Cloud three-dimensional effects evidenced in Landsat spatial power spectra and autocorrelation functions

An analysis of nadir reflectivity spatial Fourier power spectra and autocorrelation functions for solar wavelengths and cloudy conditions is presented. The data come from Landsat thematic mapper (TM) observations, while Monte Carlo (MC) simulations are used to aid the interpretation of the observations and to examine sensitivity to various factors. We show that shortwave radiative processes produce consistent signatures in power spectra and autocorrelation functions. Power spectra take a variety of shapes not shown or explained in previous observational studies. We demonstrate that TM spectra can potentially be affected by radiative “roughening” at intermediate scales (ϳ1–5 km) and radiative “smoothing” at small scales (Ͻ1 km). These processes are wavelength-dependent, with systematic differences between conservative (for cloud droplets) TM band 4 (ϳ0.8 ␮m) and absorbing band 7 (ϳ2.2 ␮m). Band 7 exhibits more roughening and less smoothing than band 4 and faster decrease in autocorrelation. Roughening is more prevalent at large solar zenith angles due to optical and/or geometrical side illumination and shadowing. MC spectra illustrate that scale invariant optical depth fields can produce complex power spectra that take a variety of shapes under different conditions. Radiative roughening increases with decreasing single scattering albedo and increasing solar zenith angle (as in the observations). For low solar zenith angles, there is a clear shift in the radiative smoothing scale to smaller values as droplet absorption increases. Power spectra also show stronger decorrelations between optical depth and reflectivity when cloud top variations are more pronounced. Finally, it is shown that power spectral analysis is a useful tool for evaluating the skill of novel optical depth retrieval techniques in removing three-dimensional radiative effects. New techniques using inverse nonlocal independent pixel approximation and normalized difference of nadir reflectivity yield optical depth fields which better match the scale-by-scale variability of the true optical depth field.