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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.

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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Radiative forcing of the Venus mesosphere. II - Thermal fluxes, cooling rates, and radiative equilibrium temperatures

A radiative heat-transfer model is presently used to ascertain the way in which radiative forcing contributes to the up to 20 K higher temperature of the Venus polar regions, by comparison with the tropics, in the 60-100 km mesospheric levels. Model global-mean radiative equilibrium temperatures for 55-100 km are compared with observations to show how each opacity source contributes to the thermal structure. The results obtained from latitude-dependent radiative equilibrium experiments indicate that meridional variations in radiative forcing obliterate observed mesospheric temperature gradients and yield polar temperatures up to 40 K cooler than the tropics.

Crisp, David↗
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 NTRS1996

Ocean observations with EOS/MODIS: Algorithm development and post launch studies

Several significant accomplishments were made during the present reporting period. We have completed our basic study of using the 1.38 micron MODIS band for removal of the effects of thin cirrus clouds and stratospheric aerosol. The results suggest that it should be possible to correct imagery for thin cirrus clouds with optical thicknesses as large as 0.5 to 1.0. We have also acquired reflectance data for oceanic whitecaps during a cruise on the RV Malcolm Baldrige in the Gulf of Mexico. The reflectance spectrum of whitecaps was found to be similar to that for breaking waves in the surf zone measured by Frouin, Schwindling and Deschamps. We installed a CIMEL sun photometer at Fort Jefferson on the Dry Tortugas off Key West in the Gulf of Mexico. The instrument has yielded a continuous stream of data since February. It shows that the aerosol optical thickness at 669 nm is often less than 0.1 in winter. This suggests that the Southern Gulf of Mexico will be an excellent winter site for vicarious calibration. In addition, we completed a study of the effect of vicarious calibration, i.e., the accuracy with which the radiance at the top of the atmosphere (TOA) can be predicted from measurement of the sky radiance at the bottom of the atmosphere (BOA). The results suggest that the neglect of polarization in the aerosol optical property inversion algorithm and in the prediction code for the TOA radiances is the largest error associated with the radiative transfer process. Overall, the study showed that the accuracy of the TOA radiance prediction is now limited by the racliometric calibration error in the sky radiometer. Finally, considerable coccolith light scattering data were obtained in the Gulf of Maine with a flow-through instrument, along with data relating to calcite concentration and the rate of calcite production.

Gordan, Howard R.↗
NASA NTRS2001

A Methodology for Surface Soil Moisture and Vegetation Optical Depth Retrieval Using the Microwave Polarization Difference Index

A methodology for retrieving surface soil moisture and vegetation optical depth from satellite microwave radiometer data is presented. The procedure is tested with historical 6.6 GHz brightness temperature observations from the Scanning Multichannel Microwave Radiometer over several test sites in Illinois. Results using only nighttime data are presented at this time, due to the greater stability of nighttime surface temperature estimation. The methodology uses a radiative transfer model to solve for surface soil moisture and vegetation optical depth simultaneously using a non-linear iterative optimization procedure. It assumes known constant values for the scattering albedo and roughness. Surface temperature is derived by a procedure using high frequency vertically polarized brightness temperatures. The methodology does not require any field observations of soil moisture or canopy biophysical properties for calibration purposes and is totally independent of wavelength. Results compare well with field observations of soil moisture and satellite-derived vegetation index data from optical sensors.

Owe, Manfred↗
NASA NTRS2011

L Band Brightness Temperature Observations Over a Corn Canopy During the Entire Growth Cycle

During a field campaign covering the 2002 corn growing season, a dual polarized tower mounted L-band (1.4 GHz) radiometer (LRAD) provided brightness temperature (T(sub B)) measurements at preset intervals, incidence and azimuth angles. These radiometer measurements were supported by an extensive characterization of land surface variables including soil moisture, soil temperature, vegetation biomass, and surface roughness. During the period from May 22, 2002 to August 30, 2002 a range of vegetation water content (W) of 0.0 to 4.3 kg/square m, ten days of radiometer and ground measurements were available. Using this data set, the effects of corn vegetation on surface emissions are investigated by means of a semi-empirical radiative transfer model. Additionally, the impact of roughness on the surface emission is quantified using T(sub B) measurements over bare soil conditions. Subsequently, the estimated roughness parameters, ground measurements and horizontally (H)-polarized T(sub B) are employed to invert the H-polarized transmissivity (gamma-h) for the monitored corn growing season.

