Independent Column Research Articles

Multi-channel counter-current chromatography for high-throughput fractionation of natural products for drug discovery

A multi-channel counter-current chromatography (CCC) method has been designed and fabricated for the high-throughput fractionation of natural products without complications sometimes encountered with other conventional chromatographic systems, such as irreversible adsorptive constituent losses and deactivation, tailing of solute peaks and contamination. It has multiple independent CCC channels and each channel connects independent separation column(s) by parallel flow tubes, and thus the multi-channel CCC apparatus can achieve simultaneously two or more independent chromatographic processes. Furthermore, a high-throughput CCC fractionation method for natural products has been developed by a combination of a new three-channel CCC apparatus and conventional parallel chromatographic devices including pumps, sample injectors, effluent detectors and collectors, and its performance has been displayed on the fractionation of ethyl acetate extracts of three natural materials Solidago canadensis, Suillus placidus, and Trichosanthes kirilowii, which are found to be potent cytotoxic to tumor cell lines in the course of screening the antitumor candidates. By combination of biological screening programs and preparative high-performance liquid chromatography (HPLC) purification, 22.8 mg 6β-angeloyloxykolavenic acid and 29.4 mg 6β-tigloyloxykolavenic acid for S. canadensis, 25.3 mg suillin for S. placidus, and 6.8 mg 23,24-dihydrocucurbitacin B for T. Kirilowii as their major cytotoxic principles were isolated from each 1000 mg crude ethyl acetate exctract. Their chemical structures were characterized by electrospray ionization mass spectrometry, one- and two-dimensional nuclear magnetic resonance. The overall results indicate the multi-channel CCC is very useful for high-throughput fractionation of natural products for drug discovery in spite of the solvent balancing requirement and the lower resolution of the shorter CCC columns.

The Plane-Parallel Albedo Bias of Liquid Clouds from MODIS Observations

Abstract The authors present the global plane-parallel shortwave albedo bias of liquid clouds for two months, July 2003 and January 2004. The cloud optical properties necessary to perform the bias calculations come from the operational Moderate Resolution Imaging Spectroradiometer (MODIS) Terra and MODIS Aqua level-3 datasets. These data, along with ancillary surface albedo and atmospheric information consistent with the MODIS retrievals, are inserted into a broadband shortwave radiative transfer model to calculate the fluxes at the atmospheric column boundaries. The plane-parallel homogeneous (PPH) calculations are based on the mean cloud properties, while independent column approximation (ICA) calculations are based either on 1D histograms of optical thickness or joint 2D histograms of optical thickness and effective radius. The (positive) PPH albedo bias is simply the difference between PPH and ICA albedo calculations. Two types of biases are therefore examined: 1) the bias due to the horizontal inhomogeneity of optical thickness alone (the effective radius is set to the grid mean value) and 2) the bias due to simultaneous variations of optical thickness and effective radius as derived from their joint histograms. The authors find that the global bias of albedo (liquid cloud portion of the grid boxes only) is ∼+0.03, which corresponds to roughly 8% of the global liquid cloud albedo and is only modestly sensitive to the inclusion of horizontal effective radius variability and time of day, but depends strongly on season and latitude. This albedo bias translates to ∼3–3.5 W m−2 of bias (stronger negative values) in the diurnally averaged global shortwave cloud radiative forcing, assuming homogeneous conditions for the fraction of the grid box not covered by liquid clouds; zonal values can be as high as 8 W m−2. Finally, the (positive) broadband atmospheric absorptance bias is about an order of magnitude smaller than the albedo bias. The substantial magnitude of the PPH bias underlines the importance of predicting subgrid variability in GCMs and accounting for its effects on cloud–radiation interactions.

