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At least 163 records · Page 9

Developing Fast and Accurate Radiative Transfer Models to Meet the Needs of Modern Satellite Remote Sensing Applications

Modern hyperspectral satellite remote sensors provide highly accurate measurements the Earth’s Top-of-Atmosphere (TOA) radiance, reflectance, or polarized spectra with hundreds to thousands of spectral channels and with millions of observations per day. The large data volume and high spectral dimensionality of the data pose challenges for retrieval algorithms. To process the satellite Level-1 data (e.g. calibrated TOA spectra) into Level-2 products (e.g. atmospheric and surface properties) using physical-based retrieval algorithms, accurate and fast Radiative Transfer Models (RTMs) are needed. RTMs are usually the limiting factor in determining the speed of a level-2 algorithm. For example, more than one million Line-by-Line (LBL) radiative transfer (RT) calculations are needed in order to properly capture the spectral contributions of important atmospheric molecules for an IR hyperspectral sensor with a spectral coverage from 3.5 m to 15 m or a solar hyperspectral sensor with spectral coverage from 0.25 m to 2.5 m. In this presentation, we will discuss advantages and disadvantages of different ways (e.g. correlated k and effective transmittance) to accelerate the speed of a fast RTM. We finally describe a Principal Component-based Radiative Transfer Model (PCRTM), which can calculate TOA radiance or reflectance spectra from 50 cm-1 to 40,000 cm-1 (200 m to 0.25 m). It has demonstrated very good accuracy relative to reference LBL RTMs and saves orders of magnitude in computational time. The PCRTM has been used in many satellite remote sensing applications. Examples include forward modeling in Level-2 and Level-3 retrieval algorithms, high fidelity satellite instrument simulators and instrument performance trade studies, spectral and radiometric accuracy characterizations of satellite Level-1 data, tools for inter-satellite calibrations, tools for satellite RTM lookup table generations, and tools for generating physically based training datasets for Artificial Intelligence (AI) algorithms.

climate data record↗

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Siegel, R.↗

Three-dimensional radiative transfer calculations on an SIMD machine applied to accretion disks

We have developed a tool to solve the radiative transfer equation for a three-dimensional astrophysical object on the SIMD computer MasPar MP-1. With this tool we can rapidly calculate the image of such an object as seen from an arbitrary direction and at an arbitrary wavelength. Such images and spectra can then be used to directly compare observations with the model. This tool can be applied to many different areas in astrophysics, e.g., HI disks of galaxies and polarized radiative transfer of accretion columns onto white dwarfs. Here we use this tool to calculate the image and spectrum of a simple model of an accretion disk.

Vath, H.↗

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Cogley, A. C.↗

An Analytical Solution of Radiative Transfer in the Coupled Atmosphere-Ocean System with Rough Surface

Using the efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on radiation field in the atmosphere and ocean are studied and compared with 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 ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as depth in ocean 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.

Jin, Zhonghai↗

Radiative transfer in the surfaces of atmosphereless bodies. I - Theory. II - Interpretation of phase curves

A generalized theory of radiative transfer is presented which includes single and multiple scattering of light in particulate surfaces, and is applicable to both the surfaces of atmosphereless bodies and to laboratory samples. Single scattering is described in terms of the effects of porosity and roughness, and is formulated by means of a probabilistic method. It is shown that, for low-albedo surfaces, the effects of porosity and roughness are separable, the opposition effect is caused by the former, and the slope of the linear part of the phase curve is mainly controlled by the latter. The theory, which is applicable to all albedos and phase angles, may be used in both surface brightness and integrated brightness studies. The limiting case of roughness and volume density tending to zero yields the results of classical radiative transfer theory.

Lumme, K.↗

A Fourier-Riccati approach to radiative transfer. I - Foundations

The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens' work this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

Gabriel, P. M.↗

Polarimetric signatures of a coniferous forest canopy based on vector radiative transfer theory

Complete polarization signatures of a coniferous forest canopy are studied by the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (leaves, branches, stems, and trunk) are embedded in a multi-layered medium over a rough interface. The branches, stems and trunk scatterers are modeled as finite randomly oriented cylinders. The leaves are modeled as randomly oriented needles. For a plane wave exciting the canopy, the average Mueller matrix is formulated in terms of the iterative solution of the radiative transfer solution and used to determine the linearly polarized backscattering coefficients, the co-polarized and cross-polarized power returns, and the phase difference statistics. Numerical results are presented to investigate the effect of transmitting and receiving antenna configurations on the polarimetric signature of a pine forest. Comparison is made with measurements.

Karam, M. A.↗

Efficient stream distributions in radiative transfer theory

This paper discusses a new, computationally-efficient method for approximating the integro-differential equation of radiative transfer with a finite set of coupled differential equations for discrete streams. The method uses recommended spatial distributions of streams that are quite different from those typically used in that they are based on the symmetry of several regular Platonic solids. To facilitate the use of such distributions, an explicit, one-parameter relationship between the physical radiance and the abstract stream is formulated. The parameter is used to determine the minimum number of streams required in the radiative transfer model. Accuracy and computational efficiency are shown to be served best by choosing a stream distribution that is invariant to a large number of three space rotations. For various values of the above-mentioned parameter, the resulting recommended stream distribution is shown to be more computationally efficient than more conventional stream distributions. Finally, the incorporation of polarization in the stream definition is described.

