Plane-parallel Clouds Research Articles

Liquid cloud optical property retrieval and associated uncertainties using multi-angular and bispectral measurements of the airborne radiometer OSIRIS

Abstract. In remote sensing applications, clouds are generally characterized by two properties: cloud optical thickness (COT) and effective radius of water–ice particles (Reff), as well as additionally by geometric properties when specific information is available. Most of the current operational passive remote sensing algorithms use a mono-angular bispectral method to retrieve COT and Reff. They are based on pre-computed lookup tables while assuming a homogeneous plane-parallel cloud layer. In this work, we use the formalism of the optimal estimation method, applied to airborne near-infrared high-resolution multi-angular measurements, to retrieve COT and Reff as well as the corresponding uncertainties related to the measurement errors, the non-retrieved parameters, and the cloud model assumptions. The measurements used were acquired by the airborne radiometer OSIRIS (Observing System Including PolaRization in the Solar Infrared Spectrum), developed by the Laboratoire d'Optique Atmosphérique. It provides multi-angular measurements at a resolution of tens of meters, which is very suitable for refining our knowledge of cloud properties and their high spatial variability. OSIRIS is based on the POLDER (POlarization and Directionality of the Earth's Reflectances) concept as a prototype of the future 3MI (Multi-viewing Multi-channel Multi-polarization Imager) planned to be launched on the EUMETSAT-ESA MetOp-SG platform in 2024. The approach used allows the exploitation of all the angular information available for each pixel to overcome the radiance angular effects. More consistent cloud properties with lower uncertainty compared to operational mono-directional retrieval methods (traditional bispectral method) are then obtained. The framework of the optimal estimation method also provides the possibility to estimate uncertainties of different sources. Three types of errors were evaluated: (1) errors related to measurement uncertainties, which reach 6 % and 12 % for COT and Reff, respectively, (2) errors related to an incorrect estimation of the ancillary data that remain below 0.5 %, and (3) errors related to the simplified cloud physical model assuming independent pixel approximation. We show that not considering the in-cloud heterogeneous vertical profiles and the 3D radiative transfer effects leads to an average uncertainty of 5 % and 4 % for COT and 13 % and 9 % for Reff.

The effect of solar zenith angle on MODIS cloud optical and microphysical retrievals within marine liquid water clouds

Abstract. In this paper we use a novel observational approach to investigate MODIS satellite retrieval biases of τ and re (using three different MODIS bands: 1.6, 2.1 and 3.7 μm, denoted as re1.6, re2.1 and re3.7, respectively) that occur at high solar zenith angles (θ0) and how they affect retrievals of cloud droplet concentration (Nd). Utilizing the large number of overpasses for polar regions and the diurnal variation of θ0 we estimate biases in the above quantities for an open ocean region that is dominated by low level stratiform clouds. We find that the mean τ is fairly constant between θ0 = 50° and ~65–70°, but then increases rapidly with an increase of over 70 % between the lowest and highest θ0. The re2.1 and re3.7 decrease with θ0, with effects also starting at around θ0 = 65–70°. At low θ0, the re values from the three different MODIS bands agree to within around 0.2 μm, whereas at high θ0 the spread is closer to 1 μm. The percentage changes of re with θ0 are considerably lower than those for τ, being around 5 % and 7% for re2.1 and re3.7. For re1.6 there was very little change with θ0. Evidence is provided that these changes are unlikely to be due to any physical diurnal cycle. The increase in τ and decrease in re both contribute to an overall increase in Nd of 40–70% between low and high θ0. Whilst the overall re changes are quite small, they are not insignificant for the calculation of Nd; we find that the contributions to Nd biases from the τ and re biases were roughly comparable for re3.7, although for the other re bands the τ changes were considerably more important. Also, when considering only the clouds with the more heterogeneous tops, the importance of the re biases was considerably enhanced for both re2.1 and re3.7. When using the variability of 1 km resolution τ data (γτ) as a heterogeneity parameter we obtained the expected result of increasing differences in τ between high and low θ0 as heterogeneity increased, which was not the case when using the variability of 5 km resolution cloud top temperature (σCTT), suggesting that γτ is a better predictor of τ biases at high θ0 than σCTT. For a given θ0, large decreases in re were observed as the cloud top heterogeneity changed from low to high values, although it is possible that physical changes to the clouds associated with cloud heterogeneity variation may account for some of this. However, for a given cloud top heterogeneity we find that the value of θ0 affects the sign and magnitude of the relative differences between re1.6, re2.1 and re3.7, which has implications for attempts to retrieve vertical cloud information using the different MODIS bands. The relatively larger decrease in re3.7 and the lack of change of re1.6 with both θ0 and cloud top heterogeneity suggest that re3.7 is more prone to retrieval biases due to high θ0 than the other bands. We discuss some possible reasons for this. Our results have important implications for individual MODIS swaths at high θ0, which may be used for case studies for example. θ0 values > 65° can occur at latitudes as low as 28° in mid-winter and for higher latitudes the problem will be more acute. Also, Level-3 daily averaged MODIS cloud property data consist of the averages of several overpasses for the high latitudes, which will occur at a range of θ0 values. Thus, some biased data are likely to be included. It is also likely that some of the θ0 effects described here would apply to τ and re retrievals from satellite instruments that use visible light at similar wavelengths along with forward retrieval models that assume plane parallel clouds, such as the GOES imagers, SEVIRI, etc.

