Radiative transfer solutions for coupled atmosphere ocean systems using the matrix operator technique

Accurate radiative transfer models are the key tools for the understanding of radiative transfer processes in the atmosphere and ocean, and for the development of remote sensing algorithms. The widely used scalar approximation of radiative transfer can lead to errors in calculated top of atmosphere radiances. We show results with errors in the order of±8% for atmosphere ocean systems with case one waters. Variations in sea water salinity and temperature can lead to variations in the signal of similar magnitude. Therefore, we enhanced our scalar radiative transfer model MOMO, which is in use at Freie Universität Berlin, to treat these effects as accurately as possible. We describe our one-dimensional vector radiative transfer model for an atmosphere ocean system with a rough interface. We describe the matrix operator scheme and the bio-optical model for case one waters. We discuss some effects of neglecting polarization in radiative transfer calculations and effects of salinity changes for top of atmosphere radiances. Results are shown for the channels of the satellite instruments MERIS and OLCI from 412.5 nm to 900 nm.     

Discrete-ordinate method with matrix exponential for a pseudo-spherical atmosphere: Scalar case

We present a discrete-ordinate algorithm using the matrix-exponential solution for pseudo-spherical radiative transfer. Following the finite-element technique we introduce the concept of layer equation and formulate the discrete radiative transfer problem in terms of the level values of the radiance. The layer quantities are expressed by means of matrix exponentials, which are computed by using the matrix eigenvalue method and the Padé approximation. These solution methods lead to a compact and versatile formulation of the radiative transfer. Simulated nadir and limb radiances for an aerosol-loaded atmosphere and a cloudy atmosphere are presented along with a discussion of the model intercomparisons and timings.     

A single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere

We present a single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere. It is based on the assumption that the upwelling internal radiation field is dominated by a surface with a uniform brightness temperature. It allows the calculation of the scattering source function for individual aerosol types, mixtures of aerosol types, and mixtures of gas and aerosol. The approximation can be applied in a Curtis-Godson radiative transfer code and is used for operational retrievals from Mars Climate Sounder measurements. Radiance comparisons with a multiple scattering model show good agreement in the mid- and far-infrared although the approximate model tends to underestimate the radiances in realistic conditions of the Martian atmosphere. Relative radiance differences are found to be about 2% in the lowermost atmosphere, increasing to ∼10% in the middle atmosphere of Mars. The increasing differences with altitude are mostly due to the increasing contribution to limb radiance of scattering relative to emission at the colder, higher atmospheric levels. This effect becomes smaller toward longer wavelengths at typical Martian temperatures. The relative radiance differences are expected to produce systematic errors of similar magnitude in retrieved opacity profiles.     

Integration of Chandrasekhar's integral equation

We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA “explicitly” in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness.     

Microwave scattering properties of sand particles: Application to the simulation of microwave radiances over sandstorms

The single-scattering properties of sand/dust particles assumed to be ellipsoids are computed from the discrete dipole approximation (DDA) method at microwave frequencies 6.9-89.0 GHz in comparison with the corresponding Lorenz-Mie solutions. It is found that the single-scattering properties of sand particles are strongly sensitive to the shapes of the particles. The bulk scattering properties of sandstorms composed of spherical or nonspherical particles are investigated by averaging the single-scattering properties of these particles over log-normal particle size distributions. Furthermore, a vector radiative transfer model is used to simulate microwave radiances. The microwave brightness temperatures in the vertical polarization model are essentially not sensitive to sand particle habit, whereas microwave brightness temperature polarization differences are influenced by particle habit. It is shown that microwave brightness temperatures and brightness temperature polarization differences may be useful for estimating the effective particle sizes and mass loading of sandstorms.     

