First geometrical path length probability density function derivation of the skylight from high-resolution oxygen A-band spectroscopy - 2. Derivationof the Levy index for the skylight transmitted by midlatitude clouds

For the first time Livy indices (gamma) of the solar light transmitted by c loudy skies at mid latitude (50 degrees N, 8.2 degrees E) are reported. The Levy index describes the dependence of the mean geometrical paths (< L-T > )of photons transmitted from cloudy skies as a function of the vertical cl oud extension (H-c) expressed by the scaling law < L-T > similar to H-c(gam ma). For a set of 33 individual cloudy sky < L-T > measurements, reported c loud types and heights, Levy indices are deduced. It is found that the infe rred Levy indices cluster into the range of 1 less than or equal to gamma l ess than or equal to 2 for "all sky" observations, and into a range 1.5 les s than or equal to gamma less than or equal to 2 for optically very thick c louds. The observations provide evidence that the cloudy sky geometrical pa th lengths are Levy distributed with the gamma value depending on the cloud morphology (the shape of individual clouds and the spatial arrangement of the clouds) but also on the internal cloud inhomogeneities, Because of a pa rticular sensitivity of our method to detect the radiative transfer (RT) ca used by clouds (rather than by the clear sky parts of the atmosphere), the inferred type of the path statistics is expected to reflect mostly the path length distribution caused by cloud inhomogeneities rather than by the clo ud morphology. Since the cloud inhomogeneities are caused by dynamic proces ses (besides other factors), the RT transfer is expected to be closely conn ected to atmospheric dynamics. From this it is concluded that the absorptio n of solar radiation in cloudy skies is connected to the dynamic state (whe ther it is stratified or convective) of the cloud cover. In particular, it is expected to be different (mostly larger) than calculated by naively assu ming homogeneous horizontally infinite cloud covers in conventional non sta tistical RT models.