Adjoint problem of radiative transfer for a pseudo-spherical atmosphere and general viewing geometries

We formulate the adjoint radiative transfer for a pseudo-spherical atmosphere and various retrieval scenarios. The single scattering radiance is computed in a spherical atmosphere by using the source integration technique, while for the multiple scattering radiance we formulate an one-dimensional adjoint radiative transfer equation in a plane-parallel atmosphere. The adjoint solution of the radiative transfer equation is obtained by employing the discrete ordinate method with matrix exponential. We provide an abbreviated derivation of our formalism as well as a discussion of the numerical implementation of the theory.     

Polarization Structure of Multiply Scattered Background Components of Lidar Signals Reflected from Cloud Ice Crystals

A numerical experiment is performed to obtain the polarization characteristics of signals of a monostatic lidar intended for homogeneous cloud sensing. It is assumed that clouds consist of monodisperse randomly-oriented hexagonal ice crystals. To solve the vector radiative transfer equation, the light scattering phase matrices, preliminary calculated with the help of the beam splitting technique, are used as input data. The formation of the polarization structure of multiply scattered background signal component is studied for different scattering orders depending on crystal shapes and sizes and optical and geometrical conditions of the experiment.     

The NIMO Monte Carlo model for box-air-mass factor and radiance calculations

A new fully spherical multiple scattering Monte Carlo radiative transfer model named NIMO (NIWA Monte Carlo model) is presented. The ray tracing algorithm is described in detail along with the treatment of scattering and absorption, and the simulation of backward adjoint trajectories. The primary application of NIMO is the calculation of box-air-mass factors (box-AMFs), which are used to convert slant column densities (SCDs) of trace gases, derived from UV–visible multiple axis Differential Optical Absorption Spectroscopy (MAX-DOAS) measurements, into vertical column densities (VCDs). Box-AMFs are also employed as weighting functions for optimal estimation retrievals of vertical trace gas profiles from SCDs. Monte Carlo models are well suited to AMF calculations at high solar zenith angles (SZA) and at low viewing elevation angles where multiple scattering is important. Additionally, the object-oriented structure of NIMO makes it easily extensible to new applications by plugging in objects for new absorbing or scattering species. Box-AMFs and radiances, calculated for various wavelengths, SZAs, viewing elevation and azimuth angles and aerosol scenarios, are compared with results from nine other models using a set of exercises from a recent radiative transfer model intercomparison. NIMO results for these simulations are well within the range of variability of the other models.     

An efficient diffusion approximation for 3D radiative transfer parameterization: application to cloudy atmospheres

The three-dimensional (3D) diffusion radiative transfer equation, which utilizes a four-term spherical harmonics expansion for the scattering phase function and intensity, has been efficiently solved by using the full multigrid numerical method. This approach can simulate the transfer of solar and thermal infrared radiation in inhomogeneous cloudy conditions with different boundary conditions and sharp boundary discontinuity. The correlated k-distribution method is used in this model for incorporation of the gaseous absorption in multiple-scattering atmospheres for the calculation of broadband fluxes and heating rates in the solar and infrared spectra. Comparison of the results computed from this approach with those computed from plane-parallel and 3D Monte Carlo models shows excellent agreement. This 3D radiative transfer approach is well suited for radiation parameterization involving 3D and inhomogeneous clouds in climate models.     

等效球模型模拟冰晶云反射的误差分析

用射线光学理论计算了具有一定尺度分布的六角冰晶粒子在可见和近红外光谱区一系列波长上(0.2～5μm)的单次散射特性.利用米氏(Mie)理论,计算了与六角冰晶具有相同截面积的球形粒子的单次散射特性.根据辐射传输理论,应用累加法,分别计算了由冰晶粒子和等效球形粒子构成的卷层云的多次散射特性,计算结果表明当入射波长λ≈3.0 μm时,等效球Mie理论可以很好地用于计算卷层云的反射特性,但是当λ＜2.8μm时,尤其在可见光区,将引起显著的误差.最后提出了计算冰云光学特性的两种方案.     

