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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Four years of global cirrus cloud statistics using HIRS

Trends in global upper-tropospheric transmissive cirrus cloud cover are beginning to emerge from a four-year cloud climatology using NOAA polar-orbiting High-Resolution Infrared Radiation Sounder (HIRS) multispectral data. Cloud occurrence, height, and effective emissivity are determined with the CO2 slicing technique on the four years of data (June 1989-May 1993). There is a global preponderance of transmissive high clouds, 42% on the average; about three-fourths of these are above 500 hPa and presumed to be cirrus. In the Inter-tropical Convergence Zone (ITCZ), a high frequency of cirrus (greater than 50%) is found at all times; a modest seasonal movement tracks the sun. Large seasonal changes in cloud cover occur over the oceans in the storm belts at midlatitudes; the concentrations of these clouds migrate north and south with the seasons following the progressions of the subtropical highs (anticyclones). More cirrus is found in the summer than in the winter in each hemisphere. A significant change in cirrus cloud cover occurs in 1991, the third year of the study. Cirrus observations increase from 35% to 43% of the data, a change of eight percentage points. Other cloud forms, opaque to terrestrial radiation, decerase by nearly the same amount. Most of the increase is thinner cirrus with infrared optical depths below 0.7. The increase in cirrus happens at the same time as the 1991-92 El Nino/Southern Oscillation (ENSO) and the eruption of Mt. Pinatubo. The cirrus changes occur at the start of the ENSO and persist into 1993 in contrast to other climatic indicators that return to near pre-ENSO and volcanic levels in 1993.

Wylie, Donald P.↗
NASA NTRS1994

Simulations of the effects of water vapor, cloud liquid water, and ice on AMSU moisture channel brightness temperatures

Radiative transfer simulations are performed to determine how water vapor and nonprecipitating cloud liquid water and ice particles within typical midlatitude atmospheres affect brightness temperatures T(sub B)'s of moisture sounding channels used in the Advanced Microwave Sounding Unit (AMSU) and AMSU-like instruments. The purpose is to promote a general understanding of passive top-of-atmosphere T(sub B)'s for window frequencies at 23.8, 89.0, and 157.0 GHz, and water vapor frequencies at 176.31, 180.31, and 182.31 GHz by documenting specific examples. This is accomplished through detailed analyses of T(sub B)'s for idealized atmospheres, mostly representing temperate conditions over land. Cloud effects are considered in terms of five basic properties: droplet size distribution, phase, liquid or ice water content, altitude, and thickness. Effects on T(sub B) of changing surface emissivity also are addressed. The brightness temperature contribution functions are presented as an aid to physically interpreting AMSU T(sub B)'s. Both liquid and ice clouds impact the T(sub B)'s in a variety of ways. The T(sub B)'s at 23.8 and 89 GHz are more strongly affected by altostratus liquid clouds than by cirrus clouds for equivalent water paths. In contrast, channels near 157 and 183 GHz are more strongly affected by ice clouds. Higher clouds have a greater impact on 157- and 183-GHz T(sub B)'s than do lower clouds. Clouds depress T(sub B)'s of the higher-frequency channels by suppressing, but not necessarily obscuring, radiance contributions from below. Thus, T(sub B)'s are less closely associated with cloud-top temperatures than are IR radiometric temperatures. Water vapor alone accounts for up to 89% of the total attenuation by a midtropospheric liquid cloud for channels near 183 GHz. The Rayleigh approximation is found to be adequate for typical droplet size distributions; however, Mie scattering effects from liquid droplets become important for droplet size distribution functions with modal radii greater than 20 micrometers near 157 and 183 GHz, and greater than 30-40 micrometers at 89 GHz. This is due mainly to the relatively small concentrations of droplets much larger than the mode radius. Orographic clouds and tropical cumuli have been observed to contain droplet size distributions with mode radii in the 30-40 micrometers range. Thus, as new instruments bridge the gap between microwave and infrared to frequencies even higher than 183 GHz, radiative transfer modelers are cautioned to explicitly address scattering characteristics of such clouds.

