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NASA NTRS2005

Scanning Backscatter Lidar Observations for Characterizing 4-D Cloud and Aerosol Fields to Improve Radiative Transfer Parameterizations

Clouds have a powerful influence on atmospheric radiative transfer and hence are crucial to understanding and interpreting the exchange of radiation between the Earth's surface, the atmosphere, and space. Because clouds are highly variable in space, time and physical makeup, it is important to be able to observe them in three dimensions (3-D) with sufficient resolution that the data can be used to generate and validate parameterizations of cloud fields at the resolution scale of global climate models (GCMs). Simulation of photon transport in three dimensionally inhomogeneous cloud fields show that spatial inhomogeneities tend to decrease cloud reflection and absorption and increase direct and diffuse transmission, Therefore it is an important task to characterize cloud spatial structures in three dimensions on the scale of GCM grid elements. In order to validate cloud parameterizations that represent the ensemble, or mean and variance of cloud properties within a GCM grid element, measurements of the parameters must be obtained on a much finer scale so that the statistics on those measurements are truly representative. High spatial sampling resolution is required, on the order of 1 km or less. Since the radiation fields respond almost instantaneously to changes in the cloud field, and clouds changes occur on scales of seconds and less when viewed on scales of approximately 100m, the temporal resolution of cloud properties should be measured and characterized on second time scales. GCM time steps are typically on the order of an hour, but in order to obtain sufficient statistical representations of cloud properties in the parameterizations that are used as model inputs, averaged values of cloud properties should be calculated on time scales on the order of 10-100 s. The Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE) provides exceptional temporal (100 ms) and spatial (30 m) resolution measurements of aerosol and cloud backscatter in three dimensions. HARLIE was used in a ground-based configuration in several recent field campaigns. Principal data products include aerosol backscatter profiles, boundary layer heights, entrainment zone thickness, cloud fraction as a function of altitude and horizontal wind vector profiles based on correlating the motions of clouds and aerosol structures across portions of the scan. Comparisons will be made between various cloud detecting instruments to develop a baseline performance metric.

Schwemmer, Geary K.↗

NASA NTRS2004

3D Cloud Radiative Effects on Aerosol Optical Thickness Retrievals in Cumulus Cloud Fields in the Biomass Burning Region in Brazil

Aerosol amount in clear regions of a cloudy atmosphere is a critical parameter in studying the interaction between aerosols and clouds. Since the global cloud cover is about 50%, cloudy scenes are often encountered in any satellite images. Aerosols are more or less transparent, while clouds are extremely reflective in the visible spectrum of solar radiation. The radiative transfer in clear-cloudy condition is highly three- dimensional (3D). This paper focuses on estimating the 3D effects on aerosol optical thickness retrievals using Monte Carlo simulations. An ASTER image of cumulus cloud fields in the biomass burning region in Brazil is simulated in this study. The MODIS products (i-e., cloud optical thickness, particle effective radius, cloud top pressure, surface reflectance, etc.) are used to construct the cloud property and surface reflectance fields. To estimate the cloud 3-D effects, we assume a plane-parallel stratification of aerosol properties in the 60 km x 60 km ASTER image. The simulated solar radiation at the top of the atmosphere is compared with plane-parallel calculations. Furthermore, the 3D cloud radiative effects on aerosol optical thickness retrieval are estimated.

Wen, Guo-Yong↗

NASA NTRS2003

Sensitivity of Precipitation Processes to Microphysics and Resolution in a Cloud Resolving Model

The Goddard Cumulus Ensemble (GCE) model examines the impact of various microphysical schemes, and vertical and horizontal resolution in the development, intensity and rainfall associated with mesoscale convective systems, idealized hurricanes and an ensemble of clouds. The model variables include horizontal and vertical velocities, potential temperature, perturbation pressure, turbulent kinetic energy, and mixing rations of all water phases (vapor, liquid and ice). The major characteristics of the GCE model are the explicit representation of warm rain and ice microphysical processes, and their complex interactions with solar and infrared radiative transfer processes and with surface processes. For idealized hurricanes, an axisymmetric version of the GCE model was developed and used to simulate the tropical cyclogenesis process using both a Rankin vortex and saturated air within a specified radius as initial conditions. For mesoscale convective systems, the 3-D version of the GCE model was use to simulate squall lines that developed in the western Pacific, South China Sea, eastern Atlantic, South America and central U.S. FOr the cloud ensemble, the GCE model was integrated for several days in order to have a good sampling of cloud statistics. In this paper, the sensitivities of hurricane intensity to various microphysical processes and model grid resolutio will be examined. This will be mainly achieved by performing sensitivity tests using various horizontal (from 1-to 5-km) and vertical resolutions (from 20- to 200-m in the lower troposphere to 200- to 500m in the middle and upper troposphere). Sensitivity test using various microphysical schemes (warm rain only, and three ice with either graupel or hail) will also be performed. The thermodynamic and water budget associated with various types of precipitation systems will also be evaluated. The budgets will be calculated for different regions (i.e., convective and stratiform regions).

