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This paper examines the tradeoffs between computational cost and accuracy for two new state-of-the-art codes for computing three-dimensional radiative transfer: a community Monte Carlo model and a parallel implementation of the Spherical Harmonics Discrete Ordinate Method (SHDOM). Both codes are described and algorithmic choices are elaborated. Two prototype problems are considered: a domain filled with stratocumulus clouds and another containing scattered shallow cumulus, absorbing aerosols, and molecular scatterers. Calculations are performed for a range of resolutions and the relationships between accuracy and computational cost, measured by memory use and time to solution, are compared. Monte Carlo accuracy depends primarily on the number of trajectories used in the integration. Monte Carlo estimates of intensity are computationally expensive and may be subject to large sampling noise from highly peaked phase functions. This noise can be decreased using a range of variance reduction techniques, but these techniques can compromise the excellent agreement between the true error and estimates obtained from unbiased calculations. SHDOM accuracy is controlled by both spatial and angular resolution; different output fields are sensitive to different aspects of this resolution, so the optimum accuracy parameters depend on which quantities are desired as well as on the characteristics of the problem being solved. The accuracy of SHDOM must be assessed through convergence tests and all results from unconverged solutions may be biased. SHDOM is more efficient (i.e., has lower error for a given computational cost) than Monte Carlo when computing pixel-by-pixel upwelling fluxes in the cumulus scene, whereas Monte Carlo is more efficient in computing flux divergence and downwelling flux in the stratocumulus scene, especially at higher accuracies. The two models are comparable for downwelling flux and flux divergence in cumulus and upwelling flux in stratocumulus. SHDOM is substantially more efficient when computing pixel-by-pixel intensity in multiple directions; the models are comparable when computing domain-average intensities. In some cases memory use, rather than computation time, may limit the resolution of SHDOM calculations.

The importance of multidimensional (MD) longwave radiative effects on cloud dynamics is evaluated in an eddy-resolving model (ERM)--the two-dimensional analog to large-eddy simulation (LES)--framework employing multidimensional radiative transfer [Spherical Harmonics Discrete Ordinate Method (SHDOM)]. Simulations are performed for a case of unbroken, marine boundary layer stratocumulus and a broken field of trade cumulus. 'Snapshot' calculations of MD and independent pixel approximation (IPA; 1D) radiative transfer applied to simulated cloud fields show that the total radiative forcing changes only slightly, although the MD effects significantly modify the spatial structure of the radiative forcing. Simulations of each cloud type employing MD and IPA radiative transfer, however, differ little. For the solid cloud case, relative to using IPA, the MD simulation exhibits a slight reduction in entrainment rate and boundary layer total kinetic energy (TKE) relative to the IPA simulation. This reduction is consistent with both the slight decrease in net radiative forcing and a negative correlation between local vertical velocity and radiative forcing, which implies a damping of boundary layer eddies. Snapshot calculations of the broken cloud case suggest a slight increase in radiative cooling, although few systematic differences are noted in the interactive simulations. This result is attributed to the fact that radiative cooling is a relatively minor contribution to the total energetics. For the cloud systems in this study, the use of IPA longwave radiative transfer is sufficiently accurate to capture the dynamical behavior of boundary layer clouds. Further investigations are required to generalize this conclusion for other cloud types and longer time integrations.

