We analyze the sensitivity of a mathematical model of volcanic ash dispersion in the atmosphere to the representation of key physical processes. These include the parameterization of subgrid-scale atmospheric processes and source parameters such as the height of the eruption column, the mass emission rate, the size of the particulates, and the amount of ash that falls out close to the source. By comparing the results of the mathematical model with satellite and airborne observations of the ash cloud that erupted from Eyjafjallajokull volcano in May 2010, we are able to gain some insight into the processes and parameters that govern the long-range dispersion of ash in the atmosphere. The structure of the ash cloud, particularly its width and depth, appears to be sensitive to the source profile (i.e., whether ash is released over a deep vertical column or not) and to the level of subgrid diffusion. Of central importance to the quantitative estimates of ash concentration in the distal ash cloud is the fallout of ash close to the source. By comparing the mass of the ash and the column loadings in the modeled and observed distal ash cloud, we estimate the fraction of fine ash that survives into the distal ash cloud albeit with considerable uncertainty. The processes that contribute to this uncertainty are discussed.