Tao, Wei-Kuo↗

NASA NTRS2003

Sensitivity of Precipitation Processes to Microphysics and Resolution in a Cloud-Resolving Model

The Goddard Cumulus Ensemble (GCE) model is used to examine the impact of various microphysical schemes, and vertical and horizontal resolution on the development, intensity and rainfall associated with mesoscale convective systems, idealized hurricanes and an ensemble of clouds. The model variables include horizontal and vertical velocities, potential temperature, perturbation pressure, turbulent kinetic energy, and mixing ratios of all water phases (vapor, liquid, and ice). The major characteristics of the GCE model are the explicit representation of warm rain and ice microphysical processes, and their complex interactions with solar and infrared radiative transfer processes, and with surface processes. For idealized hurricane, an axisymmetric version of the GCE model was developed and used successfully to simulate the tropical cyclogenesis process using both a Rankin vortex and saturated air within a specified radius as initial conditions. For mesoscale convective systems, the 3-D version of the GCE model was used to simulate squall lines that developed in the western Pacific, South China Sea, eastern Atlantic, South America and central U.S. For the cloud ensemble, the GCE model was integrated for several days in order to have good sampling of cloud statistics. In this paper, the sensitivities of hurricane intensity to various microphysical processes and model grid resolution will be examined. This will be mainly achieved by performing sensitivity tests using various horizontal (from 1- to 5-kilometers) and vertical resolutions (from 20- to 200-meters in the lower troposphere to 200- to 500-m in the middle and upper troposphere). Sensitivity tests using various microphysical schemes (warm rain only, and three ice with either graupel or hail) will also be performed. The PBL and diurnal variation of precipitation processes will also be evaluated. The budgets will be calculated for different regions (i.e., convective and stratiform regions).

Tao, Wei-Kao↗

NASA NTRS2003

Sensitivity of Precipitation Processes to Microphysics and Resolution in a Cloud-Resolving Model

The Goddard Cumulus Ensemble (GCE) model is used to examine the impact of various microphysical schemes, and vertical and horizontal resolution on the development, intensity and rainfall associated with mesoscale convective systems, idealized hurricanes and an ensemble of clouds. The model variables include horizontal and vertical velocities, potential temperature, perturbation pressure, turbulent kinetic energy, and mixing ratios of all water phases (vapor, liquid, and ice). The major characteristics of the GCE model are the explicit representation of warm rain and ice microphysical processes, and their complex interactions with solar and infrared radiative transfer processes, and with surface processes. For idealized hurricane, an axisymmetric version of the GCE model was developed and used successfully to simulate the tropical cyclogenesis process using both a Rankin vortex and saturated air within a specified radius as initial conditions. For mesoscale convective systems, the 3-D version of the GCE model was used to simulate squall lines that developed in the western Pacific, eastern Atlantic and central US. For the cloud ensemble, the GCE model was integrated for several days in order to have good sampling of cloud statistics. In this paper, the sensitivities of hurricane intensity to various microphysical processes and model grid resolution will be examined.

Tao, Wei-Kuo↗

NASA NTRS2003

Sensitivity of Precipitation Processes of Microphysics and Resolution in a Cloud-Resolving Model

