Abstract
Abstract. Most Earth system models are based on grid-averaged 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.
Highlights
The atmosphere integrates the fluxes of water, energy, and trace gases that it receives from the spatially heterogeneous landscape beneath it
Because lateral transfer will necessarily be driven by gravity, the analysis shown in Fig. 6b leads directly to a simple general rule: wherever higher locations are more humid, one should expect lateral redistribution to result in a net increase in ET, and wherever higher locations are more arid, lateral redistribution should result in a net decrease in ET
The maximum possible increase in ET from lateral redistribution exactly equals the heterogeneity bias calculated in the preceding section: both are equal to the ET function at the average P and potential evapotranspiration (PET) (e.g., Eq 16 in the case of two columns), minus the average of the ETs calculated for the individual columns using their individual P and PET values
Summary
The atmosphere integrates the fluxes of water, energy, and trace gases that it receives from the spatially heterogeneous landscape beneath it. Studies with nested high-resolution models demonstrate that this overestimation bias is largest where topographic effects play a major role (Giorgi and Avissar, 1997; Pope and Stratton, 2002; Boyle and Klein, 2010; Bacmeister et al, 2014) Another potential source of bias in Earth system models arises from their neglect of surface and subsurface flows within and between grid cells. The Earth system modeling community has recognized the need to determine how sub-grid heterogeneity and lateral redistribution affect grid-scale evapotranspiration rates as viewed from the atmosphere, and to develop schemes that can efficiently account for these effects in land surface models (Clark et al, 2015). Estimates of the potential effects of sub-grid heterogeneity and subsurface lateral redistribution on ET fluxes from heterogeneous landscapes, as seen from the atmosphere
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