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NASA NTRS1999

Modeling of Sub-Grid Heterogeneity and its Impact on GCM Global Radiation Balance

The spatial and temporal variability of high, low, and mid-level clouds is obtained from ISCCP D1 data. Monthly mean global maps of the observed cloud variability are used to re-scale GCM prognostic cloud optical depths and radiative parameters via the Monte Carlo cloud heterogeneity parameterization that utilizes the existing plane-parallel GCM radiative transfer model to compute radiative fluxes for inhomogeneous cloud distributions. The GCM radiative fluxes at TOA and the ground surface are then compared to ERBE and GEBA results. These comparisons show that including sub-grid cloud variability in the GCM radiative model improves agreement between the GCM radiative energy budget components and observations,

Lacis, Andrew↗

NASA NTRS1999

Radiation Effects: Core Project

The risks to personnel in space from the naturally occurring radiations are generally considered to be one of the most serious limitations to human space missions, as noted in two recent reports of the National Research Council/National Academy of Sciences. The Core Project of the Radiation Effects Team for the National Space Biomedical Research Institute is the consequences of radiations in space in order to develop countermeasure, both physical and pharmaceutical, to reduce the risks of cancer and other diseases associated with such exposures. During interplanetary missions, personnel in space will be exposed to galactic cosmic rays, including high-energy protons and energetic ions with atomic masses of iron or higher. In addition, solar events will produce radiation fields of high intensity for short but irregular durations. The level of intensity of these radiations is considerably higher than that on Earth's surface, and the biological risks to astronauts is consequently increased, including increased risks of carcinogenesis and other diseases. This group is examining the risk of cancers resulting from low-dose, low-dose rate exposures of model systems to photons, protons, and iron by using ground-based accelerators which are capable of producing beams of protons, iron, and other heavy ions at energies comparable to those encountered in space. They have begun the first series of experiments using a 1-GeV iron beam at the Brookhaven National Laboratory and 250-MeV protons at Loma Linda University Medical Center's proton synchrotron facility. As part of these studies, this group will be investigating the potential for the pharmaceutical, Tamoxifen, to reduce the risk of breast cancer in astronauts exposed to the level of doses and particle types expected in space. Theoretical studies are being carried out in a collaboration between scientists at NASA's Johnson Space Center and Johns Hopkins University in parallel with the experimental program have provided methods and predictions which are being used to assess the levels of risks to be encountered and to evaluate appropriate strategies for countermeasures. Although the work in this project is primarily directed toward problems associated with space travel, the problem of protracted exposures to low-levels of radiation is one of national interest in our energy and defense programs, and the results may suggest new paradigms for addressing such risks.

Dicello, John F.↗

NASA NTRS1999

Quantitation of Radiation Induced Deletion and Recombination Events Associated with Repeated DNA Sequences

Manned exploration of space exposes the explorers to a complex and novel radiation environment. The galactic cosmic ray and trapped belt radiation (predominantly proton) components of this environment are relatively constant, and the variations with the solar cycle are well understood and predictable. The level of radiation encountered in low earth orbits is determined by several factors, including altitude, inclination of orbit with respect to the equator, and spacecraft shielding. At higher altitudes, and on a Mars mission, the level of radiation exposure will increase significantly. A significant fraction of the dose may be delivered by solar particle events which vary dramatically in dose rate and incident particle spectrum. High-LET radiation is of particular concern. High-LET radiation, a component of galactic cosmic rays (GCR), is comprised of a variety of charged particles of various energies (10 MeV/n to 10 GeV/n), including about 87% photons, 12% helium ions, and heavy ions (including iron). These high energy particles can cause significant damage to target cells. The different particle types and energies result in different patterns of energy deposition at the molecular and cellular level in a primary target cell. They can also cause significant damage to other, nearby cells as a result of secondary particles. Protons, for instance produce secondaries that include photons, neutrons, pions, heavy particles, as well as gamma rays. Heavy ions deposit energy in a "track" in which the magnitude of the damage varies as the particle loses energy. Heavy ions produce secondary delta rays, or electrons. The distribution of damage through tissue is described by a Bragg curve which will be characteristic for different energies. Needless to say there are differences in the RBE of protons and a particles. High-LET heavy ions are particularly damaging to cells as they do continual damage throughout their track. Differences in these energy deposition patterns can significantly influence the nature of DNA damage and the ability of cellular systems to repair such damage. It has been suspected that these differences also affect the spatial distribution of damage within the DNA of the interphase cell nucleus and produce corresponding differences in endpoints related to health effects. The interaction of a single high-LET particle with chromatin has been suggested to cause multiple double strand breaks within a relatively short distance. In part this is due to the organization of DNA into chromatin fibers in which distant regions of the DNA helix can be physically juxtaposed by the various levels of coiling of the DNA. This prediction was confirmed by the detection of the generation of double strand DNA fragments of 100-2000 bp following exposure to high-LET ions (including iron).

