For under a stratus cloud cover and for identical solar heights, irradiation values are about 70% higher in spring than in late summer at Barrow in northern Alaska. A possible explanation for these differences is by interseasonal variations in cloud thickness and water content in the atmosphere. However, we demonstrate that multiple reflection is mostly responsible for it. In spring there is a very high surface albedo (~80%), while in summer the surface albedo is los (~15%). Hence multiple reflection between the surface and the lower extent of the stratus cloud cover is important when snow is on the ground but fairly unimportant after the snow has melted. To verify our assumption, airborne measurements were carried out for the same cloud but over surfaces of different albedos, namely, snow covered tundra (~80%), broken sea ice (20--40%), and open water (4--16%). These data show clearly that if the surface albedo is raised, multiple reflection is the cause of the strong increase in irradiation. The interaction by multiple reflections of the spectral characteristics of various ground surfaces with the stratus clouds also was found to be displayed in the spectral irradiance received from the cloud cover.