The Multiangle Imaging Spectroradiometer (MISR) views the earth with nine cameras, ranging from a 70[degrees] zenith angle viewing forward through nadir to 70[degrees] viewing aft. MISR does not have an operational cloud optical depth retrieval algorithm, but previous research has hinted that solar reflection measured in multiple directions might improve cloud optical depth retrievals. This study explores the optical depth information content of MISR's multiple angles using a retrieval simulation approach. Hundreds of realistic boundarylayer cloud fields are generated with large-eddy simulation (LES) models for stratocumulus, small trade cumulus, and land surface-forced fair-weather cumulus. Reflectances in MISR directions are computed with three-dimensional radiative transfer from the LES cloud fields over an ocean surface and averaged to MISR resolution and sampled at MISR 275-m pixel spacing. Neural networks are trained to retrieve the mean and standard deviation of optical depth over different size pixel patches from the mean and standard deviation of simulated MISR reflectances. Various configurations of MISR cameras are input to the retrieval, and the rms retrieval errors are compared. For 5 x 5 pixel patches the already low mean optical depth retrieval error for stratocumulus decreases 41% and 23% (for 25[degrees] and 45[degrees] solar zenith angles, respectively) from using only the nadir camera to using seven MISR cameras. For cumulus, however, the much higher normalized optical depth retrieval error only decreases around 14%. These small improvements suggest that measurements of solar reflection in multiple directions do not contribute substantially to more accurate optical depth retrievals for small cumulus clouds. The 3D statistical retrievals, however, even with only the nadir camera, are much more accurate for small cumulus than standard nadir plane-parallel retrievals; therefore, this approach may be worth pursuing.

The spherical harmonics discrete ordinate method for plane-parallel data assimilation (SHDOMPPDA) model is an unpolarized plane-parallel radiative transfer forward model, with corresponding tangent linear and adjoint models, suitable for use in assimilating cloudy sky visible and infrared radiances. It is derived from the spherical harmonics discrete ordinate method plane-parallel (SHDOMPP, also described in this article) version of the spherical harmonics discrete ordinate method (SHDOM) model for three-dimensional atmospheric radiative transfer. The inputs to the SHDOMPPDA forward model are profiles of pressure, temperature, water vapor, and mass mixing ratio and number concentration for a number of hydrometeor species. Hydrometeor optical properties, including detailed phase functions, are determined from lookup tables as a function of mass mean radius. The SHDOMPP and SHDOMPPDA algorithms and construction of the tangent-linear and adjoint models are described. The SHDOMPPDA forward model is validated against the Discrete Ordinate Radiative Transfer Model (DISORT) by comparing upwelling radiances in multiple directions from 100 cloud model columns at visible and midinfrared wavelengths. For this test in optically thick clouds the computational time for SHDOMPPDA is comparable to DISORT for visible reflection, and roughly 5 times faster for thermal emission. The tangent linear and adjoint models are validated by comparison to finite differencing of the forward model.

Cumulus clouds can become tilted or elongated in the presence of wind shear. Nevertheless, most studies of the interaction of cumulus clouds and radiation have assumed these clouds to be isotropic, This paper describes an investigation of the effect of fair-weather cumulus cloud field anisotropy on domain-averaged solar fluxes and atmospheric heating rate profiles. A stochastic field generation algorithm was used to produce 20 three-dimensional liquid water content fields based on the statistical properties of cloud scenes from a large eddy simulation. Progressively greater degrees of x-z plane tilting and horizontal stretching were imposed on each of these scenes, so that an ensemble of scenes was produced for each level of distortion. The resulting scenes were used as input to a three-dimensional Monte Carlo radiative transfer model. Domain-averaged transmission, reflection, and absorption of broadband solar radiation were computed for each scene along with the average heating rate profile. Both tilt and horizontal stretching were found to significantly affect calculated fluxes, with the amount and sign of flux differences depending strongly on sun position relative to cloud distortion geometry. The mechanisms by which anisotropy interacts with solar fluxes were investigated by comparisons to independent pixel approximation and tilted independent pixel approximation computations for the same scenes. Cumulus anisotropy was found to most strongly impact solar radiative transfer by changing the effective cloud fraction (i.e., the cloud fraction with respect to the solar beam direction).

Causes of anisotropy in fair-weather cumulus cloud fields were investigated using quantitative measures of anisotropy and a large-eddy simulation (LES) model. Case six of the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study Working Group 1 was used as the standard model scenario. This case represents radiatively forced development of cumulus clouds over the southern Great Plains. Cloud formation under a variety of environmental conditions was simulated and the degree of anisotropy in the output fields was calculated as a function of spatial scale. Wind shear was found to be the single greatest factor in the development of both vertically tilted and horizontally stretched cloud structures. Other factors included mean wind speed, initial water vapor mixing ratio, and the magnitude of the surface forcing.

