Search NASA⌕ Search

SEARCH · Search NASA

Results for “parallel planes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

An Efficient and Accurate Algorithm for Computing Grid-Averaged Solar Fluxes for Horizontally Inhomogeneous Clouds

A computationally efficient method is presented to account for the horizontal cloud inhomogeneity by using a radiatively equivalent plane parallel homogeneous (PPH) cloud. The algorithm can accurately match the calculations of the reference (rPPH) independent column approximation (ICA) results, but use only the same computational time required for a single plane parallel computation. The effective optical depth of this synthetic sPPH cloud is derived by exactly matching the direct transmission to that of the inhomogeneous ICA cloud. The ffective9 scattering asymmetry factor is found from a pre-calculated albedo inverse look-up-table that is allowed to vary over the range from -1.0 to 1.0. In the special cases of conservative scattering and total absorption, the synthetic method is exactly equivalent to the ICA, with only a small bias (about 0.2% in flux) relative to ICA due to imperfect interpolation in using the look-up tables. In principle, the ICA albedo can be approximated accurately regardless of cloud inhomogeneity. For a more complete comparison, the broadband shortwave albedo and transmission calculated from the synthetic sPPH cloud and averaged over all incident directions, have the RMS biases of 0.26% and 0.76%, respectively, for inhomogeneous clouds over a wide variation of particle size. The advantages of the synthetic PPH method are that (1) it is not required that all the cloud subcolumns have uniform microphysical characteristic, (2) it is applicable to any 1D radiative transfer scheme, and (3) it can handle arbitrary cloud optical depth distributions and an arbitrary number of cloud subcolumns with uniform computational efficiency.

cloud inhomogeneity↗
NASA NTRS2000

Influence of the Surface and Cloud Nonuniformities in the Solar Energy Fluxes in the Arctic

Solar energy fluxes reaching the surface and absorbed by it are basic components of the energy balance of the Arctic. They depend mainly on the solar zenith angle, a state of the atmosphere, especially the cloudiness, and the surface albedo. However, they can also be modified by variabilities in the surface albedo and cloud optical thickness. The surface of the Arctic can be highly nonuniform. The surface of the Arctic Ocean, which covers the huge part of the Arctic can be view as a mosaic of sea water, sea ice, snow and, in the melting period, melting ponds. In our paper, results are presented of Monte Carlo simulations of the expected influence of nonuniform cloud structure and nonuniform surface albedo on radiative fluxes at the Arctic surface. In particular, the plane parallel biases in the surface absorptance and atmospheric transmittance are studied. The bias is defined as the difference between the real absorptance or transmittance (i.e. nonuniform conditions) averaged over a given area, and the uniform or plane parallel case with the same mean cloud optical thickness and the same mean surface albedo. The dependence of the biases is analysed with respect to the following: domain averaged values of the cloud optical thickness and surface albedo, scales of their spatial variabilities, correlation between cloud optical thickness and cloud albedo variabilities, cloud height, and the solar zenith angle. Ranges of means and standard deviations of the input parameters typical of Arctic conditions are obtained from the SHEBA experiment.

Rozwadowska, A.↗
NASA NTRS1984

Stratocumulus cloud field reflected fluxes - The effect of cloud shape

The reflected fluxes of stratocumulus cloud fields are calculated as a function of sky cover aspect ratio and cloud shape. In order to obtain a better fit with general circulation models (GCMs), cloud liquid water volume values were kept invariant relative to cloud shape. On the basis of the required accuracy of the Earth Radiation Budget Experiment (ERBE), an order of magnitude value of 10 W per sq m was used to estimate the difference between plane-parallel and broken cloudiness reflected fluxes. An empirical relationship for effective cloud cover at a solar zenith angle of 60 deg is derived. The relationship allows for the accurate computation of broken cloud field reflected fluxes using plane-parallel calculations. It is predicted that more accurate estimates of broken cloud field radiative properties may be possible in the future.