Multilayer Cloud Detection with the MODIS Near-Infrared Water Vapor Absorption Band

Abstract Data Collection 5 processing for the Moderate Resolution Imaging Spectroradiometer (MODIS) on board the NASA Earth Observing System (EOS) Terra and Aqua spacecraft includes an algorithm for detecting multilayered clouds in daytime. The main objective of this algorithm is to detect multilayered cloud scenes, specifically optically thin ice cloud overlying a lower-level water cloud, that present difficulties for retrieving cloud effective radius using single-layer plane-parallel cloud models. The algorithm uses the MODIS 0.94-μm water vapor band along with CO2 bands to obtain two above-cloud precipitable water retrievals, the difference of which, in conjunction with additional tests, provides a map of where multilayered clouds might potentially exist. The presence of a multilayered cloud results in a large difference in retrievals of above-cloud properties between the CO2 and the 0.94-μm methods. In this paper the MODIS multilayered cloud algorithm is described, results of using the algorithm over example scenes are shown, and global statistics for multilayered clouds as observed by MODIS are discussed. A theoretical study of the algorithm behavior for simulated multilayered clouds is also given. Results are compared to two other comparable passive imager methods. A set of standard cloudy atmospheric profiles developed during the course of this investigation is also presented. The results lead to the conclusion that the MODIS multilayer cloud detection algorithm has some skill in identifying multilayered clouds with different thermodynamic phases.

Investigation of Regional and Seasonal Variations in Marine Boundary Layer Cloud Properties from MODIS Observations

Abstract To aid in understanding the role that marine boundary layer (MBL) clouds play in climate and assist in improving their representations in general circulation models (GCMs), their long-term microphysical and macroscale characteristics are quantified using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument aboard the National Aeronautics and Space Administration’s (NASA’s) Terra satellite. Six years of MODIS pixel-level cloud products are used from oceanic study regions off the west coasts of California, Peru, the Canary Islands, Angola, and Australia where these cloud types are common. Characterizations are given for their organization (macroscale structure), the associated microphysical properties, and the seasonal dependencies of their variations for scales consistent with the size of a GCM grid box (300 km × 300 km). MBL mesoscale structure is quantified using effective cloud diameter CD, which is introduced here as a simplified measure of bulk cloud organization; it is straightforward to compute and provides descriptive information beyond that offered by cloud fraction. The interrelationships of these characteristics are explored while considering the influences of the MBL state, such as the occurrence of drizzle. Several commonalities emerge for the five study regions. MBL clouds contain the best natural examples of plane-parallel clouds, but overcast clouds occur in only about 25% of the scenes, which emphasizes the importance of representing broken MBL cloud fields in climate models (that are subgrid scale). During the peak months of cloud occurrence, mesoscale organization (larger CD) increases such that the fractions of scenes characterized as “overcast” and “clumped” increase at the expense of the “scattered” scenes. Cloud liquid water path and visible optical depth usually trend strongly with CD, with the largest values occurring for scenes that are drizzling. However, considerable interregional differences exist in these trends, suggesting that different regression functionalities exist for each region. For peak versus off-peak months, the fraction of drizzling scenes (as a function of CD) are similar for California and Angola, which suggests that a single probability distribution function might be used for their drizzle occurrence in climate models. The patterns are strikingly opposite for Peru and Australia; thus, the contrasts among regions may offer a test bed for model simulations of MBL drizzle occurrence.