Tests of Monte Carlo Independent Column Approximation in the ECHAM5 Atmospheric GCM

Abstract The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes allows a flexible treatment of unresolved cloud structure, and it is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Here, tests of McICA in the ECHAM5 atmospheric GCM are reported. ECHAM5 provides an interesting test bed for McICA because it carries prognostic variables for the subgrid-scale probability distribution of total water content, which allows us to determine subgrid-scale cloud variability directly from the resolved-scale model variables. Three experiments with differing levels of radiative noise, each consisting of ten 6-yr runs, are performed to estimate the impact of McICA noise on simulated climate. In an experiment that attempted to deliberately maximize McICA noise, a systematic reduction in low cloud fraction occurred. For a more reasonable implementation of McICA, the impact of noise is very small, although statistically discernible. In terms of the impacts of noise, McICA appears to be a viable approach for use in ECHAM5. However, to improve the simulation of cloud radiative effects, realistic representation of both unresolved and resolved cloud structures is needed, which remains a challenging problem. Comparison of ECHAM5 data with a global cloud system–resolving model dataset and with International Satellite Cloud Climatology Project data suggested two problems related to unresolved cloud structures. First, ECHAM5 appears to underestimate subgrid-scale cloud variability. This problem seems partly related to the use of the beta distribution scheme for total water content in ECHAM5: in its current form, the scheme is unable to generate highly inhomogeneous clouds (relative standard deviation of condensate amount >1). Second, it appears that in ECHAM5, overcast cloud layers occur too frequently and partially cloudy layers too rarely. This problem is not unique to the beta distribution scheme; in fact, it is more pronounced when using an alternative, relative humidity–based cloud fraction scheme.

Performance comparison of aperture codes for multimodal, multiplex spectroscopy

We experimentally evaluate diverse static independent column codes in a coded aperture spectrometer. The performance of each code is evaluated based on the signal-to-noise ratio (SNR), defined as the peak value in the spectrum to the standard deviation of the background noise, as a function of subpixel vertical misalignments. Among the code families tested, an S-matrix-based code produces spectral reconstructions with the highest SNR. The SNR is least sensitive to vertical subpixel misalignments on the detector with a Hadamard-matrix-based code. Finally, the increased sensitivity of a spectrometer using a coded aperture instead of a slit is demonstrated.

Recovery of trifluoroacetic acid from dilute aqueous solutions by reactive distillation

It is difficult to recover trifluoroacetic acid (TFA) from its dilute aqueous solutions by conventional techniques. This work investigates the feasibility of using reactive distillation to recover TFA through esterification with 2-propanol. A kinetic model is proposed based on batch reactor data. Experiments performed using reactive distillation in batch and continuous modes, show significant recovery. Independent column simulations, based on kinetics and vapor–liquid equilibrium (VLE) developed in this work, agree well with our experimental results. The validated model is further used to obtain suitable design and operating parameters to give nearly complete recovery. A complete process recovery process sheet is suggested based on the results obtained.

Adsorption equilibrium of fructosyltransferase on a weak anion-exchange resin

The adsorption equilibrium of a glycoprotein, fructosyltransferase from Aureobasidium pullulans, on an anion-exchange resin, Sepabeads FP-DA activated with 0.1 M NaOH, was investigated. The adsorption isotherms were determined at 20 °C in a phosphate–citrate buffer with pH 6.0 using the static method. Sodium chloride was used to adjust the ionic strength in the range from 0.0215 to 0.1215 mol dm −3 which provided conditions varying from a weak effect of salt concentration on protein binding to its strong suppression. The equilibrium data were very well fitted by means of the steric mass-action model when the ion-exchange capacity of 290 mmol dm −3 was obtained from independent frontal column experiments. The model fit provided the protein characteristic charge equal to 1.9, equilibrium constant 0.326, and steric factor 1.095 × 10 5.

A Sensitivity Study of the Effect of Horizontal Photon Transport on the Radiative Forcing of Contrails

Abstract With the rapid growth in air travel, there is concern over the radiative impact of contrails and aircraft-induced cirrus on climate. Previous radiation calculations on contrails have almost all used the independent column approximation, which neglects the transport of photons through the sides of the contrail, but in this study the 3D effects are quantified using the Spherical Harmonic Discrete Ordinate Method (SHDOM). The authors have investigated the dependence of shortwave and longwave radiative forcing on contrail aspect ratio, optical depth, solar zenith angle, solar azimuth angle relative to contrail orientation, particle size, particle habit, surface albedo, and surface temperature. It is found that inclusion of 3D transport results in an increase in the positive longwave radiative forcing of the contrail and either an increase or a decrease in the magnitude of the negative shortwave radiative forcing depending on the orientation of the contrail with respect to the sun. Although these two effects are individually quite modest (of order 10%), the fact that the total shortwave and longwave forcings largely cancel during the day means that the relative change in the net radiative forcing due to the 3D effect is substantial; in some cases this results in a doubling of the net forcing of the contrail, in other cases changing its sign. On a more general note, the relatively simple geometry of contrail cirrus provides an ideal test case for explaining the various mechanisms by which 3D photon transport can change the radiative effect of clouds, which can be rather difficult to visualize for more complex cloud scenarios.