Improving the description of sunglint for accurate prediction of remotely sensed radiances

The bidirectional reflection distribution function (BRDF) of the ocean is a critical boundary condition for radiative transfer calculations in the coupled atmosphere-ocean system. Existing models express the extent of the glint-contaminated region and its contribution to the radiance essentially as a function of the wind speed. An accurate treatment of the glint contribution and its propagation in the atmosphere would improve current correction schemes and hence rescue a significant portion of data presently discarded as “glint contaminated”. In current satellite imagery, a correction to the sensor-measured radiances is limited to the region at the edge of the glint, where the contribution is below a certain threshold. This correction assumes the sunglint radiance to be directly transmitted through the atmosphere. To quantify the error introduced by this approximation we employ a radiative transfer code that allows for a user-specified BRDF at the atmosphere-ocean interface and rigorously accounts for multiple scattering. We show that the errors incurred by ignoring multiple scattering are very significant and typically lie in the range 10-90%. Multiple reflections and shadowing at the surface can also be accounted for, and we illustrate the importance of such processes at grazing geometries.     

A strong ice cloud event as seen by a microwave satellite sensor: Simulations and observations

In this article, brightness temperatures observed by channels of the Advanced Microwave Sounding Unit-B (AMSU-B) instrument are compared to those simulated by a radiative transfer model, which can take into account the multiple scattering due to ice particles by using a discrete ordinate iterative solution method. The input fields, namely, the pressure, temperature, humidity, and cloud water content are taken from the short range forecast from the Met Office mesoscale model (UKMES). The comparison was made for a case study on the 25 January 2002 when a frontal system associated with significant cloud was present over the UK. It is demonstrated that liquid clouds have maximum impact on channel 16 of AMSU whereas ice clouds have maximum impact on channel 20. The main uncertainty for simulating microwave radiances is the assumptions about microphysical properties, such as size distribution, shape and orientation of the cloud particles, which are not known in the mesoscale model. The article examines the impact of these parameters on the cloud signal. The polarisation signal due to oriented ice particles at these frequencies is also discussed.     

Noninvasive determination of tissue optical properties based on radiative transfer theory

We present a feasibility study of a new method for determining the tissue optical properties, including the absorption and scattering coefficients and the scattering asymmetry factor. A state-of-the-art radiative transfer model for the coupled air/tissue system, based on rigorous radiative transfer theory, is used in our forward modeling simulations. The concept of the effective photon penetration depth is introduced and used to help determine the depth below, which information about the tissue will not be available through noninvasive imaging of a biological tissue using reflected diffuse light. Simulation results show that for accurate determination of tissue optical properties, one can use radiative transfer theory in conjunction with measurements of reflected radiances as well as other existing techniques.     

Visualization of Ocean Colour and Temperature from multi-spectral imagery captured by the Japanese ADEOS satellite

The Ocean Colour and Temperature Scanner on board of the Japanese Advanced Earth Observing Satellite has been designed to provide frequent global measurements of marine chlorophyll levels and ocean temperature and created a means for visualizing the biological activity in the upper ocean. Over the time of its operation, the sensor captured the coverage of global oceans suitable for studies of the marine primary production and monitoring of fishery sites and environmental changes. Current radiative transfer techniques modelling marine chlorophyll levels based on optical reflectances captured by satellite sensors have to account for atmospheric path radiances superimposed onto the waterleaving radiance and a diversity of water suspended particles. Detailed modelling of geophysical processes and empirically constrained algorithms sometimes produce misclassifications. This paper presents chlorophyll concentration for several sites around the Pacific Ocean. Where the skill of the conventional chlorophyll algorithm is uncertain, the results given by an unsupervised neural network classification scheme are also provided. The hierarchical neural network introduced in the text extracts water pixels from images and reclassifies them to separate case 1 and case 2 waters and water radiances with the significant influence of the atmospheric attenuation.     

On similarity and scaling of the radiative transfer equation

The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced.     

Forward Monte Carlo computations of fully polarized microwave radiation in non-isotropic media

A completely forward Monte Carlo radiative transfer code has been developed with biasing techniques to efficiently solve the polarized radiative transfer equation for the full Stokes vector. The code has been adapted to accommodate plane parallel/3-D vertically/horizontally inhomogeneous scattering atmospheres in Cartesian geometries. Particular attention has been paid in stochastically treating the propagation, the emission and the scattering through anisotropic media particularly suited for clouds containing perfectly or partially oriented particles. Our modelling is very appealing because all its biasing techniques do not introduce unphysical Stokes vector. Numerical results and comparisons with benchmark tests are presented for verification.     