Welch, R. M.↗
NASA NTRS2011

Faraday-Active Fabry-Perot Resonator: Transmission, Reflection, and Emissivity

The propagation of light within a semiconductor Faraday-active Fabry-Perot resonator (FAFR) is investigated theoretically and experimentally. It is shown that an external magnetic field radically changes the angular and spectral characteristics of transmission, reflection and emissivity of the resonator not only for polarized, but also for unpolarized light. Suppression of interference patterns and phase inversion of the interference extrema were observed in both monochromatic and polychromatic light. The investigations were carried out for the plane-parallel plates of n-InAs in the spectral range of free charge carrier absorption. The results can be used to create new controllable optical and spectroscopic devices for investigation of Faraday-active material properties and for control of parameters of plane-parallel layers and structures.

Liptuga, Anatoliy↗
NASA NTRS2007

The Effects of Rainfall Inhomogeneity on Climate Variability of Rainfall Estimated from Passive Microwave Sensors

Passive microwave rainfall estimates that exploit the emission signal of raindrops in the atmosphere are sensitive to the inhomogeneity of rainfall within the satellite field of view (FOV). In particular, the concave nature of the brightness temperature (T(sub b)) versus rainfall relations at frequencies capable of detecting the blackbody emission of raindrops cause retrieval algorithms to systematically underestimate precipitation unless the rainfall is homogeneous within a radiometer FOV, or the inhomogeneity is accounted for explicitly. This problem has a long history in the passive microwave community and has been termed the beam-filling error. While not a true error, correcting for it requires a priori knowledge about the actual distribution of the rainfall within the satellite FOV, or at least a statistical representation of this inhomogeneity. This study first examines the magnitude of this beam-filling correction when slant-path radiative transfer calculations are used to account for the oblique incidence of current radiometers. Because of the horizontal averaging that occurs away from the nadir direction, the beam-filling error is found to be only a fraction of what has been reported previously in the literature based upon plane-parallel calculations. For a FOV representative of the 19-GHz radiometer channel (18 km X 28 km) aboard the Tropical Rainfall Measuring Mission (TRMM), the mean beam-filling correction computed in this study for tropical atmospheres is 1.26 instead of 1.52 computed from plane-parallel techniques. The slant-path solution is also less sensitive to finescale rainfall inhomogeneity and is, thus, able to make use of 4-km radar data from the TRMM Precipitation Radar (PR) in order to map regional and seasonal distributions of observed rainfall inhomogeneity in the Tropics. The data are examined to assess the expected errors introduced into climate rainfall records by unresolved changes in rainfall inhomogeneity. Results show that global mean monthly errors introduced by not explicitly accounting for rainfall inhomogeneity do not exceed 0.5% if the beam-filling error is allowed to be a function of rainfall rate and freezing level and does not exceed 2% if a universal beam-filling correction is applied that depends only upon the freezing level. Monthly regional errors can be significantly larger. Over the Indian Ocean, errors as large as 8% were found if the beam-filling correction is allowed to vary with rainfall rate and freezing level while errors of 15% were found if a universal correction is used.

Kummerow, Christian↗
NASA NTRS2000

Forward Monte Carlo Computations of Polarized Microwave Radiation

Microwave radiative transfer computations continue to acquire greater importance as the emphasis in remote sensing shifts towards the understanding of microphysical properties of clouds and with these to better understand the non linear relation between rainfall rates and satellite-observed radiance. A first step toward realistic radiative simulations has been the introduction of techniques capable of treating 3-dimensional geometry being generated by ever more sophisticated cloud resolving models. To date, a series of numerical codes have been developed to treat spherical and randomly oriented axisymmetric particles. Backward and backward-forward Monte Carlo methods are, indeed, efficient in this field. These methods, however, cannot deal properly with oriented particles, which seem to play an important role in polarization signatures over stratiform precipitation. Moreover, beyond the polarization channel, the next generation of fully polarimetric radiometers challenges us to better understand the behavior of the last two Stokes parameters as well. In order to solve the vector radiative transfer equation, one-dimensional numerical models have been developed, These codes, unfortunately, consider the atmosphere as horizontally homogeneous with horizontally infinite plane parallel layers. The next development step for microwave radiative transfer codes must be fully polarized 3-D methods. Recently a 3-D polarized radiative transfer model based on the discrete ordinate method was presented. A forward MC code was developed that treats oriented nonspherical hydrometeors, but only for plane-parallel situations.