The Goddard Cumulus Ensemble (GCE) model is used to examine the impact of various microphysical schemes, and vertical and horizontal resolution ion the development, intensity and rainfall associated with mesoscale convective systems, idealized hurricanes and an ensemble f clouds. The model variables include horizontal and vertical velocities, potential temperatures, perturbation pressure, turbulent kinetic energy, and mixing ratios of all water phases (vapor, liquid, and ice). The major characteristics of the GCE model are the explicit representation of warm rain and ice microphysical processes, and their complex interactions with solar and infrared radiative transfer processes, and with surface processes. For idealized hurricane, an axisymmetric version of the GCE model was developed and used successfully to simulate the tropical cyclogenesis process using both a Rankin vortex and saturated air within a specified radius as initial conditions. For mesoscale convective systems, the 3-D version of the GCE model was used to simulated squall lines that developed in the western Pacific, eastern Atlantic and central US. For the cloud ensemble, the GCE model was integrated for several days in order to have good sampling of cloud statistics. In this paper, the sensitivities of hurricane intensity to various microphysical processes and model grid resolution will be examined. This will be mainly achieved by performing sensitivity tests using various horizontal (from 1- to 5-km) and vertical resolutions (from 20- to 200-m in the lower troposphere to 200- to 500-m in the middle and upper troposphere). Sensitivity tests using various microphysical schemes (warm rain only, and three ice with either graupel or hail) will also be performed. The thermodynamic and water budget associated with various types of precipitation systems will also be evaluated. The budgets will be calculated for different regions (i.e., convective and stratiform regions).

Tao, Wei-Kuo↗

NASA NTRS2011

Eta Carinae: An Observational Testbed for 3-D Interacting Wind Modeling

Eta Car, with its very massive interacting winds, provides shocked arc-like structures dense enough to trace in forbidden emission lines out to 0.7" (1700 AU). As the massive binary is in a very elliptical orbit (e approx. 0.9), the spatial and velocity structures of these winds change over the 5.54 year period. We can tract ionization structures by several forbidden emission lines. With the addition of radiative transfer on a time-step frame-by-frame basis, we are learning much new information on the ballistic structures, and may gain insight on how molecules and dust might form in these very massive systems.

Gull, Theodore↗

NASA NTRS1988

Tabulation of Mie scattering calculation results for microwave radiative transfer modeling

In microwave radiative transfer model simulations, the Mie calculations usually consume the majority of the computer time necessary for the calculations (70 to 86 percent for frequencies ranging from 6.6 to 183 GHz). For a large array of atmospheric profiles, the repeated calculations of the Mie codes make the radiative transfer computations not only expensive, but sometimes impossible. It is desirable, therefore, to develop a set of Mie tables to replace the Mie codes for the designated ranges of temperature and frequency in the microwave radiative transfer calculation. Results of using the Mie tables in the transfer calculations show that the total CPU time (IBM 3081) used for the modeling simulation is reduced by a factor of 7 to 16, depending on the frequency. The tables are tested by computing the upwelling radiance of 144 atmospheric profiles generated by a 3-D cloud model (Tao, 1986). Results are compared with those using Mie quantities computed from the Mie codes. The bias and root-mean-square deviation (RMSD) of the model results using the Mie tables, in general, are less than 1 K except for 37 and 90 GHz. Overall, neither the bias nor RMSD is worse than 1.7 K for any frequency and any viewing angle.

Yeh, Hwa-Young M.↗

NASA NTRS2006

Radiative Effect of Clouds on Tropospheric Chemistry in a Global Three-Dimensional Chemical Transport Model

Clouds exert an important influence on tropospheric photochemistry through modification of solar radiation that determines photolysis frequencies (J-values). We assess the radiative effect of clouds on photolysis frequencies and key oxidants in the troposphere with a global three-dimensional (3-D) chemical transport model (GEOS-CHEM) driven by assimilated meteorological observations from the Goddard Earth Observing System data assimilation system (GEOS DAS) at the NASA Global Modeling and Assimilation Office (GMAO). We focus on the year of 2001 with the GEOS-3 meteorological observations. Photolysis frequencies are calculated using the Fast-J radiative transfer algorithm. The GEOS-3 global cloud optical depth and cloud fraction are evaluated and generally consistent with the satellite retrieval products from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the International Satellite Cloud Climatology Project (ISCCP). Results using the linear assumption, which assumes linear scaling of cloud optical depth with cloud fraction in a grid box, show global mean OH concentrations generally increase by less than 6% because of the radiative effect of clouds. The OH distribution shows much larger changes (with maximum decrease of approx.20% near the surface), reflecting the opposite effects of enhanced (weakened) photochemistry above (below) clouds. The global mean photolysis frequencies for J[O1D] and J[NO2] in the troposphere change by less than 5% because of clouds; global mean O3 concentrations in the troposphere increase by less than 5%. This study shows tropical upper tropospheric O3 to be less sensitive to the radiative effect of clouds than previously reported (approx.5% versus approx.20-30%). These results emphasize that the dominant effect of clouds is to influence the vertical redistribution of the intensity of photochemical activity while global average effects remain modest, again contrasting with previous studies. Differing vertical distributions of clouds may explain part, but not the majority, of these discrepancies between models. Using an approximate random overlap or a maximum-random overlap scheme to take account of the effect of cloud overlap in the vertical reduces the impact of clouds on photochemistry but does not significantly change our results with respect to the modest global average effect.