Molecular dark matter in galaxies

Clouds containing molecular dark matter in quantities relevant for star formation may exist in minihaloes of the type of cold dark matter included in many cosmological simulations or in the regions of some galaxies extending far beyond their currently known boundaries. We have systematically explored parameter space to identify conditions under which plane-parallel clouds contain sufficient column densities of molecular dark matter that they could be reservoirs for future star formation. Such clouds would be undetected or at least appear by current observational criteria to be uninteresting from the perspective of star formation. We use a time-dependent PDR code to produce theoretical models of the chemistry and emission arising in clouds for our chosen region of parameter space. We then select a subset of model clouds with levels of emission that are low enough to be undetectable or at least overlooked by current surveys. The existence of significant column densities of cold molecular dark matter requires that the background radiation field be several or more orders of magnitude weaker than that in the solar neighbourhood. Lower turbulent velocities and cosmic ray induced ionization rates than typically associated with molecular material within a kpc of the Sun are also required for the molecular matter to be dark. We find that there is a large region within the parameter space that results in clouds that might contain a significant mass of molecular gas whilst remaining effectively undetectable or at least not particularly noticeable in surveys. We note briefly conditions under which molecular dark matter may contain a dynamically interesting mass.

Estimate of satellite‐derived cloud optical thickness and effective radius errors and their effect on computed domain‐averaged irradiances

The process of retrieving cloud optical thickness and effective radius from radiances measured by satellite instruments is simulated to determine the error in both the retrieved properties and in the irradiances computed with them. The radiances at 0.64 μm and 3.7 μm are computed for three cloud fields (stratus, stratocumulus, and cumulus) generated by large eddy simulation models. When overcast pixels are assumed and the horizontal flux is neglected in the retrieval process, the error in the domain‐averaged retrieved optical thickness from nadir is 1% to −32% (1% to −27%) and the error in the retrieved effective radius is 0% to 67% (0% to 63%) for the solar zenith angle of 30° (50°). Using the radiance averaged over a 1 km size pixel also introduces error in the optical thickness because of the nonlinear relation between the reflected radiance and optical thickness. Both optical thickness and effective radius errors increase with increasing horizontal inhomogeneity. When the 0.64 μm albedo is computed with the independent column approximation using retrieved properties from nadir (oblique) view for a solar zenith angle of 50°, the error is −0.3% to 14% (−5% to −30%) relative to the albedo from 3‐D radiative transfer computations with the true cloud properties. The albedo error occurs even though the radiance at one angle is forced to agree because a plane parallel cloud with a single value of optical thickness and effective radius cannot consistently match the radiance angular distribution. In addition, the error in the retrieved cloud properties contributes to the albedo error. When albedos computed with cloud properties derived from nadir and oblique views are averaged, the albedo error can partially cancel. The absolute error in the narrowband 0.64 μm (3.7 μm) albedo averaged over a 1° × 1° domain is less than 1.5% (0.6%), 5.0% (4.1%), and 7.1% (11%) in order of increasing inhomogeneity, when albedos computed with cloud properties derived from viewing zenith angles between 0° and 60° are averaged and when the solar zenith angle is between 10° and 50°. When the solar zenith angle is 70°, the error increases to up to +24% (+37%) for all three scenes.

The Impact of Ice Crystal Shapes, Size Distributions, and Spatial Structures of Cirrus Clouds on Solar Radiative Fluxes

AbstractThe solar radiative properties of cirrus clouds depend on ice particle shape, size, and orientation, as well as on the spatial cloud structure. Radiation schemes in atmospheric circulation models rely on estimates of cloud optical thickness only. In the present work, a Monte Carlo radiative transfer code is applied to various cirrus cloud scenarios to obtain the radiative response of uncertainties in the above-mentioned microphysical and spatial cloud properties (except orientation). First, plane-parallel homogeneous (0D) clouds with different crystal shapes (hexagonal columns, irregular polycrystals) and 114 different size distributions have been considered. The resulting variabilities in the solar radiative fluxes are in the order of a few percent for the reflected and about 1% for the diffusely transmitted fluxes. Largest variabilities in the order of 10% to 30% are found for the solar broadband absorptance. However, these variabilities are smaller than the flux differences caused by the choice of ice particle geometries.The influence of cloud inhomogeneities on the radiative fluxes has been examined with the help of time series of Raman lidar extinction coefficient profiles as input for the radiative transfer calculations. Significant differences between results for inhomogeneous and plane-parallel clouds were found. These differences are in the same order of magnitude as those arising from using extremely different crystal shapes for the radiative transfer calculations. From this sensitivity study, the ranking of cirrus cloud properties according to their importance in solar broadband radiative transfer is optical thickness, ice crystal shape, ice particle size, and spatial structure.