Battaglia, A.↗
NASA NTRS1989

Reflected fluxes for broken clouds over a Lambertian surface

Reflected fluxes are calculated for broken cloudiness (i.e., nonplane parallel) as a function of cloud cover, cloud optical depth, solar zenith angle and surface albedo. These calculations extend previous results for broken cloud reflected fluxes over a black surface. The present study demonstrates that not only radiances but also radiative fluxes over high albedo surfaces may be decreased by the presence of broken cloudiness. Conventional wisdom states that cloud radiances (brightnesses) are always greater than the background. While most cloud retrieval schemes are built around this assumption, it is incorrect for clouds over high albedo surfaces such as found in polar regions. However, the most startling and counterintuitive conclusion of this study is that nonabsorbing finite clouds over a highly reflecting surface will decrease the system albedo. As a result, surface absorption is increased, the result of multiple scattering between surface and cloud layer, controlled by cloud morphology and cloud optical thickness. A simple parameterization of the effects of cloud contamination upon retrieved albedo is given in terms of solar zenith angle, cloud optical depth, surface albedo, cloud cover, and plane-parallel cloud albedo. In this way, the effects of broken cloudiness are modeled in terms of easily computed plane-parallel values.

Welch, Ronald M.↗
NASA NTRS1998

Computation of the Effects of Inhomogeneous Clouds on Retrieval of Remotely Sensed Properties

Current and future earth observation programs depend on satellite measurements of radiance to retrieve the properties of clouds on a global basis. At present, this retrieval is made assuming that the clouds in the instrument field of view are plane parallel and independent of adjacent pixels. While this assumption is known to be false except in very limited cases, its impact can be evaluated, and if possible corrected, based on emerging theoretical techniques. In this study, the Spherical Harmonic Discrete Ordinate Method (SHDOM, Evans, 1996) has been used to assess the sensitivity of the retrieval to a variety of cloud parameters. SHDOM allows the plane parallel assumption to be relaxed and makes 2D and even 3D radiative solutions practical. A previous study (Chambers et al., 1996) assessed the effect of horizontal inhomogeneity in 45 LANDSAT scenes of boundary layer clouds over ocean. The four scenes studied here represent overcast, broken, scattered and strongly thermally forced cloud fields and are used to perform sensitivity studies to a wider variety of parameters. Comparisons are made at three solar zenith angles (theta (sub 0) = 0, 49, and 63 degrees) to avoid ambiguity in the results due to solar zenith angle.

Chambers, Lin H.↗
NASA NTRS1994

Model atmosphere analysis of selected luminous B stars

The general scientific goal of this program has been to determine whether the atmospheric structure of the B-type stars can be represented by the current generation of plane parallel, line-blanketed, LTE stellar atmosphere models sufficiently well to allow accurate effective temperatures and surface gravities to be deduced. The B stars cover a wide range of temperature and luminosity. For the hottest such stars (with T approximately 30,000 K) the applicability of the models may be compromised by departures from LTE in the stellar atmospheres ('non-LTE effects'). At the highest luminosities (the B 'super giants'), the models may be invalidated by departures from plane parallel geometry. Thus we seek to identify the temperature and luminosity range within which these effects are unimportant and where the models may be relied upon.

Fitzpatrick, Edward L.↗
NASA NTRS1991

Bi-directional reflectance of finite and infinite clouds

The transfer of solar irradiance in plane parallel and broken cloud fields is modeled using a Monte Carlo method. The angular distribution pattern of radiances exiting the cloud layer is studied with varying cloud geometries, optical thicknesses, cloudiness and solar zenith angles. A rather large anisotropy of the reflected flux is found, usually increasing with solar zenith angle and with patterns that strongly depend on cloud geometry. The main features are: a local maximum of reflected intensity in the forward direction for all cases; a limb darkening for the plane parallel case; and a limb brightening and a local maximum of reflected intensity in the backward direction for broken clouds. The method is used to study the cloud reflectance sensitivity to various parameters. A more precise description of cloud field internal and external structure is needed in order to obtain accurate bi directional reflectance diagrams.

