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NASA NTRS1973

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗
NASA NTRS2007

Self-consistent Model of Magnetospheric Electric Field, RC and EMIC Waves

Electromagnetic ion cyclotron (EMIC) waves are an important magnetospheric emission, which is excited near the magnetic equator with frequencies below the proton gyro-frequency. The source of bee energy for wave growth is provided by temperature anisotropy of ring current (RC) ions, which develops naturally during inward convection from the plasma sheet These waves strongly affect the dynamic s of resonant RC ions, thermal electrons and ions, and the outer radiation belt relativistic electrons, leading to non-adiabatic particle heating and/or pitch-angle scattering and loss to the atmosphere. The rate of ion and electron scattering/heating is strongly controlled by the Wave power spectral and spatial distributions, but unfortunately, the currently available observational information regarding EMIC wave power spectral density is poor. So combinations of reliable data and theoretical models should be utilized in order to obtain the power spectral density of EMIC waves over the entire magnetosphere throughout the different storm phases. In this study, we present the simulation results, which are based on two coupled RC models that our group has developed. The first model deals with the large-scale magnetosphere-ionosphere electrodynamic coupling, and provides a self-consistent description of RC ions/electrons and the magnetospheric electric field. The second model is based on a coupled system of two kinetic equations, one equation describes the RC ion dynamics and another equation describes the power spectral density evolution of EMIC waves, and self-consistently treats a micro-scale electrodynamic coupling of RC and EMIC waves. So far, these two models have been applied independently. However, the large-scale magnetosphere-ionosphere electrodynamics controls the convective patterns of both the RC ions and plasmasphere altering conditions for EMIC wave-particle interaction. In turn, the wave induced RC precipitation Changes the local field-aligned current distributions and the ionospheric conductances, which are crucial for a large-scale electrodynamics. The initial results from this new self-consistent model of the magnetospheric electric field, RC and EMIC waves will be shown in this presentation.

Gamayunov, K. V.↗
NASA NTRS1975

Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.

Canuto, V.↗
NASA NTRS1989

Development of a numerical solution to the time dependent kinetic equation

A numerical solution was developed for the time dependent Fokker-Planck equation for arbitrary distributions of electrons injected into a magnetized plasma. The code which includes energy loss and pitch angle scattering due to Coulomb collisions and changes in pitch angle due to inhomogeneous magnetic fields was calibrated and tested. The numerical method is versatile so that other scattering or radiation terms can be easily included. Using this code many processes associated with the impulsive phase of solar flares will be investigated.

Hamilton, Russell J.↗
NASA NTRS1995

A theoretical derivation of the dependence of the remotely sensed reflectance of the ocean on the inherent optical properties

An expression for the ratio of the upwelling nadir radiance L(pi, z) and the downwelling scalar irradiance E(sub od)(Z) is derived from the following equation of radiative transfer. This expression is given by RSR(z) = (L(pi, z))/E(sub od) = (f(sub b)(z)b(sub b)(z))/2 pi(k(pi, z) + c(z) - F(sub L)(z)b(sub f)(z)), where b(sub b)(z) is the backscattering coefficient, k(pi, z) is the vertical attenuation coefficient of the nadir radiance, c(z) is the beam attenuation coefficient, and f(sub b)(z) and f(sub L)(z) are shape parameters that depend on the shape of the volume scattering function and the radiance distribution. Successive approximations are subsequently applied to the above exact equation. These are f(sub b)(z) = (2 pi beta(pi - theta(sub m), z)/(b(sub b)(z))), where beta(pi - theta(sub m), z) is the volume scattering function at 180 deg minus the zenith angle of the maximum radiance, and k(pi, z) = am = c(1 - 0.52 b/c - 0.44 (b/c)(exp 2)), where m is a parameter that is numerically equal to the inverse of the average cosine of the asymptotic light field for a medium with the same inherent optical properties, a is the absorption coefficient, and b/c is the single scattering albedo. Together with f(sub L)(z) = 1.05 and application of Gershun's equation, it is shown that for nearly all oceanic cases RSR(z) identical to L(pi, z)/E(sub od)(z) = (Beta(pi - theta(sub m), z))/(a(z)(1 + m(z))).

Zaneveld, J. Ronald V.↗
NASA NTRS1986

Field experiment for measurement of the radiative characteristics of a hazy atmosphere

Theoretical two-dimensional and three-dimensional solutions to the radiative-transfer equation have been applied to the earth-atmosphere system. A field experiment was conducted to test this theory. In the experiment the upward radiance was measured above and below a haze layer during simultaneous measurements of the haze characteristics. The measurements were conducted at a narrow near-IR channel (773 + or - 22 nm) which represents the visible and near-IR spectral region. The aerosol vertical optical thickness at eight wavelengths, as well as the vertical and horizontal profiles of the scattering coefficient, the temperature, and dew point were measured at several locations. These measurements quantified the vertical and spatial structure of the atmospheric haze and the atmospheric radiation. The result was a well-defined radiative-transfer experiment. The experimental data set is used to quantify the haze effect on upward radiance, including the adjacency effect (the effect of a bright area on the upward radiance measured above a dark adjacent area), and to test radiative-transfer models for a plane-parallel atmosphere above a nonuniform surface. A comparison is given between the theoretical prediction of upward radiance above the haze and the measurement. Agreement between theory and the experiment is discussed.