Spectral properties of backscattered UV radiation in cloudy atmospheres

We use a Plane‐Parallel Cloud (PPC) model to illustrate how Mie scattering from cloud particles interacts with Rayleigh scattering in the atmosphere and produces a complex wavelength dependence in the top‐of‐the‐atmosphere (TOA) reflectances measured by satellite instruments that operate in the ultraviolet (UV) part of the spectrum. Comparisons of the PPC‐model‐derived spectral dependence of reflectances with the Total Ozone Mapping Spectrometer (TOMS) measurements show surprisingly good agreement over a wide range of observational conditions. The PPC model results also are compared with the results of two other cloud models: Lambert Equivalent Reflectivity (LER) and Modified LER (MLER) that have been used to analyze satellite data in the UV. These models assume that clouds are opaque Lambertian reflectors rather than Mie scattering particles. Although one of these models (MLER) can be adjusted to agree reasonably well with the TOMS data, the adjustments are somewhat arbitrary and may not be suitable for interpreting satellite data if one desires high accuracy. We also use the PPC model to illustrate how clouds can perturb tropospheric O3 absorption in complex ways that cannot be explained by models that treat them as reflecting surfaces rather than as volume scatterers.

Monte Carlo Radiative Transfer Modeling of Lightning Observed in Galileo Images of Jupiter

We study lightning on Jupiter and the clouds illuminated by the lightning using images taken by the Galileo orbiter. The Galileo images have a resolution of ∼25 km/pixel and are able to resolve the shape of single lightning spots, which have half widths (radii) at half the maximum intensity in the range 45–80 km. We compare the shape and width of lightning flashes in the images with simulated flashes produced by our 3D Monte Carlo light-scattering model. The model calculates Monte Carlo scattering of photons in a 3D opacity distribution. During each scattering event, light is partially absorbed. The new direction of the photon after scattering is chosen according to a Henyey–Greenstein phase function. An image from each direction is produced by accumulating photons emerging from the cloud in a small range (bins) of emission angles. The light source is modeled either as a point or a vertical line. A plane-parallel cloud layer does not always fit the data. In some cases the cloud over the light source appears to resemble cumulus clouds on Earth. Lightning is estimated to occur at least as deep as the bottom of the expected water cloud. For the six flashes studied, we find that the clouds above the lightning are optically thick (τ>5). Jovian flashes are more regular and circular than the largest terrestrial flashes observed from space. On Jupiter there is nothing equivalent to the 30–40-km horizontal flashes that are seen on Earth.

Space–Time Characteristics of Light Transmitted through Dense Clouds: A Green's Function Analysis

Here, previous work using photon diffusion theory to describe radiative transfer through dense plane-parallel clouds at nonabsorbing wavelengths is extended. The focus is on the scaling of space- and time-domain moments for transmitted light with respect to cloud thickness H and optical depth τ; and the new results are as follows: accurate prefactors for asymptotic scaling, preasymptotic correction terms in closed form, 3D effects for internal variability in τ, and the rms transit time or pathlength. Mean pathlength is ∝H for dimensional reasons and, from random-walk theory, we already know that it is also ∝(1 – g)τ for large enough τ (g being the asymmetry factor). Here, it is shown that the prefactor is precisely 1/2 and that corrections are significant for (1 – g)τ < 10, which includes most actual boundary layer clouds. It is also shown that rms pathlength is not much larger than the mean for transmittance (its prefactor is ≈ 0.59); this proves that, in sharp contrast with reflection, pathlength distributions are quite narrow in transmission. If the light originates from a steady point source on a cloud boundary, a fuzzy spot is observed on the opposite boundary. This problem is formally mapped to the pulsed source problem, and it is shown that the rms radius of this spot slowly approaches H as τ increases; it is also shown that the transmitted spot shape has a flat top and an exponential tail. Because all preasymptotic corrections are computed here, the diffusion results are accurate when compared to Monte Carlo counterparts for τ ≥ 5, whereas the classic scaling relations apply only for τ ≥ 70, assuming g = 0.85. The temporal quantities shed light on observed absorption properties and optical lightning waveforms. The spatial quantity controls the three-dimensional radiative smoothing process in transmission, which was recently observed in spectral analyses of time series of zenith radiance at 725 nm. Opportunities in ground-based cloud remote sensing using the new developments are described and illustrated with simulations of 3D solar radiative transfer in realistic models of stratocumulus. Finally, since this analytical diffusion study applies only to weakly variable stratus layers, extensions to more complex cloud systems using anomalous diffusion theory are discussed.

