Multiple-scattering transmission and an effective average photon path length of a plane-parallel beam in a homogeneous medium

A two-stream radiative transfer model is used to derive expressions for the multiple-scattered transmitted flux (including single-scattering contributions) and the total effective average photon path length on transmission of a normally incident plane-parallel beam on a homogeneous layer characterized by the optical depth, the single-scattering albedo, and the asymmetry parameter of the scatterers. The results are simple analytical expressions that are useful for modifying the Beer-Lambert transmission law for a thick scattering medium in which the multiple-scattering contribution to the transmission is not negligible.     

Radiative transfer model for aerosols in infrared wavelengths for passive remote sensing applications

A comprehensive analytical radiative transfer model for isothermal aerosols and vapors for passive infrared remote sensing applications (ground-based and airborne sensors) has been developed. The theoretical model illustrates the qualitative difference between an aerosol cloud and a chemical vapor cloud. The model is based on two and two/four stream approximations and includes thermal emission-absorption by the aerosols; scattering of diffused sky radiances incident from all sides on the aerosols (downwelling, upwelling, left, and right); and scattering of aerosol thermal emission. The model uses moderate resolution transmittance ambient atmospheric radiances as boundary conditions and provides analytical expressions for the information on the aerosol cloud that is contained in remote sensing measurements by using thermal contrasts between the aerosols and diffused sky radiances. Simulated measurements of a ground-based sensor viewing Bacillus subtilis var. niger bioaerosols and kaolin aerosols are given and discussed to illustrate the differences between a vapor-only model (i.e., only emission-absorption effects) and a complete model that adds aerosol scattering effects.     

Radiative properties of snow for clear sky solar radiation

Spectral and integrated radiative properties (reflection, transmission, and the rate of heating) of finegrained wind-packed snow typical of subpolar regions are studied through a model taking into account surface reflection and volumetric multiple scattering. The surface reflection is modeled by a bidirectional reflectance distribution function applicable to powdered dielectric material. For the volumetric multiple scattering, the radiative transfer equation designed for strongly asymmetric scattering is solved. All multiple scattering parameters (single scattering albedo, various moments of the scattering phase function, and optical depth) are related to measurable physical characteristics (density, grain size, and the absorption coefficient of pure ice).Parameterized atmospheric spectral transmission coefficients for scattering and absorption by aerosols and gases are used to obtain the direct and diffuse components of solar flux, incident on the snow-cover. Calculated values of spectral and integrated visible and near infrared reflection and flux attenuation coefficients of snow are compared with observations. The rate of radiative heating at different depths within the snowcover is calculated from the net flux divergence. It is shown that the conventional method of calculating this rate using measured bulk extinction coefficients grossly underestimates the amount of heating within the top few millimeters. This study provides a better overall understanding of the radiative properties of snow under clear sky conditions in terms of the physical characteristics of the snowcover.     

Retrieval of the scattering and microphysical properties of aerosols from ground-based optical measurements including polarization. I. Method

A method has been developed for retrieving the scattering and microphysical properties of atmospheric aerosol from measurements of solar transmission, aureole, and angular distribution of the scattered and polarized sky light in the solar principal plane. Numerical simulations of measurements have been used to investigate the feasibility of the method and to test the algorithm's performance. It is shown that the absorption and scattering properties of an aerosol, i.e., the single-scattering albedo, the phase function, and the polarization for single scattering of incident unpolarized light, can be obtained by use of radiative transfer calculations to correct the values of scattered radiance and polarized radiance for multiple scattering, Rayleigh scattering, and the influence of ground. The method requires only measurement of the aerosol's optical thickness and an estimate of the ground's reflectance and does not need any specific assumption about properties of the aerosol. The accuracy of the retrieved phase function and polarization of the aerosols is examined at near-infrared wavelengths (e.g., 0.870 mum). The aerosol's microphysical properties (size distribution and complex refractive index) are derived in a second step. The real part of the refractive index is a strong function of the polarization, whereas the imaginary part is strongly dependent on the sky's radiance and the retrieved single-scattering albedo. It is demonstrated that inclusion of polarization data yields the real part of the refractive index.     

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer from measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with our computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.     

