Empirical Orthogonal Function Analysis of the Weakly Convective Atmospheric Boundary Layer. Part I: Eddy Structures

Abstract

Three-dimensional empirical orthogonal functions (EOFs), representing atmospheric turbulence structures, are determined from a large-eddy simulation of a weakly convective, planetary boundary layer. The method of analysis is based on Lumley's proper orthogonal decomposition (POD) but has been extended to include temperature as well as velocity structure. The horizontal domain of the simulation is a square with side length equal to 30 times the inversion height in order to allow for the formation of multiple large-scale structures. The geostrophic wind is 22.5 m s?1 and the surface temperature flux is 0.03 K m s?1. Among the structures revealed by the analysis are longitudinal roll vortices, apparently in both inflection-point and thermal modes, and gravity waves in the capping temperature inversion. Modes associated with wave breaking and entrainment at the inversion may also be present. Spatially compact characteristic structures (thermal plumes) are constructed from the EOFs using a maximum-spatial-compactness method, and the resulting structures are compared with the simpler spatial compositing (conditional sampling) method. The two methods are found to give very similar results in this case, hence leading to the conclusion that the 3D EOF analysis is best suited to studying quasi-periodic structures such as rolls and gravity waves, whereas compositing is best suited to studying spatially compact structures such as the plumes.