The Shape of Averaged Drop Size Distributions

Henri Sauvageot Université.Paul Sabatier, Laboratoire d'Aérologie (URA CNRS 354), Toulouse, France

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Jean-Pierre Lacaux Université.Paul Sabatier, Laboratoire d'Aérologie (URA CNRS 354), Toulouse, France

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Abstract

The shape of averaged drop size distributions (DSD) is studied from a large sample of data (892 h) collected at several sites of various latitudes. The results show that neither the hypothesis of an exponential distribution to represent rainfall with a high rain raw (R) nor the concept of equilibrium distribution arising from the various models using the parameterization of Low and List is compatible with the observations. To describe the DSD two regions have to be distinguished: a small-drop region, for diameter D smaller than a threshold Dc, and a large-drop region, for diameter D larger than Dc. For D<Dc the distributions are strongly dependent on R and on z0, the height of fall of the rain from the base of the melting level. The decrease in the relative number of small drops with increasing R suggests that in this region the depletion of the small drops by the big ones is not totally compensated for by the input of small drops due to the collisions breakup process; there is no stationary state for D<Dc. In the big-drop region, for D>Dc, the slope of the distributions is almost independent of D. At low values of R (<20 mm h−1) it decreases when R increases, and not much depends on z0. For increasing values of R beyond about 20 mm h−1, the slope of the distributions tends toward a constant value of about 2.2–2.3 mm−1. This suggests a certain stationarity between the coalescence and collisional breakup processes in intense rainfalls. It also appears that the two regions are not much influenced by each other. The value of Dc increases with R and with z0. The relation between the radar reflectivity factor (Z) and R obtained from the averaged DSDs are close to those calculated from nonaveraged data and compatible with those proposed in the literature. The differences observed between the coefficients of Z–R relations for various types of rain are essentially due to the differences in small-drop concentration.

Abstract

The shape of averaged drop size distributions (DSD) is studied from a large sample of data (892 h) collected at several sites of various latitudes. The results show that neither the hypothesis of an exponential distribution to represent rainfall with a high rain raw (R) nor the concept of equilibrium distribution arising from the various models using the parameterization of Low and List is compatible with the observations. To describe the DSD two regions have to be distinguished: a small-drop region, for diameter D smaller than a threshold Dc, and a large-drop region, for diameter D larger than Dc. For D<Dc the distributions are strongly dependent on R and on z0, the height of fall of the rain from the base of the melting level. The decrease in the relative number of small drops with increasing R suggests that in this region the depletion of the small drops by the big ones is not totally compensated for by the input of small drops due to the collisions breakup process; there is no stationary state for D<Dc. In the big-drop region, for D>Dc, the slope of the distributions is almost independent of D. At low values of R (<20 mm h−1) it decreases when R increases, and not much depends on z0. For increasing values of R beyond about 20 mm h−1, the slope of the distributions tends toward a constant value of about 2.2–2.3 mm−1. This suggests a certain stationarity between the coalescence and collisional breakup processes in intense rainfalls. It also appears that the two regions are not much influenced by each other. The value of Dc increases with R and with z0. The relation between the radar reflectivity factor (Z) and R obtained from the averaged DSDs are close to those calculated from nonaveraged data and compatible with those proposed in the literature. The differences observed between the coefficients of Z–R relations for various types of rain are essentially due to the differences in small-drop concentration.

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