Ole Peters, J. David Neelin and Stephen W. Nesbitt
J. Atmos. Sci., 2008, submitted.
Preprint (PDF 1.1MB)
Abstract. Size distributions and other geometric properties of mesoscale convective sys- tems (MCS), identified as clusters of adjacent pixels exceeding a precipitation threshold in satellite radar images, are examined with respect to a recently iden- tified critical range of water vapor. Satellite microwave estimates of column water vapor and precipitation show that the onset of convection and precipitation in the tropics can be described as a phase transition, where the rain rate and likeli- hood of rainfall suddenly increase as a function of water vapor. This is confirmed in Tropical Rainfall Measuring Mission radar data used here. As is known from percolation theory, cluster properties are highly sensitive to changes in the rain- fall probability, and thereby to changes in the water vapor. To confirm this we categorize clusters by their prevalent water vapor. As expected, mean cluster size and radius of gyration strongly increase as the critical water vapor is approached from below. In the critical region we find scale-free size distributions spanning several orders of magnitude. Large clusters are typically from the critical re- gion: at low water vapor most clusters are small, and super-critical water vapor values are too rare to contribute much. The perimeter of the clusters confirms previous observations in field- and model-data of robust non-trivial scaling. The well-known area-perimeter scaling is fully compatible with the quantitative pre- diction from the plausible null-model of gradient percolation, where the accessible hull is a fractal object with dimension 4/3.
Citation. Peters, O., J. D. Neelin, and S. W. Nesbitt: Mesoscale convective systems and critical clusters. J. Atmos. Sci., submitted, Feb. 2008.
Acknowledgements. This work was supported in part by the National Science Foundation grant ATM-0645200, National Oceanic and Atmospheric Administration grant NA05OAR431-1134 (JDN and OP) and NA07OAR431-0214 (SN) and the Guggenheim Foundation (JDN). DN thanks J. L. Lin for asking what the PN results imply for cluster size distributions. OP would like to thank G. Pruessner, M. Gastner, and B. Oborny for helpful discussions on a related problem in ecology. We thank B. Stevens for discussions.