Radiative perturbation theory for polarized radiances: 1. Theory

Radiative perturbation theory has proven to be a useful tool in radiative transfer calculations, especially in situations where repeated solution of the radiative transfer equation is required. So far however, its use has been restricted to non-polarized situations, including such applications as surface fluxes, UV indices, and the inversion of satellite radiance observations. Here, we extend the structure of radiative perturbation theory to incorporate the full Stokes formalism of polarization, to obtain the relevant equations for the first order term. This formalism will be applied to fluxes in a follow-up paper, and eventually to satellite observations.     

Numerical optimization of the extracavity Raman laser with barium nitrate crystal

The radiation transfer equations of the extracavity Raman laser including up to the third Stokes beams and backward Raman scattering terms were deduced in detail from the wave equation and material equations of stimulated Raman scattering. The radiation transfer equations were solved numerically to optimize the performance of the extracavity Raman lasers with barium nitrate crystal as the nonlinear medium. The optimum reflectivity of the output coupler at the first Stokes was figured out numerically to achieve the maximum conversion efficiency of the first Stokes, and found to be closely related to the pump pulse duration, peak intensity of the pump pulse, and Raman crystal length. With the resonator mirrors highly reflective at the first Stokes, the highest conversion efficiency of the second Stokes was obtained when the input mirror was highly reflective at second Stokes, whereas the output coupler was highly transmissive at the second Stokes. It was found that too high intracavity intensity of the second Stokes would impede the efficient energy extraction from the pump pulse to the first Stokes, and consequently, limit the conversion efficiency of the second Stokes.     

VLIDORT: A linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media

We describe a new vector discrete ordinate radiative transfer model with a full linearization facility. The VLIDORT model is designed to generate simultaneous output of Stokes vector light fields and their derivatives with respect to any atmospheric or surface property. We develop new implementations for the linearization of the vector radiative transfer solutions, and go on to show that the complete vector discrete ordinate solution is analytically differentiable for a stratified multilayer multiply scattering atmospheric medium. VLIDORT will generate all output at arbitrary viewing geometry and optical depth. The model has the ability to deal with attenuation of solar and line-of-sight paths in a curved atmosphere, and includes an exact treatment of the single scatter computation. VLIDORT also contains a linearized treatment for non-Lambertian surfaces. A number of performance enhancements have been implemented, including a facility for multiple solar zenith angle output. The model has been benchmarked against established results in the literature.     

The Joint Airborne IASI Validation Experiment: An evaluation of instrument and algorithms

The Joint Airborne IASI Validation Experiment (JAIVEx) was designed to investigate the absolute radiometric accuracy of the Infrared Atmospheric Sounding Interferometer (IASI) and test the radiative transfer algorithms on which applications using IASI radiances rely. Two comprehensively instrumented research aircraft participated in coordinated measurements co-aligned with overpasses on the IASI instrument, with airborne interferometers obtaining radiance observations alongside intensive measurements of the atmospheric state. The JAIVEx data set has been used to place an upper bound on the absolute radiometric accuracy of IASI radiances. Further, a set of clear air case studies have been used to test competing formulations of the CO₂ line shape, water vapor spectroscopic line parameters and continuum. The current state-of-the art performance of line-by-line models is established with implications for optimal use of IASI radiances in numerical weather prediction.     

Photon conservation in scattering by large ice crystals with the SASKTRAN radiative transfer model

The scattering of visible light by ice crystals and dust in radiative transfer models is challenging in part due to the large amount of scattering in the forward direction. We introduce a technique that ensures numerical conservation of photons in any radiative transfer model and that quantifies the integration error associated with highly asymmetric phase functions. When applied to a successive-orders of scatter model, the technique illustrates the high accuracy obtained in numerical integration of molecular and aerosol scattering. As well, a phase function truncation and renormalization technique is applied to scattering by ice crystals with very large size parameters, between 100 and 1000, and the scaled radiative transfer equation is solved with the spherical successive-orders model, SASKTRAN. Since computations shown this work are performed in a fully spherical model atmosphere, the computed radiances are not subject to the discontinuity at the horizon that is inherent in models using a plane–parallel assumption. The methods introduced in this work are of particular interest in modeling limb radiances in the presence of thin cirrus clouds.     

Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials

We demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.     

The influence of broken cloudiness on cloud top height retrievals using nadir observations of backscattered solar radiation in the oxygen A-band

The paper is devoted to theoretical studies of the influence of cloud inhomogeneities on cloud top height (CTH) retrievals based on top-of-atmosphere nadir reflectance observations in the oxygen A-band. A three-demensional (3D) Monte Carlo code is used to simulate highly resolved spectral measurements in the oxygen A-band. These synthetic radiances are used as input for the retrieval code SACURA based on asymptotic radiative transfer theory and the independent pixel approximation. The results show that the effect of cloud inhomogeneity on the derived CTHs is small. While we found considerable 3D effects in the reflectance of more than 30% compared to the independent column approximation, the spectral dependence of the difference was small. As SACURA is mainly based on spectral ratios, the retrieval results are hardly affected by the large absolute deviations. In consequence, SACURA is capable to retrieve CTHs with an accuracy of better than 1.5 km for overcast and also most partially cloudy cases.     

Finite element method for the two-dimensional atmospheric radiative transfer

The finite element method is applied to the solution of the two-dimensional atmospheric radiative transfer. The analysis is mainly focussed on the derivation of the cell or element equation. The Galerkin method and several hybrid methods using the integral and finite difference form of the radiative transfer equation are employed to obtain the cell equation. The assembled system of equations relating the radiances at the lower and upper boundary of the domain is solved by a direct method.     

Development of a GPU-based high-performance radiative transfer model for the Infrared Atmospheric Sounding Interferometer (IASI)

Satellite-observed radiance is a nonlinear functional of surface properties and atmospheric temperature and absorbing gas profiles as described by the radiative transfer equation (RTE). In the era of hyperspectral sounders with thousands of high-resolution channels, the computation of the radiative transfer model becomes more time-consuming. The radiative transfer model performance in operational numerical weather prediction systems still limits the number of channels we can use in hyperspectral sounders to only a few hundreds. To take the full advantage of such high-resolution infrared observations, a computationally efficient radiative transfer model is needed to facilitate satellite data assimilation. In recent years the programmable commodity graphics processing unit (GPU) has evolved into a highly parallel, multi-threaded, many-core processor with tremendous computational speed and very high memory bandwidth. The radiative transfer model is very suitable for the GPU implementation to take advantage of the hardware’s efficiency and parallelism where radiances of many channels can be calculated in parallel in GPUs.In this paper, we develop a GPU-based high-performance radiative transfer model for the Infrared Atmospheric Sounding Interferometer (IASI) launched in 2006 onboard the first European meteorological polar-orbiting satellites, METOP-A. Each IASI spectrum has 8461 spectral channels. The IASI radiative transfer model consists of three modules. The first module for computing the regression predictors takes less than 0.004% of CPU time, while the second module for transmittance computation and the third module for radiance computation take approximately 92.5% and 7.5%, respectively. Our GPU-based IASI radiative transfer model is developed to run on a low-cost personal supercomputer with four GPUs with total 960 compute cores, delivering near 4 TFlops theoretical peak performance. By massively parallelizing the second and third modules, we reached 364× speedup for 1 GPU and 1455× speedup for all 4 GPUs, both with respect to the original CPU-based single-threaded Fortran code with the –O₂ compiling optimization. The significant 1455× speedup using a computer with four GPUs means that the proposed GPU-based high-performance forward model is able to compute one day’s amount of 1,296,000 IASI spectra within nearly 10 min, whereas the original single CPU-based version will impractically take more than 10 days. This model runs over 80% of the theoretical memory bandwidth with asynchronous data transfer. A novel CPU–GPU pipeline implementation of the IASI radiative transfer model is proposed. The GPU-based high-performance IASI radiative transfer model is suitable for the assimilation of the IASI radiance observations into the operational numerical weather forecast model.