Three-dimensional radiative transfer calculations are accurate, though computationally expensive, if the spatial distribution of cloud properties is known. The difference between these calculations and those using the much less expensive independent column approximation is called the 3D radiative transfer effect. Assessing the magnitude of this effect in the real atmosphere requires that many realistic cloud fields be obtained, and profiling instruments such as ground-based radars may provide the best long-term observations of cloud structure. Cloud morphology can be inferred from a time series of vertical profiles obtained from profilers by converting time to horizontal distance with an advection velocity, although this restricts variability to two dimensions. This paper assesses the accuracy of estimates of the 3D effect in shallow cumulus clouds when cloud structure is inferred in this way. Large-eddy simulations provide full three-dimensional, time-evolving cloud fields, which are sampled every 10 s to provide a 'radar's eye view' of the same cloud fields. The 3D effect for shortwave surface fluxes is computed for both sets of fields using a broadband Monte Carlo radiative transfer model, and intermediate calculations are made to identify reasons why estimates of the 3D effect differ in these fields. The magnitude of the 3D effect is systematically underestimated in the two-dimensional cloud fields because there are fewer cloud edges that cause the effect, while the random error in hourly estimates is driven by the limited sample observed by the profiling instrument.

The datasets currently being collected by the Atmospheric Radiation Measurement (ARM) program on the islands of Nauru and Manus represent the longest time series of ground-based cloud measurements in the tropical western Pacific region. In this series of papers, a shortwave flux closure study is presented using observations collected at the Nauru site between June 1999 and May 2000. The first paper presented frequency of occurrence of nonprecipitating clouds detected by the millimeter-wavelength cloud radar (MMCR) at Nauru and statistics of their retrieved microphysical properties. This paper presents estimates of the cloud radiative effect over the study period and results from a closure study in which retrieved cloud properties are input to a radiative transfer model and the modeled surface fluxes are compared to observations. The average surface shortwave cloud radiative forcing is 48,2 W [m.sup.-2], which is significantly smaller than the cloud radiative forcing estimates found during the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) field project. The difference in the estimates during the two periods is due to the variability in cloud amount over Nauru during different phases of the El Nino-Southern Oscillation (ENSO). In the closure study, modeled and observed surface fluxes show large differences at short time scales, due to the temporal and spatial variability of the clouds observed at Nauru. Averaging over 60 min reduces the average root-mean-square difference in total flux to 10% of the observed flux. Modeled total downwelling fluxes are unbiased with respect to the observed fluxes while direct fluxes are underestimated and diffuse fluxes are overestimated. Examination of the differences indicates that cloud amount derived from the ground-based measurements is an overestimate of the radiatively important cloud amount due to the anisotropy of the cloud field at Nauru, interpolation of the radar data, uncertainty in the microwave brightness temperature measurements for thin clouds, and the uncertainty in relating the sixth moment of the droplet size distribution observed by the radar to the more radiatively important moments.

The datasets currently being collected at the Atmospheric Radiation Measurement (ARM) program's sites on the islands of Nauru and Marius represent the longest time series of ground-based cloud measurements available in the tropical western Pacific region. In this and a companion paper, a shortwave flux closure study is presented using observations collected at the Nauru site between June 1999 and May 2000. This paper presents frequency of occurrence of nonprecipitating liquid and ice clouds detected by the millimeter wavelength cloud radar (MMCR) and statistics of retrieved microphysical properties. The companion paper presents results from a closure study in which the retrieved cloud properties are input to a radiative transfer model, and the modeled surface fluxes are compared to observations. The liquid cloud properties are retrieved from MMCR and microwave radiometer (MWR) measurements using a Bayesian retrieval technique. Properties of ice phase clouds are retrieved from MMCR measurements using regression equations based on in situ observations taken during the Central Equatorial Pacific Experiment (CEPEX). Nonprecipitating liquid clouds were observed at Nauru in 35% of the radar observations. These clouds were primarily shallow cumulus with bases less than 1 km. Of the retrieved liquid clouds, 90% had liquid water path less than 100 g [m.sup.-2]. The average retrieved effective radius was 7.5 [micro]m. The frequency of liquid cloud detection and height of the liquid cloud base showed a clear diurnal cycle, which is most likely related to the island effect and the existence of the Nauru cloud plume. Ice clouds with no underlying liquid clouds were detected in 16.5% of the radar observations and ice clouds above liquid clouds in 7.7% of the observations. The mean retrieved IWP of the radar-detected ice clouds was 22.1 g [m.sup.-2] and the mean effective diameter retrieved was 72 [micro]m. Large monthly variability was seen in both the amount of cirrus detected and the retrieved ice water path. Ice clouds were observed by the radar more frequently at night than during the day at Nauru, but there was no clear diurnal trend in the retrieved microphysical properties.

