A numerical analysis of aggregation error in evapotranspiration estimates due to heterogeneity of soil moisture and leaf area index

Abstract

Land Surface Models which determine evapotranspiration (ET) by neglecting the sub-grid heterogeneity of land-atmosphere parameters will cause aggregation biases in spatially-averaged ET estimates, considering the nonlinear dependences of ET on the heterogeneous land-atmosphere parameters. One frequently adopted strategy clusters the heterogeneous surface within a model grid into several tiles, assumed to be homogeneous, usually based on high-resolution land cover data. While the differences in bulk-averaged parameters between different tiles are considered, the heterogeneity within each tile is neglected. This study evaluated in detail the aggregation biases in the tile mean ET estimates due to applying bulk-averages of the Saturation degree of surface Soil Moisture (SSM) and Leaf Area Index (LAI) for each tile through numerical experiments. Four types of Probability Distribution Function (PDF) were used to simulate different scenarios on the heterogeneity (within a tile) of SSM and LAI, i.e., from water scarcity to wet, and from sparse to dense vegetation covered surfaces. Aggregation bias was calculated by comparing ET estimates based on bulk-averaged SSM and LAI with the one obtained by aggregation of the flux estimates based on the PDFs, which complies with energy conservation. In addition, a wide range of meteorological conditions was applied in our numerical experiments and the impacts were evaluated by binning results according to the reference ET (ET
₀
). We found that potentially significant bias can be found in semi-arid areas. Neglecting the actual spatial variability of both SSM and LAI within tiles can lead to both large relative error (> 20%) and absolute error (> 1 mm/day) in the estimated ET. A negative bias is expected at low ET / ET
₀
and a positive bias is expected at large ET / ET
₀
, regardless of climate conditions (i.e., ET
₀
).