Muller, Bradley M.↗
NASA NTRS2004

Simple Models of the Spatial Distribution of Cloud Radiative Properties for Remote Sensing Studies

This project aimed to assess the degree to which estimates of three-dimensional cloud structure can be inferred from a time series of profiles obtained at a point. The work was motivated by the desire to understand the extent to which high-frequency profiles of the atmosphere (e.g. ARM data streams) can be used to assess the magnitude of non-plane parallel transfer of radiation in thc atmosphere. We accomplished this by performing an observing system simulation using a large-eddy simulation and a Monte Carlo radiative transfer model. We define the 3D effect as the part of the radiative transfer that isn't captured by one-dimensional radiative transfer calculations. We assess the magnitude of the 3D effect in small cumulus clouds by using a fine-scale cloud model to simulate many hours of cloudiness over a continental site. We then use a Monte Carlo radiative transfer model to compute the broadband shortwave fluxes at the surface twice, once using the complete three-dimensional radiative transfer F(sup 3D), and once using the ICA F (sup ICA); the difference between them is the 3D effect given.

Source record↗
NASA NTRS1999

Analysis of Cirrus Cloud Microphysical Data

The First International Satellite Cloud Climatology Regional Experiment (FIRE) program has the goal of improving our capabilities to understand, model and detect the properties of climatically-important clouds. This is being undertaken through a three-pronged effort of modeling, long-term observations and short-term intensive field studies. Through examination of satellite and other data it is apparent that stratus and cirrus cloud types have the greatest impact on climate due to their radiative effects and ubiquitous nature. As a result, the FIRE program has developed two paths of investigation, each having its own subset of research objectives and measurement programs. The work conducted under this grant was directed toward furthering our understanding of cirrus cloud systems. While it is known that cirrus are climatically important, the magnitude and even sign of the impact is unclear. Cirrus clouds affect the transfer of radiation according to their physical depth and location in the atmosphere and their microphysical composition. However, significant uncertainties still exist in how cirrus clouds form and how they are maintained, what their physical properties are and how they can be parameterized in numerical models. Better remote sensing techniques for monitoring cirrus cloud systems and improved modeling of radiative transfer through ice particles are also needed. A critical element in resolving these issues is a better understanding of cirrus cloud microphysical properties and how they vary. The focus of the research to be conducted under this grant was th data collected in situ by the University of North Dakota Citation aircraft. The goals of this research were to add to the body of knowledge of cirrus cloud microphysics, particularly at the small end of the size spectrum; and analyze the spatial variation of cirrus clouds.

Poellot, Michael R.↗
NASA NTRS1998

The Effect of Clouds Upon Limb Scattered Radiances and the Retrieval of Ozone Profiles Using These Radiances

The use of limb scattered radiance profiles to retrieve ozone profiles is currently being investigated. The goal is to produce ozone profiles with better vertical resolution than is available with the Backscattered Ultraviolet (BUV) technique and with much greater spatial and temporal coverage than with the solar occultation method (i.e. SAGE II). This method, which uses UV and visible light scattered from the earth's limb, has recently been proven to work for clear sky cases with data from the STS-87 flight of the Shuttle Ozone Sounding Limb Experiment/Limb Ozone Retrieval Experiment (SOLSE/LORE). As to be expected, clouds have a substantial impact upon the limb radiance (increasing the radiance as much as 80-100% is some cases). Here we use a variety of radiative transfer models and limited SOLSE/LORE data to investigate the effect of clouds upon the limb radiance at wavelengths used in the ozone retrieval (approximately 600 nm). Though the presence of clouds can greatly increase the limb radiance, they have a minimal effect upon the retrieved ozone profile, since the retrieval uses a differential absorption technique.

