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Vertical velocities and microphysical processes within deep convection are intricately linked, having wide-ranging impacts on water and mass vertical transport, severe weather, extreme precipitation, and the global circulation. The goal of this research is to investigate the functional form of the relationship between vertical velocity (w) and microphysical processes that convert water vapor into condensed water (M) in deep convection. We examine an ensemble of high-resolution simulations spanning a range of tropical and midlatitude environments, a variety of convective organizational modes, and different model platforms and microphysics schemes. The results demonstrate that the relationship between w and M is robustly linear, with the slope of the linear fit being primarily a function of temperature and secondarily a function of supersaturation. The R2 of the linear fit is generally above 0.6 except near the freezing and homogeneous freezing levels. The linear fit is examined both as a function of local in-cloud temperature and environmental temperature. The results for in-cloud temperature are more consistent across the simulation suite, although environmental temperatures are more useful when considering potential observational applications. The linear relationship between w and M is substituted into the condensate tendency equation and rearranged to form a diagnostic equation for w. The performance of the diagnostic equation is tested in several simulations, and it is found to diagnose the storm-scale updraft speeds to within 1 m s−1 throughout the upper half of the clouds. Potential applications of the linear relationship between w and M and the diagnostic w equation are discussed.

The latest configuration of the Hadley Centre Global Environmental Model version 3 (HadGEM3) contains significant changes in the formulation of warm rain processes and aerosols. We evaluate the impacts of these changes in the simulation of warm rain formation processes using A-Train observations. We introduce a new model evaluation tool, quartile-based Contoured Frequency by Optical Depth Diagrams (CFODDs), in order to fill in some blind spots that conventional CFODDs have. Results indicate that HadGEM3 has weak linkage between the size of particle radius and warm rain formation processes, and switching to the new warm rain microphysics scheme causes more difference in warm rain formation processes than switching to the new aerosol scheme through reducing overly produced drizzle mode in HadGEM3. Finally, we run an experiment in which we perturb the second aerosol indirect effect (AIE) to study the rainfall-aerosol interaction in HadGEM3. Since the large changes in the cloud droplet number concentration (CDNC) appear in the AIE experiment, a large impact in warm rain diagnostics is expected. However, regions with large fractional changes in CDNC show a muted change in precipitation, arguably because large-scale constraints act to reduce the impact of such a big change in CDNC. The adjustment in cloud liquid water path to the AIE perturbation produces a large negative shortwave forcing in the midlatitudes.

This study examines the warm rain formation process over the global ocean in global climate models. Methodologies developed to analyze CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) satellite observations are employed to investigate the cloud-to-precipitation process of warm clouds and are applied to the model results to examine how the models represent the process for warm stratiform clouds. Despite a limitation of the present study that compares the statistics for stratiform clouds in climate models with those from satellite observations, including both stratiform and (shallow) convective clouds, the statistics constructed with the methodologies are compared between the models and satellite observations to expose their similarities and differences. A problem common to some models is that they tend to produce rain at a faster rate than is observed. These model characteristics are further examined in the context of cloud microphysics parameterizations using a simplified one-dimensional model of warm rain formation that isolates key microphysical processes from full interactions with other processes in global climate models. The one-dimensional model equivalent statistics reproduce key characteristics of the global model statistics when corresponding autoconversion schemes are assumed in the one-dimensional model. The global model characteristics depicted by the statistics are then interpreted as reflecting behaviors of the autoconversion parameterizations adopted in the models. Comparisons of the one-dimensional model with satellite observations hint at improvements to the formulation of the parameterization scheme, thus offering a novel way of constraining key parameters in autoconversion schemes of global models.

Observations from multiple satellites and large-eddy simulations (LESs) from the Regional Atmospheric Modeling System (RAMS) are used to determine the extent to which free-tropospheric clouds (FTCs) affect the properties of stratocumulus. Overlying FTCs decrease the cloud-top radiative cooling in stratocumulus by an amount that depends on the upper-cloud base altitude, cloud optical thickness, and abundance of moisture between the cloud layers. On average, FTCs increase the downward longwave radiative flux above stratocumulus clouds (at 3.5 km) by approximately 30 W m−2. As a consequence, this forcing translates to a relative decrease in stratocumulus cooling rates by about 20%. Overall, the reduced cloud-top radiative cooling decreases the turbulent mixing, vertical development, and precipitation rate in stratocumulus clouds at night. During the day these effects are greatly reduced because the overlying clouds shade the stratocumulus from strong solar radiation, thus reducing the net radiative effect by the upper cloud. Differences in liquid water path are also observed in stratocumulus; however, the response is tied to the diurnal cycle and the time scale of interaction between the FTCs and the stratocumulus. Radiative effects by FTCs tend to be largest in the midlatitudes where the clouds overlying stratocumulus tend to be more frequent, lower, and thicker on average. In conclusion, changes in net radiation and moisture brought about by FTCs can significantly affect the dynamics of marine stratocumulus and these processes should be considered when evaluating cloud feedbacks in the climate system.

