Analysis of patterns of atmospheric motions at different scales

Applications and limitations of fractal concepts to the study of atmospheric motions on scales of tens of meters to a few kilometers and the use of multiresolution feature analysis (MFA) for estimating fractal dimension are described. MFA applies specified correlation filters to a data field at different resolutions to allow the analyst to choose physically significant features for filtering. The scaling of the intensities of the spatial peaks in the filter outputs at the different scales are used to define fractal properties. MFA was extended from two-dimensional scalar applications to three-dimensional vector fields, and applied to observations of motions in sheared atmospheric boundary layers obtained by two National Atmospheric and Oceanic Administration Doppler radar systems (reduced to Cartesian coordinates by Schneider at the University of Oklahoma), and to a corresponding large eddy simulation (LES) data from Costigan and coworkers at Colorado State University. MFA requires definition of physically significant features, that take the form of small scale patterns of motion. Statistical techniques similar to principal component analysis were applied to small subvolumes of data to identify motion patterns that could be used as filters. These small scale patterns differ from case to case, depending on the prevailing boundary layer stability. The most important features exhibit local enhancement and weakening of shear for the more stable conditions, while vortex-like features, tilted in the direction of the shear, are also important for unstable cases. Observed spatial variability of feature intensity patterns at different scales were compared with the LES results, to help understand the energy cascade. Observations suggest a support dimension between 2.3 and 2.5 for the unstable atmosphere's turbulent motions on spatial scales from about 200 m to 1000 m. Corresponding LES values indicate less intermittency.