Liu, Hongyu↗

NASA NTRS2001

Laser Powered Launch Vehicle Performance Analyses

The purpose of this study is to establish the technical ground for modeling the physics of laser powered pulse detonation phenomenon. Laser powered propulsion systems involve complex fluid dynamics, thermodynamics and radiative transfer processes. Successful predictions of the performance of laser powered launch vehicle concepts depend on the sophisticate models that reflects the underlying flow physics including the laser ray tracing the focusing, inverse Bremsstrahlung (IB) effects, finite-rate air chemistry, thermal non-equilibrium, plasma radiation and detonation wave propagation, etc. The proposed work will extend the base-line numerical model to an efficient design analysis tool. The proposed model is suitable for 3-D analysis using parallel computing methods.

Chen, Yen-Sen↗

NASA NTRS1992

Radiation model predictions and validation using LDEF data

Radiation dosimetry aboard LDEF, as well as post-flight measurements of the radioactivity induced in numerous LDEF spacecraft components, provide unique data for evaluating the accuracy of current models for predicting both the space radiation environments (trapped proton intensity, spectra, and directionality; cosmic ray fluence) and the radiation environments induced in spacecraft components (fluence, energy spectra, secondary particle, linear energy transfer, etc.). By determining the accuracy of such models using LDEF data, and with model updates where required, improved radiation environment predictions can be made for future missions, which in turn allows improved predictions for specific radiation effects for future spacecraft components (single event upsets of microelectronics, radiation damage to focal plane arrays, noise in sensitive instrumentation, etc.). Herein, the status and results from radiation model predictions and comparisons with LDEF data is given. The calculations are made using radiation transport codes coupled with a 3-D geometry/mass model of LDEF, together with current models of the space radiation environment.

Armstrong, T. W.↗

NASA NTRS1989

Image-based terrain modeling with thematic mapper applied to resolving the limit of Holocene Lake expansion in the Great Salt Lake Desert, Utah, part 1

The LANDSAT Thematic Mapper (TM) scanner records reflected solar energy from the earth's surface in six wavelength regions, or bands, and one band that records emitted energy in the thermal region, giving a total of seven bands. Useful research was extracted about terrain morphometry from remote sensing measurements and this information is used in an image-based terrain model for selected coastal geomorphic features in the Great Salt Lake Desert (GSLD). Technical developments include the incorporation of Aerial Profiling of Terrain System (APTS) data in satellite image analysis, and the production and use of 3-D surface plots of TM reflectance data. Also included in the technical developments is the analysis of the ground control point spatial distribution and its affects on geometric correction, and the terrain mapping procedure; using satellite data in a way that eliminates the need to degrade the data by resampling. The most common approach for terrain mapping with multispectral scanner data includes the techniques of pattern recognition and image classification, as opposed to direct measurement of radiance for identification of terrain features. The research approach in this investigation was based on an understanding of the characteristics of reflected light resulting from the variations in moisture and geometry related to terrain as described by the physical laws of radiative transfer. The image-based terrain model provides quantitative information about the terrain morphometry based on the physical relationship between TM data, the physical character of the GSLD, and the APTS measurements.

Merola, John A.↗

NASA NTRS2002

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

We study lightning on Jupiter and the clouds illuminated by the lightning using images taken by the Galileo orbiter. The Galileo images have a resolution of 25 km/pixel and axe able to resolve the shape of the single lightning spots in the images, which have full widths at half the maximum intensity in the range of 90-160 km. We compare the measured lightning flash images with simulated images produced by our ED Monte Carlo light-scattering model. The model calculates Monte Carlo scattering of photons in a ED opacity distribution. During each scattering event, light is partially absorbed. The new direction of the photon after scattering is chosen according to a Henyey-Greenstein phase function. An image from each direction is produced by accumulating photons emerging from the cloud in a small range (bins) of emission angles. Lightning bolts are modeled either as points or vertical lines. Our results suggest that some of the observed scattering patterns axe produced in a 3-D cloud rather than in a plane-parallel cloud layer. Lightning is estimated to occur at least as deep as the bottom of the expected water cloud. For the six cases studied, we find that the clouds above the lightning are optically thick (tau > 5). Jovian flashes are more regular and circular than the largest terrestrial flashes observed from space. On Jupiter there is nothing equivalent to the 30-40-km horizontal flashes which axe seen on Earth.

