## 1. Introduction

[2] In recent years, the formalism of nonextensive statistical mechanics, first introduced by *Tsallis* [1988] and later further developed by others [*Abe*, 2000; *Abe et al.*, 2001; *Tsallis et al.*, 1998], has gained considerable interest [*Beck*, 2000, 2001a, 2001b, 2001c, 2002a, 2002b, 2002c, 2004; *Arimitsu and Arimitsu*, 2000a, 2000b, 2001, 2002, 2006; *Wilk and Wlodarczyk*, 2000; *Daniels et al.*, 2004]. The new theoretical approach is suitable to treat physical systems of sufficient complexity that cannot maximize the usual Boltzmann-Gibbs-Shannon (BGS) entropy, the latter leading to the usual statistical mechanics. In such a case, the system maximizes some other, more general entropy measure, such as the Tsallis entropies _{q}, which have the BGS as a limit. Various reasons may cause some physical systems not to maximize the BGS entropy, for example, long-range correlations, multifractality [*Lyra and Tsallis*, 1998; *Campos Velho et al.*, 2001; *Meson and Vericat*, 2002; *Arimitsu and Arimitsu*, 2000a, 2000b, 2006], or simply the fact that the system is not in equilibrium owing to some external forcing [*Tsallis and Bukman*, 1996]. Recently it has been shown that nonextensive statistical mechanics is particularly useful in describing two-dimensional Eulerian turbulence [*Boghosian*, 1996] and the stochastic properties of fully developed turbulent flows [*Beck*, 2000, 2001a, 2001b, 2001c, 2002a, 2002c, 2004; *Beck et al.*, 2001; *Arimitsu and Arimitsu*, 2000a, 2000b, 2001; *Ramos et al.*, 2001a; *Bolzan et al.*, 2002], including dislocation motion in defect turbulence in inclined layer convection [*Daniels et al.*, 2004].

[3] In this study, we apply the Beck dynamical model [*Beck*, 2000, 2001a, 2002a] to liquid water path fluctuations in stratus clouds in the framework of nonextensive statistical mechanics. As introduced to describe fully developed turbulence, the Beck dynamical model aims neither to solve the turbulence problem nor to reproduce fully the spatiotemporal dynamics of the Navier-Stokes equations, but rather to provide a simple model that captures some of the most important statistical properties of the phenomena in an analytically tractable manner [*Beck*, 2004].

[4] Stratus overcast conditions are associated with a neutral boundary layer. The turbulence in such a layer is generated predominately by shear production from the atmosphere toward the Earth's surface. In classical studies, the phenomenology of turbulence has been described by self-similar cascades, in which an identical, scale-invariant step is repeated from large scales to small ones, as the small ones produce even smaller ones until the turbulent flow energy gets dissipated on the smallest scale [*Mandelbrot*, 1974]. More realistic description of turbulence is achieved by generalization of this approach to anisotropic scaling and multiplicative cascade models [*Schertzer and Lovejoy*, 1987]. Cascade processes generically give rise to multifractals. The resulting multifractal behavior of a random variable is scale invariant and can be determined either by the scaling of its probability distribution functions or by the scaling of its structure functions. In hydrodynamics, the velocity structure functions are expected to exhibit multiaffine scaling, for example, nonlinear scaling of the structure function exponents [*Frisch*, 1995].

[5] In contrast, the probability distribution functions that are obtained within the nonextensive statistical mechanics approach are not scale invariant [*Tsallis*, 1988]. The Beck dynamical model in the framework of Tsallis statistics describes the evolution of the time-dependent probability distribution functions of a random variable for different delay times [*Beck*, 2000, 2001a]. The purpose of this study is to present empirical evidence that the probability distribution functions of the liquid water path fluctuations in stratus clouds are time-dependent and their evolution can be sufficiently well described in the framework of Tsallis statistics.