Structural characteristics of rain fields

Abstract

[1] This paper analyzes the shape of rain area size distributions (RASDs) observed by radar in tropical and midlatitude regions. The rain area is defined, with respect to a rain threshold t, as the area, inside a contour, where the rain rate is higher than t. The size considered is the diameter of the equivalent circular area D. The reflectivity peaks inside the rain areas are numbered and the rain areas put together by classes having the same peak number. The size distributions of the rain areas containing the same number of peaks p are well fitted by lognormal functions, the parameters of which, m p and s p , are weakly dependent on the conditions of the peak determination. The parameters m p and s p are found to be linked by a power relation. For D < 6 km most of the rain areas are single peaked. The RASD without peak number distinction is a lognormal mixture. Using the relations obtained for m p , s p , and the rain area number as functions of p enables one to simulate RASDs with results in good agreement with the observations. Because of the limitation in the radar sampling at both ends of the RASD and the decrease of area number with increasing size, the radar-observed RASDs are severely truncated. The possibility of an approximate fitting of the truncated RASD with diverse functions is discussed. At the intermediary values of the threshold, i.e., for t ranging between 3 and 12 mm h À1 , where the RASD is easiest to compute, the slope of these truncated distributions is not strongly dependent on the threshold. This slope appears not to be very sensitive to the minimum and maximum distances bounding the domain where the rain field is observed. The RASD is found to be sloping more over sea than over land. The slope of the RASDs shows a small diurnal variation but no significant annual variation. The ''perimeter to area'' (fractal) dimension of the rain area for the sample without peak number distinction is around 1.35. Single-peaked and multipeaked rain areas have different perimeter to area dimensions, $1.23 and 1.38, respectively. These values are almost independent from the threshold and from the location of the domain observed.

Comparing Simulated Size Distributions of Precipitation Systems at Different Model Resolution

“…Previous studies revealed that lognormal distributions were frequently observed (López 1977;Houze and Cheng 1977;Mapes and Houze 1993;Mesnard and Sauvageot 2003;Cetrone and Houze 2006;Holder et al 2008). Other functional forms such as a power law (Machado and Rossow 1993), a double power law (Benner and Curry 1998), and an exponential form (Mesnard and Sauvageot, 2003) were also reported.…”

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 2. Statistical modeling of the rain rate field

“…Mesnard and Sauvageot [2003] answered this question and showed that the RCSD is in fact best fitted by a lognormal function, whose modal value is less than about 2 km, that is located at a diameter smaller than the minimum size that can be resolved by most of the radars at the farthest part of their observation area. In such a way, (2) corresponds to the analytical fitting of a (lognormal) distribution truncated on the left, at size larger than the modal value, so that the validity domain of (2) has to be restrained to the diameter interval 2 km D 20 km.…”

“…[15] Many authors [Dennis and Fernald, 1963;Miller et al, 1975;Konrad, 1978;Goldhirsh and Musiani, 1986;Tenorio et al, 1995;Sauvageot et al, 1999;Mesnard and Sauvageot, 2003] have considered that rain cells can be approximated by a circular shape. The diameter of the circular cell of equivalent area is used as a characteristic measure of the rain cell size.…”

HYCELL—A new hybrid model of the rain horizontal distribution for propagation studies: 1. Modeling of the rain cell

“…Figure 2 can be seen as a typical example. Nevertheless, from radar observations of rain fields in tropical and midlatitudes areas, Mesnard and Sauvageot [2003] show that 95% of the rain cells having an equivalent diameter smaller than 5 km -which represents the majority of the cells -are single-peaked. Moreover, they show that, in average, the relative frequency of the rain cell as a function of their peak number p, that is N A (p), is well-approximated by the power distribution:…”

“…Thus, for example, many authors have developed empirical or statistical models of rain cell size distribution based on radar measurements [Konrad, 1978;Goldhirsh and Musiani, 1986;Crane, 1996;Mesnard and Sauvageot, 2003].…”