Multiscale decomposition for heterogeneous land‐atmosphere systems

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.