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

For the first time Levy indices (γ) of the solar light transmitted by cloudy skies at mid latitude (50°N, 8.2°E) are reported. The Levy index describes the dependence of the mean geometrical paths ( ) of photons transmitted from cloudy skies as a function of the vertical cloud extension (Hc) expressed by the scaling law ∼ Hcγ. For a set of 33 individual cloudy sky measurements, reported cloud types and heights, Levy indices are deduced. It is found that the inferred Levy indices cluster into the range of 1 ≤ γ ≤ 2 for “all sky” observations, and into a range 1.5 ≤ γ ≤ 2 for optically very thick clouds. The observations provide evidence that the cloudy sky geometrical path lengths are Levy distributed with the γ 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 particular sensitivity of our method to detect the radiative transfer (RT) caused 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 cloud morphology. Since the cloud inhomogeneities are caused by dynamic processes (besides other factors), the RT transfer is expected to be closely connected to atmospheric dynamics. From this it is concluded that the absorption of solar radiation in cloudy skies is connected to the dynamic state (whether it is stratified or convective) of the cloud cover. In particular, it is expected to be different (mostly larger) than calculated by naively assuming homogeneous horizontally infinite cloud covers in conventional non statistical RT models.