In certain drylands around the globe vegetation is distributed in bands that are regularly spaced and oriented transverse to a gentle slope. The limited water resource ends up concentrated in the bands via feedback mechanisms that act on the fast timescales of the rare storms. In our modeling framework, we treat the storms as kicks that add water to the soil in a heterogeneous fashion that depends on the biomass distribution. These kicks then determine the initialization of a reaction diffusion PDE model that captures the slow dynamics of the vegetation distribution during the long dry periods between the storms. This modeling framework is designed so we can explore possible impacts of storm variability. In particular we introduce randomness to the kick strength and the subsequent flow duration. We are interested in how these random aspects of storm strength and timing impact the resilience of these fragile ecosystems, particularly in the face of climate change.