Cloud 3D Effects Evidenced in Landsat Power Spectra and Autocorrelation Functions

An analysis of nadir reflectivity Fourier spatial power spectra and autocorrelation functions at solar wavelengths and for cloudy conditions has been carried out. The data come from Landsat Thematic Mapper (TM) observations, while Monte Carlo (MC) simulations are used to aid the interpretation of the Landsat results. We show that radiative processes produce consistent signatures on power spectra and autocorrelation functions. The former take a variety of forms not shown or explained in previous observational studies. We demonstrate that the TM spectra can potentially be affected by both radiative "roughening" at intermediate scales (approx. 1 -5 km), being more prevalent at large solar zenith angles, and the already documented radiative "smoothing" at small scales (less than 1 km). These processes are wavelength dependent, as shown by systematic differences between conservative (for cloud droplets) TM band 4 (approx. 0.8 microns) and absorbing band 7 (approx. 2.2 microns): band 7 exhibits more roughening and less smoothing. This is confirmed quantitatively by comparing least-squared fitted power spectral slopes for the two bands. It is also corroborated by a slower decrease with distance of autocorrelation function values for band 4 compared to band 7. The appearance of roughening at large solar zenith angles is a result of side illumination and shadowing and adds an additional complexity to the power spectra. MC spectra are useful in illustrating that scale invariant optical depth fields can produce complex power spectra that take a variety of shapes under different conditions. We show that radiative roughening increases with the decrease of single scattering albedo and with the increase of solar zenith angle (as in the observations). For high Sun there is also a clear shift of the radiative smoothing scale to smaller values as droplet absorption increases. The shape of the power spectrum is sensitive to the magnitude and type of cloud top height variability, with the spectral signatures of decorrelation between reflectance and optical depth at large scales becoming stronger as the magnitude of cloud top variations increase. Finally, the usefulness of power spectral analysis in evaluating the skill of novel optical depth retrieval techniques in removing 3D radiative effects is demonstrated. New techniques using inverse Non-local Independent Pixel Approximation (NIPA) and Normalized Difference of Nadir Reflectivity (NDNR) yield optical depth fields which better match the scale-by-scale variability of the true optical depth field.