Principal component-based radiative transfer model for hyperspectral sensors: theoretical concept

Modern infrared satellite sensors such as the Atmospheric Infrared Sounder (AIRS), the Cross-Track Infrared Sounder (CrIS), the Tropospheric Emission Spectrometer (TES), the Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS), and the Infrared Atmospheric Sounding Interferometer (IASI) are capable of providing high spatial and spectral resolution infrared spectra. To fully exploit the vast amount of spectral information from these instruments, superfast radiative transfer models are needed. We present a novel radiative transfer model based on principal component analysis. Instead of predicting channel radiance or transmittance spectra directly, the principal component-based radiative transfer model (PCRTM) predicts the principal component (PC) scores of these quantities. This prediction ability leads to significant savings in computational time. The parameterization of the PCRTM model is derived from the properties of PC scores and instrument line-shape functions. The PCRTM is accurate and flexible. Because of its high speed and compressed spectral information format, it has great potential for superfast one-dimensional physical retrieval and for numerical weather prediction large volume radiance data assimilation applications. The model has been successfully developed for the NAST-I and AIRS instruments. The PCRTM model performs monochromatic radiative transfer calculations and is able to include multiple scattering calculations to account for clouds and aerosols.     

Radiative transfer. I. Atmospheric transmission monitoring with modeling and ground-based multispectral measurements

Existing solar radiative codes such as lowtran allow us to model the radiative properties of the atmosphere and its constituents for standard atmospheric conditions. The increase in urbanization and air pollution has led to changes in the distribution, type, and concentration of the atmospheric constituents, affecting spectral atmospheric transmission and modifying weather and climate. This requires knowledge of the real optical properties of atmospheric transmission. We have developed a model for the radiative properties of atmospheric transmission, with ground-based multispectral measurements of direct solar radiation in the 310-830-nm range. An application of this model to Athens' urban atmosphere is described. The radiative properties of a U.S. Standard Atmosphere are also simulated by use of the lowtran 7 code; simulations and calculations are compared. The total ozone retrieval scheme and the algorithm for retrieving the spectral transmission function and optical thickness, considering multiple scattering, are given. Results for the spectral atmospheric transmission and aerosol and gas transmission functions as well as optical-thickness measurements for the Athens area are also presented as an application of the proposed methodology.     

Radiative heat transfer in splash and dilution zones of the pressurized oxy-fuel combustion CFB considering particle-dependent scattering

Radiative heat transfer is dominant in splash and dilution zones of the oxy-fuel combustion pressurized circulating fluidized bed (PCFB). However, the particle radiation fields interact with each other due to the high particle concentration. Moreover, the particle concentration distribution, the flue gas components and pressure change drastically due to pressurized oxy-fuel combustion technology. In this paper, the radiative heat transfer in splash and dilution zones of the oxy-fuel combustion PCFB is investigated when particle-dependent scattering is considered. The results show that the maximum error of the particle radiation model is less than 1% in predicting the incident heat flux at the wall when particle-dependent scattering is considered. The particle concentration distribution has a significant impact on the radiative heat transfer in splash and dilution zones of oxy-fuel combustion PCFB. The simplified particle concentration distribution model cannot capture the zero-source term phenomenon in the core region and has a large error in the annular region. In addition, the mechanism and importance of the flue gas composition and pressure on the radiative heat transfer in splash and dilution zones of oxy-fuel combustion PCFB are analyzed.     

Measuring and modeling twilight's purple light

During many clear twilights, much of the solar sky is dominated by pastel purples. This purple light's red component has long been ascribed to transmission through and scattering by stratospheric dust and other aerosols. Clearly the vivid purples of post-volcanic twilights are related to increased stratospheric aerosol loading. Yet our time-series measurements of purple-light spectra, combined with radiative transfer modeling and satellite soundings, indicate that background stratospheric aerosols by themselves do not redden sunlight enough to cause the purple light's reds. Furthermore, scattering and extinction in both the troposphere and the stratosphere are needed to explain most purple lights.     

