## 6 Discussion  
The lidar technology is a key technology for autonomous driving. Although this type of sensor compensates for the weaknesses of previous technologies, it is still subject to weather phenomena. As the lidar relies on the detection of self-emitted laser pulses, airborne particles, such as water droplets in fog and rain, can scatter or absorb the photons of the laser beam. This effect has the following two consequences: firstly, a loss of detectable signal intensity, which can be calculated using the extinction coefficient \(\alpha\) and the distance to the object. Secondly, backscattered photons add noise, depending on the backscattering coefficient \(\beta\), to the point cloud, which is constructed inside the lidar. Both coefficients can be calculated using either Mie scattering theory or empirical models. A main contribution of this work is to propose a full set of empirical models for the coefficients, adding to the limited set previously available in the literature, as shown in Table 4.  
The comparison of the theoretical and empirical approaches shows that the models for the extinction coefficient for fog are very similar, as depicted in Figure 4; however, the model for the backscattering coefficient appears to be too small. Using the ratio of the calculation of \(\alpha/\beta\), a constant factor was calculated to approximate the backscattering coefficient. The empirical models of rain for the extinction coefficient yield very different results depending on the mean drop size. Here, many small raindrops cause more scattering events, resulting in a large extinction coefficient, whereas the same precipitation rate with a few large drops results in a smaller coefficient. For the backscattering coefficient \(\beta_{\rm rain}\), no model could be found and was therefore calculated in the same way as for fog. Depending on the temperature of the atmosphere, either dry or wet snow occurs. Here, dry snowfall results in a higher extinction coefficient \(\alpha_{\rm snow}\) due to its lower density, and hence the higher amount of flakes to achieve the same precipitation. For the backscattering coefficient \(\beta_{\rm snow}\), no model could be found in the literature, so it was calculated similarly to fog. For dust storms no applicable empirical models could be found in the literature. Using related work of different areas of a simple approach was developed, which considers industry standard type of dust, to calculate both extinction coefficients. Although particulate matter is in some regions a common man-made environmental phenomenon, no related literature could be found. A similar approach to that for dust was used to derive empirical models for the coefficients. Figure 17: Simulated lidar during smog. The spread stands for the standard deviation of the number of detected points. In this work, we have implemented a rigorous simulation approach to validate the usefulness of the proposed models for lidar detection. We have presented a comprehensive simulation framework using the virtual environment Carla and ROS2. To evaluate the performance of the simulation, it was compared with real experiments by recreating the real scenarios in the simulation, which showed that the simulation of fog is very similar to the real experiments. Although the results of the simulation of rain do not contradict the experimental results available, it appears to be a bit more complicated, as several unknown factors might affect the real experiment, which were not known and hence not considered in the simulation experiment. For dust, snow, and particulate matter, no real-world experiment could be found, and therefore, the simulation results can be considered as a prediction of the lidar detect captionabilities. As the derivation of the models has shown, the calculated coefficients depend heavily on the particle distributions of the respective weather phenomena.