Joseph, Alicia T.↗
NASA NTRS2012

Iterative Atmospheric Correction Scheme and the Polarization Color of Alpine Snow

Characterization of the Earth's surface is crucial to remote sensing, both to map geomorphological features and because subtracting this signal is essential during retrievals of the atmospheric constituents located between the surface and the sensor. Current operational algorithms model the surface total reflectance through a weighted linear combination of a few geometry-dependent kernels, each devised to describe a particular scattering mechanism. The information content of these measurements is overwhelmed by that of instruments with polarization capabilities: proposed models in this case are based on the Fresnel reflectance of an isotropic distribution of facets. Because of its remarkable lack of spectral contrast, the polarized reflectance of land surfaces in the shortwave infrared spectral region, where atmospheric scattering is minimal, can be used to model the surface also at shorter wavelengths, where aerosol retrievals are attempted based on well-established scattering theories. In radiative transfer simulations, straightforward separation of the surface and atmospheric contributions is not possible without approximations because of the coupling introduced by multiple reflections. Within a general inversion framework, the problem can be eliminated by linearizing the radiative transfer calculation, and making the Jacobian (i.e., the derivative expressing the sensitivity of the reflectance with respect to model parameters) available at output. We present a general methodology based on a Gauss-Newton iterative search, which automates this procedure and eliminates de facto the need of an ad hoc atmospheric correction. In this case study we analyze the color variations in the polarized reflectance measured by the NASA Goddard Institute of Space Studies Research Scanning Polarimeter during a survey of late-season snowfields in the High Sierra. This insofar unique dataset presents challenges linked to the rugged topography associated with the alpine environment and a likely high water content due to melting. The analysis benefits from ancillary information provided by the NASA Langley High Spectral Resolution Lidar deployed on the same aircraft. The results obtained from the iterative scheme are contrasted against the surface polarized reflectance obtained ignoring multiple reflections, via the simplistic subtraction of the atmospheric scattering contribution. Finally, the retrieved reflectance is modeled after the scattering properties of a dense collection of ice crystals at the surface. Confirming that the polarized reflectance of snow is spectrally flat would allow to extend the techniques already in use for polarimetric retrievals of aerosol properties over land to the large portion of snow-covered pixels plaguing orbital and suborbital observations.

Polarized BRDF↗
NASA NTRS2022

Numerical Results for Polarized Light Scattering in a Spherical Atmosphere

We report numerical results for polarized light reflection from the top of a Rayleigh scattering spherical atmosphere with height-dependent single scattering albedo over a dark surface. Michael Mishchenko considered this scenario back in the 1990’s, for a plane-parallel atmosphere of unit optical thickness (OT), for which radiance errors arising from neglecting polarization reaches their highest values. To further extend Mishchenko’s results, we consider a value of OT = 0.25, for which the effect of atmospheric curvature is pronounced. New results are generated using three state-of-the art radiative transfer (RT) codes. These are: the MYSTIC and MCSSA models, which simulate light scattering in a true- spherical atmosphere using Monte Carlo methods; and the discrete ordinate code VLIDORT, operating with a new multiple-scatter spherical correction designed to deliver reasonable approximations to spherical-medium scattering. In this work, we report results for both single and multiple scattering; this will help to support the validation of existing and future polarized spherical RT codes, especially those using approximative methods to deal with sphericity.