This study examines the warm rain formation process in global and regional cloud-resolving models. Methodologies developed to analyze CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) satellite observations are employed to investigate the cloud-to-precipitation processes and are applied to model results for comparisons with corresponding statistics from the observations. Three precipitation categories of no precipitation, drizzle, and rain are defined according to nonattenuated near-surface radar reflectivity, and their fractional occurrences and the probability of precipitation are investigated as a function of cloud properties such as droplet size, optical thickness, droplet number concentration, and liquid water path. The comparisons reveal how the models are qualitatively similar to, but quantitatively different from, observations in terms of cloud-to-rainwater conversion processes. Statistics from one model reveal a much faster formation of rain than observed, with drizzle occurrence being much less frequent, whereas statistics from the other model illustrate rain formation closer to satellite observations but still faster formation of drizzle water. Vertical profiles of radar reflectivity that are rescaled as a function of in-cloud optical depth and classified according to particle size are also compared. The results show that each model indicates systematically faster formation of rain and drizzle, respectively, than observed in vertical profiles although they indicate that the cloud-to-rain transitions are qualitatively similar to observations. These results characterize the model behavior in terms of warm cloud microphysics and then point to a possible area of model improvement for more realistic representation of warm rain formation processes.

The impacts of enhanced aerosol concentrations such as those associated with dust intrusions on the trimodal distribution of tropical convection have been investigated through the use of large-domain (10 000 grid points), fine-resolution (1 km), long-duration (100 days), two-dimensional idealized cloud-resolving model simulations conducted under conditions of radiative–convective equilibrium (RCE). The focus of this research is on those aerosols that serve primarily as cloud condensation nuclei (CCN). The results demonstrate that the large-scale organization of convection, the domain-averaged precipitation, and the total cloud fraction show only show a weak response to enhanced aerosol concentrations. However, while the domainwide responses to enhanced aerosol concentrations are weak, aerosol indirect effects on the three tropical cloud modes are found to be quite significant and often opposite in sign, a fact that appears to contribute to the weaker domain response. The results suggest that aerosol indirect effects associated with shallow clouds may offset or compensate for the aerosol indirect effects associated with congestus and deep convection systems and vice versa, thus producing a more moderate domainwide response to aerosol indirect forcing. Finally, when assessing the impacts of aerosol indirect forcing associated with CCN on the characteristics of tropical convection, several aspects need to be considered, including which cloud mode or type is being investigated, the field of interest, and whether localized or systemwide responses are being examined.

Aerosols are known to have both direct and indirect effects on clouds through their role as cloud condensation nuclei. This study examines the effects of differing aerosol concentrations on convective storms developing under different environments. The Regional Atmospheric Modeling System (RAMS), a cloud-resolving model with sophisticated microphysical and aerosol parameterization schemes, was used to achieve the goals of this study. A sounding that would produce deep convection was chosen and consistently modified to obtain a variety of CAPE values. Additionally, the model was initiated with varying concentrations of aerosols that were available to act as cloud condensation nuclei. Each model run produced long-lived convective storms with similar storm development, but they differed slightly based on the initial conditions. Runs with higher initial CAPE values produced the strongest storms overall, with stronger updrafts and larger amounts of accumulated surface precipitation. Simulations initiated with larger concentrations of aerosols developed similar storm structures but showed some distinctive dynamical and microphysical changes because of aerosol indirect effects. Many of the changes seen because of varying aerosol concentrations were of either the same order or larger magnitude than those brought about by changing the convective environment.

This study describes an approach for combining CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) satellite observations to investigate the microphysical processes of warm clouds on the global scale. MODIS column optical thickness is vertically distributed between the cloud top and cloud bottom according to adiabatic and condensational growth assumptions and used as a vertical coordinate system to analyze profiles of CloudSat-observed radar reflectivity. The reflectivity profiles thus rescaled as a function of the in-cloud optical depth clearly depict how the cloud-to-rain particle growth processes take place within the cloud layer and how these processes vary systematically with variations in MODIS-derived effective particle radius. It is also found that the effective radii retrieved using two different wavelengths of MODIS tend to trace the microphysical change of reflectivity profiles in a different way because of the difference in the layer depth that characterizes these two effective radii. The reflectivity profiles as a function of optical depth are also interpreted in terms of drop collection processes based on the continuous collection model. The slope of the reflectivity change with optical depth provides a gross measure of the collection efficiency factor. The systematic changes of reflectivity profiles with MODIS-derived particle sizes are then interpreted as demonstrating a strong dependency of the collection efficiency on particle size. These results provide a quantitative insight into the drop collection process of warm clouds in the real atmosphere.

