## 1. Introduction

[2] Precipitation is commonly classified in two main categories, *stratiform* and *convective*, according to the strength (convective indicating the stronger case) of the updraft motion generating atmospheric vapor condensation and eventually rainfall drops. Updraft velocities ∼2 m/s are commonly considered as the threshold separating the two cases [*Houze*, 1997]. In terms of the microphysical dynamics of drop formation, stratiform rain is characterized by aggregation and a small degree of riming, while convective rain by accretion and high degree of riming [*Steiner and Smith*, 1998]. It is worth noting that updraft velocities in dying convective cells can be of the order or smaller than 2 m/s. Thus stratiform rain can occur also in clouds of convective origin [*Houze*, 1997]. Moreover, a synoptic formation may present a mix of both types of precipitation [e.g., *Williams*, 2009].

[3] The separation between stratiform and convective precipitation is relevant for global circulation, climatological, hydrological models, and for a proper retrieval of rainfall rates from remote sensing measurements [*Steiner and Smith*, 1998]. Different criteria have been proposed for separating these two types of precipitation. Large (small) values of rainfall rate, *R*, are typically generated by convective (stratiform) rain. However there is a considerable overlap in the range of rainfall rates which may be generated by the two mechanisms, e.g., *Tokay and Short* [1996] report a range of 1–10 mm/h for 1 minute-resolution data of tropical rain.

[4] The process of aggregation, which is peculiar of stratiform precipitation, produces a thin horizontal (fixed altitude) layer of enhanced reflectivity in radar retrievals, the “bright band” [*Steiner and Smith*, 1998]. Reflectivity maps from vertically pointed radar can resolve the presence of the bright band, and help differentiating stratiform from convective precipitation [e.g., *Houze*, 1997; *Williams*, 2009]). Several criteria have indeed been developed during the years based on direct observations or statistical properties, yet the discrimination between the two types of precipitation remains somewhat “arbitrary” (see, e.g., *Lang et al.* [2003] for a review).

[5] If a large body of literature is dedicated to the difference between stratiform and convective precipitation, and in general to the time variability of the rainfall phenomenon, very few works explore the possibility of describing/capturing this variability in a parsimonious mathematical model. Efforts in this direction use 1) the “instantaneous” drop size distribution, _{I}(*D*), namely the number of drops per unit volume and diameter in an interval of time *I* which is usually the instrument time resolution [*Joss and Gori*, 1978]; 2) a rescaling by different factors of both the abscissa and the ordinate of _{I}(*D*) versus *D* to obtain the appearance of an approximately invariant shape [*Sekhon and Srivastava*, 1971; *Sempere Torres et al.*, 1994].

[6] Following this idea some studies compare “renormalized” instantaneous drop size distributions for convective and stratiform precipitation, where the two types of precipitation are separated using rainfall rates [e.g., *Maki et al.*, 2001; *Testud et al.*, 2001; *Willis*, 1984] or radar reflectivity [e.g., *Campos et al.*, 2006]. However, while *Willis* [1984] and *Testud et al.* [2001] conclude that the average curves for stratiform and convective precipitation are somewhat similar, *Maki et al.* [2001] and *Campos et al.* [2006] reach the opposite conclusion.

[7] The possibility of finding a renormalization procedure resulting in an “universal” drop size distribution is attractive for many reasons. For modeling purposes the existence of an universal distribution allows to split rainfall dynamics into two contributions: an invariant component and a contribution which can be modeled by few parameters describing the variability of the phenomenon. In this manuscript we adopt a renormalization procedure which is different in spirit and substance from that of *Sekhon and Srivastava* [1971]: 1) We consider the probability density *p*_{G}(*D*) of observing, at the ground, a drop diameter in the range *D*, *D* + *dD* instead of the concentration (*D*). 2) Instead of rescaling separately (by multiplication of two different factors) the diameter *D* and the concentration (*D*), we make a change of variable, *D* → *D*_{R}, and plot the probability density *p*_{G}(*D*_{R}) versus *D*_{R}: no rescaling of *p*_{G}(*D*_{R}) is adopted. We use data from a RD69 Joss–Waldvogel (JW) disdrometer to show that the probability density for the renormalized diameter is, within the statistical significance, invariant in stratiform and convective intervals, and also independent from a classification based on the rainfall rate range.