Cumulus cloud radiative properties and the characteristics of satellite radiance wavenumber spectra

Visible and infrared wavenumber spectra were examined for two AVHRR images (256 × 256 pixels; 1.1 km resolution) of single layer, shallow-cumuliform clouds from off the east coast of North America. For each image, both spectra are almost identical in form for scales between 2 and 256 km. For scales greater than ∼5 km, spectral slopes can vary widely between cloud types, but for smaller scales they follow ∼ k −3 in constancy with previous results. It is argued that abrupt scaling changes are to be expected at about typical cloud cell size, thus implying that satellite radiance variability is scale dependent. Furthermore, it is argued that application of existing generalized scale invariance techniques to satellite imagery should avoid crossing over the scale associated with typical cloud cell size. Monte Carlo methods of photon transport were used to demonstrate the similarities between spectral slopes for a cloud's vertical integral of optical depth τ υ and its corresponding reflected and emitted radiation fields. This suggests that the k −3 radiance spectra for shallow cumuliform clouds derives from cloud optical depths varying as ∼k −3 also. This, in turn, implies that if in shallow cumulus liquid water content (LWC) variability is isotropic, spectra of LWC transects should be close to k −2, as is often the case. Despite the spectral similarities, it is shown that the many-to-many relation between reflected radiance and τ υ can be quite pronounced, thus making inference of τ υ difficult.