The ongoing development of self driving cars requires accurate measuring devices and the objective of this thesis was to investigate how di↵erent weather will affect one of these devices, known as a LiDAR. A LiDAR uses pulsed laser light to measure the distance to an object. The main goal of this thesis was to solve the transient radiative transfer equation (TRTE) that describes the propagation of radiation in a scattering, absorbing and emitting media. The TRTE was solved in the frequency domain using the discrete ordinate method (DOM) and a matrix formulation. An alternative model to estimate the amplitude of the return pulse is to use the LiDAR equation which describes the attenuation of a laser pulse in a similar way as Beer-Lamberts law. The difference between the models are that the TRTE accounts for multiple scattering whereas the LiDAR equation only accounts for single scattering. This has the effect that the LiDAR equation only models the change in amplitude of the return pulse whereas the TRTE also models the broadening and shift of the pulse. Experiments were performed with a LiDAR in foggy, rainy and clear weather conditions and compared with the theoretical models. The results from the measurements showed how the amplitude of the pulse decreased in denser fog. However, no tendency to a change in pulse shift and pulse width could be seen from the measured data. Additionally, the measurements showed the effect of ambient light and temperature to the LiDAR signal and also that, even after averaging 300 waveforms, noisy data were a problem. The results from the transient radiative transfer equation showed that in a medium with large optical depth the shift and width of the pulse are highly affected. It was also shown that the amplitude of the pulse calculated with the TRTE seemed to better approximate the experimental data in fog than the LiDAR equation.