## Appendix A
### Basis for Parameter Selection of Synthesis Methods  
Based on the Imgaug library, for corruption types with relatively clear generation reasons, such as noise, contrast, and compression transform, we adopt its predefined synthesis methods under the premise of being as realistic as possible. For those with complex generation reasons, such as rain, snow, fog, darkness, or occlusion, we add some additional conditions to ensure that they approximate the real situation while using the predefined synthesis methods. And we verified their rationality by evaluating real corruption images. As shown in Table 1, we provide simple and fast data generation methods for reasonably evaluating the robustness of vehicle detection models in deployment. The following are the basis for parameter selection when we add additional conditions. How to synthesize realistic corrupted images for various types of corruption is complex. Although this paper focuses on basic types of corruption. However, when synthesizing corrupted data, in order to be as consistent with real-world scenarios as possible, synthesis methods for most corruption are actually the superposition of multiple basic corruptions, as shown in Table 1. The synthesis method for rain is to add raindrop (size = (0.025, 0.05), speed = (0.25, 0.05)), add splatter with predefined severities {1, 2, 3}, add motion blur (k = 3), and reduce the brightness by 20%. For rain, we add the occlusion caused by raindrops and the splashing of raindrops, the blur caused by the movement of raindrops, and the dim light caused by the decrease in brightness on rainy days. For fog, snow, and frost, based on the predefined synthesis methods in Imgaug [51], we additionally add different opacity gray mask layers according to the severity to reduce the image contrast and brightness and also reduce the brightness to simulate dark. The synthesis method for darkness is: The brightness is multiplied by (0.7, 0.5, 0.3), Gaussian noise is added with (1-5, 5-10, 10-20), and hue and saturation are adjusted with (\(-\)10\(+\)10, \(-\)20\(+\)20, \(-\)30\(+\)30). For darkness, we consider the decrease in brightness, the Gaussian noise brought by the sensor, and the changes in hue and contrast. **Fog. ** According to the atmospheric scattering model [51], the concentration of fog is inversely proportional to the transmittance. Changing the transmittance is equivalent to adding a grayscale mask layer. Based on multiple experimental observations, adding an opacity gray mask layer with 20% transparency is consistent with the fog concentration (middle class) with a visibility of 100m in Foggy Cityscapes [52]. Therefore, for the predefined fog levels, for light fog (visibility of 200 m), add an opacity gray mask layer with 10% transparency; for moderate fog (visibility of 100 m), add an opacity gray mask layer with 20% transparency; for heavy fog (visibility of 50 m), add an opacity gray mask layer with 30% transparency; in addition, considering that foggy days are often accompanied by decreased brightness, we reduce the image brightness by 20% to ensure consistency with the light intensity distribution of real foggy-day images. **Rain. ** The synthesis of rain is relatively complex. According to [53], the proportion of raindrops in the image is set to be between 0.025 and 0.05, and the falling speed of raindrops is set to be between 0.25 and 0.5. In addition, because the falling of raindrops will cause motion blur, the blur kernel is set to k = 3 with reference to the medium blur intensity in RainCityscapes [54]. Considering the splashing characteristics of raindrops, predefined splashing effects of different levels are added. Finally, image brightness is reduced by 20% to ensure consistency with the light intensity distribution of real rainy-day images. **Snow. ** The brightness decrease in snow is related to the snowflake density. On real snowy days, the increase in the ground reflectance leads to a decrease in the overall brightness by about 15-25%. Therefore, the brightness of the image is reduced by 20%.