Estimates of radiation over clouds and dust aerosols: Optimized number of terms in phase function expansion

The bulk-scattering properties of dust aerosols and clouds are computed for the community radiative transfer model (CRTM) that is a flagship effort of the Joint Center for Satellite Data Assimilation (JCSDA). The delta-fit method is employed to truncate the forward peaks of the scattering phase functions and to compute the Legendre expansion coefficients for re-constructing the truncated phase function. Use of more terms in the expansion gives more accurate re-construction of the phase function, but the issue remains as to how many terms are necessary for different applications. To explore this issue further, the bidirectional reflectances associated with dust aerosols, water clouds, and ice clouds are simulated with various numbers of Legendre expansion terms. To have relative numerical errors smaller than 5%, the present analyses indicate that, in the visible spectrum, 16 Legendre polynomials should be used for dust aerosols, while 32 Legendre expansion terms should be used for both water and ice clouds. In the infrared spectrum, the brightness temperatures at the top of the atmosphere are computed by using the scattering properties of dust aerosols, water clouds and ice clouds. Although small differences of brightness temperatures compared with the counterparts computed with 4, 8, 128 expansion terms are observed at large viewing angles for each layer, it is shown that 4 terms of Legendre polynomials are sufficient in the radiative transfer computation at infrared wavelengths for practical applications.     

Fast and accurate 4 and 6 stream linearized discrete ordinate radiative transfer models for ozone profile retrieval

The global and long-term measurement of ozone vertical and horizontal distributions is one of the most important tasks in the monitoring of the earth's atmosphere. A number of satellite instruments are capable of delivering ozone profile distributions from UV nadir backscatter measurements. Retrieval algorithms should be efficient enough to deliver profiles in real-time without compromising accuracy. Such algorithms require a radiative transfer model that can generate quickly and accurately both simulated radiances and Jacobian matrices of weighting functions. We develop fast and analytic 4 stream and 6 stream linearized discrete ordinate models designed to satisfy performance and accuracy requirements for such an algorithm. The models have the pseudo-spherical treatment of the direct beam attenuation. For anisotropic scattering we use the delta-M scaling method to deal with strong forward scattering peaks. We demonstrate that the accuracy of the models is improved greatly upon application of a single scatter correction based on an exact specification of the phase function. For wide-angle off-nadir viewing, a sphericity correction is developed to deal more precisely with attenuation in a curved atmosphere. Radiances and weighting functions for the 4 and 6 stream models are compared with 20 stream output from the LIDORT model. We show that for the UV range pertinent to ozone profile retrieval from space, the 4 stream model generates backscatter radiances to an accuracy >1.25% for all viewing situations in a clear sky Rayleigh and background aerosol reference atmosphere, and up to 1.75% for a number of special scenarios with optically thick particulate layers. Six stream radiances are accurate to the 0.25% level for clear sky situations, and 0.65% for the special cases; weighting functions for the 6 stream output are accurate to ±2% in all cases. We discuss the implications of these comparisons regarding the performance and accuracy of the radiative transfer forward model in the ozone profile retrieval context.     

基于六角形和球形冰晶模型的卷云辐射特征研究

卷云中冰晶粒子的单次光散射计算是卷云辐射传输及云微物理参数反演的重要基础。近年,利用高观测频率的静止气象卫星数据来反演水云和卷云的光学和微物理参数,进而计算地表光通量的研究倍受重视。然而,很多研究中卷云的冰晶用球形模型来模拟。由于不同形状和尺度大小的冰晶对电磁波的散射特征的不同,导致不同冰晶模型计算的卷云环境下卫星观测的辐射值及地表光通量的不同。利用不同尺度大小和电磁波波长的球形和六角形冰晶的单次散射数据,结合RSTAR辐射传输模式来定量分析了卷云环境下不同形状的冰晶模型对计算卫星观测的辐射和地表光通量中的影响。结果显示利用不同形状的冰晶模块来计算的卫星观测的辐射,地表向下辐射通量明显不同。波长在0.4～1.0 μm之间的大气窗口部分的光谱辐射通量的差距最大。总辐射通量受云粒子形状的影响显著。研究证实了正确选择冰晶模型对卫星反演卷云微物理和光学参数的反演及计算地表光通量的重要性。该结果对于云微物理参数的反演及地表向下辐射通量的模拟具有参考价值。     

