The Effects of Surface Heterogeneity Scale on the Flux Imbalance under Free Convection

Abstract

It is well known that the available energy (i.e., the net radiation minus the ground heat flux) is often 10-30% larger than the sum of turbulent fluxes measured by the eddy-covariance method. Although field observations and previous large-eddy simulation studies have shown that surface heterogeneity can induce flux imbalance, the relationship between the flux imbalance magnitude and the surface heterogeneity scale remains to be investigated in more detail. Here we examine the flux imbalance over landscapes characterized by different surface heterogeneity scales in a dry freely convective boundary layer. We reveal that the flux imbalance initially increases with increasing surface heterogeneity scale. However, when the surface heterogeneity scale becomes larger than the boundary layer height, the surface starts to behave locally homogeneous, which leads to a lower flux imbalance. Based on large-eddy simulation results, we propose a conceptual model to explain how the domain average flux imbalance is influenced by surface heterogeneity. The flux imbalance is found to be controlled by the ratio of the boundary layer height to the Obukhov length (−z i /L), the integral length scale of vertical velocity (l w ), the mean horizontal speed (U), and the time averaging interval (T). Among these four variables, l w determines the size of turbulent coherent structures (i.e., large eddies), whereas −z i /L affects the form of these large eddies. Meanwhile, the U and T determine how many these large eddies can be sampled by the eddy covariance. This finding indicates that it may be possible to diagnose the flux imbalance using these four variables under convective conditions. Key Points: • The relation between flux imbalance and surface heterogeneity scale is investigated using large-eddy simulations and a cospectral model • A diagnostic equation for flux imbalance is proposed • The qualitative relations between flux imbalance and various factors reported in the literature can be explained by this equation

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