## 4 Results and Discussion
### Simplified Prediction Formula Based on Experimental and Theoretical Models  
To develop a practical and simplified prediction formula for estimating the onset time of pavement icing at airports, we first conducted a thorough analysis of the experimental  
Figure 13: Comparison of experimental results and theoretical solutions: (**a–d**), respectively, show the results under different combinations of air temperature, wind speed and deicing salt concentration, with values of (\(-15\,^{\circ}\)C, 2 m/s, 0%), (\(-15\,^{\circ}\)C, 6 m/s, 0%), (\(-20\,^{\circ}\)C, 2 m/s, 0%), and (\(-15\,^{\circ}\)C, 2 m/s, 80%) for each condition.  
results in comparison with the theoretical models. This analysis enabled us to identify the key factors that significantly impact the icing onset time. These factors include the pavement surface temperature (\(T_{s}\)), wind speed (\(v_{wind}\)), deicing salt concentration (\(r_{salt}\)), and air temperature (\(T_{a}\)).  
The results indicate an exponential relationship between the pavement surface temperature and the onset time of icing. As the temperature decreases, the icing onset time occurs earlier, prompting us to adopt an exponential function to describe this relationship. Additionally, an increasing wind speed accelerates the heat loss from the pavement surface, thereby shortening the icing onset time; the experimental results demonstrate that the effect of the wind speed on the icing time is approximately linear. The concentration of deicing salt directly influences the freezing point of the salt solution, affecting the icing onset time, with a linear relationship observed between the salt concentration and the icing time. Moreover, the air temperature impacts the cooling rate of the pavement surface, thereby impacting the icing onset time; this relationship is also linear.  
To determine the specific values of the fitting parameters, we employed the Least Squares Method (LSM) using the experimental data. This method minimizes the discrepancy between the predicted icing onset time and the observed experimental results, resulting in the most accurate fitting parameters. The Simplified Prediction Formula is presented in Equation (6), where b\({}_{1}\)-b\({}_{5}\) are fitting parameters determined as follows: 0.8104, \(-\)7.3345, 6.4675, 2.422 \(\times\) 10\({}^{-8}\), 24.3328;  
\[t_{ic-start}=b_{1}v_{wind}^{2}+b_{2}v_{wind}+b_{3}\tau_{salt}e^{\frac{(T_{a}-T _{a})}{T_{a}}}+b_{5} \tag{6}\]  
The proposed simplified prediction formula for the onset time of pavement icing demonstrates strong accuracy when compared to the experimental data. As illustrated in Figure 14, the predicted values closely align with the actual measured values, as evidenced by the data points clustering around the line \(y=x\), which represents perfect prediction accuracy. The dashed lines indicating the boundaries of \(y=0.8x\) and \(y=1.2x\) show that the majority of the predicted values fall within a \(\pm 20\%\) error range, confirming the model's reliability for practical applications. The average error between the predicted and actual values is approximately 16.8%, with a maximum deviation of 22.4%, both of which are within acceptable limits for engineering purposes. This level of accuracy suggests that the simplified prediction model is not only effective but also practical for real-world scenarios, enabling airport operators to anticipate and respond to pavement icing conditions with a high degree of confidence. The model's ability to account for critical factors such as the surface temperature, wind speed, salt concentration, and air temperature makes it a valuable tool for enhancing the safety and operational efficiency of airport runways during winter weather conditions.  
Figure 14: Comparison of calculation results for icing onset time with measured values.