Errors in liquid water path retrieval arising from cloud inhomogeneities: The beam-filling effect

In this modelling study the effects of cloud inhomogeneities on the observations of the passive microwave radiometer SSM/I (Special Sensor Microwave/Imager) are investigated. Brightness temperatures in the radiometer's field-of-view are calculated by using the results of a numerical cloud model as input for a 3-dimensional radiative transfer model. These brightness temperatures are compared with those obtained by the assumption of a plane parallel homogeneous cloud with the equivalent mean liquid water path (LWP). Differences between the two temperatures (the so-called 'beam-filling effect') are related to the mean LWP and to cloud inhomogeneity. It was found that not only the strength of the beam-filling effect but also its dependencies on mean LWP and its inhomogeneity are different for the different microwave frequencies. For 19 and 22 GHz the beam-filling effect increases monotonically with the mean LWP and inhomogeneity, while the beam-filling effect decreases with increased LWP at 37 and 85 GHz at large LWP. In general the beam-filling effect is more pronounced in the horizontal polarisation. Its maximum is found for 37 GHz with differences up to -60 Kelvin compared to the homogeneous case. The effect of the lowered brightness temperatures of inhomogeneous clouds in a LWP algorithm (WENG and GRODY, 1994) is analysed. The largest effect arises from decreased 37 GHz brightness temperature. The mean underestimation of LWP is 0.0179 kg/m 2 and the maximum amounts to 0.7 kg/m 2 .

Angular Variability of the Liquid Water Cloud Optical Thickness Retrieved from ADEOS–POLDER

Abstract The usual procedure for retrieving the optical thickness of liquid water clouds from satellite-measured radiances is based on the assumption of plane-parallel layers composed of liquid water droplets. This study investigates the validity of this assumption from Advanced Earth Orbiting Satellite–Polarization and Directionality of the Earth's Reflectances (ADEOS–POLDER) observations. To do that, the authors take advantage of the multidirectional viewing capability of the POLDER instrument, which functioned nominally aboard ADEOS from November 1996 to June 1997. The usual plane-parallel cloud model composed of water droplets with an effective radius of 10 μm provides a reasonable approximation of the angular dependence in scattering at visible wavelengths from overcast liquid water clouds for moderate solar zenith angles. However, significant differences between model and observations appear in the rainbow direction and for the smallest observable values of scattering angle (Θ < 90°). A better overa...

Parametrization of solar radiation in inhomogeneous stratocumulus: Albedo bias

Low-level cloud fields with typical albedos between 50% and 70% contribute significantly to short-wave cloud radiative forcing. Consequently, the earth's radiative budget is sensitive to extended stratocumulus which typically occurs in sub-tropical subsidence regions over the oceans. It is therefore vital to represent the cloud albedo of such cloud fields accurately in climate models. Nevertheless, cloud fields are modelled as homogeneous plane-parallel clouds, which leads to an overestimation of the albedo by up to 15% compared with real inhomogeneous clouds, both types of cloud fields having the same mean cloud optical depth. This so-called plane-parallel cloud albedo bias has given rise to a number of studies that present methods for reducing the albedo bias for stratiform clouds in climate models. Using Monte Carlo simulations and the Independent Pixel Approximation (IPA) the inhomogeneous cloud albedo is investigated with the aim of deriving a parametrization of the albedo bias. The new approach used here is that the variance of the cloud optical depth is parametrized as a function of grid size and mean cloud liquid-water content. The variance of the cloud optical depth is derived from turbulence processes. For the determination of the albedo bias an analytical solution is presented which is based on a simplified distribution function of the cloud optical depth and the IPA method. When used in conjunction with the parametrized variance of the cloud optical depth, a box function, which replaces the distribution function, produces comparable results to Monte Carlo simulations within an acceptable accuracy of a few per cent.

