Averaging over spatiotemporal heterogeneity substantially biases evapotranspiration rates in a mechanistic large-scale land evaporation model

Abstract

Evapotranspiration (ET) influences land-climate interactions, regulates the hydrological cycle, and contributes to the Earth's energy balance. Due to its feedback to large-scale hydrological processes and its impact on atmospheric dynamics, ET is one of the drivers of droughts and heatwaves. Existing land surface models differ substantially, both in their estimates of current ET fluxes and in their projections of how ET will evolve in the future. Any bias in estimated ET fluxes will affect the partitioning between sensible and latent heat and thus alter model predictions of temperature and precipitation. One potential source of bias is the so-called "aggregation bias"that arises whenever nonlinear processes, such as those that regulate ET fluxes, are modeled using averages of heterogeneous inputs. Here we demonstrate a general mathematical approach to quantifying and correcting for this aggregation bias, using the GLEAM land evaporation model as a relatively simple example. We demonstrate that this aggregation bias can lead to substantial overestimates in ET fluxes in a typical large-scale land surface model when sub-grid heterogeneities in land surface properties are averaged out. Using Switzerland as a test case, we examine the scale dependence of this aggregation bias and show that it can lead to an average overestimation of daily ET fluxes by as much as 10% across the whole country (calculated as the median of the daily bias over the growing season). We show how our approach can be used to identify the dominant drivers of aggregation bias and to estimate sub-grid closure relationships that can correct for aggregation biases in ET estimates, without explicitly representing sub-grid heterogeneities in large-scale land surface models.