S Korkin↗
NASA NTRS2001

Bio-Optical Measurement and Modeling of the California Current and Polar Oceans

The principal goals of our research are to validate standard or experimental products through detailed bio-optical and biogeochemical measurements, and to combine ocean optical observations with advanced radiative transfer modeling to contribute to satellite vicarious radiometric calibration and advanced algorithm development. To achieve our goals requires continued efforts to execute complex field programs globally, as well as development of advanced ocean optical measurement protocols. We completed a comprehensive set of ocean optical observations in the California Current, Southern Ocean, Indian Ocean requiring a large commitment to instrument calibration, measurement protocols, data processing and data merger. We augmented separately funded projects of our own, as well as others, to acquire ill situ data sets we have collected on various global cruises supported by separate grants or contracts. In collaboration with major oceanographic ship-based observation programs funded by various agencies (CalCOFI, US JGOFS, NOAA AMLR, INDOEX and Japan/East Sea) our SIMBIOS effort has resulted in data from diverse bio-optical provinces. For these global deployments we generate a high-quality, methodologically consistent, data set encompassing a wide-range of oceanic conditions. Global data collected in recent years have been integrated with our on-going CalCOFI database and have been used to evaluate SeaWiFS algorithms and to carry out validation studies. The combined database we have assembled now comprises more than 700 stations and includes observations for the clearest oligotrophic waters, highly eutrophic blooms, red-tides and coastal case 2 conditions. The data has been used to validate water-leaving radiance estimated with SeaWiFS as well as bio-optical algorithms for chlorophyll pigments. The comprehensive data is utilized for development of experimental algorithms (e.g. high-low latitude pigment transition, phytoplankton absorption, and cDOM). During this period we completed 9 peer-reviewed publications in high quality journals, and presented aspects of our work at more than 10 scientific conferences.

Mitchell, B. Greg↗
NASA NTRS1990

Tropical Pacific moisture variability: Its detection, synoptic structure and consequences in the general circulation

Satellite data analysis tools are developed and implemented for the diagnosis of atmospheric circulation systems over the tropical Pacific Ocean. The tools include statistical multi-variate procedures, a multi-spectral radiative transfer model, and the global spectral forecast model at NMC. Data include in-situ observations; satellite observations from VAS (moisture, infrared and visible) NOAA polar orbiters (including Tiros Operational Satellite System (TOVS) multi-channel sounding data and OLR grids) and scanning multichannel microwave radiometer (SMMR); and European Centre for Medium Weather Forecasts (ECHMWF) analyses. A primary goal is a better understanding of the relation between synoptic structures of the area, particularly tropical plumes, and the general circulation, especially the Hadley circulation. A second goal is the definition of the quantitative structure and behavior of all Pacific tropical synoptic systems. Finally, strategies are examined for extracting new and additional information from existing satellite observations. Although moisture structure is emphasized, thermal patterns are also analyzed. Both horizontal and vertical structures are studied and objective quantitative results are emphasized.

Mcguirk, James P.↗
NASA NTRS1992

Effects of weather on the retrieval of sea ice concentration and ice type from passive microwave data

Effects of wind, water vapor, and cloud liquid water on ice concentration and ice type calculated from passive microwave data are assessed through radiative transfer calculations and observations. These weather effects can cause overestimates in ice concentration and more substantial underestimates in multi-year ice percentage by decreasing polarization and by decreasing the gradient between frequencies. The effect of surface temperature and air temperature on the magnitudes of weather-related errors is small for ice concentration and substantial for multiyear ice percentage. The existing weather filter in the NASA Team Algorithm addresses only weather effects over open ocean; the additional use of local open-ocean tie points and an alternative weather correction for the marginal ice zone can further reduce errors due to weather. Ice concentrations calculated using 37 versus 18 GHz data show little difference in total ice covered area, but greater differences in intermediate concentration classes. Given the magnitude of weather-related errors in ice classification from passive microwave data, corrections for weather effects may be necessary to detect small trends in ice covered area and ice type for climate studies.

Maslanik, J. A.↗
NASA NTRS1999

Estimates of Long Term Surface Soil Moisture in the Midwestern U.S. Derived from Satellite Microwave Observations