Effect of Transient Irrigation on Boron Transport in Soils

Water redistribution and solute concentration changes caused by water evaporation can affect B transport in unsaturated soils under a subsurface transient water flow regime. Our objective was to assess the effect of nonequilibrium adsorption on B transport in unsaturated, homogeneous soil under periodic infiltration cycles using adsorption and transport parameters obtained from independent batch and column experiments. Column experiments using flow interruption were conducted at two pore‐water velocities: 0.25 and 2.5 cm h−1 Transport of B at low velocity was unaffected by flow interruption, whereas interruption of fast flow resulted in appreciable perturbation of the B concentration in outflows. The convection–dispersion equation (CDE) with a rate‐limited reaction term was fitted to the fast‐flow B breakthrough curves (BTCs) to determine the mass‐transfer rate coefficients controlling nonequilibrium B transport behavior in soils. This CDE, coupled with the Richards equation, was used to simulate B transport in unsaturated soils under irrigation cycles consisting of water infiltration, internal drainage (redistribution), and evaporation. The B transport under transient nonmonotonic flow depended strongly on the rate‐limited step of B adsorption. At a small value of the mass‐transfer coefficient, the B BTCs had a characteristically jagged shape, showing increase–decrease cycles in solution B concentrations. The B adsorption tended to balance the solution B concentration increase caused by water evaporation. The final B concentrations, however, exceeded unity in the upper part of the BTCs that were obtained at different soil depths. The results revealed that deviation from adsorption equilibrium may lead to appreciable changes in solution B concentration, especially in the topsoil where the water flow is explicitly transient and nonmonotonic.

Longwave infrared (LWIR) coded aperture dispersive spectrometer

We describe a static aperture-coded, dispersive longwave infrared (LWIR) spectrometer that uses a microbolometer array at the detector plane. The two-dimensional aperture code is based on a row-doubled Hadamard mask with transmissive and opaque openings. The independent column code nature of the matrix makes for a mathematically well-defined pattern that spatially and spectrally maps the source information to the detector plane. Post-processing techniques on the data provide spectral estimates of the source. Comparative experimental results between a slit and coded aperture for emission spectroscopy from a CO(2) laser are demonstrated.

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 influence of broken cloudiness on cloud top height retrievals using nadir observations of backscattered solar radiation in the oxygen A-band

The paper is devoted to theoretical studies of the influence of cloud inhomogeneities on cloud top height (CTH) retrievals based on top-of-atmosphere nadir reflectance observations in the oxygen A-band. A three-demensional (3D) Monte Carlo code is used to simulate highly resolved spectral measurements in the oxygen A-band. These synthetic radiances are used as input for the retrieval code SACURA based on asymptotic radiative transfer theory and the independent pixel approximation. The results show that the effect of cloud inhomogeneity on the derived CTHs is small. While we found considerable 3D effects in the reflectance of more than 30% compared to the independent column approximation, the spectral dependence of the difference was small. As SACURA is mainly based on spectral ratios, the retrieval results are hardly affected by the large absolute deviations. In consequence, SACURA is capable to retrieve CTHs with an accuracy of better than 1.5 km for overcast and also most partially cloudy cases.

Anomalous Distortion and Stacking Column Formation of [Ni(dmit)2]− Induced by Propeller-Shaped Dye Cations, Crystal Violet and Basic Fuchsin

Abstract (CV+)[Ni(dmit)2]·1/2(C6H6) (1) and (BF+)[Ni(dmit)2] (2) (dmit = 2-thioxo-1,3-dithiole-4,5-dithiolato, CV+ = cation of Crystal Violet, BF+ = cation of Basic Fuchsin) were prepared and characterized by X-ray crystal structural analysis. In the crystal structure of 1, the Ni(dmit)2 unit was bent at Ni in a V shape with an angle of 13.7° and tetrahedral distortion of 8.8° around Ni was also present that originated from the steric effect of the propeller-shaped CV cation. In the case of 2, BF and [Ni(dmit)2]− formed an independent stacking column in which [Ni(dmit)2]− were stacked alternately rotated with an angle of 90° to each other. 1 and 2 exhibited semiconducting behavior with room-temperature conductivities of 2.9 × 10−7 and 9.0 × 10−5 S cm−1, respectively.

