Retrieval of urban boundary layer structures from Doppler lidar data. Part II: Proper orthogonal decomposition

The proper orthogonal decomposition technique is applied to 74 snapshots of 3D wind and temperature fields to study turbulent coherent structures and their interplay in the urban boundary layer over Oklahoma City, Oklahoma. These snapshots of data are extracted from single-lidar data via a four-dimensional variational data assimilation technique. The total velocities and fluctuating temperature are used to construct the data matrix for the decomposition; thus the first eigenmode represents the temporal mean of these data. Roll vortices with a wavelength-height ratio of 3.2 are identified in the first, most energetic eigenmode and are attributed to the inflection-point instability. The second and third spatial eigenmodes also exhibit roll characteristics with different time and length scales, resulting in clockwise- and counterclockwise-rotating roll vortices above the airport and the central business districts. Their positive correlation with temperature fluctuation suggests that those roll structures are driven by thermal as well as wind shear. Their limited horizontal extent seems to coincide with the path of the Oklahoma River. With decreasing rank, coherent structures undergo a transition from roll to polygon patterns. A localized downdraft or updraft located above a cluster of restaurants is captured by the fourth eigenmode. In the capping inversion layer, gravity wave eigenmodes are observed and may be attributed to convection waves. The representation of instantaneous snapshots by high-ranking eigenmodes is then examined by reconstruction of reduced-order fields. It is found that the first four eigenmodes are sufficient to capture the overall characteristics of the 74 snapshots of data.