## 3 Theory of Solar Radiation Intensity and Sunshine Temperature Field
### Solar Radiation Intensity Theory and Test Comparison
#### 3.1.2 Comparison of Actual and Theoretical Solar Radiation Intensity  
In the computation of solar radiation intensity using the ASHRAE clear sky model, it is necessary to choose a series of model parameters that are typically associated with geographic location, atmospheric conditions, and solar position. [PERSON] et al. (2018) proposed a set of model parameters to describe these conditions, expressed as follows:  
\[\left\{\begin{array}{l}A=1370[1+0.034\cos(2\pi N/365)]\\ B=0.2051-4.0537\times 10^{-4}N+3.5186\times 10^{-5}N^{2}\\ -1.9832\times 10^{-7}N^{3}+2.8939\times 10^{-10}N^{4}\\ C=7.8763\times 10^{-2}-4.2177\times 10^{-4}N+1.9908\times 10^{-5}N^{2}\\ -1.0607\times 10^{-7}N^{3}+1.5024\times 10^{-10}N^{4}\end{array}\right. \tag{6}\]  
where \(N\) represents the day of the year starting from 1 January. The combined calculation of Equations (1)-(6) can obtain the total solar radiation intensity that can be received at any time and any structural position.  
The amount of solar radiation absorbed by concrete structures can be calculated using Equation (7):  
\[G_{abs}=\zeta G_{t} \tag{7}\]  
where \(G_{abs}\) represents the solar radiation absorbed by the concrete structure, \(G_{t}\) is the total radiation intensity on the structure surface, which is related to the vertical incidence angle and direct solar radiation intensity \(G_{D}\). \(\zeta\) is the solar radiation absorption coefficient for concrete materials. The shortwave absorption coefficient is 0.65, and the longwave absorption coefficient is 0.88 ([PERSON] et al., 2018).  
During the solar radiation intensity experiment, the study was continuously observed for 365 days. The direct solar radiation intensity was selected for 22 April and 5 October, which are two days that usually present clear weather conditions, ideal for measuring direct solar radiation intensity. The theoretical calculations using the ASHRAE clear sky model were performed, with the comparison of actual and theoretical data illustrated in Figure 4. It can be seen that the actual direct radiation intensity initially shows a small discrepancy when compared to those calculated using the ASHRAE clear sky model in Qingdao, but both exhibit similar trends of variation. This demonstrates that the ASHRAE clear sky model is generally suitable for calculating the direct radiation intensity on U-shaped girder bridges. At the same time, the parameters A, B, and C in the model can adopt the recommended values from the Li-model parameters.  
The Li-model parameters were combined with the ASHRAE clear sky model to calculate the theoretical scattered radiation intensity, and were compared with the actual data, with the results shown in Figure 5. The scattered radiation intensity calculated using Li-model parameters and the ASHRAE clear sky model shows considerable deviation from the actual data in Qingdao. This deviation can be attribu  
Figure 4: Comparison between actual and theoretical direct radiation intensities: **(a)** 22 April; **(b)** 5 October.  
the model and variations in instrument calibration. However, multiplying the theoretical scattered radiation intensity by 1.5 results in a close match with the actual data. Therefore, the scattered radiation intensity in the Qingdao area can be calculated by multiplying the theoretical values from the ASHRAE clear sky model based on Li-model parameters by 1.5.