The Monte Carlo Independent Column Approximation’s Conditional Random Noise: Impact on Simulated Climate

Abstract The Monte Carlo Independent Column Approximation (McICA) method for computing domain-average radiative fluxes is unbiased with respect to the full ICA, but its flux estimates contain conditional random noise. Results for five experiments are used to assess the impact of McICA-related noise on simulations of global climate made by the NCAR Community Atmosphere Model (CAM). The experiment with the least noise (an order of magnitude below that of basic McICA) is taken as the reference. Two additional experiments help demonstrate how the impact of noise depends on the time interval between calls to the radiation code. Each experiment is an ensemble of seven 15-month simulations. Experiments with very high noise levels feature significant reductions to cloudiness in the lowermost model layer over tropical oceans as well as changes in highly related quantities. This bias appears immediately, stabilizes after a couple of model days, and appears to stem from nonlinear interactions between clouds and radiative heating. Outside the Tropics, insignificant differences prevail. When McICA sampling is confined to cloudy subcolumns and when, on average, 50% more samples, relative to basic McICA, are drawn for selected spectral intervals, McICA noise is much reduced and the results of the simulation are almost statistically indistinguishable from the reference. This is true both for mean fields and for the nature of fluctuations on scales ranging from 1 day to at least 30 days. While calling the radiation code once every 3 h instead of every hour allows the CAM additional time to incorporate McICA-related noise, the impact of noise is enhanced only slightly. In contrast, changing the radiative time step by itself produces effects that generally exceed the impact of McICA’s noise.

Atmospheric radiative transfer through global arrays of 2D clouds

Shortwave and longwave 2D radiative transfer calculations were performed using Monte Carlo radiative transfer models and output from a global climate model (GCM) that employed, in each of its columns, a 2D cloud system‐resolving model (CSRM) with a horizontal grid‐spacing Δx of 4 km. CSRM output were sampled every 9 hours for December 2000. Radiative fluxes were averaged to the GCM's grid. Monthly‐mean top of atmosphere (TOA) shortwave flux differences between 2D radiative transfer and the Independent Column Approximation (ICA) are at most 5 W m−2 in the tropics with a zonal‐average of 1.5 W m−2. These differences are 2 to 10 times smaller than those stemming from the maximum‐random overlap model and neglect of horizontal variability of cloud. Corresponding longwave differences are approximately 3 times smaller than their shortwave counterparts. Use of CSRM data with Δx < 4 km may roughly double the reported differences between 2D and ICA TOA SW fluxes.

Radiative sensitivities for cloud structural properties that are unresolved by conventional GCMs

AbstractThe Independent Column Approximation (ICA), a stochastic subgrid‐scale cloudy column generator, and a dataset produced by an array of two‐dimensional cloud system‐resolving models are used to estimate radiative sensitivities and uncertainties for parameters that describe the macrostructure of layered cloud at scales unresolved by conventional global climate models (GCMs). Three cloud structural parameters are considered: vertical overlap of fractional cloud, vertical overlap of cloud condensate, and horizontal variability of condensate. Radiative sensitivity is the derivative of top of atmosphere (TOA) fluxes with respect to a cloud structural parameter. Radiative uncertainty is defined as the product of radiative sensitivity and corresponding uncertainty in structural parameter. It is argued that radiative sensitivities and uncertainties can help direct and prioritize development of subgrid‐scale parametrizations.Using estimates of sensitivities and uncertainties for structural parameters, it is shown that uncertainties in TOA short‐wave fluxes for cloud fraction overlap and horizontal variability are of similar magnitude averaged over the globe but display distinct spatial differences. Corresponding values for overlap of condensate are smaller and thus less important. For long‐wave radiation, cloud horizontal variability is generally the most important of the three parameters considered here, but sensitivities, and thus uncertainties, are smaller than those for short‐wave radiation. It is estimated that uncertainties associated with overlap of fractional cloud and horizontal variability are approximately as large as those associated with effective size of cloud particles. These results reinforce prior claims that GCM parametrizations for cloud overlap and horizontal variability should be addressed together, especially at solar wavelengths. These results are echoed in the appendix which examines TOA forcings that would arise in a GCM if the maximum‐random overlap of homogeneous clouds model was replaced by a model that addresses the cloud parameters mentioned above. Copyright © 2005 Royal Meteorological Society.

