# Risk Propagation Mechanism and Prediction Model for the Highway Merging Area
## 3 Highway Merging Area Accident Impact Range Model
### Parameter Adjustment  
When building a Gaussian plume model for analyzing the impact range of traffic accidents in highway merging areas, specific adjustments of variables should be made based on the real accidents. This optimization process can refine the Gaussian plume model and make it applicable to this research. The specific adjustments are as follows.  
1. Adjustment of the source strength parameter  
The release intensity of the pollutant diffusion source can be directly replaced with the impact of the accident diffusion source. This variable is used to characterize the radiation ability of the accident, which is the source strength \(q\) reflecting the accident's own strength. It is mainly related to the type of accident and the surrounding traffic conditions.
2. Adjustment of the average wind speed parameter  
The average wind speed parameter in the plume model is not suitable for defining the accident impact range and cannot be directly replaced. However, the average wind speed is mainly related to the speed of pollutant propagation. The average traffic speed at the accident source reflects the initial spread speed of accident. It is related to the traffic conditions. If the average travel speed is high, the diffusion speed will be fast. Therefore, the parameter of average wind speed can be replaced with the average speed \(u\) of the traffic flow at the accident position.
3. Adjustment of the diffusion coefficient parameters  
The diffusion coefficients in the plume model characterize the relationship between the pollutant gas and the propagation area. These parameters have a significant impact on the diffusion effect and propagation range of accidents. The following two parameters characterize the relationship between the accident source and the diffusion area, which replaces the diffusion coefficient in the original plume model.  
Let \(y\) and \(z\) be the distribution parameters of the traffic volume at the accident point in the \(y\) and \(z\) directions, respectively. \(C(x,y,z)\) is defined as the affected degree of the merging area during an accident. \(H^{\prime}\) is the source height of toxic gases in the original plume model and is taken as 0. Then, the improved plume model is as follows:  
\[C(x,y,z)=\frac{q}{\pi u\omega_{y}\sigma_{x}}\exp\left[-\frac{1}{2}(\frac{y^{2 }}{\sigma_{y}^{2}}+\frac{z^{2}}{\sigma_{z}^{2}})\right] \tag{4}\]  
Based on the deduction in the literature [32], a model for the accident impact range for the highway merging area was obtained after adjustment, as shown in Equation (5):  
\[X_{i}=\sqrt[3]{\frac{\xi Pab_{i}}{4\sqrt{\pi C_{d}}}} \tag{5}\]  
In Equation (5), \(X\) represents the impact range of an accident; \(\xi\) represents the diffusion traffic ratio (between 0 and 1) of the accident, which depends on the type of accident; \(P\) represents the potential energy of the accident source point; \(a\) is related to the proportion of road occupied by the accident; \(C_{d}\) represents the degree to which the maximum range of the accident is affected by traffic, which is close to 0; \(b\) is an adjusting parameter, which can be divided by different impact degrees; and \(i\) represents the level of impact areas.