Polarization of skylight in the O(2)A band: effects of aerosol properties

Motivated by several observations of the degree of linear polarization of skylight in the oxygen A (O(2)A) band that do not yet have a quantitative explanation, we analyze the influence of aerosol altitude, microphysics, and optical thickness on the degree of linear polarization of the zenith skylight in the spectral region of the O(2)A band, between 755 to 775 nm. It is shown that the degree of linear polarization inside the O(2)A band is particularly sensitive to aerosol altitude. The sensitivity is strongest for aerosols within the troposphere and depends also on their microphysical properties and optical thickness. The polarization of the O(2)A band can be larger than the polarization of the continuum, which typically occurs for strongly polarizing aerosols in an elevated layer, or smaller, which typically occurs for depolarizing aerosols or cirrus clouds in an elevated layer. We show that in the case of a single aerosol layer in the atmosphere a determination of the aerosol layer altitude may be obtained. Furthermore, we show limitations of the aerosol layer altitude determination in case of multiple aerosol layers. To perform these simulations we developed a fast method for multiple scattering radiative transfer calculations in gaseous absorption bands including polarization. The method is a combination of doubling-adding and k-binning methods. We present an error estimation of this method by comparing with accurate line-by-line radiative transfer simulations. For the Motivated by several observations of the degree of linear polarization of skylight in the oxygen A (O(2)A) band that do not yet have a quantitative explanation, we analyze the influence of aerosol altitude, microphysics, and optical thickness on the degree of linear polarization of the zenith skylight in the spectral region of the O(2)A band, between 755 to 775 nm. It is shown that the degree of linear polarization inside the O(2)A band is particularly sensitive to aerosol altitude. The sensitivity is strongest for aerosols within the troposphere and depends also on their microphysical properties and optical thickness. The polarization of the O(2)A band can be larger than the polarization of the continuum, which typically occurs for strongly polarizing aerosols in an elevated layer, or smaller, which typically occurs for depolarizing aerosols or cirrus clouds in an elevated layer. We show that in the case of a single aerosol layer in the atmosphere a determination of the aerosol layer altitude may be obtained. Furthermore, we show limitations of the aerosol layer altitude determination in case of multiple aerosol layers. To perform these simulations we developed a fast method for multiple scattering radiative transfer calculations in gaseous absorption bands including polarization. The method is a combination of doubling-adding and k-binning methods. We present an error estimation of this method by comparing with accurate line-by-line radiative transfer simulations. For the O(2)A band, the errors in the degree of linear polarization are less than 0.11% for transmitted light, and less than 0.31% for reflected light. band, the errors in the degree of linear polarization are less than 0.11% for transmitted light, and less than 0.31% for reflected light.     

Detection,identification, and estimation of biological aerosols and vapors with a Fourier-transform infrared spectrometer

Two experiments were conducted with a Fourier-transform infrared (FTIR) spectrometer. The purpose of the first experiment was to detect and identify Bacillus subtilis subsp. niger (BG) bioaerosol spores and kaolin dust in an open-air release for which the thermal contrast between the aerosol temperature and background brightness temperature is small. The second experiment estimated the concentration of a small amount of triethyl phosphate (TEP) vapor in a closed chamber in which an external blackbody radiation source was used and where the thermal contrast was large. The deduced BG (TEP) extinction spectrum (identification) showed an excellent match to the library BG (TEP) extinction spectrum. Analysis of the time sequence of the measurements coincided well with the presence (detection) of the BG during the measurements, and the estimated concentration of time-dependent TEP vapor was excellent. The data were analyzed with hyperspectral detection, identification, and estimation algorithms. The algorithms were based on radiative transfer theory and statistical signal-processing methods. A subspace orthogonal projection operator was used to statistically subtract the large thermal background contribution to the measurements, and a robust maximum-likelihood solution was used to deduce the target (aerosol or vapor cloud) spectrum and estimate its mass-column concentration. A Gaussian-mixture probability model for the deduced mass-column concentration was computed with an expectation-maximization algorithm to produce the detection threshold, the probability of detection, and the probability of false alarm. The results of this study are encouraging, as they suggest for the first time to the authors' knowledge the feasibility of detecting biological aerosols with passive FTIR sensors.     

