Fractal Characteristics of Ice-Supersaturated Regions in the Tropopause Region of the northern midlatitudes

Ice supersaturated regions (ISSRs) are air masses in the upper troposphere and lower stratosphere (UTLS) where relative humidity with respect to ice (RHi) exceeds 100 %, i.e. regions with enhanced water vapor concentrations. These are potential formation regions of cirrus clouds and contrails. While the impact of cloud free regions of enhanced water vapor on the planetary radiation balance is small to negligible, thin cirrus clouds and aircraft induced contrail cirrus formed within them might have a large radiative impact. Understanding the characteristics of ISSRs, including their geometry and seasonal variability, is essential for improving atmospheric models in representing ice clouds correctly. While ISSR’s path-length statistics, i.e. 1D characteristics, have been studied, their geometric properties, particularly fractal properties as self-similarity, and their seasonal variability remain largely unexplored. We identify ISSRs using ERA5 reanalysis data spanning from 2010 to 2020 at three pressure levels. An area-perimeter method is employed to compute fractal dimensions. The results reveal slopes equaling fractal dimensions with high coefficients of determination, strongly suggesting that ISSRs in the UTLS exhibit fractal behavior. A seasonal cycle in both dimension and total count of observed ISSRs was found. We hypothesize that this is caused by the seasonal variation of convective and frontal activity. We further analyzed the latitudinal and longitudinal spans of ISSRs and the path lengths of modeled flights along commercial flight routes. The results of the horizontal extensions are consistent with the fractal properties, and suggest distinct formation processes for ISSRs.