Spatial statistics of marine boundary layer clouds
G. M. Lewis, P. H. Austin and M. Szczodrak
Journal of Geophysical Research 109, D04104, doi:10.1029/2003JD003742, 2004.

Abstract

An analysis is presented of the structure functions and scalar spectra for 25 satellite-derived marine stratocumulus cloud optical depth fields. The scenes, which cover a horizontal domain of 58 $\times$ 58 km at a resolution of 28.5 m, are partitioned into two ensembles based on cloud fraction. For the fully cloudy scenes, although there is wide scene-to-scene variability, both the average isotropic scalar spectrum and the average isotropic second-order structure function exhibit power-law behavior over approximately two decades, with scale-invariant exponents equal to those expected for inertial-subrange passive tracer fluctuations. Higher-order structure functions show anomalous scaling that closely matches that observed for wind-tunnel temperature fluctuations and for other fully cloudy observations. The partly cloudy scenes, while scaling, show different behavior. The average isotropic second-order structure function and average isotropic scalar spectrum have scale-invariant exponents that are significantly smaller than those of the fully cloudy scenes, and the analysis of the higher-order structure functions indicates that the field has much more intermittent fluctuations than the fully cloudy scenes. Fits to random cascade models for the fully cloudy scenes show that the increment statistics are consistent with an underlying lognormal distribution. For the partly cloudy scenes, a divergence of higher-order moments is predicted, indicating that the field fluctuations are necessarily derived from fat-tailed distributions, and that there will be significant realization dependence of the measured statistics. In addition, the presence of long-range correlations in all the data predicts that single-point histograms of the field values will have significant scene-to-scene variability, or equivalently, the use of spatial averages in the approximation of the parameters of the single-point probability density function of the field will result in random fluctuations of the estimated parameters.

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