Kaufman, Y. J.↗
NASA NTRS1988

Acoustical scattering from finite compliant surfaces bounding a duct

Acoustic radiation effects of a finite compliant surface covering a transverse slot in a two-dimensional parallel walled rigid duct are investigated. Radiation from a harmonic source external to the duct is shown to impinge on the slot, reradiating to the half plane and propagating through the duct. Integral equation techniques are employed to study the cases of an open slot, a membrane cover, and a flexible plate cover. The total power radiated to the half plane external to the duct and to the region internal to the duct is determined, taking into account slot-width and fluid-loading variations and the effect of the surface on the power radiated.

Smith, M. E.↗
NASA NTRS1980

Application of the method of discrete ordinates to the solution of the transport equation in the case of an inhomogeneous planetary atmosphere

A version of the method of discrete ordinate (MDO) which can be used for an optically thick inhomogeneous atmosphere was developed. The MDO may be implemented as an algorithm simpler than those proposed earlier. The algorithm is the same for each azimuth dependent component of intensity. The MDO can determine the scattered radiation field over its entire length along the vertical. It is shown the MDO, when used for homogeneous atmospheres is in agreement with the results obtained by other methods.

Zasova, L. V.↗
NASA NTRS2014

Assessment of the Accuracy of the Conventional Ray-Tracing Technique: Implications in Remote Sensing and Radiative Transfer Involving Ice Clouds.

A fundamental problem in remote sensing and radiative transfer simulations involving ice clouds is the ability to compute accurate optical properties for individual ice particles. While relatively simple and intuitively appealing, the conventional geometric-optics method (CGOM) is used frequently for the solution of light scattering by ice crystals. Due to the approximations in the ray-tracing technique, the CGOM accuracy is not well quantified. The result is that the uncertainties are introduced that can impact many applications. Improvements in the Invariant Imbedding T-matrix method (II-TM) and the Improved Geometric-Optics Method (IGOM) provide a mechanism to assess the aforementioned uncertainties. The results computed by the II-TMþIGOM are considered as a benchmark because the IITM solves Maxwell's equations from first principles and is applicable to particle size parameters ranging into the domain at which the IGOM has reasonable accuracy. To assess the uncertainties with the CGOM in remote sensing and radiative transfer simulations, two independent optical property datasets of hexagonal columns are developed for sensitivity studies by using the CGOM and the II-TMþIGOM, respectively. Ice cloud bulk optical properties obtained from the two datasets are compared and subsequently applied to retrieve the optical thickness and effective diameter from Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Additionally, the bulk optical properties are tested in broadband radiative transfer (RT) simulations using the general circulation model (GCM) version of the Rapid Radiative Transfer Model (RRTMG) that is adopted in the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM, version 5.1). For MODIS retrievals, the mean bias of uncertainties of applying the CGOM in shortwave bands (0.86 and 2.13 micrometers) can be up to 5% in the optical thickness and as high as 20% in the effective diameter, depending on cloud optical thickness and effective diameter. In the MODIS infrared window bands centered at 8.5, 11, and 12 micrometers biases in the optical thickness and effective diameter are up to 12% and 10%, respectively. The CGOM-based simulation errors in ice cloud radiative forcing calculations are on the order of 10Wm(exp 2).

remote sensing↗
NASA NTRS1973

Note on the modified two-stream approximation of Sagan and Pollack.

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order l equal to or greater than 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic scattering.

Lyzenga, D. R.↗
NASA NTRS2003

An Introduction to Atmospheric Radiation: Review for the Bulletin of AMS

Whether you like a certain geophysical book or not, largely depends on your background. The field of radiative transfer and atmospheric radiation, in particular, combines people with a wide range of mathematical skills: from theoretical astrophysicists and nuclear physicists to meteorologists and ecologists. There is always a delicate balance between physical explanations and their mathematical interpretations. This balance is very personal and is based on your background. I came to the field of atmospheric radiative transfer as a mathematician with little knowledge of atmospheric physics. After being in the field for more than a decade, I still have gaps in my atmospheric science education. Thus I assess a radiative transfer book fi-om two main criteria: how well does it describe the material that is familiar to me (the radiative transfer equation and its numerical solutions) and how well does it help me to fill the gaps in my personal knowledge. So I present this review fi-om the perspective of a former mathematician working in the field of atmospheric radiation. . After being asked to review the book, my first intention was to compare the new edition with the previous one (Liou, 1980). In doing so, you can clearly follow the progress made in the field of atmospheric radiation over the past two decades. If there are few changes (as in Fundamental Radiative Transfer) or no changes at all (as in the Maxwell s equations), then the field has not seen much development. To the contrary, many differences between the two editions illustrate areas of major progress in the field, such as evidenced in Thermal Ineared Radiative Transfer and even in the creations of completely new fields like Three-Dimensional Radiative Transfer or Light Scattering by Nonspherical Particles. Obviously, the major changes happened not in the theory, which is at least half a century old, but in data quality and completely new measurements (mostly due to new satellite data) with higher accuracy and more reliability. The new edition illustrates this progress well.