Breon, Francois-Marie↗
NASA NTRS1992

Reflectance of broken cloud fields - Simulation and parameterization

The transfer of solar irradiance in plane parallel and broken cloud fields is simulated using a Monte Carlo method. The angular distribution pattern of radiances exiting the cloud layer is studied with varying cloud geometries, optical thicknesses, cloudiness, and solar zenith angles. A rather large anisotropy of the reflected flux is found, usually increasing with solar zenith angle and with patterns that strongly depend on cloud geometry. The main features are (1) a local maximum of reflected intensity in the forward direction for all cases, (2) a limb darkening for the plane parallel case, and (3) a limb brightening and a local maximum of reflected intensity in the backward direction for broken clouds. A parameterization for the azimuth-average reflectance function is developed. It reproduces the Monte Carlo simulation with a reasonable accuracy and illustrates that, when azimuthally averaged, the reflectance function is dominated by side viewing and intercloud shadowing effects.

Breon, Francois-Marie↗
NASA NTRS1994

Solar flare model atmospheres

Solar flare model atmospheres computed under the assumption of energetic equilibrium in the chromosphere are presented. The models use a static, one-dimensional plane-parallel geometry and are designed within a physically self-consistent coronal loop. Assumed flare heating mechanisms include collisions from a flux of nonthermal electrons and X-ray heating of the chromosphere by the corona. The heating by energetic electrons accounts explicitly for variations of the ionized fraction with depth in the atmosphere. X-ray heating of the chromosphere by the corona incorporates a flare loop geometry by approximating distant portions of the loop with a series of point sources, while treating the loop leg closest to the chromospheric footpoint in the plane-parallel approximation. Coronal flare heating leads to increased heat conduction, chromospheric evaporation and subsequent changes in coronal pressure; these effects are included self-consistently in the models. Cooling in the chromosphere is computed in detail for the important optically thick H I, Ca II and Mg II transitions using the non-local thermodynamic equilibrium (non-LTE) prescription in the program MULTI. Hydrogen ionization rates from X-ray photoionization and collisional ionization by nonthermal electrons are included explicitly in the rate equations. The models are computed in the 'impulsive' and 'equilibrium' limits, and in a set of intermediate 'evolving' states. The impulsive atmospheres have the density distribution frozen in the pre-flare configuration, while the equilibrium models assume the entire atmosphere is in hydrostatic and energetic equilibrium. The evolving atmospheres represent intermediate stages where hydrostatic equilibrium has been established in the chromosphere and corona, but the corona is not yet in energetic equilibrium with the flare heating source. Thus, for example, chromospheric evaporation is still in the process of occurring. We have computed the chromospheric radiation that results from a range of coronal heating rates, with particular emphasis on the widely observed diagnostic H(alpha). Our conclusion is that the H(alpha) fluxes and profiles actually observed in flares can only be produced under conditions of a low-pressure corona with strong beam heating. Therefore we suggest that H(alpha) in flares is produced primarily at the footprints of newly heated loops where significant evaporation has not yet occurred. As a single loop evolves in time, no matter how strong the heating rate may become, the H(alpha) flux will diminish as the corona becomes denser and hence more effective at stopping the beam. This prediction leads to several observable consequences regarding the spatial and temporal signatures of the X-ray and H(alpha) radiation during flares.

Hawley, Suzanne L.↗
NASA NTRS1975

The He II lines in the spectrum of zeta Puppis

The observed He II line spectrum in zeta Pup is compared with that predicted from model atmospheres in an attempt to establish the parameters (effective temperature, log g) which characterize the model that best represents this star's atmosphere. The study is conducted by compiling equivalent widths of the He II lines in the series (n = 2,3,4,5) and comparing them with predictions from plane-parallel static model atmospheres using a non-LTE theory of line formation. Good agreement between observation and prediction for a model atmosphere with an effective temperature of 50,000 K and log of 4.0 is found for the upper members of the n = 3 and n = 5 series, but discrepancies are found for the two lines of the n = 2 series and the upper members of the n = 4 series. It is shown that the n = 4 level appears to be more overpopulated at moderate atmospheric depths than the non-LTE calculations with plane-parallel layers indicate. It is suggested that this may be due to an overlap of the H and He II lines in the even-even series caused by macroturbulent velocities of the hydrogen and helium atoms.

Snijders, M. A. J.↗
NASA NTRS1982

Model atmospheres, predicted spectra, and colors

Theoretical models of stellar atmospheres and the process of forming a spectrum are reviewed with particular reference to the spectra of B stars. In the case of classical models the stellar atmosphere is though to consist of plane parallel layers of gas in which radiative and hydrostatic equilibrium exists. No radiative energy is lost or gained in the model atmosphere, but the detailed shape of the spectrum is changed as a result of the interactions with the ionized gas. Predicted line spectra using statistical equilibrium local thermodynamic equilibrium (LTE), and non-LTE physics are compared and the determination of abundances is discussed. The limitations of classical modeling are examined. Models developed to demonstrate what motions in the upper atmosphere will do to the spectrum and to explore the effects of using geometries different from plane parallel layer are reviewed. In particular the problem of radiative transfer is addressed.

