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

meteorological station from 2000 to 2021. According to reported data, the three hottest months are June (17.944 C˚), July (20.799 C˚), and August (19.408 C˚) while the coldest months in this case study are December (-10.901 C˚), January (-13.018 C˚), and February (-12.847 C˚). Furthermore, the recorded air temperatures have extreme values (far from the mean) in four months (i.e., December to March). In these months, the standard deviation val- ues of the data are very high compared to other months. Nevertheless, the dispersion of the data through June (St. D = 3.626), July (St. D = 2.916), and August (St. D = 3.248) is very little, which means that the data are more consistent with their normal rates. Notably, the utilized data in this study are collected from the open-source website of the Crary station [43]. Finally, the location of the studied region is shown in Fig 1. 2.2 Support vector regression Support vector regression (SVR) is considered a powerful and efficient tool based on the notion of statistical learning and was first introduced by Vapnik [44] to describe regression as a part of the support vector machine (SVM). Based on the principle of structural risk minimi- zation (SRM), SVR has been successfully implemented in real-world challenge modeling by overcoming classification and regression tasks [45]. The linear relationship between indepen- dent variables (x1, x2, x3, � � �, xr) and dependent variable (y) is given in the equation below. y ¼ f x ð Þ ¼ w; x ð Þ þ b ð1Þ Where wi and b are the weight and bias of the model, respectively. ;(x) is the higher dimen-

sional feature space converted from the independent vector (input). These parameters can be determined by minimizing kwk2 = (w.w) as follows min 1 2 k w2 k þC X r i¼1 xi þ xi � ð Þ ð2Þ under the constraints yi w; x ð Þ b � ε þ xi yi w; x ð Þ b � ε xi � 8i xi ; xi � � 0 8 > < > : 2 1; . . . n f g ð3Þ Table 2. Statistical characteristics of Crary station: Weekly scale. Month/statics Min Average Max St. D Skewness Jan -28.23 -13.112 -1.84 5.882 -0.070 Feb -27.35 -13.191 0.26 6.093 0.111 Mar -20.56 -5.287 11.32 6.311 -0.115 Apr -10.33 3.833 12.74 4.926 -0.383 May 3.22 11.185 21.55 3.879 0.101 Jun 10.28 17.461 23.22 2.743 -0.133 Jul 15.76 20.644 24.47 1.949 -0.384 Aug 13.98 19.650 25.50 2.292 -0.056 Sep 6.20 15.149 22.96 3.319 -0.229 Oct -3.89 7.212 18.09 4.414 0.036 Nov -14.03 -1.822 8.59 5.210 -0.133 Dec -22.77 -9.993 1.34 5.816 -0.380 https://doi.org/10.1371/journal.pone.0277079.t002 PLOS ONE Air temperature forecasting: Mutli-time scale PLOS ONE | https://doi.org/10.1371/journal.pone.0277079 November 3, 2022 4 / 31