Hydrometeor droplet growth processes are inferred from a combination of Aqua/Moderate Resolution Imaging Spectroradiometer (MODIS) cloud particle size observations and CloudSat/Cloud Profiling Radar (CPR) observations of warm water clouds. This study supports the inferences of a related paper (Part I) (i) that MODIS-retrieved cloud droplet radii (CDR) from the 3.7-μm channel (R37) are influenced by the existence of small droplets at cloud top and (ii) that the CDR obtained from 1.6- (R16) and 2.1-μm (R21) channels contain information about drizzle droplets deeper into the cloud as well as cloud droplets. This interpretation is shown to be consistent with radar reflectivities when matched to CDR that were retrieved from MODIS data. This study demonstrates that the droplet growth process from cloud to rain via drizzle proceeds monotonically with the evolution of R16 or R21 from small cloud drops (on the order of 10–12 μm) to drizzle (CDR greater than 14 μm) to rain (CDR greater than 20 μm). Thus, R16 or R21 is an indicator of hydrometeor droplet growth processes whereas R37 does not contain information about coalescence. A new composite analysis, the contoured frequency diagram, is introduced to combine CloudSat/CPR reflectivity profiles and reveals a distinct trimodal population of reflectivities corresponding to cloud, drizzle, and rain modes.

This study examines the sensitivity of the retrieved cloud droplet radii (CDR) to the vertical inhomogeneity of droplet radii, including the existence of a drizzle mode in clouds. The focus of this study is warm water-phase clouds. Radiative transfer simulations of three near-infrared Moderate Resolution Imaging Spectroradiometer (MODIS) channels centered on wavelengths of 1.6, 2.1, and 3.7 μm reveal that the retrieved CDR are strongly influenced by the vertical inhomogeneity of droplet size including (i) the existence of small cloud droplets at the cloud top and (ii) the existence of the drizzle mode. The influence of smaller droplets at cloud top affects the 3.7-μm channel most, whereas the presence of drizzle influences radiances of both the 2.1- and 1.6-μm channels more than the 3.7-μm channel. Differences in the CDR obtained from MODIS 1.6-, 2.1-, and 3.7-μm channels that appear in global analysis of MODIS retrievals and the CDR derived from data collected during the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) intensive observation period in 1987 can be explained by the results obtained from the sensitivity experiments of this study.

Observations by Johnson et al. depict regions of active tropical convection as possessing increased relative humidity through a deep layer and reduced low-level static stability when compared to nonconvecting regions. Shallow cumulus clouds, congestus clouds, and deep convection all coexist within these convecting regions. This investigation explores the effect that radiation might have on the tropical cloud distributions by using large-domain (20 000 km) radiative–convective equilibrium cloud-resolving model (RCE-CRM) experiments that reproduce similar moisture, stability, and cloud structures to those observed. Radiation is found to significantly increase the amount of shallow and intermediate-level clouds (tops between 1.5 and 5 km) by increasing low-level stability and thus promoting additional low-level cloud detrainment. The mechanism by which radiation stabilizes the low levels is found to differ between convectively suppressed and active regions. In convectively suppressed regions, strong relative humidity gradients within the trade inversion layer produce a low-level cooling maximum that further stabilizes the stable layer, much as proposed by Mapes and Zuidema. In convectively active regions, sufficiently moist columns with no relative humidity gradients are also found to produce a low-level cooling maximum that stabilizes the lower levels. This cooling maximum is due to the complicated effects of the water vapor continuum and is sensitive to the absolute moisture path. Because of the dependence on absolute moisture, the radiative enhancement of shallow and intermediate-level clouds in convectively active regions is potentially sensitive to SSTs.

This paper examines feedbacks between the radiative heating of clouds and convection in the context of numerical radiative–convective equilibrium experiments conducted using both 2D and 3D versions of a cloud-resolving model. The experiments are conducted on a large domain, and equilibria develop as juxtaposed regions of dry and moist air that are connected and sustained by circulations between them. The scales of such variability are large and differ significantly between the 2D and 3D versions of the experiments. Three sensitivity experiments were conducted which, when compared to the control experiment, provide insight into the relative influences of cloud–radiation feedback mechanisms on the equilibrium state achieved. It emerges from the experiments conducted that radiation feedbacks operate via two main pathways, with the radiative heating by high clouds being the governing process of both. The predominant bimodal nature of the moist equilibrium is established by gradients in radiative heating that, in turn, are determined by high cloud differences between wet and dry regions that, in turn, are controlled by convection. Convection, on the other hand, is also influenced by the localized effects of cloud radiative heating by these extended layers of high clouds. The results of the experiments demonstrate how high cloud radiative heating, which is a by-product of the convection itself, provides a feedback that acts to regulate the high clouds produced in the wet convective areas of the equilibrium.

