Time correlations and 1/f behavior in backscattering radar reflectivity measurements from cirrus cloud ice fluctuations

The state of the atmosphere is governed by the classical laws of fluid motion and exhibits correlations in various spatial and temporal scales. These correlations are crucial to understand the short- and long-term trends in climate. Cirrus clouds are important ingredients of the atmospheric boundary layer. To improve future parameterization of cirrus clouds in climate models, it is important to understand the cloud properties and how they change within the cloud. We study correlations in the fluctuations of radar signals obtained at isodepths of winter and fall cirrus clouds. In particular, we focus on three quantities: (1) the backscattering cross-section, (2) the Doppler velocity, and (3) the Doppler spectral width. They correspond to the physical coefficients used in Navier Stokes equations to describe flows, i.e., bulk modulus, viscosity, and thermal conductivity. In all cases we find that power law time correlations exist with a crossover between regimes at about 3 to 5 min. We also find that different type of correlations, including 1/f behavior, characterize the top and the bottom layers and the bulk of the clouds. The underlying mechanisms for such correlations are suggested to originate in ice nucleation and crystal growth processes.