Internal variability and pattern identification in cirrus cloud structure: The Fokker-Planck equation approach

Using 35-GHz millimeter wave radar observations collected at the Southern Great Plains site of the Atmospheric Radiation Measurements (ARM) program, we study physical processes in cirrus cloud layers having different stratifications. The time-dependent probability distribution functions of the backscattering cross section within different layers in the cloud describe the dynamics of the pertinent physical processes. The time-dependent tails of the probability distribution functions provide the signature of intermittency characterizing turbulent flows. In the framework of the Fokker-Planck equation approach, we derive the behavior of the drift D⁽¹⁾ and diffusion D⁽²⁾ terms that characterize the deterministic and stochastic parts, respectively, of the dynamics of the probability distribution functions directly from the time series of observed backscattering cross section. We derive the Langevin equation that governs the temporal evolution of the backscattering cross-section signal in cloud layers having different stratification. Finally, we ascertain that the drift γ and diffusion β coefficients of the backscattering cross-section signal in the upper well-mixed, neutrally stratified layer of the cirrus cloud satisfy the relationship γ = 2β, which is valid for fully developed turbulence owing to the Kolmogorov -4/5 law.