Sinden, Richard R.↗

NASA NTRS2000

North Atlantic Aerosol Properties for Radiative Impact Assessments. Derived from Column Closure Analyses in TARFOX and ACE-2

Aerosol effects on atmospheric radiative fluxes provide a forcing function that can change the climate in potentially significant ways. This aerosol radiative forcing is a major source of uncertainty in understanding the climate change of the past century and predicting future climate. To help reduce this uncertainty, the 1996 Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) and the 1997 Aerosol Characterization Experiment (ACE-2) measured the properties and radiative effects of aerosols over the Atlantic Ocean. Both experiments used remote and in situ measurements from aircraft and the surface, coordinated with overpasses by a variety of satellite radiometers. TARFOX focused on the urban-industrial haze plume flowing from the United States over the western Atlantic, whereas ACE-2 studied aerosols over the eastern Atlantic from both Europe and Africa. These aerosols often have a marked impact on satellite-measured radiances. However, accurate derivation of flux changes, or radiative forcing, from the satellite measured radiances or retrieved aerosol optical depths (AODs) remains a difficult challenge. Here we summarize key initial results from TARFOX and ACE-2, with a focus on closure analyses that yield aerosol microphysical models for use in improved assessments of flux changes. We show how one such model gives computed radiative flux sensitivities (dF/dAOD) that agree with values measured in TARFOX and preliminary values computed for the polluted marine boundary layer in ACE-2. A companion paper uses the model to compute aerosol-induced flux changes over the North Atlantic from AVHRR-derived AOD fields.

Russell, Philip A.↗

NASA NTRS2000

North Atlantic Aerosol Properties and Direct Radiative Effects: Key Results from TARFOX and ACE-2

Aerosol effects on atmospheric radiative fluxes provide a forcing function that can change the climate In potentially significant ways. This aerosol radiative forcing is a major source of uncertainty in understanding the observed climate change of the past century and in predicting future climate. To help reduce this uncertainty, the International Global Atmospheric Chemistry Project (IGAC) has endorsed a series of multiplatform aerosol field campaigns. The Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) and the second Aerosol Characterization Experiment (ACE-2) were the first IGAC campaigns to address the impact of anthropogenic aerosols, Both TARFOX and ACE-2 gathered extensive data sets on aerosol properties and radiative effects, TARFOX focused on the urban-industrial haze plume flowing from the eastern United States over the western Atlantic Ocean, whereas ACE-2 studied aerosols carried over the eastern Atlantic from both European urban/industrial and African mineral sources. These aerosols often have a marked influence on the top-of-atmosphere radiances measured by satellites. Shown there are contours of aerosol optical depth derived from radiances measured by the AVHRR sensor on the NOAA-11 satellite. The contours readily show that aerosols originating in North America, Europe, and Africa impact the radiative properties of air over the North Atlantic. However, the accurate derivation of flux changes, or radiative forcing, from the satellite measured radiances or retrieved optical depths remains a difficult challenge. In this paper we summarize key initial results from TARFOX and, to a lesser extent, ACE-2, with a focus on those results that allow an improved assessment of the flux changes caused by North Atlantic aerosols at middle latitudes.