Soil moisture is a key component of the water and energy balances of the Earth's surface, and has been identified as a parameter of significant potential for improving the accuracy of large-scale land surface-atmosphere interaction models. However, soil moisture is often somewhat difficult to measure accurately in both space and time, especially at large spatial scales. Soil moisture is highly variable, and while point measurements are typically quite accurate, subsequent areal averaging of these measurements often leads to large errors. Since remotely sensed land surface observations are already a spatially averaged or areally integrated value, they are a logical input parameter to regional or larger scale land process models. A database of long-term soil moisture was compared to satellite microwave observations over test sites in the Midwestern United States. Ground measurements of average volumetric surface soil moisture in the top ten cm were made bimonthly at 19 locations throughout the state of Illinois. Nighttime microwave brightness temperatures were observed at a frequency of 6.6 GHz, by the Scanning Multichannel Microwave Radiometer (SMMR), onboard the Nimbus 7 satellite. The life of the SMMR instrument spanned from Nov. 1978 to Aug. 1987. At 6.6 GHz, the instrument provided a spatial resolution of approximately 150 km, and a temporal frequency over the test area of about 3 nighttime orbits per week. Vegetation radiative transfer characteristics, such as the canopy transmissivity, were estimated from vegetation indices such as the Normalized Difference Vegetation Index (NDVI) and the 37 GHz Microwave Polarization Difference Index (MPDI). Because the time of satellite coverage does not always coincide with the ground measurements of soil moisture, the existing ground data were used to calibrate a water balance for the top IO cm surface layer in order to interpolate daily surface moisture values. Such a climate-based approach is often more appropriate for estimating large-area average soil moisture because meteorological data are generally more spatially representative than isolated point measurements of soil moisture, Passive microwave remote sensing presents the greatest potential for providing regular spatially representative estimates of surface soil moisture at global scales. Real time estimates should improve weather and climate modelling efforts, while the development of historical data sets will provide necessary information for simulation and validation of long-term climate and global change studies.

Owe, M.↗
NASA NTRS2000

Estimating Long Term Surface Soil Moisture in the GCIP Area From Satellite Microwave Observations

Soil moisture is an important component of the water and energy balances of the Earth's surface. Furthermore, it has been identified as a parameter of significant potential for improving the accuracy of large-scale land surface-atmosphere interaction models. However, accurate estimates of surface soil moisture are often difficult to make, especially at large spatial scales. Soil moisture is a highly variable land surface parameter, and while point measurements are usually accurate, they are representative only of the immediate site which was sampled. Simple averaging of point values to obtain spatial means often leads to substantial errors. Since remotely sensed observations are already a spatially averaged or areally integrated value, they are ideally suited for measuring land surface parameters, and as such, are a logical input to regional or larger scale land process models. A nine-year database of surface soil moisture is being developed for the Central United States from satellite microwave observations. This region forms much of the GCIP study area, and contains most of the Mississippi, Rio Grande, and Red River drainages. Daytime and nighttime microwave brightness temperatures were observed at a frequency of 6.6 GHz, by the Scanning Multichannel Microwave Radiometer (SMMR), onboard the Nimbus 7 satellite. The life of the SMMR instrument spanned from Nov. 1978 to Aug. 1987. At 6.6 GHz, the instrument provided a spatial resolution of approximately 150 km, and an orbital frequency over any pixel-sized area of about 2 daytime and 2 nighttime passes per week. Ground measurements of surface soil moisture from various locations throughout the study area are used to calibrate the microwave observations. Because ground measurements are usually only single point values, and since the time of satellite coverage does not always coincide with the ground measurements, the soil moisture data were used to calibrate a regional water balance for the top 1, 5, and 10 cm surface layers in order to interpolate daily surface moisture values. Such a climate-based approach is often more appropriate for estimating large-area spatially averaged soil moisture because meteorological data are generally more spatially representative than isolated point measurements of soil moisture. Vegetation radiative transfer characteristics, such as the canopy transmissivity, were estimated from vegetation indices such as the Normalized Difference Vegetation Index (NDVI) and the 37 GHz Microwave Polarization Difference Index (MPDI). Passive microwave remote sensing presents the greatest potential for providing regular spatially representative estimates of surface soil moisture at global scales. Real time estimates should improve weather and climate modelling efforts, while the development of historical data sets will provide necessary information for simulation and validation of long-term climate and global change studies.

