Number Fluxes in Equilibrium Raindrop Populations: A Markov Chain Analysis

Marc P. Valdez Department of Atmospheric Sciences, University of Arizona, Tucson, AZ 85721

Search for other papers by Marc P. Valdez in
Current site
Google Scholar
PubMed
Close
and
Kenneth C. Young Department of Atmospheric Sciences, University of Arizona, Tucson, AZ 85721

Search for other papers by Kenneth C. Young in
Current site
Google Scholar
PubMed
Close
Full access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

Four raindrop distributions at equilibrium are studied using a Markov chain model adapted from the cloud parcel model of Young. The model uses collisional drop breakup as specified by Low and List. The shape of the equilibrium distributions is determined by the birth and death fluxes of drops, the expected lifetimes of the drops, and at diameters greater than 1.5 mm, by the net flux of drops from size to size. The shape of the distributions is sensitive to the fraction of mass lost by the colliding drops in sheet breakup.A proposition inspired by Marshall and Palmer, that exponential spectra result from increasing chances of drop identity loss with increasing diameter, is found to be incomplete. Of greater importance is an exponential decrease with diameter of drop births. A constant N0 among observed raindrop distributions may result from the different stage of evolution each distribution represents. At low liquid-water contents (LWCs), distributions are far from equilibrium and reflect the cloud environment (large N0). At low LWCs, N0 will be inversely proportional to rain intensity. At higher LWCs, distributions are closer to equilibrium, where N0 is proportional to LWC. The decline of N0 with higher LWCs may match the increase of N0 resulting with greater maturity, creating the appearance of a constant N0. Due to the extreme times and LWCs required, raindrop distributions will never achieve complete equilibrium. Difficulties with the Low and List parameterizations strongly suggest their usefulness may be limited.

Abstract

Four raindrop distributions at equilibrium are studied using a Markov chain model adapted from the cloud parcel model of Young. The model uses collisional drop breakup as specified by Low and List. The shape of the equilibrium distributions is determined by the birth and death fluxes of drops, the expected lifetimes of the drops, and at diameters greater than 1.5 mm, by the net flux of drops from size to size. The shape of the distributions is sensitive to the fraction of mass lost by the colliding drops in sheet breakup.A proposition inspired by Marshall and Palmer, that exponential spectra result from increasing chances of drop identity loss with increasing diameter, is found to be incomplete. Of greater importance is an exponential decrease with diameter of drop births. A constant N0 among observed raindrop distributions may result from the different stage of evolution each distribution represents. At low liquid-water contents (LWCs), distributions are far from equilibrium and reflect the cloud environment (large N0). At low LWCs, N0 will be inversely proportional to rain intensity. At higher LWCs, distributions are closer to equilibrium, where N0 is proportional to LWC. The decline of N0 with higher LWCs may match the increase of N0 resulting with greater maturity, creating the appearance of a constant N0. Due to the extreme times and LWCs required, raindrop distributions will never achieve complete equilibrium. Difficulties with the Low and List parameterizations strongly suggest their usefulness may be limited.

Save