This scenario investigates the capability of the AI models to predict the one-step ahead values for daily and weekly temperature. In this part of the work, we divide the data into two phases: training and testing. The classical method is used to separate the data into two steps; the first 70% of the recorded temperature is used for training, and the last 30% of the data is used for testing. In this scenario, the effect of the current temperature trends is not considered. In other words, the current records of temperatures are used in the testing phase. Thus, the models are tested and evaluated based on their ability to predict the current temperature values of the time series data. Furthermore, the input lags were determined by AFC and produced to the adopted models like RF, SVR, GBR, RT, and QRT. Different statistical parameters and compa- rable figures are used to assess the models’ performances. This part discusses the performance of the proposed models for predicting the daily and weekly temperature over the training and testing phases for different input lags. Tables 4 and 5

show the performance of the proposed models during the training phase for both daily and PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 13 / 31