The Earth is incredibly complex, with geophysical processes occurring at many different scales that contribute to determining the eventual observed behavior. For example, the rate at which ice sheets contribute to sea level rise depends crucially on a heterogeneous, time varying subglacial water network, and the damaging effects of earthquakes depend crucially on complex, intertwining fault zone structure. Due to this complexity, many attempts to model Earth systems rely on an empirical, observationally driven approach. However, such empirical models fail when applied to conditions that have not been observed, making prediction of future behavior and related hazards challenging. Here I discuss how simple physical models are useful for modeling complex geophysical processes like ice sheet motion and earthquakes, particularly with the goal of robust prediction. On the ice sheet side, I show that one can account for a heterogeneous, time varying subglacial hydrologic system in a simplified manner that nonetheless produces accurate predictions when applied to the Greenland Ice Sheet. On the earthquake side, I show that the effects of complex fault zone structure on earthquake damage can be evaluated using statistical mechanics and yields predictions of high-frequency ground motions that compare more favorably with observed ground motions than more complex numerical simulations.