Source record↗
NASA NTRS1993

Solar flare model atmospheres

Solar flare model atmospheres computed under the assumption of energetic equilibrium in the chromosphere are presented. The models use a static, one-dimensional plane parallel geometry and are designed within a physically self-consistent coronal loop. Assumed flare heating mechanisms include collisions from a flux of non-thermal electrons and x-ray heating of the chromosphere by the corona. The heating by energetic electrons accounts explicitly for variations of the ionized fraction with depth in the atmosphere. X-ray heating of the chromosphere by the corona incorporates a flare loop geometry by approximating distant portions of the loop with a series of point sources, while treating the loop leg closest to the chromospheric footpoint in the plane-parallel approximation. Coronal flare heating leads to increased heat conduction, chromospheric evaporation and subsequent changes in coronal pressure; these effects are included self-consistently in the models. Cooling in the chromosphere is computed in detail for the important optically thick HI, CaII and MgII transitions using the non-LTE prescription in the program MULTI. Hydrogen ionization rates from x-ray photo-ionization and collisional ionization by non-thermal electrons are included explicitly in the rate equations. The models are computed in the 'impulsive' and 'equilibrium' limits, and in a set of intermediate 'evolving' states. The impulsive atmospheres have the density distribution frozen in pre-flare configuration, while the equilibrium models assume the entire atmosphere is in hydrostatic and energetic equilibrium. The evolving atmospheres represent intermediate stages where hydrostatic equilibrium has been established in the chromosphere and corona, but the corona is not yet in energetic equilibrium with the flare heating source. Thus, for example, chromospheric evaporation is still in the process of occurring.

Hawley, Suzanne L.↗
NASA NTRS1987

Light scattering in cometary dust comae

Single and multiple scattering calculations were performed for a spherically symmetric cometary atmosphere irradiated by a plane parallel source. It is suggested that the increased flux found for anisotropic phase functions is due to the effect of directional scattering in the forward sun-comet axis. The isotropic multiply scattered flux at the surface is shown to be an increasing function of the opacity (tau) for tau of less than about 2.5. At large tau values, the maximum in the downward directed scattered flux still increases, but occurs at a height of several radii above the nucleus, resulting in a reduction at the surface. Results suggest that, except in the vicinity of the sun-comet axis, the plane parallel geometry tends to underestimate the degree of scattering.

Herman, Gary↗
NASA NTRS1977

Multiple scattering in reflection nebulae. IV - The multiplicity of scattering

The characteristics of higher order scattering in plane-parallel reflection nebulae of finite optical thickness have been examined. Measured both by the mean number of scatterings and the effective multiplicity, the importance of multiple scattering in such systems varies strongly with position as well as direction, and the effects cannot be taken into account by simple corrections only. It is found that the amount of higher order scattering is relatively insensitive to the shape of the phase function over a wide range of asymmetries, while the dependence of multiplicity on particle albedo, optical thickness of the nebula, and other geometrical factors is as expected. Pronounced asymmetries in the surface brightness distribution of strongly tilted plane-parallel nebulae are explained by different radial variations of the effective multiplicity along opposite radii on the projected nebular face.

Witt, A. N.↗
NASA NTRS1990

Reflectivities of uniform and broken marine stratiform clouds

Plane-parallel radiative transfer models are often used to estimate the effects of clouds on the earth's energy budget and to retrieve cloud properties from satellite observations. An attempt is made to assess the performance of such models by using AVHRR data collected during the FIRE MARINE Stratus IFO to determine the reflectivities and, in particular, the anisotropy of the reflected radiances for the clouds observed during the field experiment. The intent is to determine the anisotropy for conditions that are overcast and to compare this anisotropy with that produced by the same cloud when broken. The observations are used to quantify aspects of the differences between reflection by plane-parallel clouds and non-planar clouds expected on the basis of theoretical studies.

Coakley, James A., Jr.↗