Owe, Manfred↗
NASA NTRSDate not supplied

Development of Micro Pulse Lidar Network (MPLNET) Level 3 Satellite Validation Products in Advance of the EarthCARE Mission

Assessing the cirrus cloud radiative effect is crucial to establish their feedback on the Earth- atmosphere system. For this reason, cirrus clouds are of paramount importance in climate. Moreover, these tiny ice clouds are the most common cloud gene, continuously covering 30% of the Earth’s surface, peaking to 70% in the tropical and equatorial regions. The same authors, in three different recent studies, assessed the yearly cirrus cloud radiative effects characteristics for different NASA MPLNET permanent observational sites, deployed at different latitudes, e. g. Goddard Space Flight Center, Singapore, and Fairbanks Alaska. The analysis put in evidence that the cirrus cloud can be both cooling or warming agents of the Earth-atmosphere system during the daytime, depending on their latitude. The cirrus clouds are warming agents in equatorial/tropical regions because of the higher averaged solar zenith angle, and become neutral at mid-latitudes. At polar latitudes instead, cirrus clouds become cooling agents because of the lower solar zenith angle. In this analysis instead, using the Fu-Liou-Gu radiative transfer model, we assess how the cirrus cloud radiative effects, both at the top of the atmosphere and surface, changed over twenty years. The analysis is extended also to evaluate also changes in cloud optical depth over the same period. This is unprecedented research, because to our knowledge, no other analysis has been carried out from ground-based measurement for such a long period. As a future perspective, the analysis will be repeated for the different observational sites of the MPLNET lidar network to evaluate cirrus cloud radiative effects at a global scale.

Jasper R. Lewis↗
DOE OSTI2020

CosTuuM: Polarized Thermal Dust Emission by Magnetically Oriented Spheroidal Grains

We present the new open-source C++-based Python library CosTuuM that can be used to generate infrared absorption and emission coefficients for arbitrary mixtures of spheroidal dust grains that are (partially) aligned with a magnetic field. We outline the algorithms underlying the software, demonstrate the accuracy of our results using benchmarks from literature, and use our tool to investigate some commonly used approximative recipes. We find that the linear polarization fraction for a partially aligned dust grain mixture can be accurately represented by an appropriate linear combination of perfectly aligned grains and grains that are randomly oriented, but that the commonly used picket fence alignment breaks down for short wavelengths. We also find that for a fixed dust grain size, the absorption coefficients and linear polarization fraction for a realistic mixture of grains with various shapes cannot both be accurately represented by a single representative grain with a fixed shape, but that instead an average over an appropriate shape distribution should be used. Insufficient knowledge of an appropriate shape distribution is the main obstacle in obtaining accurate optical properties. CosTuuM is available as a standalone Python library and can be used to generate optical properties to be used in radiative transfer applications.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2022

Snow Microphysical Retrieval from the NASA D3R Radar During ICE-POP 2018

A method is developed to use both polarimetric and dual-frequency radar measurements to retrieve microphysical properties of falling snow. It is applied to the Ku- and Ka-band measurements of the NASA dual-polarization, dual-frequency Doppler radar (D3R) obtained during the International Collaborative Experiments for PyeongChang 2018 Olympic and Paralympic winter games (ICE-POP 2018) field campaign and incorporates the Atmospheric Radiative Transfer Simulator (ARTS) microwave singles cattering property database for oriented particles. The retrieval uses optimal estimation to solve for several parameters that describe the particle size distribution (PSD), relative contribution of pristine, aggregate, and rimed ice species, and the orientation distribution along an entire radial simultaneously. Examination of Jacobian matrices and averaging kernels shows that the dual-wavelength ratio (DWR) measurements provide information regarding the characteristic particle size, and to a lesser extent, the rime fraction and shape parameter of the size distribution, whereas the polarimetric measurements provide information regarding the mass fraction of pristine particles and their characteristic size and orientation distribution. Thus, by combining the dual-frequency and polarimetric measurements, some ambiguities can be resolved that should allow a better determination of the PSD and bulk microphysical properties (e.g., snowfall rate) than can be retrieved from single-frequency polarimetric measurements or dual-frequency, single-polarization measurements. The D3R ICE-POP retrievals were validated using Precipitation Imaging Package (PIP) and Pluvio weighing gauge measurements taken nearby at the May Hills ground site. The PIP measures the snow PSD directly, and its measurements can be used to derived the snowfall rate (volumetric and water equivalent), mean volume-weighted particle size, and effective density, as well as particle aspect ratio and orientation. Four retrieval experiments were performed to evaluate the utility of different measurement combinations: Kuonly, DWR-only, Ku-pol, and All-obs. In terms of correlation, the volumetric snowfall rate (r D 0:95) and snow water equivalent rate (r D 0:92) were best retrieved by the Ku-pol method, while the DWR-only method had the lowest magnitude bias for these parameters (-31% and -8 %, respectively). The methods that incorporated DWR also had the best correlation to particle size (r D 0:74 and r D 0:71 for DWR-only and All-obs, respectively), although none of the methods retrieved density particularly well (r D 0:43 for Allobs). The ability of the measurements to retrieve mean aspect ratio was also inconclusive, although the polarimetric methods (Ku-pol and All-obs) had reduced biases and mean absolute error (MAE) relative to the Ku-only and DWR-only methods. The significant biases in particle size and snowfall rate appeared to be related to biases in the measured DWR, emphasizing the need for accurate DWR measurements and frequent calibration in future D3R deployments.