Multiple field of view lidar returns from atmospheric aerosols

As a laser pulse propagates into the atmosphere, it becomes broader in the lateral direction as a result of scattering by aerosols. The laser pulse may be described as the superposition of a central, unscattered component of reduced intensity and a surrounding scattered component. A multiple field of view lidar has been developed that makes simultaneous measurements of the backscattered power from the central pulse and multiply scattered power arising from the scattered component. Measurements from various types of atmospheric aerosols and precipitation are presented and compared with simulated returns. The results show how the multiply scattered signals are influenced by the distribution of the aerosols along the lidar path, the characteristic size of the aerosols, and the optical depth. It is shown that the multiple field of view lidar can provide meaningful, additional information about the aerosols that is not available from a conventional single field of view lidar.     

Integrating biomass, sulphate and sea-salt aerosol responses into a microphysical chemical parcel model: implications for climate studies

Aerosols are known to influence significantly the radiative budget of the Earth. Although the direct effect (whereby aerosols scatter and absorb solar and thermal infrared radiation) has a large perturbing influence on the radiation budget, the indirect effect (whereby aerosols modify the microphysical and hence the radiative properties and amounts of clouds) poses a greater challenge to climate modellers. This is because aerosols undergo chemical and physical changes while in the atmosphere, notably within clouds, and are removed largely by precipitation. The way in which aerosols are processed by clouds depends on the type, abundance and the mixing state of the aerosols concerned. A parametrization with sulphate and sea-salt aerosol has been successfully integrated within the Hadley Centre general circulation model (GCM). The results of this combined parametrization indicate a significantly reduced role, compared with previous estimates, for sulphate aerosol in cloud droplet nucleation and, consequently, in indirect radiative forcing. However, in this bicomponent system, the cloud droplet number concentration, N(d) (a crucial parameter that is used in GCMs for radiative transfer calculations), is a smoothly varying function of the sulphate aerosol loading. Apart from sea-salt and sulphate aerosol particles, biomass aerosol particles are also present widely in the troposphere. We find that biomass smoke can significantly perturb the activation and growth of both sulphate and sea-salt particles. For a fixed salt loading, N(d) increases linearly with modest increases in sulphate and smoke masses, but significant nonlinearities are observed at higher non-sea-salt mass loadings. This non-intuitive N(d) variation poses a fresh challenge to climate modellers.     

Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with a rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind conditions.     

Spatial distribution of doubly scattered polarized laser radiation in the focal plane of a lidar receiver

Depolarization lidars are widely used to study clouds and aerosols because of their ability to discriminate between spherical particles and particles of irregular shape. Depolarization of cloud backscattered radiation can be caused also by multiple scattering events. One of the ways to gain information about particle parameters in the presence of strong multiple scattering is the measurement of radial and azimuthal dependence of the polarization patterns in the focal plane of receiver. We present an algorithm for the calculation of corresponding polarized patterns in the frame of double scattering approximation. Computations are performed for various receiver field of views, for different parameters of the scattering geometry, e.g., cloud base and sounding depth, as well as for different values of cloud particle size and refractive index. As the spatial distribution of cross-polarized radiation is of cross shape and rotated at 45 degrees with respect to laser polarization, the use of a properly oriented cross-shaped mask in the receiver focal plane allows the removal of a significant portion of the depolarized component of the backscattered radiation produced by double scattering. This has been verified experimentally based on cloud depolarization measurements performed at different orientations of the cross-shaped mask. Results obtained from measurements are in agreement with model predictions.     

Remote sensing of aerosol plumes: a semianalytical model

A semianalytical model, named APOM (aerosol plume optical model) and predicting the radiative effects of aerosol plumes in the spectral range [0.4,2.5 microm], is presented in the case of nadir viewing. It is devoted to the analysis of plumes arising from single strong emission events (high optical depths) such as fires or industrial discharges. The scene is represented by a standard atmosphere (molecules and natural aerosols) on which a plume layer is added at the bottom. The estimated at-sensor reflectance depends on the atmosphere without plume, the solar zenith angle, the plume optical properties (optical depth, single-scattering albedo, and asymmetry parameter), the ground reflectance, and the wavelength. Its mathematical expression as well as its numerical coefficients are derived from MODTRAN4 radiative transfer simulations. The DISORT option is used with 16 fluxes to provide a sufficiently accurate calculation of multiple scattering effects that are important for dense smokes. Model accuracy is assessed by using a set of simulations performed in the case of biomass burning and industrial plumes. APOM proves to be accurate and robust for solar zenith angles between 0 degrees and 60 degrees whatever the sensor altitude, the standard atmosphere, for plume phase functions defined from urban and rural models, and for plume locations that extend from the ground to a height below 3 km. The modeling errors in the at-sensor reflectance are on average below 0.002. They can reach values of 0.01 but correspond to low relative errors then (below 3% on average). This model can be used for forward modeling (quick simulations of multi/hyperspectral images and help in sensor design) as well as for the retrieval of the plume optical properties from remotely sensed images.     