Russell, P. B.↗

NASA NTRS2000

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Gould, Dana C.↗

NASA NTRS1999

Single Bubble Sonoluminescence in Low Gravity and Optical Radiation Pressure Positioning of the Bubble

Several groups of researchers have demonstrated that high frequency sound in water may be used to cause the regular repeated compression and luminescence of a small bubble of gas in a flask. The phenomenon is known as single bubble sonoluminescence (SBSL). It is potentially important because light emitted by the bubble appears to be associated with a significant concentration of energy within the volume of the bubble. Unfortunately, the detailed physical mechanisms causing the radiation of light by oscillating bubbles are poorly understood and there is some evidence that carrying out experiments in a weightless environment may provide helpful clues. In addition, the radiation pressure of laser beams on the bubble may provide a way of simulating weightless experiments in the laboratory. The standard model of SBSL attributes the light emission to heating within the bubble by a spherically imploding shock wave to achieve temperatures of 50,000 K or greater. In an alternative model, the emission is attributed to the impact of a jet of water which is required to span the bubble and the formation of the jet is linked to the buoyancy of the bubble. The coupling between buoyancy and jet formation is a consequence of the displacement of the bubble from a velocity node (pressure antinode) of the standing acoustic wave that drives the radial bubble oscillations. One objective of this grant is to understand SBSL emission in reduced buoyancy on KC-135 parabolic flights. To optimize the design of those experiments and for other reasons which will help resolve the role of buoyancy, laboratory experiments are planned in simulated low gravity in which the radiation pressure of laser light will be used to position the bubble at the acoustic velocity node of the ultrasonic standing wave. Laser light will also be used to push the bubble away from the velocity node, increasing the effective buoyancy. The original experiments on the optical levitation and radiation pressure on bubbles in water by Unger and Marston noted above were carried out using a continuous wave (CW) beam of an Argon laser. For lateral stability the beam had a intensity minimum along its axis. Calculations of the optical radiation force on an SBSL bubble indicate that ion laser technology is a poor choice for providing the magnitude of the average optical radiation force required. Consequently it is necessary to examine various diode-pumped solid state laser technologies. The approach for this part of the research will be to achieve optical levitation of a quiescent bubble based on contemporary laser technology and then to strobe the laser synchronously with the SBSL bubble oscillations.

Thiessen, D. B.↗

NASA NTRS2000

Earth Radiation Measurement Science

This document is the final report for NASA Grant NAG1-1959, 'Earth Radiation Measurement Science'. The purpose of this grant was to perform research in this area for the needs of the Clouds and Earth Radiant Energy System (CERES) project and for the Earth Radiation Budget Experiment (ERBE), which are bing conducted by the Radiation and Aerosols Branch of the Atmospheric Sciences Division of Langley Research Center. Earth Radiation Measurement Science investigates the processes by which measurements are converted into data products. Under this grant, research was to be conducted for five tasks: (1) Point Response Function Measurements; (2) Temporal Sampling of Outgoing Longwave Radiation; (3) Spatial Averaging of Radiation Budget Data; (4) CERES Data Validation and Applications; and (5) ScaRaB Data Validation and Application.

Smith, G. Louis↗

NASA NTRS1994

Comparison of Coupled Radiative Navier-Stokes Flow Solutions with the Project Fire II Flight Data

A nonequilibrium, axisymmetric, Navier-Stokes flow solver with coupled radiation has been developed to use in the design of thermal protection systems for vehicles where radiation effects are important. The present method has been compared with an existing flow and radiation solver and with the Project Fire II experimental data. Very good agreement has been obtained over the entire Fire II trajectory with the experimentally determined values of the stagnation radiation intensity in the .2 to 6.2 eV range and with the total stagnation heating. The agreement was significantly better than previous numerical predictions. The effects of a number of flow models are examined to determine which combination of physical models produces the best agreement with the experimental data. These models include radiation coupling, multi-temperature thermal models, finite-rate chemistry, and a quasi-steady-state or Boltzmann assumption for the calculation of the excited electronic states. Finally, the computational efficiency of the present model is evaluated. The radiation properties model developed for this study is shown to offer significant computational savings compared to existing codes.

