The energy balance of an alpine snow cover significantly changes once the snow cover gets patchy. The local advection of warm air causes above-average snow ablation rates at the upwind edge of the snow patch. As lateral transport processes are typically not considered in models describing surface exchange, e. g., for hydrological or meteorological applications, small-scale variations in snow ablation rates are not resolved. The overall model error in the hydrological model Alpine3D is split into a contribution from the pure " leading edge effect" and a contribution from an increase in the mean air temperature due to a positive snow-albedo feedback mechanism. We found an overall model error for the entire ablation period of 4% for the almost flat alpine test site Gletschboden and 14% for the Wannengrat area, which is located in highly complex terrain including slopes of different aspects. Terrestrial laser scanning measurements at the Gletschboden test site were used to estimate the pure " leading edge effect" and reveal an increase in snow ablation rates of 25-30% at the upwind edge of a snow patch and a total of 4-6% on a catchment scale for two different ablation days with a snow cover fraction lower than 50%. The estimated increase of local snow ablation rates is then around 1-3% for an entire ablation period for the Gletschboden test site and approximately 4% for the Wannengrat test site. Our results show that the contribution of lateral heat advection is smaller than typical uncertainties in snow melt modeling due to uncertainties in boundary layer parameters but increases in regions with smaller snow patch sizes and long-lasting patchy snow covers in the ablation period. We introduce a new temperature footprint approach, which reproduces a 15% increase of snow ablation rates at the upwind edge of the snow patch, whereas observations indicate that this value is as large as 25%. This conceptual model approach could be used in hydrological models. In addition to improved snow ablation rates, the footprint model better represents snow mask maps and turbulent sensible heat fluxes from eddy-covariance measurements.