## 5 Methods for Predicting Pavement Temperature
### Statistical and Probabilities Techniques  
The current empirical models consist of three categories, non-linear regression, linear regression, and neural network [65]. The simplest method for developing empirical models is linear regression, which predicts the minimum or maximum temperature at a particular depth [63; 90; 91; 92]. Linear regression models typically comprise several parameters and are used in real-time situations to predict surface temperature [93]. A drawback of using this method is that the daily pavement temperature through depth is non-linear and complex. Therefore, linear regression to predict pavement temperature is not encouraged as it depends on time as an independent variable factor [94]. Since the predicted pavement temperature changes over time, advanced empirical models generally include the sine terms [95; 96]. However, the statistical analysis method is commonly developed using a large amount of measured field data on asphalt pavement details and climate database. It considers geographical and meteorological factors such as wind speed, ambient temperature, location and solar radiation [5; 97; 98; 99]. Table 3 presents a list of researches that used statistical methods to predict the pavement temperature. The regression method establishes a quantitative relationship between the temperature data and the asphalt pavement [100; 101]. Furthermore, formulas are also applied to provide a mathematical solution for real-world problems and express relationships between various quantities in order to predict asphalt pavement temperatures for a particular area [102]. The advantage of using mathematical models is that they facilitate the analysis and interpretation of the observed data as they describe the evolution law as a function of only a few statistically compared [103]. Generally, statistical methods can provide reliable predictions of temperature with input data, including the original pattern databases [63]. Hence it is observed that this method can evaluate pavement temperature prediction models without requiring multiple inputs such as numerical computation and analytical deviation. Thus, empirical models are used extensively in practice [65]. The Strategic Highway Research Program (SHRP) was introduced in Canada and the United States in 1987. It is a 20-year study to improve the on-site performance description of pavements [104]. Apart from this, the study introduced a new bitumen classification system called Performance Grading (PG) [105]. Consequently, the PG number helps road engineers to locate the minimum and maximum temperatures of pavement that have been selected. Therefore, the appropriate bituminous binder was chosen at a specified temperature to prevent pavement rutting and cracking in hot and cold temperatures [59; 106]. Most recently, AASHTO updated the associated pavement design manual called Mechanistic-Empirical Pavement Design Guide. This new guide helped to exploit the benefits of adopting the PG classification system and utilising the actual weather record. \begin{table}
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**Ref, Year** & **Location** & **Model and Influencing Factors** & **Summary and Findings** \\ \hline SHRP (1987) [104] & USA & \(1331\pi\pi^{2}\)\(\simeq\)\(cos2+\alpha\)\(\tau\)\(T_{d}^{4}-hc(Ts-Ta)-164k-\alpha\)\(\tau\)\(T_{d}^{4}=0\) & The model based on the assumption of a balance of energy during the highest temperatures, which is an erroneous assumption \\ SHRP (1987) [104] & USA & \(T_{d}\) is a 20 degrees latitude, \(c\) is movement surface emissivity, \(\sigma\) is the Stefan-Boltzmann constant (5.7 \(\times\) 10\({}^{-8}\) W/m\({}^{2}\)), \(k\) is surface coefficient of solar radiation, wind speed and atmospheric circumstances. \\  & heat transfer (W/m\({}^{2}\) C), \(k\) is heat conduction coefficient (W/m\({}^{2}\) C), \(T_{h}\) is air temperature (K), and \(T_{d}\) is surface temperature (K). & The model could predict maximum and minimum temperatures that play an essential role in asphalt pavement.