Olynick, David R.↗

NASA NTRS1994

Collisional-Radiative Nonequilibrium and Precursor Effects in a Nitrogen Shock Wave

Improvements to a plasma code with a Collisional-Radiative (CR) non-equilibrium model are made, allowing for a more accurate description of the physical processes. The code allows for non-Boltzmann distributions of the electronic excited states by convecting separately each excited state, as a pseudo-specie. Each molecular state has also its own vibrational temperature, while a global rotational temperature is assumed. The free electron temperature is different from those of the excited states, and the electron heat conduction is also included. The CR model also uses a unique coupling between chemistry and vibrational energy (C-V coupling), which is fully coherent, and has the property of establishing thermal equilibrium as well as chemical equilibrium, on its own. We have also included a coupling between electronic excitations and vibrational energy (X-V coupling), which can have a strong influence on the vibrational temperature of some states. The recent improvements include the multi- temperature dependence of the chemical rates for associative ionization, as well as the estimation of the internal energies transferred during this process. Additionally, the distribution of energy into different translational modes (electron and heavy particles) is now correctly modeled. This provides a very rapid heating mechanism for the free electrons, since it is found that the electrons are generated with an average thermal energy of the same order as the heavy particle translational energy. This effect was observed by Gorelov et al in a recent paper, and lead to pronounced peaks in electron temperature immediately behind the shock. We will attempt ro reproduce this phenomenon. The last modification concerns the inclusion of the radiative terms into the calculations, thus enabling us to observe the effect of radiative losses and radiation transport. Preliminary tests have shown that the radiative losses are not negligible, i.e. the shock velocity drops when the radiative emission is included. In addition, we have observed some precursor excitation and ionization phenomena. These may be important at high shock velocities, and this will be investigated in detail. Precursor phenomena were also observed (in air) by Gorelov et al, and our results (for pure nitrogen) will be qualitatively compared with theirs.

Cambier, Jean-Luc↗

NASA NTRS2001

Do Fractal Models of Clouds Produces the Right 3D Radiative Effects?

Stochastic fractal models of clouds are often used to study 3D radiative effects and their influence on the remote sensing of cloud properties. Since it is important that the cloud models produce a correct radiative response, some researchers require the model parameters to match observed cloud properties such as scale-independent optical thickness variability. Unfortunately, matching these properties does not necessarily imply that the cloud models will cause the right 3D radiative effects. First, the matched properties alone only influence the 3D effects but do not completely determine them. Second, in many cases the retrieved cloud properties have been already biased by 3D radiative effects, and so the models may not match the true real clouds. Finally, the matched cloud properties cannot be considered independent from the scales at which they have been retrieved. This paper proposes an approach that helps ensure that fractal cloud models are realistic and produce the right 3D effects. The technique compares the results of radiative transfer simulations for the model clouds to new direct observations of 3D radiative effects in satellite images.

Varnai, Tamas↗

NASA NTRS1994

Measurements of Ice Particles in Tropical Cirrus Anvils: Importance in Radiation Balance