Flittner, D. E.↗
NASA NTRS2017

Atmospheric Collapse on Early Mars: The Role of CO2 Clouds

The abundance of evidence that liquid water flowed on the surface early in Mars' history strongly implies that the early Martian atmosphere was significantly more massive than it is today. While it seems clear that the total CO2 inventory was likely substantially larger in the past, the fundamental question about the physical state of that CO2 is not completely understood. Because the temperature at which CO2 condenses increases with surface pressure, surface CO2 ice is more likely to form and persist as the atmospheric mass increases. For the atmosphere to remain stable against collapse, there must be enough energy, distributed planet wide, to stave off the formation of permanent CO2 caps that leads to atmospheric collapse. The presence of a "faint young sun" that was likely about 25 percent less luminous 3.8 billion years ago than the sun today makes this even more difficult. Several physical processes play a role in the ultimate stability of a CO2 atmosphere. The system is regulated by the energy balance between solar insolation, the radiative effects of the atmosphere and its constituents, atmospheric heat transport, heat exchange between the surface and the atmosphere, and latent heating/cooling. Specific considerations in this balance for a given orbital obliquity/eccentricity and atmospheric mass are the albedo of the caps, the dust content of the atmosphere, and the presence of water and/or CO2 clouds. Forget et al. show that, for Mars' current obliquity (in a circular orbit), CO2 atmospheres ranging in surface pressure from 500 hectopascals to 3000 hectopascals would have been stable against collapsing into permanent surface ice reservoirs. Soto et al. examined a similar range in initial surface pressure to investigate atmospheric collapse and to compute collapse rates. CO2 clouds and their radiative effects were included in Forget et al. but they were not included in Soto et al. Here we focus on how CO2 clouds affect the stability of the atmosphere against collapse.

Kahre, M. A.↗
NASA NTRS1989

A self-consistency approach to improve microwave rainfall rate estimation from space

A multichannel statistical approach is used to retrieve rainfall rates from the brightness temperature T(B) observed by passive microwave radiometers flown on a high-altitude NASA aircraft. T(B) statistics are based upon data generated by a cloud radiative model. This model simulates variabilities in the underlying geophysical parameters of interest, and computes their associated T(B) in each of the available channels. By further imposing the requirement that the observed T(B) agree with the T(B) values corresponding to the retrieved parameters through the cloud radiative transfer model, the results can be made to agree quite well with coincident radar-derived rainfall rates. Some information regarding the cloud vertical structure is also obtained by such an added requirement. The applicability of this technique to satellite retrievals is also investigated. Data which might be observed by satellite-borne radiometers, including the effects of nonuniformly filled footprints, are simulated by the cloud radiative model for this purpose.

Kummerow, Christian↗
NASA NTRS2012

Simulating Mars' Dust Cycle with a Mars General Circulation Model: Effects of Water Ice Cloud Formation on Dust Lifting Strength and Seasonality

The dust cycle is critically important for the current climate of Mars. The radiative effects of dust impact the thermal and dynamical state of the atmosphere [1,2,3]. Although dust is present in the Martian atmosphere throughout the year, the level of dustiness varies with season. The atmosphere is generally the dustiest during northern fall and winter and the least dusty during northern spring and summer [4]. Dust particles are lifted into the atmosphere by dust storms that range in size from meters to thousands of kilometers across [5]. Regional storm activity is enhanced before northern winter solstice (Ls~200 degrees - 240 degrees), and after northern solstice (Ls~305 degrees - 340 degrees ), which produces elevated atmospheric dust loadings during these periods [5,6,7]. These pre- and post- solstice increases in dust loading are thought to be associated with transient eddy activity in the northern hemisphere with cross-equatorial transport of dust leading to enhanced dust lifting in the southern hemisphere [6]. Interactive dust cycle studies with Mars General Circulation Models (MGCMs) have included the lifting, transport, and sedimentation of radiatively active dust. Although the predicted global dust loadings from these simulations capture some aspects of the observed dust cycle, there are marked differences between the simulated and observed dust cycles [8,9,10]. Most notably, the maximum dust loading is robustly predicted by models to occur near northern winter solstice and is due to dust lifting associated with down slope flows on the flanks of the Hellas basin. Thus far, models have had difficulty simulating the observed pre- and post- solstice peaks in dust loading.

