On the angular radiance closure of tropical cumulus congestus clouds observed by the Multiangle Imaging Spectroradiometer

Monte Carlo reflectance simulations of three tropical cumulus congestus clouds reconstructed from Multiangle Imaging Spectroradiometer (MISR) data are compared to the domain-averaged MISR reflectance measurements. The goal of the comparison is to evaluate the nadir-view pixel cloud optical depth retrievals derived using plane-parallel radiative transfer theory, and the assumptions for vertically distributing the optical depth. Cloud heights are operationally retrieved using a stereo-imaging algorithm. The cloud heights and optical depths are at a 275 m spatial resolution, and for most simulations a vertical resolution of 250 m is applied. Five different but common three-dimensional cloud representations are assessed, using (1) a column vertical-mean volume extinction coefficient (b) value (the reference case), (2) a volume extinction coefficient proportional to the two-thirds power of height (the adiabatic assumption), (3) the adiabatic assumption at a 25 m vertical resolution, (4) a vertical-mean b retrieved from reflectances averaged over a (2.2 km)2 area, and (5) a vertical-mean b retrieved using off-nadir reflectances. An asymmetry about nadir in the observed reflectance means and skewnesses is not reproduced by any Monte Carlo simulation. The lack of symmetry can be related to differing proportions of unobscured sunlit and shadowed cloudy areas within the different views, even for these cases with viewing angles close to the perpendicular plane. The Monte Carlo simulations do not appear to capture the observed fraction of unobscured sunlit and shadowed cloudy areas, suggesting that radiatively significant cloud variability is occurring at scales smaller than the height field resolution of ±550 m. Results from the Monte Carlo simulation done at a higher vertical resolution are consistent with this. The cases examined also contain a nadir maximum in the observed reflectance skewnesses and a relative maximum for the observed nadir reflectances, attributed to the solar illumination of some optically thick cloud surfaces and to specular reflection pervading through the optically thin cloudy regions. This contrasts with previous modeling results that assume a Lambertian surface.