Whitney, C.↗

Developing a Radar Signal Simulator for the Community Radiative Transfer Model

Active radar instruments provide vertically resolved clouds and precipitation measurements that cannot be provided by the passive instruments. These active measurements are not conventionally assimilated into the data assimilation systems because of the lack of fast forward radiative transfer models and also difficulties in the error modelling of the measurements. This paper describes the development, evaluation, and sensitivity analysis for a forward radar model implemented in the Community Radiative Transfer Model (CRTM). The scattering properties required by the forward model are provided by the hydrometeor lookup tables that were generated using the discrete dipole approximation. The model is able to calculate both the reflectivity and the attenuated reflectivity for any given radar instrument at any given zenith angles as long as CRTM instrument specific coefficients are available. The evaluation using CloudSat measurements shows a very good agreement between the simulations and measurements as long as the input profiles of hydrometeors are consistent with the measured reflectivity profiles. Major sources contributing to the differences between the measured and simulated reflectivities are input hydrometeor profiles, scattering lookup tables, lack of melting layer in the forward model, CRTM scattering solvers, and attenuation calculations. In addition to the forward model, both Tangent Linear and Adjoint of the model are also implemented and tested within CRTM. These components may be required by some data assimilation systems for the assimilation of radar measurements.

radar↗

Atmospheric Radiative Transfer for Satellite Remote Sensing

I will discuss the science of satellite remote sensing which involves the interpretation and inversion of radiometric measurements made from space. The goal of remote sensing is to retrieve some physical aspects of the medium which are sensitive to the radiation at specific wavelengths. This requires the use of fundamentals of atmospheric radiative transfer. I will talk about atmospheric radiation or, more specifically, about the interactions of solar radiation with aerosols and cloud particles. The focus will be more on cloudy atmospheres. I will also show how a standard one-dimensional approach, that is traced back at least 100 years, can fail to interpret the complexity of real clouds. I n these cases, three-dimensional radiative transfer should be used. Examples of satellite retrievals will illustrate the cases.

Marshak, Alexander↗

Microwave radiative transfer through horizontally inhomogeneous precipitating clouds

Recent advances in cloud microphysical models have led to realistic three-dimensional distributions of cloud constituents. Radiative transfer schemes can make use of this detailed knowledge in order to study the effects of horizontal as well as vertical inhomogeneities within clouds. This study looks specifically at the differences between three-dimensional radiative transfer results and those obtained by plane parallel, independent pixel approximations in the microwave spectrum. A three-dimensional discrete ordinates method as well as a backward Monte Carlo method are used to calculate realistic radiances emerging from the cloud. Analyses between these models and independent pixel approximations reveal that plane parallel approximations introduce two distinct types of errors. The first error is physical in nature and is related to the fact that plane parallel approximations do not allow energy to leak out of dense areas into surrouding areas. In general, it was found that these errors are quite small for emission-dominated frequencies (37 GHz and lower) and that physical errors are highly pronounced only at scattering frequencies (85 GHz) where large deviations and biases up to 8 K averaged over the entire cloud were found. The second error is more geometric in nature and is related to the fact that plane parallel approximations cannot accommodate physical boundaries in the horizontal dimension for off-nadir viewing angles. The geometric errors were comparable in magnitude for all frequencies. Their magnitude, however, depends on a number of factors including the scheme used to deal with the edge, the nature of the surface, and the viewing angle.

Roberti, Laura↗

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

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

Schwemmer, Geary K.↗

Implications of a quadratic stream definition in radiative transfer theory.

An explicit definition of the radiation-stream concept is stated and applied to approximate the integro-differential equation of radiative transfer with a set of twelve coupled differential equations. Computational efficiency is enhanced by distributing the corresponding streams in three-dimensional space in a totally symmetric way. Polarization is then incorporated in this model. A computer program based on the model is briefly compared with a Monte Carlo program for simulation of horizon scans of the earth's atmosphere. It is found to be considerably faster.

Whitney, C.↗

The diffusion approximation. An application to radiative transfer in clouds

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

Arduini, R. F.↗

Diffusion approximation for large absorption in radiative transfer

A new diffusion model is developed for radiative transfer in particulate media. It includes the effects of higher Legendre moments while avoiding the mathematical complexities of solving multiple coupled differential moment equations and satisfying higher-order boundary conditions. The method accurately extrapolates the conventional Eddington approximation to problems involving large absorption. Although the simplifying assumptions limit the model to nonbeam incidence and spatial homogeneity of the scattering material, they are nonrestrictive with regard to the size and shape of the medium, the character of background reflections, and the type of phase function.

Meador, W. E.↗