Fine structure of cloud droplet concentration as seen from the Fast-FSSP measurements. Part I: Method of analysis and preliminary results

A statistical analysis of a series of droplet arrival times measured by the Fast Forward-Scattering Spectrometer Probe (FSSP) during aircraft flights in cumulus clouds was conducted. The main purpose of the analysis was to determine whether droplet concentration fluctuates at small scales on the order of a few centimeters or whether these fluctuations are negligible as compared with the mean concentration. In the analysis, the series of droplet arrival times is regarded as a generalized Poisson random process with time-dependent (or space dependent) parameters. The method developed is based on the representation of droplet concentration in a cloud along the aircraft track as the sum of three components: average droplet concentration in a cloud, large-scale fluctuations of droplet concentrations described by the Fourier series, and a small-scale noncoherent fraction of concentration fluctuation characterized by the energy spectrum and the correlation function. The efficiency of the method to estimate the amplitude and spatial characteristics of small-scale droplet concentration fluctuations and to calculate the profile of large-scale components of droplet concentration along the aircraft track was carefully tested using model-simulated series of droplet arrival times. The method was used to analyze a measurement sample in a cumulus cloud on a 350-m segment. The properties of droplet concentration were calculated both over the whole cloud traverse and within the adiabatic core. The results of the calculations show the existence of pronounced small-scale droplet concentration fluctuations in the case study. The rms of small-scale droplet concentration fluctuations was estimated to be about 31% of the mean values of droplet concentration both over the whole cloud and in a more homogeneous adiabatic core. The power spectrum shows that fluctuations with spatial scales within the 0.5-5-cm range contain over 80% of the energy of small-scale fluctuations.