# Solar Radiation Parameters for Assessing Temperature Distributions on Bridge Cross-Sections
## 1 Introduction  
Temperature distribution in bridge structures built in the outdoor environment are appreciably influenced by solar radiation and ambient temperature variations [1]. The thermal energy associated with solar radiation can result in an increase in temperature at the top surfaces of the structure beyond the ambient temperature. Solar radiation is one of the most important factors affecting the temperature distribution in bridge structures [2]. Heat conduction can further affect the temperature distribution. Although there are many experimental studies that address temperature distribution in bridges [3; 4; 5; 6; 7; 8], few consider and measure solar radiation when assessing bridge temperature distributions. When carrying out a dynamic heat transfer analysis on bridge structures, the geometry of cross-section, initial thermal state, varying boundary conditions, thermal properties of materials, etc. should be input into any Finite Element Method (FEM) software used. The solar radiation levels on different parts of bridge structures represent one of the time-varying boundary conditions, which can be estimated by considering the various model parameters. Taking box girder bridges as example, the external surface of the top flange is influenced by both the beam and diffuse solar radiation, while the external surface of the web is influenced by a combination of the beam solar radiation, diffusesolar radiation and reflection from the ground. The undersides of the top and bottom flanges are influenced by ground reflection. The geometry of the cross-section, thermal parameters of materials, and bridge location are all determined or known at the beginning of the design process; however, the solar radiation must be estimated or measured. The accuracy of heat transfer analysis using FEM is influenced by the precision of solar radiation estimates. At present, there is a lack of measured solar radiation data in most parts of China. There are 756 meteorological stations in China, but only 122 of those stations monitor solar radiation data [9]. In Fujian, there are more than 60 meteorological stations, with only the Fuzhou and Jian'ou stations monitoring the solar radiation levels. Therefore, engineers usually establish estimation models of solar radiation for engineering applications or scientific research. However, choosing the appropriate estimation models for solar radiation from among those proposed by researchers is a key problem. Some are empirical models based on different meteorological parameters, while others are established using numerical simulation involving different types of artificial intelligence methodologies.  
In this paper, the similarities and differences of various estimation models for solar radiation are summarized, including models for global, beam, and diffuse solar radiation, all of which should be considered in the analyses of temperature distribution on bridge girder cross-sections. Based on the solar radiation data obtained from eight cities in Fujian, China, estimation models of solar radiation applicable for Fujian, China were proposed. The monitoring of some bridges was carried out to obtain the temperature distribution on bridge girder cross-sections. The FEM of cross-sections of bridge girders were built using the Midas software. The influence of solar radiation on bridge temperature distribution in different seasons was analyzed. The results can be considered as a model for future development of specifications and estimation models for solar radiation in different regions in China and elsewhere.