Analytical solution to the optical transfer function of a scattering medium with large particles

A new analytical expression for the optical transfer function of multiple-scattering media such as clouds, mists, and dust aerosols is given in terms of their microphysical characteristics. The geometrical optics approximation is used to find local optical parameters of a scattering medium, including the simple approximation of the phase function, which is the key to the solution of the problem considered here. The optical transfer function is taken within a small-angle approximation of the radiative transfer theory. A comparison with Monte Carlo data shows a fairly satisfactory accuracy of our analytic formulas.     

Combined Henyey-Greenstein and Rayleigh phase function

The phase function is an important parameter that affects the distribution of scattered radiation. In Rayleigh scattering, a scatterer is approximated by a dipole, and its phase function is analytically related to the scattering angle. For the Henyey-Greenstein (HG) approximation, the phase function preserves only the correct asymmetry factor (i.e., the first moment), which is essentially important for anisotropic scattering. When the HG function is applied to small particles, it produces a significant error in radiance. In addition, the HG function is applied only for an intensity radiative transfer. We develop a combined HG and Rayleigh (HG-Rayleigh) phase function. The HG phase function plays the role of modulator extending the application of the Rayleigh phase function for small asymmetry scattering. The HG-Rayleigh phase function guarantees the correct asymmetry factor and is valid for a polarization radiative transfer. It approaches the Rayleigh phase function for small particles. Thus the HG-Rayleigh phase function has wider applications for both intensity and polarimetric radiative transfers. For microwave radiative transfer modeling in this study, the largest errors in the brightness temperature calculations for weak asymmetry scattering are generally below 0.02 K by using the HG-Rayleigh phase function. The errors can be much larger, in the 1-3 K range, if the Rayleigh and HG functions are applied separately.     

Radiances simulated in the presence of clouds by use of a fast radiative transfer model and a multiple-scattering scheme

A fast-forward radiative transfer (RTF) model is presented that includes cloud-radiation interaction for any number of cloud layers. Layer cloud fraction and transmittance are treated separately and combined with that of gaseous transmittances. RTF is tested against a reference procedure that uses line-by-line gaseous transmittances and solves the radiative transfer equation by use of the adding-doubling method to handle multiple-scattering conditions properly. The comparison is carried out for channels 8, 12, and 14 of the High Resolution Infrared Radiation Sounder (HIRS/2) and for the geostationary satellite METEOSAT thermal infrared and water vapor channels. Fairly large differences in simulated radiances by the two schemes are found in clear conditions for upper- and mid-tropospheric channels; the cause of the differences is discussed. For cloudy situations an improved layer source function is shown to be required when rapid changes in atmospheric transmission are experienced within the model layers. The roles of scattering processes are discussed; results with and without scattering, both obtained by use of a reference code, are compared. Overall, the presented results show that the fast model is capable of reproducing the cloudy results of the much more complex and time-consuming reference scheme.     

Computation of hypersonic flow and radiation of viscous chemically reacting gas in a channel modeling a section of a scramjet

This work is devoted to a consideration of flow and combustion of a hydrogen-air mixture in a channel modeling a section of a supersonic combustion ramjet (scramjet). Fields of concentrations, pressure, and temperature are obtained. Based on them, the thermal radiation of gas within a scramjet combustor is computed. The density of the radiative heat flux to the chamber wall is computed by two methods, i.e., in a P1 approximation of the spherical harmonics method and in an approximation of the plane layer. It has been shown that the radiative heat flux contribute significantly to the total heating of the jet wall.