Scale-Dependent Estimability of Turbulent Flux in the Unstable Surface Layer for Land Surface Modeling

Surface flux estimation is essential to land surface modeling in earth system models. In practice, parameterizations of surface turbulent fluxes are almost all based on the similarity theory. That is, the grid or subgrid mean surface-layer flow is assumed at equilibrium with the underlying earth surface, and therefore some empirical relations can be used to estimate surface fluxes. In this paper, scale-dependent estimability of turbulent flux in the unstable surface layer is systematically investigated based on high-resolution large-eddy simulation data over a flat and homogeneous domain, representing a typical land surface modeling grid. It is found that turbulent flow in the unstable surface layer inherently fluctuates over a wide range of scales. This kind of fluctuation affects the steady-state relations between mean atmospheric quantities and underlying earth surface, and hence affects the estimability of surface fluxes. Sensitivity tests show that the relative root mean square error of the estimated surface friction velocity for a subdomain generally increases as the subdomain becomes smaller. The error can be as high as 35% as the subdomain size decreases to the order of the surface layer height. To achieve an error of 10% for all cases, the subdomain size should be at least on the order of the boundary layer height. These findings imply that estimability-based strategies may be needed for representing subgrid heterogeneity for surface flux estimation in land surface modeling.