Fractal dimension of rainbands over Hilly terrain

Abstract

The fractal geometry of nature has been discerned in a bewildering variety of places. Perhaps the most fundamental property is the existence of structure at almost every space or time scale. It is generally accepted today for convective cloud and rain areas to have fractal structure with dimensionD∼4/3 for many orders of magnitude in area. During the ALPEX-SOP the Vienna airport weather radar's echoes on a PPI display were evaluated within a range of 150 km. The results indeed confirm the general thesis, but sometimes exhibit considerable deviations both in space and in time from the expected fractal dimension. AsD ought to be determined by the physical processses (includinginteraction with orography) which shape clouds, we have split the data set according to different orographic regions (upstream side, ridge, lee-side), and weather process types (prefrontal, frontal, postfrontal; type of organization of precipitation). Hence follows a moderate reduction in fractal dimension on the upwind side, a substantial growth ofD on the lee-side, especially in situations with strong vertical shear of flow velocities, e.g. characteristic of narrow cold-frontal precipitation bands. There is evidence that the individual change in shape of clouds and precipitation patterns is related to mesoscale variability of physical parameters involved. Furthermore there might be a possibility to interpret this transitory modification from the rule during the flow over hills in terms of turbulence alternation in the boundary layer.