Surface heterogeneity is present on every scale of the land surface. However, its role in the exchange processes between the land surface and the atmosphere is still an open question. In this paper, we present a method, which combines the decomposition of land-surface heterogeneity into fine and coarse structures with the quantification of the structures using information entropy. The resulting entropy spectrum allows the assessment of the amount of information on different scales. The wavelet transformation and the most frequent-value method are used as filters for the decomposition. We also derive an analytical formula for estimation of the probability density function (PDF) of filtered random surface parameters using the most frequent-value method. By analyzing the entropy spectrum of synthetic data, we derive rules for the interpretation of the entropy spectrum. We then apply them to real data and appraise, which scale of the heterogeneity is important for land surface and atmosphere interactions.
The land-atmosphere system is characterized by pronounced land surface heterogeneity and vigorous atmospheric turbulence both covering a wide range of scales. The multiscale surface heterogeneities and multiscale turbulent eddies interact nonlinearly with each other. Understanding these multiscale processes quantitatively is essential to the subgrid parameterizations for weather and climate models. In this paper, we propose a method for surface heterogeneity quantification and turbulence structure identification. The first part of the method is an orthogonal transform in the probability density function (PDF) domain, in contrast to the orthogonal wavelet transforms which are performed in the physical space. As the basis of the whole method, the orthogonal PDF transform (OPT) is used to asymptotically reconstruct the original signals by representing the signal values with multilevel approximations. The "patch" idea is then applied to these reconstructed fields in order to recognize areas at the land surface or in turbulent flows that are of the same characteristics. A patch here is a connected area with the same approximation. For each recognized patch, a length scale is then defined to build the energy spectrum. The OPT and related energy spectrum analysis, as a whole referred to as the orthogonal PDF decomposition (OPD), is applied to two-dimensional heterogeneous land surfaces and atmospheric turbulence fields for test. The results show that compared to the wavelet transforms, the OPD can reconstruct the original signal more effectively, and accordingly, its energy spectrum represents the signal's multiscale variation more accurately. The method we propose in this paper is of general nature and therefore can be of interest for problems of multiscale process description in other geophysical disciplines.
Atmosphere-land interactions simulated by an LES model are evaluated from the perspective of heterogeneity propagation by comparison with airborne measurements. It is found that the footprints of surface heterogeneity, though as 2D patterns can be dissipated quickly due to turbulent mixing, as1D projections can persist and propagate to the top of the atmospheric boundary layer. Direct comparison and length scale analysis show that the simulated heterogeneity patterns are comparable to the observation. The results highlight the model's capability in simulating the complex effects of surface heterogeneity on atmosphere-land interactions.Key words: atmosphere-land interaction, heterogeneity, large-eddy simulation Citation: Liu, S. F., M. Hintz, and X. L. Li, 2016: Evaluation of atmosphere-land interactions in an LES from the perspective of heterogeneity propagation.
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