A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds

AbstractThe three‐dimensional structure of clouds is known to be important for determining their radiative effects, but it is difficult to obtain this structure directly from observations. In this paper a stochastic model is described that is capable of simulating the structural properties unique to cirrus: fallstreak geometry and shear‐induced mixing. We first present an analysis of time–height cloud radar sections from southern England to extract the cirrus parameters of interest. It is found that horizontal power spectra of the logarithm of ice‐water content (estimated from radar reflectivity factor and temperature) typically exhibit a spectral slope of around −5/3 near cloud top that decreases with depth into the cloud, to values as low as −3.5 in some cases. This decrease can be explained by wind shear coupled with a spread of particle fall speeds leading to a homogenization that acts preferentially at smaller scales. The power spectra exhibit a distinct scale break, becoming flat at scales larger than around 50 km (the ‘outer scale’). The orientation of the fallstreaks may be predicted from the profile of mean wind and mean ice fall speed. We then describe the stochastic model, which takes as input profiles of the mean and fractional standard deviation of ice‐water content, spectral slope, outer scale and wind speed. It first generates an isotropic 3‐D fractal field by performing an inverse 3‐D Fourier transform on a matrix of simulated Fourier coefficients with amplitudes consistent with the observed 1‐D spectra. Random phases for the coefficients allow multiple realizations of a cloud with the same statistical properties to be generated. Then horizontal slices from the domain are manipulated in turn to simulate horizontal displacement and changes to the spectra with height. Finally the field is scaled to produce the observed mean and fractional standard deviation of ice‐water content. Vertical 2‐D slices extracted from the domain are very similar in appearance to cloud radar observations. Radiative‐transfer calculations using the independent column approximation are used to show that the different fallstreak orientation resulting from different wind shears can change mean top‐of‐atmosphere radiative fluxes by in excess of 45 W m−2 in the short‐wave and 15 W m−2 in the long‐wave. The effect of wind shear to induce horizontal mixing causes an additional but smaller radiative effect. We also investigate the biases that would be expected from the assumptions made in the radiation schemes of general‐circulation models (GCMs). It is found that there is some compensation between the errors arising from the assumptions of horizontal homogeneity and maximum‐random overlap; if a GCM were to improve the overlap assumption but still assume clouds to be horizontally homogeneous then the total error in cloud radiative effect would be likely to increase. Copyright © 2005 Royal Meteorological Society.

The Impact of Model Resolution on Differences between Independent Column Approximation and Monte Carlo Estimates of Shortwave Surface Irradiance and Atmospheric Heating Rate

Abstract Within general circulation models (GCMs), domain average radiative fluxes are computed using plane-parallel radiative transfer algorithms that rely on cloud overlap schemes to account for clouds not resolved at the horizontal resolution of a grid cell. These parameterizations have a strong statistical approach and have difficulty being applied well to all cloudy conditions. A more physically based superparameterization has been developed that captures subgrid cloud variability using an embedded cloud system resolving model (CSRM) within each GCM grid cell. While plane-parallel radiative transfer computations are generally appropriate at the scale of a GCM grid cell, their suitability for the much higher spatially resolved CSRMs (2–4 km) is unknown because they ignore photon horizontal transport effects. The purpose of this study is to examine the relationship between model horizontal resolution and 3D radiative effects by computing the differences between independent column approximations (ICA) and 3D Monte Carlo estimates of shortwave surface irradiance and atmospheric heating rate. Shortwave radiative transfer computations are performed on a set of six 2D fields composed of stratiform and convective liquid water and ice clouds. To establish how 3D effects vary with the size of a grid cell, this process is repeated as the model resolution is progressively degraded from 200 to 20 km. For shortwave surface irradiance, the differences between the 3D and ICA results can reach 500 W m−2. At model resolutions of between 2.0 and 5.0 km the difference for almost all columns is reduced to a maximum of ±100 W m−2. For atmospheric heating rates assessed at the level of individual model cells, 3D radiative effects can approach a maximum value of ±1.2 K h−1 when the horizontal column size is 200 m. However, between model resolutions of 2.0 and 5.0 km, 3D radiative effects are reduced to well below ±0.1 K h−1 for a large majority of the cloudy cells. While this finding seems to bode well for the CSRM, the results ultimately need to be understood within the context of how 3D radiative effects impact not only heating rates but also cloud dynamics.