Dyudine, U. A.↗

NASA NTRS2013

Modeling of 2008 Kasatochi Volcanic Sulfate Direct Radiative Forcing: Assimilation of OMI SO2 Plume Height Data and Comparison with MODIS and CALIOP Observations

Volcanic SO2 column amount and injection height retrieved from the Ozone Monitoring Instrument (OMI) with the Extended Iterative Spectral Fitting (EISF) technique are used to initialize a global chemistry transport model (GEOS-Chem) to simulate the atmospheric transport and lifecycle of volcanic SO2 and sulfate aerosol from the 2008 Kasatochi eruption, and to subsequently estimate the direct shortwave, top-of-the-atmosphere radiative forcing of the volcanic sulfate aerosol. Analysis shows that the integrated use of OMI SO2 plume height in GEOS-Chem yields: (a) good agreement of the temporal evolution of 3-D volcanic sulfate distributions between model simulations and satellite observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and Cloud-Aerosol Lidar with Orthogonal Polarisation (CALIOP), and (b) an e-folding time for volcanic SO2 that is consistent with OMI measurements, reflecting SO2 oxidation in the upper troposphere and stratosphere is reliably represented in the model. However, a consistent (approx. 25 %) low bias is found in the GEOS-Chem simulated SO2 burden, and is likely due to a high (approx.20 %) bias of cloud liquid water amount (as compared to the MODIS cloud product) and the resultant stronger SO2 oxidation in the GEOS meteorological data during the first week after eruption when part of SO2 underwent aqueous-phase oxidation in clouds. Radiative transfer calculations show that the forcing by Kasatochi volcanic sulfate aerosol becomes negligible 6 months after the eruption, but its global average over the first month is -1.3W/sq m, with the majority of the forcing-influenced region located north of 20degN, and with daily peak values up to -2W/sq m on days 16-17. Sensitivity experiments show that every 2 km decrease of SO2 injection height in the GEOS-Chem simulations will result in a approx.25% decrease in volcanic sulfate forcing; similar sensitivity but opposite sign also holds for a 0.03 m increase of geometric radius of the volcanic aerosol particles. Both sensitivities highlight the need to characterize the SO2 plume height and aerosol particle size from space. While more research efforts are warranted, this study is among the first to assimilate both satellite-based SO2 plume height and amount into a chemical transport model for an improved simulation of volcanic SO2 and sulfate transport.

Wang, J.↗

NASA NTRS2009

Evaluation of Low Altitude Cloud Amount Using CALIPSO Observations

Clouds strongly modulate the transfer of solar and thermal radiation within the atmosphere. Changes in the distribution and properties of clouds in a changing climate represent climate feedbacks affecting climate sensitivity, but the predicted responses of clouds from current climate models are inconsistent. Of particular concern is the response of low clouds, and it is recognized that proper representation of low clouds in global models is in need of improvement. Accurate satellite cloud climatologies are necessary to evaluate model performance, but existing climatologies require validation and are inadequate in some respects for model evaluation. CALIPSO and CloudSat have been acquiring high vertical resolution cloud profiles since launch in 2006. These global cloud datasets represent a new tool for evaluation of both models and existing satellite climatologies. While a recently available merged CALIPSO-CloudSat cloud climatology provides the most comprehensive view of global 3-D cloud distribution, the CALIPSO dataset set on its own has several unique characteristics, including profiles of the atmospheric boundary layer with 30 meter vertical resolution. In this paper we investigate the use of CALIPSO data to characterize boundary layer clouds, looking toward the development of a reliable global dataset suitable for evaluation of model performance.

