A Budyko framework for estimating how spatial heterogeneity and lateral moisture redistribution affect average evapotranspiration rates as seen from the atmosphere

Most Earth system models are based on gridaveraged soil columns that do not communicate with one another, and that average over considerable sub-grid heterogeneity in land surface properties, precipitation (P), and potential evapotranspiration (PET). These models also typically ignore topographically driven lateral redistribution of water (either as groundwater or surface flows), both within and between model grid cells. Here, we present a first attempt to quantify the effects of spatial heterogeneity and lateral redistribution on grid-cell-averaged evapotranspiration (ET) as seen from the atmosphere over heterogeneous landscapes. Our approach uses Budyko curves, as a simple model of ET as a function of atmospheric forcing by P and PET. From these Budyko curves, we derive a simple sub-grid closure relation that quantifies how spatial heterogeneity affects average ET as seen from the atmosphere. We show that averaging over sub-grid heterogeneity in P and PET, as typical Earth system models do, leads to overestimations of average ET. For a sample high-relief grid cell in the Himalayas, this overestimation bias is shown to be roughly 12 %; for adjacent lower-relief grid cells, it is substantially smaller. We use a similar approach to derive sub-grid closure relations that quantify how lateral redistribution of water could alter average ET as seen from the atmosphere. We derive expressions for the maximum possible effect of lateral redistribution on average ET, and the amount of lateral redistribution required to achieve this effect, using only estimates of P and PET in possible source and recipient locations as inputs. We show that where the aridity index P/PET increases with altitude, gravitationally driven lateral redistribution will increase average ET (and models that overlook lateral redistribution will underestimate average ET). Conversely, where the aridity index P/PET decreases with altitude, gravitationally driven lateral redistribution will decrease average ET. The effects of both sub-grid heterogeneity and lateral redistribution will be most pronounced where P is inversely correlated with PET across the landscape. Our analysis provides first-order estimates of the magnitudes of these sub-grid effects, as a guide for more detailed modeling and analysis.