Approximations for horizontal photon transport in cloud remote sensing problems

The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. In this paper, analytic approximations for the root-mean-square horizontal displacement of reflected and transmitted photons, relative to the incident cloud-top location, are derived for plane-parallel cloud layers. With anisotropic scattering, separate approximations are needed depending on the order of scattering. When sufficient numbers of photon scatterings occur, an approximation based on random walk theory (photon diffusion) is applicable; when scattering numbers are relatively small, a modification to the diffusion result is used. The resulting formulae are a function of the average number of photon scatterings, as well as particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings from plane-parallel, vertically inhomogeneous cloud layers can be determined from efficient adding/doubling radiative transfer procedures. The transport approximations are applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximations are applicable to general anisotropic, multiple scattering, plane-parallel radiative transfer problems. Approximations useful for three-dimensional transport are also given. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average radial displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.

A superposition technique for deriving mean photon scattering statistics in plane-parallel cloudy atmospheres

Photon transport in a multiple scattering medium is critically dependent on scattering statistics, in particular the average number of scatterings. A superposition technique is derived to accurately determine the average number of scatterings encountered by reflected and transmitted photons within arbitrary layers in plane-parallel, vertically inhomogeneous clouds. As expected, the resulting scattering number profiles are highly dependent on cloud particle absorption and solar/viewing geometry. The technique uses efficient adding and doubling radiative transfer procedures, avoiding traditional time-intensive Monte Carlo methods. Derived superposition formulae are applied to a variety of geometries and cloud models, and selected results are compared with Monte Carlo calculations. Cloud remote sensing techniques that use solar reflectance or transmittance measurements generally assume a homogeneous plane-parallel cloud structure. The scales over which this assumption is relevant, in both the vertical and horizontal, can be obtained from the superposition calculations. Though the emphasis is on photon transport in clouds, the derived technique is applicable to any multiple scattering plane-parallel radiative transfer problem, including arbitrary combinations of cloud, aerosol, and gas layers in the atmosphere.

Radiative Horizontal Transport and Absorption in Stratocumulus Clouds

The equation of radiative energy balance in a homogeneous plane-parallel cloud accounts for the photon transport in the vertical direction only. From this equation, the absorption can be evaluated as a difference between the net radiative fluxes measured on the cloud top and bottom. Real clouds exhibit extreme horizontal variability of their optical and, hence, radiative properties. So the radiative energy balance equation for inhomogeneous clouds includes an extra term to describe the net energy transport in the horizontal directions (radiative horizontal transport). This study investigates the horizontal transport in nonhomogeneous stratocumulus clouds and its influence on the accuracy of absorption estimates. Using a realistic fractal model of marine stratocumulus clouds and Monte Carlo method, it is shown that the magnitude of horizontal transport 1) is comparable with those of albedo, transmittance, and absorptance and 2) depends strongly on the fractal dimension of cloud optical depth. Because of the horizontal transport, there is no unique dependence between optical and radiative properties of given pixel. The neglect of the horizontal transport is a major source of uncertainty in absorption estimates. Two possible ways of improving the inhomogeneous cloud absorption estimates from field measurements are discussed.

Radiative transfer in multifractal clouds

We studied effects of the cloud inhomogeneity in subcloud scale on the reflectance, transmittance, and absorptance of two‐dimensional, inhomogeneous clouds. We generated the inhomogeneous clouds as multifractal clouds with a lognormal multiplicative process. For such clouds, the information codimension C1 is a measure of the cloud inhomogeneity. Radiative transfer through the multifractal clouds was computed with a discrete angle radiative transfer model. The average reflectance, transmittance, and absorptance of multifractal clouds with a given codimension were estimated as averages of 200 realizations. They were computed for different sets of the C1 parameter, cloud total optical thickness, and asymmetry factor of cloud scatterers. An effective optical thickness of inhomogeneous clouds was defined empirically in the framework of a homogeneous, plane parallel cloud model. Consequently, computation of radiative flux in an inhomogeneous cloud could be transformed into that of an equivalent homogeneous, plane parallel cloud. For a two‐dimensional, inhomogeneous, absorbing cloud we found that an inhomogeneous cloud absorbs generally less energy than its homogeneous counterpart. An exception was found for inhomogeneous clouds characterized by a small information codimension, a large cloud optical thickness, and a large single‐scattering albedo and for which absorptance is much larger than for their homogeneous counterpart. However, this increase was less than 5% of the homogeneous cloud absorptance. The use of the effective optical thickness also enabled us to treat an inhomogeneous absorbing cloud as an equivalent homogeneous absorbing cloud and to estimate the radiative flux of the equivalent homogeneous cloud as an approximation to the one in the inhomogeneous cloud. We found no immediate need to conceive of a direct effect of the cloud inhomogeneity on the single‐scattering albedo, as far as we considered this treatment as a first‐order approximation. We discussed the use of the effective optical thickness in two‐stream radiative approximations. We also compared our results with those based on the independent pixel approximation.