This paper presents a critical review of a number of popular methods that have been developed to retrieve cloud and precipitation properties from satellite radiance measurements. The emphasis of the paper is on the retrieval uncertainties associated with these methods, as these shape future data assimilation applications, either in the form of direct radiance assimilation or assimilation of retrieved geophysical data, or even in the use of retrieved information as a source of model error characterization. It is demonstrated throughout the paper how cloud and precipitation observing systems developed around seemingly simple concepts are in fact very complex and largely underconstrained, which explains, in part, why assigning realistic errors to these properties has been so elusive in the past. Two primary sources of error that define the observing system are highlighted throughout: (i) the first source is errors associated with the identification of cloudy scenes from clear scenes and the identification of precipitation in cloudy scenes from nonprecipitating cloudy scenes. The problems of discriminating of cloud clear and cloud precipitation are illustrated using examples drawn from microwave cloud liquid water path and precipitation retrievals. (ii) The second source is errors introduced by the forward model and its related parameters. The forward model generally contains two main components: a model of the atmosphere and the cloud and precipitation structures imbedded in that atmosphere and a forward model of the radiative transfer that produces the synthetic measurement that is ultimately compared to the measurement. The vast majority of methods developed for deriving cloud and precipitation information from satellite measurements is highly sensitive to these model parameters, which merely reflects the underconstrained nature of the problem and the need for other information in deriving solutions. The cloud and precipitation retrieval examples presented in this paper are most often constructed around very unrealistic atmosphere models typically composed of just a few layers. The consequence is that the retrievals become too sensitive to the unobserved parameters of those layers and the atmosphere above and below. Clearly a better definition of the atmospheric state, and the vertical structure of clouds and precipitation, are needed to improve the information extracted from satellite observations, and it is for this reason that the combination of active and passive measurements offers much hope for improving cloud and precipitation retrievals.

The role of horizontal inhomogeneity in radiative transfer through cloud fields is investigated within the context of the two-stream approximation. Spatial correlations between cloud optical properties and the radiance field are introduced in the three-dimensional radiative transfer equation and lead to a two-stream model in which the correlations are represented by parameterizations. The behavior of the model is examined using simple single-layer single-column atmospheres. Positive correlations between extinction or scattering and the radiance field are shown to decrease transmission, increase reflection, and increase absorption within inhomogeneous media. The parameterization is used to evaluate the characteristics of inhomogeneous cloud fields observed by radar and lidar over a number of different locations and seasons, revealing that shortwave transfer is generally characterized by negative correlations between extinction and radiance, while longwave transfer is characterized by positive correlations. The results from this characterization are applied to the integration of an atmospheric general circulation model. Model surface temperatures are significantly affected, largely in response to changes in downwelling radiative fluxes at the surface induced by changes in cloud cover and water vapor distributions.

Different approaches for parameterizing the effects of vertical variability of cloudiness on radiative transfer are assessed using a database constructed from observations derived from lidar and millimeter cloud radar data collected from three different locations. Five different methods for dealing with the vertical overlap of clouds were incorporated into a single radiation model that was applied to the lidar/radar data averaged in time. The calculated fluxes and heating rates derived with this model are compared to broadband fluxes and heating rates calculated with the independent column approximation using the time-resolved cloud data. These comparisons provide a way of evaluating the effects of different overlap assumptions on the calculation of domain-mean fluxes. It was demonstrated how two of the most commonly used overlap schemes, the random and maximum-random methods, suffer a severe problem in that the total cloud amount defined by these methods depends on the vertical resolution of the...

The paper analyzes the influence of horizontal variability of clouds on sunlight reflected in a narrow portion of the solar spectrum and how this influence affects the ability to estimate cloud properties from measurements of reflection. This paper is part of a series that examines the use of high-resolution measurements of absorption lines of the oxygen A band located between 0.763 and 0.773 mm as a way of deriving information on cloud structure presently unobtainable from other passive measurements. The effects of spatial heterogeneity on reflectances and pathlength distributions are examined for marine stratocumulus cloud fields derived from Landsat data. The results showed that for the marine stratocumulus fields studied, the radiance errors were on the order of 3%‐20%, and the spectral radiance ratio (in-band to out-of-band) errors were on the order of 1%‐5%. When these errors are too large, the retrieved quantities possess too much error to be useful. The errors due to horizontal transport of photons and subpixel variability are studied independently as a function of spatial scale. Using both the radiance and radiance ratios, a technique was developed that allows the plane-parallel forward model typically used in retrieval schemes to be able to predict when its retrievals are so influenced by spatial heterogeneity that the results are invalid. This ability would represent a significant step forward in the current abilities of passive retrievals, which cannot determine the effect of cloud spatial variability on their retrievals. Lastly, a method was demonstrated that used domain-averaged measurements of absorption formed by reflection along with planeparallel theory to estimate the distribution of optical depth throughout the domain. The results for the four simulated cloud fields showed this technique to have significant promise in quickly classifying the level of cloud heterogeneity over a large area.

This paper describes simple, computationally efficient methods of calculating 2-stream broadband fluxes and heating rates in the shortwave and longwave for multilayered media. The method, herein referred to as selection rules, is used in conjunction with conventional 2-stream solvers to reduce the number of full-up radiative transfer calculations, thus decreasing the computation time.

This paper outlines a radiation parameterization method for deriving broadband fluxes that is currently being implemented in a number of global and regional atmospheric models. The rationale for the use of the 2-stream method as a way of solving the radiative transfer problem for broadband solar and longwave fluxes is presented. This rationale is based on assessment of these models in the context of a novel method of classifying radiative transfer problems that more clearly identifies the types of problems encountered in calculating globally distributed broadband fluxes. The delta-Eddington model (DEM) and the constant-hemispheric 2-stream models (CHMs) are shown to be superior to other 2-stream methods of solution under this classification and also superior to 4-stream solutions for the many classes of problems relevant to modeling the global atmosphere. These two methods are used to construct a radiation model of broadband solar and IR fluxes based on the k-distribution data of Fu and Liou. Whe...