Winker, Dave↗

NASA NTRS2010

Plasma IMS Composition Measurements for Europa and the Other Galilean Moons

NASA and ESA are planning the joint Europa Jupiter System Mission (EJSM) to the Jupiter system with specific emphasis to Europa and Ganymede, respectively. The Japanese Space Agency is also planning an orbiter mission to explore Jupiter's magnetosphere and the Galilean satellites. For NASA's Jupiter Europa Orbiter (JEO) we are developing the 3D Ion Mass Spectrometer (IMS) with two main goals which can also be applied to the other Galilean moons, 1) measure the plasma interaction between Europa and Jupiter's magnetosphere and 2) infer the 4 pi surface composition to trace elemental and significant isotopic levels. The first goal supports the magnetometer (MAG) measurements, primarily directed at detection of Europa's sub-surface ocean, while the second gives information about transfer of material between the Galilean moons, and between the moon surfaces and subsurface layers putatively including oceans. The measurement of the interactions for all the Galilean moons can be used to trace the in situ ion measurements of pickup ions back to either Europa's or Ganymede's surface from the respectively orbiting spacecraft. The IMS instrument, being developed under NASA's Astrobiology Instrument Development Program, would maximally achieve plasma measurement requirements for JEO and EJSM while moving forward our knowledge of Jupiter system composition and source processes to far higher levels than previously envisaged. The composition of the global surfaces of Europa and Ganymede can be inferred from the measurement of ejected neutrals and pick-up ions using at minimum an in situ payload including MAG and IMS also fully capable of meeting Level 1 mission requirements for ocean detection and survey. Elemental and isotopic analysis of potentially extruded oceanic materials at the moon surfaces would further support the ocean objectives. These measurements should be made from a polar orbiting spacecraft about Europa or Ganymede at height 100 km. The ejecta produced by sputtering of the surfaces of Europa and Ganymede has been shown to be representative of the surface composition. Level 2 science on surface geology and composition can then be further enhanced by addition of the following: 3D Ion Neutral Mass Spectrometer (INNS), 3D plasma electron spectrometer (ELS), and hot plasma energetic particle instrument. The measurement approach is to alternate between times measuring pickup ions and times measuring plasma and magnetic field parameters along the spacecraft trajectory. By measuring the pickup ion energy, arrival direction and mass-per-charge, the ion can be traced back along the ejection trajectory to the approximate area of origin if the 3-D electric field and magnetic field are known. In situ observations of plasma flow velocities and vector magnetic fields can be used to determine the local convective electric field (E = -VXB) along the spacecraft trajectory. By combining this information with models of the magnetospheric interaction with Europa, one can generate 3D maps of the electric and magnetic field and compute the trajectories of the pickup ions back to the surface or exospheric points of origin. In the case of Ganymede there is the additional complexity of its own internal dipole magnetic field, while Io's volcanic activity introduces the complexity of a highly structured denser atmosphere. Callisto with its less globally extended exosphere will have a simpler interaction than for Europa (i.e., more like our moon). We will discuss these differences in light of the above proposed technique. Finally, the INNS observations and neutral exosphere models are needed to estimate production rates of pickup ions. The hot plasma measurements are needed to correct for sputtering rates which can be time dependent and electron plasma observations for electron impact ionization rates. Instrument characteristics, field-of-view requirements, modes of operation and effects of radiation on instrument functionality will be discussed.

Sittler, Edward↗

NASA NTRS1982

Solar reflection from a regular array of horizontally finite clouds

The reflected flux from a regular array of 2- and 3-D clouds has been computed to estimate the effect of fractional cloud cover on albedos and the solar flux available to heat the earth's surface. The broken clouds are represented by a regular array of identical cuboids for the 3-D problem and equally spaced, infinitely long, bars for the 2-D problem. A diffusion approximation to the radiative transfer equation is used to compute the fluxes leaving each face of the cloud. Interaction between clouds is simulated by assuming diffuse exitance from the cloud faces and applying angle factors to obtain modified boundary conditions on each cloud face.

Weinman, J. A.↗

NASA NTRS1991

Formation of the protosolar nebula

Theoretical models are discussed of the collapse of a dense molecular cloud core to form the protosolar nebula that produce the sun and the planet. The theoretical models use the equations of hydrodynamics, gravitation, and radiative transfer to follow the time evolution of a cloud collapsing under its own self-gravity. Both semi-analytical and fully numerical solutions (in two and three spatial dimensions) were calculated by several workers, One challenge is to find a set of initial conditions that will lead to the formation of a suitable protosolar nebula. Detailed results are shown for 2-D models, both with and without turbulent viscosity for redistributing angular momentum, and for 3-D models investigating the strength of gravitational torques associated with nonaxisymmetry produced during the collapse phase.

Tscharnuter, Werner M.↗