Kahre, Melinda A.↗
NASA NTRS2021

An overview of the ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) project: aerosol–cloud–radiation interactions in the southeast Atlantic basin

Southern Africa produces almost a third of the Earth’s biomass burning (BB) aerosol particles, yet the fate of these particles and their influence on regional and global climate is poorly understood. ORACLES (ObseRvations of Aerosols above CLouds and their intEractionS) is a 5-year NASA EVS-2 (Earth Venture Suborbital-2) investigation with three intensive observation periods designed to study key atmospheric processes that determine the climate impacts of these aerosols. During the Southern Hemisphere winter and spring (June–October), aerosol particles reaching 3–5 km in altitude are transported westward over the southeast Atlantic, where they interact with one of the largest subtropical stratocumulus (Sc) cloud decks in the world. The representation of these interactions in climate models remains highly uncertain in part due to a scarcity of observational constraints on aerosol and cloud properties, as well as due to the parameterized treatment of physical processes. Three ORACLES deployments by the NASA P-3 aircraft in September 2016, August 2017, and October 2018 (totaling ~ 350 science flight hours), augmented by the deployment of the NASA ER-2 aircraft for remote sensing in September 2016 (totaling ~ 100 science flight hours), were intended to help fill this observational gap. ORACLES focuses on three fundamental science themes centered on the climate effects of African BB aerosols: (a) direct aerosol radiative effects, (b) effects of aerosol absorption on atmospheric circulation and clouds, and (c) aerosol–cloud microphysical interactions. This paper summarizes the ORACLES science objectives, describes the project implementation, provides an overview of the flights and measurements in each deployment, and highlights the integrative modeling efforts from cloud to global scales to address science objectives. Significant new findings on the vertical structure of BB aerosol physical and chemical properties, chemical aging, cloud condensation nuclei, rain and precipitation statistics, and aerosol indirect effects are emphasized, but their detailed descriptions are the subject of separate publications. The main purpose of this paper is to familiarize the broader scientific community with the ORACLES project and the dataset it produced.

Jens Redemann↗
NASA NTRS1990

Comparison of cloud forcing derived from the Earth Radiation Budget Experiment with that simulated by the NCAR Community Climate Model

The cloud radiative forcing derived from the Earth Radiation Budget Experiment (ERBE) data was compared with cloud forcing simulated by a T42 version of the NCAR Community Climate Model (CCM). The comparison indicates a number of deficiencies in the CCM. Namely, it is shown that the model emits substantially more long-wave radiation than is observed by ERBE. This overestimation is attributed to two model characteristics: (1) the model is too dry and thus reduces the greenhouse longwave radiation effect of the atmosphere (permitting more longwave radiation to escape into space); and (2) the effective high cloud amount is quite small in the model.

Kiehl, J. T.↗
NASA NTRS1988

A 3-dimensional numerical simulation of the atmospheric injection of aerosols by a hypothetical basaltic fissure eruption

Researchers simulated the atmospheric response to a hypothetical basaltic fissure eruption using heating rates based on the Roza flow eruption. The simulation employs the Colorado State University Regional Atmospheric Model (RAMS) with scavenging effects. The numerical model is a three-dimensional non-hydrostatic time-split compressible cloud/mesoscale model. Explicit microphysics include prediction of cloud, rain, crystal, and hail precipitation types. Nucleation and phoretic scavenging are predicted assuming that the pollutant makes an effective cloud droplet nucleus. Smoke is carried as a passive tracer. Long and short wave radiation heating tendencies, including the effects of the smoke, are parameterized. The longwave emission by the lava surface is neglected in the parameterization and included as an explicit heating term instead. A regional scale domain of 100 x 100 km in the horizontal and 22 km high is used. The horizontal grid spacing is taken to be 2 km and the vertical spacing is taken to be 0.75 km. The initial atmospheric state is taken to be horizontally homogenous and based on the standard atmospheric sounding. The fissure is assumed to be 90 km long and oriented in a zig/zag pattern.