The Accuracy of Determining Three-Dimensional Radiative Transfer Effects in Cumulus Clouds Using Ground-Based Profiling Instruments

Abstract 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.

Impact of Cloud Cover on Solar Radiative Biases in Deep Convective Regimes

Abstract Conflicting claims have been made concerning the magnitude of the bias in solar radiative transfer calculations when horizontal photon transport is neglected for deep convective scenarios. The difficulty of obtaining a realistic set of cloud scenes for situations of complex cloud geometry, while certain characteristics such as total cloud cover are systematically controlled, has hindered the attempt to reach a consensus. Here, a simple alternative approach is adopted. An ensemble of cloud scenes generated by a cloud resolving model are modified by an idealized function that progressively alters the cirrus anvil coverage without affecting the realism of the scene produced. Comparing three-dimensional radiative calculations with the independent column approximation for all cloud scenes, it is found that the bias in scene albedo can reach as much as 22% when the sun is overhead and 46% at low sun angles. The bias is an asymmetrical function of cloud cover with a maximum attained at cirrus anvil cloud cover of approximately 30%–40%. With a cloud cover of 15%, the bias is half its maximum value, while it is limited for coverage exceeding 80%. The position of the peak occurs at the cloud cover coinciding with the maximum number of independent clouds present in the scene. Increasing the cloud cover past this point produces a decrease in the number of isolated clouds because of cloud merging, with a consequential bias reduction. With this systematic documentation of the biases as a function of total cloud cover, it is possible to identify two contributions to the total error: the geometrical consequences of the effective cloud cover increase at low sun angles and the true 3D scattering effect of photons deviating from the original path direction. An attempt to account for the former geometrical contribution to the 1D bias is made by performing a simple correction technique, whereby the field is sheared by the tangent of the solar zenith angle. It is found that this greatly reduces the 1D biases at low sun angles. Because of the small aspect ratio of the cirrus cloud deck, the remaining bias contribution is small in magnitude and almost independent of solar zenith angle.

Computation of Domain-Averaged Irradiance Using Satellite-Derived Cloud Properties

Abstract The respective errors caused by the gamma-weighted two-stream approximation and the effective thickness approximation for computing the domain-averaged broadband shortwave irradiance are evaluated using cloud optical thicknesses derived from 1 h of radiance measurements by the Moderate Resolution Imaging Spectrometer (MODIS) over footprints of Clouds and the Earth’s Radiant Energy System (CERES) instruments. Domains are CERES footprints of which dimension varies approximately from 20 to 70 km, depending on the viewing zenith angle of the instruments. The average error in the top-of-atmosphere irradiance at a 30° solar zenith angle caused by the gamma-weighted two-stream approximation is 6.1 W m−2 (0.005 albedo bias) with a one-layer overcast cloud where a positive value indicates an overestimate by the approximation compared with the irradiance computed using the independent column approximation. Approximately one-half of the error is due to deviations of optical thickness distributions from a gamma distribution and the other half of the error is due to other approximations in the model. The error increases to 14.7 W m−2 (0.012 albedo bias) when the computational layer dividing the cloud layer is increased to four. The increase is because of difficulties in treating the correlation of cloud properties in the vertical direction. Because the optical thickness under partly cloudy conditions, which contribute two-thirds of cloudy footprints, is smaller, the error is smaller than under overcast conditions; the average error for partly cloudy condition is −2.4 W m−2 (−0.002 albedo bias) at a 30° solar zenith angle. The corresponding average error caused by the effective thickness approximation is 0.5 W m−2 for overcast conditions and −21.5 W m−2 (−0.018 albedo bias) for partly cloudy conditions. Although the error caused by the effective thickness approximation depends strongly on the optical thickness, its average error under overcast conditions is smaller than the error caused by the gamma-weighted two-stream approximation because the errors at small and large optical thicknesses cancel each other. Based on these error analyses, the daily average error caused by the gamma-weighted two-stream and effective thickness approximations is less than 2 W m−2.