CloudSat Cloud Length, Thickness Distributions Again Confirm the 23/9 (2.55 D) Scaling, Stratified, Turbulence Model

Nearly 100 years ago, Richardson proposed that his “scaling first”, 4/3 law of turbulent advection holds from dissipation up to planetary scales. Starting in the 1960s - due primarily to its theoretical simplicity - the atmosphere was instead modelled as an “isotropy first” hybrid of isotropic 2D and isotropic 3D turbulence. In the 1980's Schertzer and Lovejoy pointed out that since the atmosphere is stratified, scaling first implies different horizontal and vertical scaling exponents and proposed the ratio = 5/9 implying an in-between dimension $D=2+5/9= 23/9=2.55\ldots$ . By 2013 (the review [1]), the (meagre) aircraft support for the isotropic first model had been shown to be spurious, while numerous scaling first analyses (precipitation, aerosols, cloud densities, horizontal wind) vindicated Richardson and confirmed the 23/9D model over most of the horizontal and vertical ranges. I discuss new analyses of CloudSat cloud length distributions up to ≈ 2000 km (data from [2]) that yield the estimate $D=2.53\pm 0.02$ giving even more support for Richardson and the 23/9D model and excluding the (still) fashionable isotropy first ( $D=2$ , large, $D=3$ , small) model at the level of many, many, many standard deviations. Applications to remote pollution modelling and measurements are also discussed.