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An international Intercomparison of 3D Radiation Codes (I3RC) underscores the vast progress of recent years, but also highlights the challenges ahead for routine implementation in remote sensing and global climate modeling applications. Modeling atmospheric and oceanic processes is one of the most important methods of the earth sciences for understanding the interactions of the various components of the surface-atmosphere system and predicting future weather and climate states. Great leaps in the availability of computing power at continuously decreasing costs have led to widespread popularity of computer models for research and operational applications. As part of routine scientific work, output from models built for AFFILIATIONS: CAHALAN-NASA

This paper examines the processes through which cloud heterogeneities influence solar reflection. This question is important since present methods give numerical results only for the overall radiative effect of cloud heterogeneities but cannot determine the degree to which various mechanisms are responsible for it. This study establishes a theoretical framework that defines these mechanisms and also provides a procedure to calculate their magnitude. In deriving the framework, the authors introduce a one-dimensional radiative transfer approximation, called the tilted independent pixel approximation (TIPA). TIPA uses the horizontal distribution of slant optical thicknesses along the direct solar beam to describe the radiative influence of cloud heterogeneities when horizontal transport between neighbors is not considered. The effects for horizontal transport are then attributed to two basic mechanisms: trapping and escape of radiation, when it moves to thicker and thinner cloud elements, respectively. Using the proposed framework, the study examines the shortwave radiative effects of cloud-top height and cloud volume extinction coefficient variations. It is shown and explained that identical variations in cloud optical thickness can cause much stronger heterogeneity effects if they are due to variations in geometrical cloud thickness rather than in volume extinction coefficient. The differences in albedo can exceed 0.05, and the relative differences in reflectance toward the zenith can be greater than 25% for overhead sun and 50% for oblique sun. The paper also explains a previously observed phenomenon: it shows that the trapping of upwelling radiation causes the zenith reflectance of heterogeneous clouds to increase with decreasing solar elevation.

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The physical interpretation of simultaneous multiangle observations represents a relatively new approach to remote sensing of terrestrial geophysical and biophysical parameters. Multiangle measurements enable retrieval of physical scene characteristics, such as aerosol type, cloud morphology and height, and land cover (e.g., vegetation canopy type), providing improved albedo accuracies as well as compositional, morphological, and structural information that facilitates addressing many key climate, environmental, and ecological issues. While multiangle data from wide field-of-view scanners have traditionally been used to build up directional "signatures" of terrestrial scenes through multitemporal compositing, these approaches either treat the multiangle variation as a problem requiring correction or normalization or invoke statistical assumptions that may not apply to specific scenes. With the advent of a new generation of global imaging spectroradiometers capable of acquiring simultaneous visible/near-IR multiangle observations, namely, the Along-Track Scanning Radiometer-2, the Polarization and Directionality of the Earth's Reflectances instrument, and the Multiangle Imaging SpectroRadiometer, both qualitatively new approaches as well as quantitative improvements in accuracy are achievable that exploit the multiangle signals as unique and rich sources of diagnostic information. This paper discusses several applications of this technique to scientific problems in terrestrial atmospheric and surface geophysics and biophysics. 1 • Introduction With the exception of the mirrorlike surface of an absolutely calm body of water, all natural terrestrial surfaces and media reflect light diffusely. Clouds, aerosol layers, vegetation canopies, soils, snow fields-all scatter shortwave radiation into an angular reflectance pattern or Bidirectional Reflectance Distribution Function (BRDF) (Nicodemus et al.

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Abstract-The

This study directly compares plane parallel model calculations with I year of Earth Radiation Budget Satellite shortwave observations at nadir over ocean between 30øS and 30øN. When plane parallel model calculations are matched to the observations on a pixel-by-pixel basis by adjusting cloud fraction and cloud optical depth, the resulting frequency distributions of cloud optical depth show a systematic shift towards larger values with increasing solar zenith angle, regardless of the assumptions made in the calculations. This dependence is weak for thin clouds but gets progressively stronger as the clouds become thicker. For the thinnest 50% of the clouds (optical depths <• 6), it occurs only at oblique solar zenith angles, whereas it is observed at all solar zenith angles for the thickest 10% of clouds (optical depths >• 12). On average, the increase is extremely large for solar zenith angles >• 63 ø. Such behavior is unrealistic since average cloud optical depths from such an extensive data set should be almost independent of solar zenith angle. The cause is traced to a fundamental flaw in plane parallel theory applied to real clouds: the solar zenith angle dependence of model reflectance is opposite to that of the observations. The one-dimensional nadir reflectance remains within 10% of the observed reflectance for solar zenith angles <• 53 ø when applied to a general ensemble of real clouds, and for solar zenith angles <• 63 ø when applied to the thinnest 50% of such clouds. Uncertainties are found to increase rapidly as the Sun becomes more oblique, easily reaching 30% at the lowest solar elevations. Based on results from theoretical studies, it is concluded that three-dimensional cloud structures not accounted for by plane parallel theory have a statistically important effect on the radiation field. As a minimum requirement, application of one-dimensional theory to the remote sensing of cloud optical thickness from measurements of nadir reflectance should therefore be restricted to thin clouds and small solar zenith angles. address only one aspect of the dichotomy between three-dimensional reality and one-dimensional remote sensing of cloud optical properties, namely, the effect of solar zenith angle on the cloud optical depths inferred from shortwave radiance observations. ] has already shown that reflectivities from specific types of three-dimensional clouds can differ substantially from those assumed to be plane parallel. There is also increasing observational evidence [e.g., $tuhlmann et al., 1985; Coakley and Davies, 1986; Minnis, 1989; Coakley, 1991] consistent with such theory. These studies clearly demonstrate that threedimensional effects are important for certain types of clouds, so that one-dimensional retrieval of cloud optical depth may be substantially biased. Additional observational studies are now needed to quantify this bias for mixtures of cloud types that are representative of general conditions. 1621 1622 LOEB AND DAVIES: EVIDENCE OF PLANE PARALLEL MODEL BIASES In a recent study of nonsp...