Marshak, Alexander↗
NASA NTRS1973

Atmospheric effects on remote sensing of non-uniform temperature sources

The equations of transfer, for a plane-parallel scattering atmosphere with a point source of energy on the lower bounding surface, were solved for various values of sensor/point source orientation and optical depths. Applications of this analysis to Skylab and ERTS mission are discussed, and requirements for atmospheric property data and radiation transfer properties are considered.

Mcneill, W. A.↗
NASA NTRS1973

Optical transmission in a circumstellar dust cloud

It is shown from the equation of radiative transfer that the visual attenuation of an optically thick, spherically symmetric circumstellar cloud of dust can be small compared to that produced by an equal optical depth of interstellar dust. The reasons for this are the moderately large albedos of the grains and their tendency to emphasize forward scattering.

Jones, T. W.↗
NASA NTRS1977

Single scattering solution for radiative transfer through Rayleigh and aerosol atmosphere

A solution is presented to the radiative transfer of the solar irradiation through a turbid atmosphere, based on the single-scattering approximation, i.e., an assumption that a photon that underwent scattering either leaves the top of the atmosphere or strikes the surface. The solution depends on a special idealization of the scattering phase function of the aerosols. The equations developed are subsequently applied to analyze quantitatively the enhancement of the surface irradiation and the enhancement of the scattered radiant emittance as seen from above the atmosphere, caused by the surface reflectance and atmospheric back scattering. An order of magnitude error analysis is presented.

Otterman, J.↗
NASA NTRS1993

Second order distorted born approximation for backscattering from a layer of discrete random medium

In recent years there has been increasing interest in scattering and depolarization characteristics of the vegetation canopies. Scattering models applied to the microwave remote sensing of vegetation canopies showed that multiple scattering effects can be important in simulating the backscattering coefficients correctly. In particular, in most applications, the cross-polarized backscattering coefficients are often underestimated by single scattering models. Recently, there have been concerted efforts to include the second order terms in the radiative transfer models of vegetation canopies in order to account for multiple scattering within the canopy. The coherent wave theory approach is extended to include multiple scattering effects to predict the coherent and incoherent backscattering contributions from a layer of vegetation canopy. The problem is initially formulated in terms of the exact equation for the correlation function of the field, i.e., the Bethe-Salpeter equation. Using fractional volume as a small parameter, a Foldy type approximation is made to obtain a more manageable correlation equation. This equation is iterated to obtain first and second order solutions. The iteration procedure assumes the variance of the field fluctuations are small compared to the coherent intensity. This assumption proved to be particularly successful in computing backscattering coefficients. First and second order backscattering coefficients are calculated from the iterants of the correlation equation. It is shown that the first order coefficients are the same as the distorted Born results used previously by the authors. These results contained enhancement terms in the direct-reflected contributions. The important contributions to second order backscattering are examined and interpreted in terms of scattering diagrams. Examples of situations in which second order backscattering coefficients are important are given.

Lang, Roger H.↗
NASA NTRS2017

Relativistic Three-Dimensional Lippmann-Schwinger Cross Sections for Space Radiation Applications

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world’s best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three- Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scatter- ing Theory (MST) that uses 5 parameterizations—3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations—predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (TLab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which TLab > 220 MeV/n.

C M Werneth↗
NASA NTRS1987

On time-dependent radiative transfer

An integral equation is developed for application to time-dependent laboratory experiments in which partial redistribution effects are important. The equation of transport with the Heasly-Kneer (1976) emission coefficient and the equation of statistical equilibrium lead to a time-dependent redistribution function containing an absorption - reemission term which decays exponentially in time and a scattering term which is instantaneous. This integral equation does not agree with an equation written by Payne et al. (1974) that has been used to compare theory with experiments. The difference between the Payne equation and the equation developed here needs to be examined in detail, since it might under some circumstances be on the same order as the difference between partial and complete redistribution.

Streater, A.↗
NASA NTRS1988

A new approach to resonance line scattering in planetary atmospheres

The invariant imbedding technique is applied to the problem of resonance line scattering with frequency redistribution. By applying the principles of invariance to the resonance line scattering problem a set of non-linear, integrodifferential equations for the scattering and transmission functions are derived. Thus, an alternate approach to the resonance line scattering problem is presented. Rather than solving for the specific intensity directly the invariant imbedding equations may be solved for the scattering and transmission functions from which the specific intensity may be calculated. The technique is very general and in principle, can accommodate scattering in inhomogeneous atmospheres with arbitrary frequency redistribution and scattering phase functions. Solutions to the invariant imbedding equations in some simple cases are presented. If the scattering is isotropic and completely noncoherent and the atmosphere may be modeled as homogeneous, the scattering and transmission functions may be expressed in terms of generalized H, X and Y functions. This technique is extended to the problems of coupled spectral lines and scattering of radiation from internal sources.

Yelle, Roger V.↗