Some of the most challenging problems in ecology, hydrology, and geomorphology arise from processes which play out over large spatial scales and long time intervals. High-resolution global digital elevation models are becoming available. They will allow problems of broad spatial extent to be addressed, but only if we can handle the enormous volume of data. Similarly, performance gains in computers now make it feasible to test more complex theory using computational models, but only if efficient techniques are used. In this dissertation I develop and demonstrate techniques for handling large geospatial raster datasets and rapidly modeling ecological and hydrological processes, producing results that are orders of magnitude more efficient than previous work. Notably, these techniques work on both high-performance machines and laptops. Finally, I apply the techniques to a challenging problem at the interface of ecology, evolution, climate, and geology.