Gas diffusion layers (GDLs) play a significant role in the efficient operation of high-temperature polymer electrolyte fuel cells. They connect the electrodes to the gas channels of the bipolar plate by porous material with a meso-scale geometric structure. The electrodes must be sufficiently supplied by gases from the channels to operate fuel cells efficiently. Furthermore, reaction products must be transported in the other direction. The gas transport is simulated in the through-plane direction of the GDL, and its microstructure created by a stochastic model is equivalent to the structure of real GDL material. Continuum approaches in cell-scale simulations have model parameters for porous regions that can be taken from effective properties calculated from the meso-scale simulation results, as one feature of multi-scale simulations. Another significant issue in multi-scale simulations is the interface between two regions. The focus is on the gas flow at the interface between GDL and the gas channel, which is analyzed using statistical methods. Quantitative relationships between functionality and microstructure can be detected. With this approach, virtual GDL materials can possibly be designed with improved transport properties. The evaluation of the surface flow with stochastic methods offers substantiated benefits that are suitable for connecting the meso-scale to larger spatial scales.