This paper explores the feasibility of using O 2 A-band reflectance spectra in the retrieval of cloud optical and physical properties. Analyses demonstrate that these reflection spectra are sensitive to optical properties of clouds such as optical depth t c and phase function, vertical profile information including cloud-top pressure, pressure thickness, and the surface albedo. An estimation method is developed to demonstrate how well this information might be retrieved from synthetic spectra calculated by a line-by-line spectral multiple scattering model assuming realistic instrument parameters (spectral resolution, calibration accuracy, and signal-to-noise properties). The quality of the retrievals is expressed in terms of two indices, one relating to total error and another that quantifies the extent of reliance of the retrieval on the measurement, or conversely on other a priori information. Sources of total error include instrument-related errors, forward model errors including phase function errors, and errors in a priori data. The retrievals presented show the following: (i) The optical depth, surface albedo, cloud-top pressure, and cloud layer pressure thickness can be retrieved with an accuracy of approximately 5% for most cases of low cloud except when these clouds are optically thin and over bright surfaces. The spectra also contain information about the pressure thickness of the low-level cloud and this information also can be retrieved with an expected accuracy of less than 10% and with little reliance on any a priori data. (ii) Significantly larger errors result for retrievals for high clouds when no attempt is made to constrain the uncertainties associated with the unknown character of the scattering phase function. (iii) Retrieval of a limited amount of information about the phase function is possible under certain circumstances. It is possible to retrieve the asymmetry parameter sufficiently well to improve the accuracy of the forward model. This results in a shrinking of the errors in t c to less than 10% for t c . 0.1. (iv) The pressure information about scattering layers inherent in the A-band spectra is shown to provide a limited amount of vertical profiling capability (four to five layers of information at the most) provided the measurements are obtained with a spectral resolution of about 0.5 cm21 and obtained with an accuracy of 2% or better. A specific example demonstrates the capability of not only detecting the presence of thin high cloud above lower brighter cloud but also the capability of estimating the optical depths of both clouds. (v) The advantage of additional information such as provided by active profilers (radar and lidar) is explored. The advantages of this additional profile information are quantitatively shown to improve not only the retrieval of vertical profiles of extinction but also the optical properties of individual cloud layers.

This paper revisits the classical problem of particle scattering‐gaseous absorption and considers the extent to which the growth of absorption lines of a known gas can be used to obtain information about the scattering particles. The focus of the study is directed toward interpretation of the reflection spectrum of the O 2 A band located in the spectral region between 0.759 and 0.771 mm and the results provide a theoretical foundation for the retrieval of particle information described in a related study. This study demonstrates that there are six main properties that affect the absorption and reflection spectra: the optical depth of the cloud or aerosol, the pressure level of the top of this layer, the (pressure) thickness of the layer, the scattering phase function, the particle single-scatter albedo, and the surface albedo. Measured quantities, such as the spectral radiance or the ratio of in-absorption to continuum radiances are shown to be sensitive to these parameters in a manner that varies according to the O 2 optical depth. This variation sensitivity offers a way of separating the dependence of the measurements on these parameters, thereby providing some basis for their retrieval with suitable spectral measurements that resolve a sufficient range of O2 optical depth. Specifically, it is shown that radiances reflected from thin layers are sensitive to optical depth and phase function whereas the radiance ratio is sensitive to layer height. For thick layers, the sensitivity to optical depth diminishes leaving primarily a sensitivity to bulk information about the scattering phase function. By measuring radiances as a function of changing O 2 absorption, it is possible to distinguish optically thin layers above brighter lower reflecting surfaces, providing an ability to distinguish high-level thin cloud over brighter lower-level clouds or reflecting surfaces. The effects of 3D geometry on the spectral radiances is also considered in the context of photon path. It is shown how the spectral radiances provide some insight on 3D effects and the probable importance of these 3D effects on the retrievals. The equivalence theorem is illustrated and is used to provide line-by-line simulations of the reflection spectrum from hypothetical 3D clouds. A method to identify the nature of the 3D bias on retrievals of optical depth is discussed.

Recent estimates of the effect of increasing amounts of anthropogenic sulfate aerosol on the radiative forcing of the atmosphere have indicated that its impact may be comparable in magnitude to the effect from increases in CO2. Much of this impact is expected from the effects of the aerosol on cloud microphysics and the subsequent impact on cloud albedo. However, internal horizontal variations in cloud optical properties are also known to affect cloud albedo. A solar broadband version of a 2D radiative transfer model was used to quantify the impact of enhanced aerosol concentrations and horizontal inhomogeneity on the solar broadband albedo of marine stratus. The 2D cross sections of cloud physics data taken from a set of 3D RAMS/LES simulations of marine stratus provided realistic optical property data for radiative transfer simulations. A control run using typical marine CCN concentrations and a sensitivity study using enhanced concentrations of CCN were examined. The results of the radiative t...

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 mi...