Cirrus is important in the radiation balance of the global atmosphere, both at solar and thermal infrared (IR) wavelengths. In particular cirrus produced by deep convection over the oceans in the tropics may be critical in controlling processes whereby energy from warm tropical oceans is injected to different levels in the tropical atmosphere to subsequently influence not only tropical but mid latitude climate. Details of the cloud composition may differentiate between a net cooling or warming at these levels. The cloud composition may change depending on the input of nuclei from volcanic or other sources. Observations of cirrus during the FIRE-2 Project over Coffeyville, Kansas and by satellite demonstrate that cirrus, on occasion, is composed not only of larger particles with significant fall velocity (few hundred micrometers, 0.5 m/s) but much more numerous small particles, size 10-20 micrometers, with small fall velocity (cm/s), which may sometimes dominate the radiation field. This is consistent with emissivity measurements. In the thermal IR, ice absorption is strong, so that ice particles only 10 micrometers thick are opaque, at some wavelengths; on the other hand at other wavelengths and in the visible, ice is only moderately to weakly absorbing. It follows that for strongly absorbing wavelengths the average projected area of the ice particles is the important parameter, in weakly absorbing regions it is the volume (mass) of ice which is important. The shape of particles and also their internal structure may also have significant effect on their radiative properties. In order to access the role of cirrus in the radiation budget it is necessary to measure the distribution of ice particles sizes, shapes and concentrations in the regions of interest. A casual observation of any cirrus cloud shows that there is variability down to a scale of at least a few 100 m; this is confirmed by radar and lidar remote sensing. Thus aircraft measurements designed to give insight into the spatial distribution of radiation properties of ice crystals must be capable of examination of concentration, size and shape over a distance ideally of 100 m or less and to detect particles down to a size below which radiative effects are no longer significant.

Foster, Theodore↗

NASA NTRS1998

North Atlantic Aerosol Properties and Direct Radiative Effects: Key Results from TARFOX and ACE-2

Aerosol effects on atmospheric radiative fluxes provide a forcing function that can change the climate in potentially significant ways. This aerosol radiative Forcing is a major source of uncertainty in understanding the observed climate change of the past century and in predicting, future climate. To help reduce this uncertainty, the International Global Atmospheric Chemistry Project (IGAC) has endorsed a series of multiplatform aerosol field campaigns. The Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) and the second Aerosol Characterization Experiment (ACE-2) were the first IGAC campaigns to address the impact of anthropogenic aerosols. Both TARFOX and ACE-2 gathered extensive data sets on aerosol properties and radiative effects. TARFOX focused on the urban-industrial haze plume flowing from the eastern United States over the western Atlantic Ocean, whereas ACE-2 studied aerosols carried over the eastern Atlantic from both European urban/industrial and African mineral sources. These aerosols often have a marked influence on the top-of-atmosphere radiances measured by satellites, as illustrated in Figure 1. Shown there are contours of aerosol optical depth derived from radiances measured by the AVHRR sensor on the NOAA-11 satellite. The contours readily show that aerosols originating in North America, Europe, and Africa impact the radiative properties of air over the North Atlantic. However, the accurate derivation of flux chances, or radiative forcing, from the satellite-measured radiances or 'etrieved optical depths remains a difficult challenge. In this paper we summarize key Initial results from TARFOX and, to a lesser extent ACE-2, with a focus on those results that allow an improved assessment of the flux changes caused by North Atlantic aerosols at middle and high latitudes.

Russell, P. B.↗

NASA NTRS2003

Radiation Pressure Measurements on Micron Size Individual Dust Grains

Measurements of electromagnetic radiation pressure have been made on individual silica (SiO2) particles levitated in an electrodynamic balance. These measurements were made by inserting single charged particles of known diameter in the 0.2 micron to 6.82 micron range and irradiating them from above with laser radiation focused to beam-widths of approx. 175-400 micron, at ambient pressures approx. 10(exp -3) to 10(exp -4) torr. The downward displacement of the particle due to the radiation force is balanced by the electrostatic force indicated by the compensating dc potential applied to the balance electrodes, providing a direct measure of the radiation force on the levitated particle. Theoretical calculations of the radiation pressure with a least-squares fit to the measured data yield the radiation pressure efficiencies of the particles, and comparisons with Mie scattering theory calculations provide the imaginary part of the refractive index of silica and the corresponding extinction and scattering efficiencies.