A retrieval method has been developed to directly retrieve statistics of cloud parameters from Geostationary Operational Environmental Satellite (GOES) visible and infrared imager data. This method retrieves cloud parameter probability density functions (PDFs) directly from distributions of multichannel satellite-observed radiances. For example, the joint probability distribution of ice water content and effective radius can be retrieved from a four-dimensional histogram of GOES radiances. A forward radiative transfer model creates a mapping from cloud parameter space to satellite radiance space. The cloud parameter space is described by vertically inhomogeneous liquid and ice cloud layers with variable liquid water path, effective radius, height, and thickness. A Monte Carlo procedure uses the mapping to transform probability density from the observed satellite radiance histogram, or radiance PDF, to a two-dimensional cloud property PDF. An estimate of the uncertainty in the retrieved PDF is calculated from random realizations of the radiance to cloud PDF transformation given the uncertainty of the observed radiances and the nonunique mapping to cloud parameter space. The algorithm is tested with simulations from numerical cloud model output and applied to imagery from the tropical eastern Pacific.

A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds.

This paper presents the results of a detailed study of the microwave single scattering properties of ice crystals expected in cirrus clouds. The discrete dipole approximation is used to compute scattering quantities of particles ranging in size from 30 to 2000 [[micro]meter] at 85.5, 157, 220, and 340 GHz. Five shapes were simulated: solid and hollow columns, hexagonal plates, planar bullet rosettes, and equivalent-volume spheres. The scattering properties were computed for 18 Gamma size distributions with a range of characteristic particle size and distribution width. The results indicate that particle shape has a significant effect; for example, there is a range of about 3 in extinction over the five shapes for the same size distribution and ice water content. Crystal shape is the dominant effect on the polarization of the scattering, with the thinner shapes having the more polarizing effect. The characteristic particle size has the greatest impact on the extinction and single-scattering albedo, while the distribution width has only a minor effect.

This paper presents the results of polarized microwave radiative transfer modeling of cirrus clouds containing five different particle shapes and 18 Gamma size distributions. Upwelling brightness temperatures for tropical and midlatitude winter atmospheres are simulated at 85.5, 157, 220, and 340 GHz using scattering properties computed with the discrete dipole approximation (described in Part I). The key parameter for the results is the sensitivity ([Delta][T.sub.b]/IWP), which relates the modeled brightness temperature depression to the ice water path. It is shown that for the higher frequencies or distributions of larger particles (i.e., in the scattering regime) the sensitivity is nearly independent of cloud temperature and details of the underlying atmosphere. As expected from the single-scattering results, the characteristic particle size has a large effect on the sensitivity, while the distribution width has only a minor effect. The range in sensitivity over the five particle shapes is typically a factor of 2. The sensitivity for a size distribution of solid columns with a median of the third power of the dimension of 250/[[micro]meter] is about 0.1 K/(g [m.sup.-2]). Ratios of [Delta][T.sub.b]'s at adjacent frequencies can determine the characteristic size of the distribution, though the relationship is double valued for the most sensitive frequencies considered here. Ratios of [Delta][T.sub.b] at horizontal to vertical polarization contain information about particle shape primarily via the aspect ratio. Ideas concerning the development of a specific cirrus retrieval algorithm are discussed.

A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.