This research attempts to understand how nonspherical ice particles backscatter electromagnetic radiation at millimetric wavelengths. The discrete dipole approximation (DDA) is employed to examine backscattering by single particles to (i) explore the limits of the Rayleigh approximation and (ii) test the use and validity of spheroidal models to model semirealistic cirrus particles. It is shown that spheroids are reasonable models of cirrus ice particles at wavelengths of 3 and 8 mm. Furthermore, with careful consideration of optical size it is possible to exploit the Rayleigh approximation for spheroids under many circumstances. The sensitivity of backscattered radiation to variations in microphysical properties is examined, based on DDA calculations for ensembles of ice particles. The most important factor in the ice crystal size distribution is found to be the median diameter (Dm) of the ice crystal volume distribution. In particular, for values of Dm typical of cirrus, the contribution of crys...

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 µm at 85.5, 157, 220, and 340 0Hz. 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 le 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 d...

This paper presents the results of polarized microwave radiative transfer modeling of cirrus clouds containing five different particle shoes 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 (ΔTb/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 facto...

The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

A two-stream radiative transfer model is used to examine the radiative properties of cirrus clouds and compare simulations with the observations made during the cirrus FIRE IFO. The sensitivity of cirrus cloud radiative properties to altitude and size distribution changes are examined. The net radiative effect of cirrus in the infrared is largely determined by the amount of ice in the cloud and the surface—cloud base temperature difference (and thus altitude). Increases (decreases) of this temperature difference produce a net radiative heating (cooling). Cloud-top solar heating increases (decreases) with increasing (decreasing) altitude as the optical path of the atmosphere above the cloud layer decreases (increases). The impact of varying concentrations of ice particles less than 100 μm in diameter is also examined. The addition of these particles greatly enhances the longwave absorption and shortwave albedo of cirrus clouds in a manner that is spectrally dependent. Model simulations using obser...

This paper examines the effects of the relationship between cirrus cloud ice water content and cloud temperature on climate change. A simple mechanistic climate model is used to study the feedback between ice water content and temperature. The central question studied in this paper concerns the extent to which both the radiative and microphysical properties of cirrus cloud influence such a feedback. To address this question, a parameterization of the albedo and emissivity of clouds is introduced. Observations that relate the ice water content to cloud temperature are incorporated in the parameterization to introduce a temperature dependence to both albedo and emittance. The cloud properties relevant to the cloud feedback are expressed as functions of particles size re, asymmetry parameter g and cloud temperature and analyses of aircraft measurements, lidar and ground based radiometer data are used to select re and g. It was shown that scattering calculations assuming spherical particles with a di...

We employ a one-dimensional radiative-convective equilibrium model with multiple cloud layers to demonstrate that the surface equilibrium temperature is highly sensitive to the vertical distribution of effective cloud base heights. It is also demonstrated that the reflected solar flux from an ensemble of cloud layers is independent of the vertical distribution of these cloud layers and is a function only of the total water path integrated in the vertical, a property which also determines the solar radiation reaching the surface. The downward longwave radiation, on the other hand, depends strongly on the effective cloud base height as well as the background water vapor distribution. It is argued that the longwave radiative transfer processes of cloud tend to decouple the radiative budgets at the top of the atmosphere and the surface. Thus, for a given total atmospheric optical thickness, it is possible to obtain different values of surface temperature under conditions of radiative equilibrium at t...

In this paper we develop a new method for solving the transfer of radiation within a laterally finite optical medium. A new radiative transfer equation, based on a multimode approach, is developed which includes the explicit effects of the sides of the medium. This equation, derived for a box shaped medium, is exactly analogous to the plane parallel radiative transfer equation with a source term. Accordingly, the new equation is solved using the familiar plane-parallel techniques based on invariant imbedding relationships in the form of doubling and adding. The additional terms in the newly derived radiative transfer equation can be interpreted as apparent source and sink terms which arise from the lateral finiteness of the medium. The geometric and physical aspects of these source-sink terms and their influence on the solutions are discussed. Results also show that the multimode solutions compare well with the Monte Carlo simulations.

A new treatment of absorption in the window region depending on water vapor pressure is incorporated into the IR cooling rate model of Rodgers [for review see Rodgers and Walshaw (1966). The appropriate mean diffuse transmission gradient is derived. The results are presented in the form of hemispheric cross sections and indicate that for tropical climates, the new absorption has a considerable effect on radiative transfer in the lower troposphere. The results obtained are very encouraging, showing a reduction in the differences between the measured cooling rates of Cox (1969) and the calculated cooling rates in the lower troposphere.

A detailed multiple-scattering model has been employed to investigate the sensitivity of radiation profiles and flux divergences to changes in macrostructure and microstructure of basic water cloud types. The study has been performed on a range of cloud types including variable distributions of liquid water content (LWC) and drop-size distributions. Total shortwave heating rates vary from 1 to 5°C h−1 and are larger in higher clouds. IR cooling rates in the upper regions of cloud also increase with increasing elevation and are dominated by the atmospheric window contribution. Thus the typical instrument discriminating the IR radiation between 7 and 14,μm will measure almost the entire IR radiative cooling or heating of low-level water clouds. Both shortwave heating and IR cooling within cloud layers are primarily dependent on LWC and its vertical distribution and are more or less independent of drop-size distribution. Cloud albedo does vary with drop-size distribution but is virtually independent...