Abbas, M. M.↗

NASA NTRS2003

Magma Reservoirs Feeding Giant Radiating Dike Swarms: Insights from Venus

Evidence of lateral dike propagation from shallow magma reservoirs is quite common on the terrestrial planets, and examination of the giant radiating dike swarm population on Venus continues to provide new insight into the way these complex magmatic systems form and evolve. For example, it is becoming clear that many swarms are an amalgamation of multiple discrete phases of dike intrusion. This is not surprising in and of itself, as on Earth there is clear evidence that formation of both magma reservoirs and individual giant radiating dikes often involves periodic magma injection. Similarly, giant radiating swarms on Earth can contain temporally discrete subswarms defined on the basis of geometry, crosscutting relationships, and geochemical or paleomagnetic signatures. The Venus data are important, however, because erosion, sedimentation, plate tectonic disruption, etc. on Earth have destroyed most giant radiating dike swarm's source regions, and thus we remain uncertain about the geometry and temporal evolution of the magma sources from which the dikes are fed. Are the reservoirs which feed the dikes large or small, and what are the implications for how the dikes themselves form? Does each subswarm originate from a single, periodically reactivated reservoir, or do subswarms emerge from multiple discrete geographic foci? If the latter, are these discrete foci located at the margins of a single large magma body, or do multiple smaller reservoirs define the character of the magmatic center as a whole? Similarly, does the locus of magmatic activity change with time, or are all the foci active simultaneously? Careful study of giant radiating dike swarms on Venus is yielding the data necessary to address these questions and constrain future modeling efforts. Here, using giant radiating dike swarms from the Nemesis Tessera (V14) and Carson (V43) quadrangles as examples, we illustrate some of the dike swarm focal region diversity observed on Venus and briefly explore some key implications for the questions framed above.

Grosfils, E. B.↗

NASA NTRS2002

A New Look Into the Treatment of Large Drops in Radiative Transfer

One of the weakest links in conventional cloud radiation models is the way a size distribution of cloud particles is mathematically handled: one averages measured drop concentrations over space, evaluates the extinction and scattering cross sections using the mean drop size distribution function and solves the radiative transfer equation with average characteristics. This technique assumes that all drop sizes are well represented in ary given interval along the direction of photon travel. But the concentration of large drops can be so law that this assumption is significantly violated. This is clearly seen if one examines of how the appearance of drops changes with the scale. In the poster we demonstrate the results of our analysis of FSSP data acquired during FIRE'87 and both FSSP and DC1 data from cloud IOP in Spring 2000. The analysis shows that, in general, the average number of drops observed in an interval along the direction of photon travel is proportional to the interval's length (or scale) powered to a drop scaling exponent. For small droplets the scaling exponent is equal to 1, as predicted by a conventional radiative transfer model. However, for large drops, the scaling exponent can fall distinctly below 1. Since the solution of radiative transfer equation depends on the drop scaling exponent, its deviation from unity can lead to a systematic bias in estimation of cloud radiative properties. We discuss the importance of the scaling exponent for the characteristics of the small-scale drop size variability for large and small droplets. Most of the existing cloud radiation models, however, are insensitive to this parameter.

Marshak, Alexander↗

NASA NTRS2003

Radiation Pressure Measurements on Micron-Size Individual Dust Grains

Measurements of electromagnetic radiation pressure have been made on individual silica (SiO2) particles levitated in an electrodynamic balance. These measurements were made by inserting single charged particles of known diameter in the 0.2- to 6.82-micron range and irradiating them from above with laser radiation focused to beam widths of approximately 175- 400 microns at ambient pressures particle due to the radiation force is balanced by the electrostatic force indicated by the compensating dc potential applied to the balance electrodes, providing a direct measure of the radiation force on the levitated particle. Theoretical calculations of the radiation pressure with a least-squares fit to the measured data yield the radiation pressure efficiencies of the particles, and comparisons with Mie scattering theory calculations provide the imaginary part of the refractive index of SiO2 and the corresponding extinction and scattering efficiencies.

Abbas, M. 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.

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