Scale-by-scale analysis of probability distributions for global MODIS-AQUA cloud properties: how the large scale signature of turbulence may impact statistical analyses of clouds

Means, standard deviations, homogeneity parameters used in models based on their ratio, and the probability distribution functions (PDFs) of cloud properties from the MODerate resolution Infrared Spectrometer (MODIS) are estimated globally as function of averaging scale varying from 5 to 500 km. The properties – cloud fraction, droplet effective radius, and liquid water path – all matter for cloud-climate uncertainty quantification and reduction efforts. Global means and standard deviations are confirmed to change with scale. For the range of scales considered, global means vary only within 3% for cloud fraction, 7% for liquid water path, and 0.2% for cloud particle effective radius. These scale dependences contribute to the uncertainties in their global budgets. Scale dependence for standard deviations and generalized flatness are compared to predictions for turbulent systems. Analytical expressions are identified that fit best to each observed PDF. While the best analytical PDF fit to each variable differs, all PDFs are well described by log-normal PDFs when the mean is normalized by the standard deviation inside each averaging domain. Importantly, log-normal distributions yield significantly better fits to the observations than gaussians at all scales. This suggests a possible approach for both sub-grid and unified stochastic modeling of these variables at all scales. The results also highlight the need to establish an adequate spatial resolution for two-stream radiative studies of cloud-climate interactions.