## 1. Introduction

[2] Understanding the space-time rainfall variability over a range of scales (from seconds to several days in time and meters to several kilometers in space) has been the subject of intensive research over the past two decades [*Georgakakos and Cramer*, 1994; *Lovejoy and Scherzter*, 2006; *Lovejoy and Allaire*, 2008; *Olsson and Berndtsson*, 1993; *Over and Gupta*, 1994]. Emphasis has been placed on concise parameterization of this variability across a range of scales exploring concepts of scale invariance and statistical renormalization [*Gupta and Waymire*, 1996; *Lovejoy and Schertzer*, 1985; *Kumar and Foufoula-Georgiou*, 1993; *Venugopal and Foufoula-Georgiou*, 1996; *Ferraris et al.*, 2003]. One issue that has not been adequately addressed is the fundamental understanding of what key physical parameters of the storm environment explain most of the observed statistical variability of rainfall. Along this direction, *Over and Gupta* [1994] examined large-scale predictors of this variability, while *Perica and Foufoula-Georgiou* [1996] focused on the storm thermodynamic environment. In that latter study, the Convective Available Potential Energy (CAPE) ahead of the storm was empirically found to relate to the scaling properties of spatial rainfall. Under an energy cascading interpretation of the spatial scaling in rainfall intensity, the above finding was interpreted as saying that the larger the instability ahead of the storm, the more turbulent the storm environment and the larger the scale-to-scale change of spatial variability in rainfall fields. In this paper we pose the question as to whether the relation of the spatial rainfall multiscale variability and physical observables can be shown more rigorously in a physical rather than empirical or statistical context.

[3] Along these lines, our idea is to evaluate if, according to the moist convective scaling theory of *Parodi and Emanuel* [2009], it is possible to adopt the raindrop terminal velocity (or a related microphysical parameter) to define a relation between physical and statistical parameters of precipitation. We test this hypothesis by analysis of high-resolution simulations of an atmosphere in radiative-convective equilibrium performed using the Weather Research and Forecasting (WRF) model and prescribing different rain terminal velocity settings corresponding to small, slowly falling drops and large, quickly falling drops, respectively. This study is specifically focused on an investigation of the dependence of some basic statistics of rainfall fields (probability distribution of convective rain cell areas, power spectra and multifractal rain intensity statistics) on the raindrop terminal velocity in deep moist convective environments.