A one-dimensional radiative convective model is used to gage the influence of clouds on simple climate systems. The radiative transfer model is developed to accommodate in a systematic and consistent manner the optical properties of a hierachy of cloud types. Cloud albedo and emissivity relationships for both ice and water clouds are introduced. The model structure is highly sensitive to cloud height for all cloud types and particularly sensitive to water path for optically thin clouds. High thin clouds at low and middle latitudes in all seasons and all clouds at high latitudes in winter tend to warm the surface relative to the clear sky; all other clouds tend to cool the surface. The summer high-latitude effects are similar to the low- and middle-latitude situation. The model sensitivity is compounded by surface albedo effects. For a given cloud a critical surface albedo may exist at which the cloud transits from cooling the surface relative to clear-sky conditions to warming the surface when th...

We present a modification to the parameterization scheme of Stephens which improves on the estimation of shortwave absorption by cloud. In particular, the variation of cloud absorption with solar elevation angle is improved with the modified scheme.

The problem of radiative transfer in a horizontally infinite cloud layer possessing anisotropy with respect to volume extinction and other single-scattering properties was solved using the method of discrete space theory. The model was applied to a hypothetical ice crystal cloud composed of long cylinders displaying preferential orientation (in the horizontal) to provide the gross radiative properties of shortwave reflection, shortwave absorption, and longwave emission and reflection. These results were directly compared to clouds with the assumed microstructure of cylinders randomly orientated in three dimensions and of equivalent (by area) spheres. Generally, the gross radiative properties for clouds composed of equivalent spheres are substantially different than those for either of the cylinder models. The relative differences between the three assumed microstructures suggests that equivalent spheres cannot be employed to approximate the gross radiative properties determined for clouds compose...

In this paper we demonstrate that the anomalous diffraction theory of van de Hulst with some modifications, provides a reasonable approximation of the volume extinction and absorption coefficients. We also show how the shortwave radiative properties of a water cloud can be derived in terms of 1) cloud liquid water path, 2) the effective radius of the droplet distribution, and 3) the balk absorption coefficient of water. With the aid of the approximate diffraction theory we describe how cloud albedo and shortwave absorption depend on the droplet size. We demonstrate this dependence to be somewhat complex and show that the variation of absorption with variation of droplet size depends also on the cloud liquid water path. For “deep” or semi-infinite clouds, absorption increases monotonically with increasing effective radius, but the reverse dependence is established for thin clouds. The implications of these results to the so-called absorption paradox and to the possibility of determining droplet si...

A multiple-scattering radiative transfer model is employed to evaluate the 11 μm and the broad-band infrared (IR) fluxes, cooling rates and emittances in model cirrus clouds for a number of standard vertical atmospheric profiles of temperature and moisture. The single-scattering properties for scattering by mono- and polydispersed randomly orientated long ice columns and for the associated polydispersed equivalent spheres are used in the calculation. The results reveal IR reflectance at the cloud base of 4% (spheres) and 6% (cylinders). This reflectance modifies significantly the cloud effective emittances, cloud cooling rates and the emission by the total atmospheric column. It is shown that the radiative properties of model cirrus clouds determined under the equivalent sphere approximation represents well the properties determined for scattering by randomly orientated columns. The largest difference between the sphere and cylinder models is for reflectance which is a function of the degree of a...

The most common cloud species observed during the Winter Monsoon Experiment (WMONEX) wasthick (optically black) middle and upper tropospheric extended cloud. Data from the GeostationaryMeteorological Satellite (GMS) showed the extended cloud to occupy half the near-equatorial SouthChina Sea and Indonesia on some days with tops in the vicinity of the 200 mb level. Detailed observations from the WMONEX composite observing array indicated that the clouds extended up to 750 kmfrom the convective source regions, possessed bases in the vicinity of the freezing level and lay above agenerally suppressed and subsident lower troposphere. The observation of widespread precipitation fromthe extended cloud and the encountering of ice particles during the cloud penetrations suggest that theextended clouds are active in a diabatic heating sense.Calculations using a radiative transfer model and cloud and atmospheric states derived from WMONEXdata indicate substantial net heating at the base of the cloud (-20 K day1) and cooling at the top(-5 to -15 K day1), resulting in a heating rate differential between the base and top of the cloud of upto 35 K day". Net heating or cooling occurs depending upon the diurnal cycle. It is conjectured thatthe effect of the radiative heating is to destabilize the cloud layer. As the magnitude of the radiativeheating at the base of the cloud is at least within a factor of 2 of estimates of the cooling at the cloudbase due to melting for moderate disturbances and relatively greater for weak disturbances or in locationswell removed from the convective source in any disturbance, it is argued that radiative effects cannotbe ignored in the calculation of the total diabatic heating fields in tropical cloud systems.

