## 4 History of Asphalt Pavement Temperature Prediction Models  
Based on the research methodology and tools of analysis employed in each investigation, the prediction of asphalt pavement temperature can be divided into: (1) numerical and finite element techniques, (2) theoretical and analytical approaches, and (3) statistical and probabilistic models. Researchers began to study the effect of climate factors on asphalt pavement quite early. In 1957, [PERSON] [58] became one of the first researchers to address the internal temperature of asphalt pavements based on meteorological data measurements. Furthermore, researchers studying asphalt pavement temperature focused on temperature distribution in various depths; they adopted theoretical frameworks based on the one-dimensional thermal conduction model and Finite Difference Method (FDM) to simulate a pavement structure's temperature distribution [59].  
In 1987, the long-term pavement performance (LTPP) project in the United States began measuring asphalt pavement temperature [60]. Their study focused on a new pattern of data analysis for asphalt pavement. A large amount of became data available, including atmospheric temperature and solar radiation and their relationship to pavement temperature, comprise an essential database that facilitates and encourages the research in this field, which used the regression method to formulate models for predicting asphalt temperature [61]. The researchers attempted to develop a regression for the prediction model to correct the deviations and back-calculation of surface asphalt pavement layers [17].  
In the first stage (1950-1990), the researchers focused on the variation trend and temperature distribution. However, a small number of researchers used slope methods to predict pavement temperatures. During the 1990s, Canadian and American researchers focused on using a new method to analyse the asphalt pavements data. Consequently, a helpful database is now available to support research at pavement temperature based on a large amount of data and information about pavement temperature and climate parameters such as atmospheric temperature and solar radiation. However, most researchers in this second stage, 1990 to 2000, also made use of the regression method to create models for predicting asphalt temperature by focusing on the minimum and maximum asphalt pavement temperatures during the service period when selecting bituminous for the Superpave method. Hence in accordance, several studies also began discussing the daily prediction of pavement temperature with slight variable modifications, and they had been successfully implemented in road engineering practices. In the third stage, from the year 2000 to present, researchers have been using statistical methods to develop a regression prediction model in two applications, namely to correct the deflection measurements with back-calculation modulus in the asphalt pavement layers and to simulate temperature fluctuation distributions within the structure of the asphalt. The third phase's research is greatly influenced by those that occurred in the previous phase, despite the research metrics' scope has been dramatically expanded. To summarize, temperature prediction models had been improved and perfected owing to the rapid database development in the 1990s.