The Landsat scale break in stratocumulus as a three-dimensional radiative transfer effect: Implications for cloud remote sensing

Abstract

Several studies have uncovered a break in the scaling properties of Landsat cloud scenes at nonabsorbing wavelengths. For scales greater than 200-400 m, the wavenumber spectrum is approximately power law in k-5/3, but from there down to the smallest observable scales (50-100 m) follows another k-β law with β > 3. This implies very smooth radiance fields. The authors reexamine the empirical evidence for this scale break and explain it using fractal cloud models, Monte Carlo simulations, and a Green function approach to multiple scattering theory. In particular, the authors define the "radiative smoothing scale" and relate it to the characteristic scale of horizontal photon transport. The scale break was originally thought to occur at a scale commensurate with either the geometrical thickness Δz of the cloud, or with the "transport" mean free path lt = [(1 - g)σ]-1, which incorporates the effect of forward scattering (σ is extinction and g the asymmetry factor of the phase function). The smoothing scale is found to be approximately√ltΔz at cloud top; this is the prediction of diffusion theory which applies when (1 - g)τ = Δz/lt ≳ 1 (τ is optical thickness). Since the scale break is a tangible effect of net horizontal radiative fluxes excited by the fluctuations of τ, the smoothing scale sets an absolute lower bound on the range where one can neglect these fluxes and use plane-parallel theory locally, even for stratiform clouds. In particular, this constrains the retrieval of cloud properties from remotely sensed data. Finally, the characterization of horizontal photon transport suggests a new lidar technique for joint measurements of optical and geometrical thicknesses at about 0.5-km resolution.