Tripoli, Gregory J.↗
NASA NTRS2008

Radiative Susceptibility of Cloudy Atmospheres to Droplet Number Perturbations: 2. Global analysis from MODIS

Global distributions of albedo susceptibility for areas covered by liquid clouds are presented for 4 months in 2005. The susceptibility estimates are based on expanded definitions presented in a companion paper and include relative cloud droplet number concentration (CDNC) changes, perturbations in cloud droplet asymmetry parameter and single-scattering albedo, atmospheric/surface effects, and incorporation of the full solar spectrum. The cloud properties (optical thickness and effective radius) used as input in the susceptibility calculations come from MODIS Terra and Aqua Collection 5 gridded data. Geographical distributions of susceptibility corresponding to absolute ( absolute cloud susceptibility ) and relative ( relative cloud susceptibility ) CDNC changes are markedly different indicating that the detailed nature of the cloud microphysical perturbation is important for determining the radiative forcing associated with the first indirect aerosol effect. However, both types of susceptibility exhibit common characteristics such as significant reductions when perturbations in single-scattering properties are omitted, significant increases when atmospheric absorption and surface albedo effects are ignored, and the tendency to decrease with latitude, to be higher over ocean than over land, and to be statistically similar between the morning and afternoon MODIS overpasses. The satellite-based susceptibility analysis helps elucidate the role of present-day cloud and land surface properties in indirect aerosol forcing responses. Our realistic yet moderate CDNC perturbations yield forcings on the order of 1-2 W/sq m for cloud optical property distributions and land surface spectral albedos observed by MODIS. Since susceptibilities can potentially be computed from model fields, these results have practical application in assessing the reasonableness of model-generated estimates of the aerosol indirect radiative forcing.

Oreopoulos, Lazaros↗
NASA NTRSDate not supplied

Evaluating Subgrid-Scale Properties of Low Clouds over the Beaufort Sea in Arctic System Reanalysis using ARISE Airborne In Situ Observations

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. To better understand the magnitude and possible causes of this problem, we analyze the disagreements between the Arctic System Reanalysis version 2 (ASR) and data taken during the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign conducted over the Beaufort Sea. Previous analysis of grid scale-averaged meteorological variables revealed a lack of cloud water produced in ASR, related to warm/dry biases, a failure to produce sufficient cloud water in conditions that are observed to be favorable for large cloud water values, and sampling issues with the ARISE flight paths. However, ARISE collected meteorological observations at one second intervals, offering spatial data resolution comparable to the subgrid scale of ASR. Subgrid scale properties and processes must be parameterized in conventional atmospheric models and reanalyses such as ASR, and often rely on assumed distributions of meteorological variables about the grid box mean state. To enable an examination of the realism of ASR’s subgrid scale properties, we use high resolution data from ARISE determine the “subgrid scale” distributions of cloud water and thermodynamic variables in the real atmosphere. Preliminary results show that the subgrid scale distribution of thermodynamic variables about the grid scale mean resembles the triangular distribution assumed in many bulk microphysical parameterization schemes, but also with tails resembling Gaussian distributions. The main goal is to understand the partitioning of the total available atmospheric water into water vapor and cloud water. Models typically covert some percentage of total water in a grid box to cloud water based on the estimated amount of supersaturation from the assumed vapor distribution. The ARISE measurements can reveal the relationship between subgrid scale supersaturation and the partition between cloud water and water vapor.

Jason Brant Dodson↗
NASA NTRSDate not supplied

A Path to Improving Simulated Properties of Low Clouds over the Beaufort Sea using Airborne In Situ Observations of Subgrid-Scale Variability

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. One of the main reasons for this problem are the possible unrealistic assumptions that models/reanalyses make about the subgrid-scale (SGS) variability of meteorological properties, as well as the relationship between SGS variability and grid-scale (GS) cloud properties. We utilize cloud and thermodynamic data of low level (primarily) liquid clouds collected from two aircraft campaigns conducted over the Beaufort Sea to better understand and characterize this problem. Examining data from the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign reveals that GS cloud water variability is closely related with SGS distribution of total water (i.e. water vapor + cloud water). Multiple models/reanalyses use SGS supersaturated total water (relative to GS saturation) as a threshold for partitioning available water for condensation, and indeed we find significant correlation between GS cloud water and SGS supersaturation. However, we also find that the assumption of a static threshold of 100% saturation to be unrealistic. Empirical calculations from the ARISE data show a large sensitivity of this threshold to GS relative humidity, and so a microphysical parameterization allowing the threshold to vary according to GS thermodynamic properties may result in more realistic GS cloud water values. Finally, to determine how sensitive the ARISE-derived results are to that particular campaign, we include additional data from the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE) conducted in 1998. The inclusion of the second dataset will help with demonstrating the robustness of the results and their utility in improving the representation of Arctic clouds in models and reanalyses.