This paper extends the theoretical developments of Part I to illustrate the power of the method in solving multiple scattering problems with sources that result from i) the single scatter of a collimated beam of solar radiation that is directly transmitted to a given point in the medium and ii) thermal emission. These source terms are derived in the multimode context and solutions are presented to illustrate the effects of sun angle and infrared emission on the radiance and irradiance fields that emerge from hypothetical box shaped clouds. The results reiterate the earlier findings that the sides of clouds play an important role in the exchange of radiative energy between the cloud and its environment. The total infrared emission by cuboidal clouds, for example, is shown to be substantially larger than the emission from plane parallel clouds as a result of this additional exchange of radiant energy. The results presented in the paper, including the comparisons with available Monte Carlo calculati...

A theoretical study was carried out to investigate the effect of radiative heating and cooling on the mass and heat budgets of an ice crystal. Equations describing the radiative budget of an ice crystal were derived and particle absorption efficiencies were calculated from the scattering theories for spherical and cylindrical particles. The radiation budget equation was solved in terms of upper limits of warming and cooling. By the introduction of the cloud blackbody depth, these limits were shown to apply over depths of several kilometres for typical ice clouds. The effects of radiation on the growth and evaporation rates of ice crystals were shown to be significant. Particle growth (evaporation) is enhanced (suppressed) in a radiatively cooled (heated) environment. It was further demonstrated that the effects of radiative cooling in the upper regions of the cloud greatly enhances the particle fall distances. In addition, particle growth and evaporation with and without radiation exchange are di...

A bulk diagnostic model is presented for the evaluation of the mass and heat fluxes due to convective ensembles. The cloud model is consistent with the hot-tower hypothesis and includes a moist downdraft, the depth and intensity of which are explicitly determined. The model is applied to the composite wave data of Reed and Recker (1971) and the sensitivity of convective mass fluxes and eddy heating rates to the assumed radiative cooling rate profile is examined. The results obtained from the model using a radiative heating profile typical of clear “undisturbed” tropical regions were compared with those obtained using a radiative heating profile taken to be typical of disturbed conditions. Under such conditions, a thick cirrus shield is usually present. The model results show that the mass flux profile has a pronounced bimodal character regardless of the radiative heating rate profile (QR) employed. However, other characteristics of modeled convective ensembles are sensitive to the choice of QR. S...

Six case studies of “uniform” planetary boundary layer clouds are reported where the solar and infrared radiation fields, liquid water content, drop-size distributions and temperature and humidity profiles were measured simultaneously. The measurements are compared with theoretical prediction from a detailed radiative transfer model in an attempt to verify the performance of the model and its associated parameterization schemes (Parts 1 and 2). The measurements support the parameterization of both shortwave and longwave radiative characteristics in terms of vertical liquid water path (LWP) i.e., without the need to define cloud drop-size distributions. Within experimental error, there are no significant discrepancies between theory and measurement. However, there is some evidence in the present study, supported by measurements of others in (generally) thicker and denser clouds that solar absorption is in excess of theoretical prediction.

A general transform method is presented for studying problems of radiative transfer through absorbing, emitting and anisotropically scattering media exposed to arbitrary radiation conditions on its boundaries. The method permits quite arbitrary horizontal and vertical variability in the scattering and extinction properties of the medium bounded by a surface whose albedo and bidirectional reflection function varies from point to point. The technique developed incorporates a two-dimensional Fourier transform of the radiative transfer equation and a full Fourier expansion in azimuth. The general solution is based on the use of invariant imbedding principles in the form of doubling and adding algorithms. In developing these algorithms the principles of invariance are derived for three-dimensional geometry. Differences and similarities to the one-dimensional transfer problem are highlighted throughout. The method is applied to two special problems, namely the reflection by an atmosphere overlying or s...

The shortwave absorption, albedo and longwave emissivity of water clouds are parameterized for use in operational and climatic models of the atmosphere. The parameterization also provides the shortwave heating and longwave cooling rates within the cloud. The scheme presented in this paper assumes a prior knowledge of the broadband spectral fluxes incident on the cloud and further assumes that the atmospheric models will provide the surface albedo, solar zenith angle, cloud temperature and total vertical liquid water path. The last parameter was chosen because it likely to be available in atmospheric circulation models and both observational and theoretical evidence suggest that it is strongly related to the radiative properties of clouds (Paltridge, 1974; Platt, 1976). The parameterization of shortwave radiation resembles a two-stream approximation which has been “tuned” to match the results from a detailed theoretical model. The longwave scheme simply involves the parameterization of effective e...

The influence of cloud and moisture distribution on the radiative forcing of the atmosphere is investigated. A simple radiative transfer model is developed to calculate the radiative fluxes at the boundaries of the atmosphere and the net radiative absorption of the atmospheric column. It is of a type and simplicity which is compatible with the present climate models and is shown to compare well with more complicated multiple-scattering calculations. Details of the atmospheric temperature and moisture structure and its radiation properties are systematically relaxed to test the assumption associated with even simpler models. The radiative properties of the atmosphere are shown to be strong functions of cloud amount, cloud type, latitude and atmospheric state. Results are presented which have several implications regarding climate modeling. It appears that radiative schemes in large-scale models should take into account full vertical and horizontal variability of moisture and cloud as minimum requi...