S Joseph Munchak↗
NASA NTRS1974

A simple radiative transfer model of the high latitude mesospheric scattering layer

A simple radiative transfer model of the particle layer found at 85 km over the summer poles is presented. The effects of the layer on the global radiative temperature, the polar region temperature, and the greenhouse effect are discussed. The estimated magnitude of the global radiative temperature change is 3.5 x .001 K to 2.2 x .01 K, depending on the value of the imaginary part of the particle index of refraction. The layer is shown to have a possible secondary influence on the temperature of the polar region while the contribution which the layer makes to the greenhouse effect is shown to be negligible. The imaginary part of the particle index of refraction is shown to be important in determining the attenuation properties of the layer.

Hummel, J. R.↗
NASA NTRS1990

A semiempirical model for interpreting microwave emission from semiarid land surfaces as seen from space

A radiative-transfer model for simulating microwave brightness temperatures over land surfaces is described. The model takes into account sensor viewing conditions (spacecraft altitude, viewing angle, frequency, and polarization) and atmospheric parameters over a soil surface characterized by its moisture, roughness, and temperature and covered with a layer of vegetation characterized by its temperature, water content, single scattering albedo, structure, and percent coverage. In order to reduce the influence of atmospheric and surface temperature effects, the brightness temperatures are expressed as polarization ratios that depend primarily on the soil moisture and roughness, canopy water content, and percentage of cover. The sensitivity of the polarization ratio to these parameters is investigated. Simulation of the temporal evolution of the microwave signal over semiarid areas in the African Sahel is presented and compared to actual satellite data from the SMMR instrument on Nimbus-7.

Kerr, Yann H.↗
NASA NTRS1992

Polarimetric signatures of a canopy of dielectric cylinders based on first and second order vector radiative transfer theory

Complete polarimetric signatures of a canopy of dielectric cylinders overlying a homogeneous half space are studied with the first and second order solutions of the vector radiative transfer theory. The vector radiative transfer equations contain a general nondiagonal extinction matrix and a phase matrix. The energy conservation issue is addressed by calculating the elements of the extinction matrix and the elements of the phase matrix in a manner that is consistent with energy conservation. Two methods are used. In the first method, the surface fields and the internal fields of the dielectric cylinder are calculated by using the fields of an infinite cylinder. The phase matrix is calculated and the extinction matrix is calculated by summing the absorption and scattering to ensure energy conservation. In the second method, the method of moments is used to calculate the elements of the extinction and phase matrices. The Mueller matrix based on the first order and second order multiple scattering solutions of the vector radiative transfer equation are calculated. Results from the two methods are compared. The vector radiative transfer equations, combined with the solution based on method of moments, obey both energy conservation and reciprocity. The polarimetric signatures, copolarized and depolarized return, degree of polarization, and phase differences are studied as a function of the orientation, sizes, and dielectric properties of the cylinders. It is shown that second order scattering is generally important for vegetation canopy at C band and can be important at L band for some cases.

Tsang, Leung↗