J Brant Dodson↗
NASA NTRSDate not supplied

A Path to Improving Simulated Properties of Low Clouds over the Beaufort Sea using Airborne In Situ Observations of Subgrid-Scale Variability

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. One of the main reasons for this problem are the possible unrealistic assumptions that models/reanalyses make about the subgrid-scale (SGS) variability of meteorological properties, as well as the relationship between SGS variability and grid-scale (GS) cloud properties. We utilize cloud and thermodynamic data of low level (primarily) liquid clouds collected from two aircraft campaigns conducted over the Beaufort Sea to better understand and characterize this problem. Examining data from the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign and the 1998 First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE)–Arctic Cloud Experiment (ACE) reveals that GS cloud water variability is closely related with SGS distribution of total water (i.e. water vapor + cloud water). We investigate two related approaches to prediction of GS cloud properties from SGS variability: the critical saturation ratio method, and the critical relative humidity method. We find significant correlation between GS cloud water and SGS supersaturation when the critical saturation ratio is set at 100%, as well as a notable relationship between GS cloud water and the width of the SGS total water distribution. Critical relative humidity also compares well with GS cloud water. However, we also find that the assumptions of a static critical saturation ratio of 100% to be unrealistic, as well as a fixed SGS distribution width. Empirical calculations from the ARISE data show a large sensitivity of these SGS variables to GS relative humidity, and so a SGS parameterization allowing them to vary according to GS thermodynamic properties may result in more realistic GS cloud water values.

J. Brant Dodson↗
NASA NTRS2013

The Role of Long-Lived Greenhouse Gases as Principal LW Control Knob that Governs the Global Surface Temperature for Past and Future Climate Change

The climate system of the Earth is endowed with a moderately strong greenhouse effect that is characterized by non-condensing greenhouse gases (GHGs) that provide the core radiative forcing. Of these, the most important is atmospheric CO2. There is a strong feedback contribution to the greenhouse effect by water vapor and clouds that is unique in the solar system, exceeding the core radiative forcing due to the non-condensing GHGs by a factor of three. The significance of the non-condensing GHGs is that once they have been injected into the atmosphere, they remain there virtually indefinitely because they do not condense and precipitate from the atmosphere, their chemical removal time ranging from decades to millennia. Water vapor and clouds have only a short lifespan, with their distribution determined by the locally prevailing meteorological conditions, subject to Clausius-Clapeyron constraint. Although solar irradiance is the ultimate energy source that powers the terrestrial greenhouse effect, there has been no discernible long-term trend in solar irradiance since precise monitoring began in the late 1970s. This leaves atmospheric CO2 as the effective control knob driving the current global warming trend. Over geological time scales, volcanoes are the principal source of atmospheric CO2, and the weathering of rocks is the principal sink, with the biosphere participating as both a source and a sink. The problem at hand is that human industrial activity is causing atmospheric CO2, to increase by 2 ppm per year, whereas the interglacial rate has been 0.005 ppm per year. This is a geologically unprecedented rate to turn the CO2 climate control knob. This is causing the global warming that threatens the global environment.

Greenhouse effect↗
NASA NTRS1974

Multiple scattering in cloud layers; some results

Theoretical methods are discussed for calculating radiative effects of aerosols. Experimental determination is emphasized for relevant aerosol parameters on a global basis to arrive at realistic estimates of heating and cooling. Internal radiation fields in very thin and very thick slabs are reviewed. Phase functions, polarization, emission by internal sources, and path length distribution are also considered.

Vandehulst, H. C.↗