Spectral Reflectance and Atmospheric Energetics in Cirrus-like Clouds. Part II: Applications of a Fourier-Riccati Approach to Radiative Transfer

One of the major sources of uncertainty in climate studies is the detection of cirrus clouds and characterization of their radiative properties. Combinations of water vapor absorption channels (e.g., 1.38 µm), ice-water absorption channels (e.g., 1.64 µm), and atmospheric window channels (e.g., 11 µm) in the imager, together with a lidar profiler on future EOS platforms, will contribute to enhancing our understanding of cirrus clouds. The aforementioned spectral channels are used in this study to explore the effects exerted by uncertainties in cloud microphysical properties (e.g., particle size distribution) and cloud morphology on the apparent radiative properties, such as spectral reflectance and heating and cooling rate profiles. As in Part I of our previous study, which establishes the foundations of the Fourier-Riccati method of radiative transfer in inhomogeneous media, cloud extinction and scattering functions are characterized by simple spatial variations with measured and hypothesized microphysics to facilitate our understanding of their radiative properties. Results of this study suggest that (i) while microphysical variations in the scattering and extinction functions of clouds affect the magnitudes of their spectral reflectances, cloud morphology significantly alters the shape of their angular distribution; (ii) spectral reflectances viewed near nadir are least affected by cloud variability; and (iii) cloud morphology can load to spectral heating and cooling rate profiles that differ substantially from their plane-parallel averaged equivalents. Since there are no horizontal thermal gradients in plane-parallel clouds, it may be difficult to correct for this deficiency.

Satellite Determination of Stratus Cloud Microphysical Properties

Abstract Satellite measurements of liquid water path from SSM/I, broadband albedo from ERBE, and cloud characteristics from ISCCP are used to study stratus regions. An average cloud liquid water path of 0.120 ± 0.032 kg m−2 is derived by dividing the average liquid water path for stratus areas by the fractional area coverage of cloud in the region. The diurnal range in this average cloud liquid water path is about 25%. Stratus cloud liquid water is positively correlated with cloud amount and is negatively correlated with low cloud-top temperature. Cloud liquid water path (LWP) and cloud albedo measurements are used to derive an effective droplet radius using the plane-parallel cloud albedo model of Slingo. The 2.5;dg by 2.5;dg grid boxes are first screened for completely overcast scenes in an attempt to justify the plane-parallel assumption. The mean effective droplet radius for this sample is 10.1 ± 4.4 μm. This serves as an upper bound since small-scale LWP variability is estimated to affect the average...

Absorption of Solar Radiation by Stratocumulus Clouds: Aircraft Measurements and Theoretical Calculations

Aircraft observations of shortwave radiative properties of stratocumulus clouds were carried out over the western North Pacific Ocean during January 1991. Two aircraft were equipped with a pair of pyranometers and near-infrared pyranometers. Downward and upward shortwave fluxes above and below the cloud were synchronously measured by two aircraft. The cloud radiative properties, especially the absorptance obtained from measurements, were compared with those calculated. Aircraft measurements and Monte Carlo calculations showed that spatial inhomogeneities of clouds cause horizontal radiative convergence and divergence, and that vertical radiative convergence-that is, absorptance with a usual definition-apparently becomes extremely large or negative. The apparent absorptance could be corrected by a method that evaluates the true absorption from the difference between the apparent visible and near-infrared absorptions. The corrected absorptance agreed well with the theoretical absorptance calculated with plane-parallel cloud models. It is also inferred that the anomalous absorption pointed out by aircraft observations in previous studies does not exist.