Modeling single-scattering properties of small cirrus particles by use of a size-shape distribution of ice spheroids and cylinders

In this study, we model single-scattering properties of small cirrus crystals using mixtures of polydisperse, randomly oriented spheroids and cylinders with varying aspect ratios and with a refractive index representative of water ice at a wavelength of 1.88 μm. The Stokes scattering matrix elements averaged over wide shape distributions of spheroids and cylinders are compared with those computed for polydisperse surface-equivalent spheres. The shape-averaged phase function for a mixture of oblate and prolate spheroids is smooth, featureless, and nearly flat at side-scattering angles and closely resembles those typically measured for cirrus. Compared with the ensemble-averaged phase function for spheroids, that for a shape distribution of cylinders shows a relatively deeper minimum at side-scattering angles. This may indicate that light scattering from realistic cirrus crystals can be better represented by a shape mixture of ice spheroids. Interestingly, the single-scattering properties of shape-averaged oblate and prolate cylinders are very similar to those of compact cylinders with a diameter-to-length ratio of unity. The differences in the optical cross sections, single-scattering albedo, and asymmetry parameter between the spherical and the nonspherical particles studied appear to be relatively small. This may suggest that for a given optical thickness, the influence of particle shape on the radiative forcing caused by a cloud composed of small ice crystals can be negligible.     

Infrared radiative transfer modelling in a 3D scattering cloudy atmosphere: Application to limb sounding measurements of cirrus

The Monte Carlo cloud scattering forward model (McClouds_FM) has been developed to simulate limb radiative transfer in the presence of cirrus clouds, for the purposes of simulating cloud contaminated measurements made by an infrared limb sounding instrument, e.g. the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS). A reverse method three-dimensional Monte Carlo transfer model is combined with a line-by-line model for radiative transfer through the non-cloudy atmosphere to explicitly account for the effects of multiple scattering by the clouds. The ice cloud microphysics are characterised by a size distribution of randomly oriented ice crystals, with the single scattering properties of the distribution determined by accurate calculations accounting for non-spherical habit.A comparison of McClouds_FM simulations and real MIPAS spectra of cirrus shows good agreement. Of particular interest are several noticeable spectral features (i.e. H₂O absorption lines) in the data that are replicated in the simulations: these can only be explained by upwelling tropospheric radiation scattered into the line-of-sight by the cloud ice particles.     

Radiative transfer in a spherical, emitting, absorbing and anisotropically scattering medium

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an exact solution of the radiative transfer specific intensity at all points and directions in a finite spherical medium having arbitrary radial spectral distribution of: source (temperature), absorption, emission and anisotropic scattering. The power and efficiency of the method stems from the spherical numerical gridding used to discretize the transfer equations prior to matrix solution: the wanted ray and the rays which scatter into it both have the same physico-geometric structure. Very good agreement is found with an isotropic astrophysical benchmark [Avrett EH, Loeser R. Methods in radiative transfer. In: Kalkofen W, editor. Cambridge: Cambridge University Press; 1984. pp. 341-79]. We introduce a specimen arbitrary forward- side-back phase scattering function for future comparisons. Our method directly and exactly addresses spherical symmetry with anisotropic scattering, and could be used to study the Earth's climate, nuclear power (neutron diffusion) and the astrophysics of stars and planets.     

