The Landsat Scale Break in Stratocumulus as a Three-Dimensional Radiative Transfer Effect: Implications for Cloud Remote Sensing

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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 ... 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 ...

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