Lidar data remote sensing of aerosols and anisotropic space-time generalizations of Corrsin-Obukov and Kolmogorov laws

We use state-of-the-art lidar data of atmospheric aerosols in order to obtain a direct scale by scale characterization of atmospheric stratification. We analyze 2D vertical-horizontal and 2D vertical-time cross section data sets spanning 3 orders of magnitude in scale in horizontal, vertical and time. We find that for both cirrus and aerosols that anisotropic, multifractal extensions of the classical Corrsin-Obukhov law for passive scalars accurately follow the theoretical (anisotropic) scalings predicted by the 23/9D atmospheric model proposed over 20 years ago. This model assumes that energy fluxes dominate in the horizontal (leading to Kolmogorov, kx**-5/3 spectra), whereas buoyancy force variance fluxes dominate in the vertical (leading to Bolgiano-Obukhov kz**-11/5 spectra). In comparison to this 2.555 D model, the classical model of atmospheric dynamics assumes a transition from isotropic 3D turbulence at small scales to isotropic 2D turbulence at large scales and popular gravity wave theories predict D=7/3 corresponding to horizontal Kolmogorov, kx-5/3 spectra and vertical kz-3 spectra. Recently, we have shown that in space, D=2.55±0.02 effectively ruling out the competing theories [Lilley, et al., 2004].

The extension of 23/9D theory from space to space-time predicts Dst=23/9+2/3=29/9. In this paper, we use lidar data to test this prediction in arbitrary directions in (z,t) or (x,z) space, and in order to get more complete information about the underlying physical scale, we developed and applied a new Anisotropic Scaling Analysis Technique (ASAT) which is based on a nonlinear coordinate transformation. This transforms the original differential scaling into standard self-similar scaling; there remains only a “trivial” anisotropy. This method was used in real space on 2D structure functions as well as in fourier space on spectral densities. It was applied to both (z,t) and (x,z) data. Using the ASAT technique we verified the theory to within about 10% over more than 3 orders of magnitude of space-time scales in arbitrary directions in (x,z) and (z,t) spaces. By considering the high (and low) order structure functions, we verify the theory for both weak and strong structures (as predicted, their average anisotropies are apparently the same).

Putting together the results for (x,z) and (z,t) (and assuming that there is no overall stratification in the horizontal (x,y) plane), we find that the overall (x,y,z,t) space is found to have an “elliptical dimension” characterizing the overall space-time stratification equal to =3.21±0.05 which is close to the theoretical value Dst =1+1+5/9+2/3=29/9=3.22… corresponding (in conditions with no mean wind) to , , scaling in space and scaling in time.

Finally, we show how these scalings can be used to produce highly realistic multifractal simulations of clouds, including turbulence-wave phenomenologies.

References: Lilley, M., et al. (2004), 23/9 dimensional anisotropic scaling of passive admixtures using lidar aerosol data, Phys. Rev. E, 70, 036307-036301-036307.