abstract
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Structural properties and solar radiative fluxes for broken, inhomogeneous cloud fields (primarily fairweather cumulus) are examined from the point of view of sub-grid parameterization for global climate models (GCMs). AVHRR satellite visible and infrared radiances (256x256 km images) display almost identical one and two-dimensional wavenumber spectra. For scales greater than ~4 km, radiance spectra follow k⁻¹ to k⁻⁵/³ where k is wavenumber (at scales greater than ~40 km, radiance spectra for stratocumulus and stratocumulus of open polygonal cells behave as white noise). At scales between ~4 km and ~2 km, spectra follow ~k⁻⁴. Aircraft observations of cloud microphysics and temperature, however, suggest that these fields follow closely Kolmogorov's classic k⁻⁵/³ law down to at least ~120 m. The dramatic scaling change in radiance fields may, therefore, be due to horizontal variation in the vertical integral of liquid water content.
Based on the empirical data, a phenomonological scaling cloud field model which produces three different forms of a cloud field is developed and demonstrated. The cloud fields produced by this model are used ultimately in a three-dimensional atmospheric Monte Carlo photon transport model which is developed and validated. Also, two methods of including an underlying reflecting surface are developed and validated.
Using the models mentioned above, fluxes for various scaling, random, regular, and plane-parallel broken cloud fields are compared. Scaling cloud fields span a spectrum from white noise fields to plane-parallel. If most cloud fields scale between k⁻⁰.⁵ and k⁻⁵/³ over regions the size of GCM grids, as they probably do, neither the plane-parallel nor the random array models yield adequate flux estimates.
If a scaling cloud field with horizontally variable optical depth is transformed so that all cells with optical depth greater than zero are replaced by cells with optical depth equal to grid-averaged optical depth, reflectance is increased by 10 to 20%. This is due to the non-linearity of radiative transfer and the fact that photons are more likely to encounter liquid water in the homogenized case. Accounting for variable geometric depth of cloud may be important in warm regions where substantial towering clouds occur regularly. Also, at GCM gridbox scales it is probably just as important to account for low frequency whitish noise in cloud fields as it is to account for high frequency smoothing at scales below typical cloud cell diameter.
The convenient Lambertian surface approximation is probably adequate for most broken cloud scenarios. Expected errors in fluxes probably will not exceed a few percent. A method is developed for calculating cloudbase reflectance in a Monte Carlo simulation. For the widely used geometric sum formulae for flux calculation to be applicable, cloudbase reflectance must be independent of the number of internal reflections. For broken scaling clouds, however, this is violated. Fortuitously and fortunately, if cloudbase reflectance in the geometric sum formulae is set to the spherical albedo of the cloud field, errors in flux estimates should be small (≲ 5%) in most cases. Finally, it is shown analytically that reduction in system albedo due to the introduction of broken, non-absorbing clouds is possible but highly unlikely to occur with any importance on Earth.