Radiative transfer through an arbitrarily thick,scattering atmosphere

A method is presented for solving the equation of radiative transfer in a vertically inhomogeneous planetary atmosphere. The method, based on the spherical harmonics expansion, can be used to compute models with an arbitrarily large optical thickness and any scattering phase function. It is extremely efficient, requiring the equivalent of only two matrix multiplications per layer. This efficiency combined with its stability makes the method useful for computing realistic models of planetary atmospheres. To illustrate the range of validity of this method, we compute the plane albedo from model atmospheres containing clouds with optical thicknesses ranging from 0 to 10⁶.     

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.     

Effect of ice crystal shape and effective size on snow bidirectional reflectance

We tested the applicability of three rigorous radiative transfer computational approaches, namely, the discrete ordinates radiative transfer (DISORT) method, the adding–doubling approach, and an efficient computational technique based on Ambartsumian's nonlinear integral equation for computing the bidirectional reflectance of a semi-infinite layer. It was found that each of these three models, in a combination with the truncation of the forward peak of the bulk scattering phase functions of ice particles, can be used to simulate the bidirectional reflectance of a semi-infinite snow layer with appropriate accuracy. Furthermore, we investigate the sensitivity of the bidirectional reflectance of a homogeneous and optically infinite snow layer to ice crystal habit and effective particle size. It is shown that the bidirectional reflectance is not sensitive to the particle effective size in the visible spectrum. The sensitivity of the bidirectional reflectance in the near-infrared spectrum to the particle effective size increases with the increase of the incident wavelength. The sensitivity of the bidirectional reflectance to the effective particle size and shape is attributed fundamentally to the sensitivity of the single-scattering properties to particle size and shape. For a specific ice crystal habit, the truncated phase function used in the radiative transfer computations is not sensitive to particle effective size. Thus, the single-scattering albedo is primarily responsible for the sensitivity of the bidirectional reflectance to particle size, particularly, at a near-infrared wavelength.     

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.     

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.     

Control volume finite element method for radiation

In this paper a new methodology is presented by the authors for the numerical treatment of radiative heat transfer in emitting, absorbing and scattering media. This methodology is based on the utilisation of Control Volume Finite Element Method (CVFEM) and the use, for the first time, of matrix formulation of the discretized Radiative Transfer Equation (RTE). The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. Besides, the new formulation of the discretized RTE presented in this paper makes it possible to solve the algebraic system by direct or iterative numerical methods. The theoretical background of CVFEM and matrix formulation is presented in the text. The proposed technique is applied to different test problems, and the results compared favourably against other published works. Moreover this paper discusses in detail the effects of some radiative parameters, such as optical thickness and walls emissivities on the spatial evolution of the radiant heat flux. The numerical simulation of radiative heat transfer for different cases using the algorithm proposed in this work has shown that the developed computer procedure needs an accurate CPU time and is exempt of any numerical oscillations.     

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.     

An efficient method for computing atmospheric radiances in clear-sky and cloudy conditions

A computationally efficient method is developed to simulate the radiances in a scattering and absorbing atmosphere along an arbitrary path in the spectral region ranging from visible to far-infrared with a spectral resolution of 1 cm⁻¹. For a given spectral region, the method is based on fitting radiances pre-calculated from the discrete ordinate radiative transfer (DISORT) at several wavenumbers. Radiances at other wavenumbers are interpolated based on the pre-computed total absorption and scattering optical thicknesses and the surface albedo. The computational efficiency and accuracy of the method are tested in comparison with rigorous simulations for various scenarios under the same conditions. For both clear-sky and cloud atmospheres, the present method is at least 140 times faster than the direct application of DISORT. Across the spectral range, the standard relative differences between the new method and the DISORT are less than 2% for clear-sky conditions. Root-mean-square (RMS) differences of the top of the atmosphere (TOA) brightness temperatures between the new method and DISORT, for atmospheric infrared sounder (AIRS) channels over clear-sky, ice cloudy and water cloudy skies, are within the noise equivalent differential temperature (NEDT) of the AIRS sensor. The fast method is also applied to simulations of the spectral downwelling radiance measured by the Fourier transform infrared (FTIR) interferometer, and to the simulations of the AIRS upwelling radiances under clear-sky and cloudy conditions.