Exact results in modeling planetary atmospheres—II. Semi-gray atmospheres

We solve the radiative transfer equation for a semi-gray planetary atmosphere in radiative equilibrium, in an attempt to define an entirely analytical non-gray model atmosphere of finite optical thickness. The salient feature of the model is that the incident solar radiation is partitioned between two adjacent spectral domains—the “visible” and the “infrared”—in each of which the atmosphere's (effective) opacity is assumed to be independent of frequency (the semi-gray assumption). We envisage a plane-parallel atmosphere illuminated by a beam of parallel radiation and bounded below by a partially reflecting and emitting ground. The former emits infrared radiation, induced by the absorption of radiation both visible and infrared, deriving from the external irradiation as well as from the emission of the planet's surface layer. For an atmosphere with given single-scattering albedos and optical thicknesses in both the visible and infrared domains, we compute the temperature at every depth of the atmosphere, as well as the ground's temperature.     

K. Schwarzschild's problem in radiation transfer theory

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem—to be more precise the calculation of the source function within the slab—was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it, (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere.     

Extension of the discrete-ordinate algorithm and efficient radiative transfer calculation

As an accurate and efficient algorithm, the discrete-ordinate method (DOM) has been used to solve the radiative transfer problem of plane-parallel scattering atmosphere illuminated by a parallel beam, an idealized case of the sun, from above the atmosphere. In this paper, we extend this algorithm so that radiative problems of more general sources, such as parallel surface sources that illuminate with a parallel beam in any direction from any vertical position, and general surface sources that illuminate continuously in a hemisphere, can be solved. For a problem where intensity distributions are sought for a number of different sources within the same atmosphere-surface system, the intrinsic properties of DOM are used so that the time required for the solution for extra sources is reduced to a substantially small amount. In the case of parallel surface sources, numerical testing has shown that the amount can be reduced to as little as 15% of a full solution. Examples of applications are presented.     

Exact results in modeling planetary atmospheres—III.: The general theory applied to the Earth's semi-gray atmosphere

We apply the semi-gray model of our previous paper to the particular case of the Earth's atmosphere, in order to illustrate quantitatively the inverse problem associated with the direct problem we dealt with before. From given climatological values of the atmosphere's spherical albedo and transmittance for visible radiation, the single-scattering albedo and the optical thickness in the visible are inferred, while the infrared optical thickness is deduced for given global average surface temperature. Eventually, temperature distributions in terms of the infrared optical depth will be shown for a terrestrial atmosphere assumed to be semi-gray and, locally, in radiative and thermodynamic equilibrium.     

The DRESOR method for radiative heat transfer in a one-dimensional medium with variable refractive index

This paper extends the DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method to radiative transfer in a variable refractive index medium. In this method, the intensity is obtained from the source term along the curved integration paths determined only by the variable refractive index, and the DRESOR values are calculated by the Monte Carlo method in which the propagation of the energy bundles are affected by Snell's law. With given temperatures on the black boundaries of a one-dimensional medium, the temperature distribution inside the medium with a variable scattering property is calculated under the condition of radiative equilibrium. It is shown that the DRESOR method has a good accuracy in the cases studied. For an isotropic-scattering medium with the same optical thickness, the scattering albedo has no effect on the temperature distribution, which can be obtained from the general equations and can be seen as an extension of what exists for a constant refractive index; however, the different refractive index causes obvious changes in the temperatures inside the medium. The effect of anisotropic scattering on the temperature distribution cannot be ignored, although it is still weaker than the effect caused by variation in the refractive index.     

Influence of the vertical profile of Saharan dust on the visible direct radiative forcing

The vertical profile of Saharan dust in the atmosphere is generally characterized by a large aerosol concentration in the mid troposphere, differently from the climatological distribution of other types of particles, that show a peak at the surface and a rapid decrease with height. Saharan dust is also characterized by particles of relatively large size of irregular shape, and variable values of the single scattering albedo (the ratio between radiation scattering and extinction). The dust's peculiar vertical distribution is expected to produce an effect on the calculation of the direct aerosol radiative forcing at the surface and at the top of the atmosphere. This effect is investigated by comparing estimates of aerosol direct visible radiative forcing at the surface and at the top of the atmosphere for dust vertical profiles measured in the Mediterranean, and for the climatological profile. The radiative forcing is estimated by means of an accurate radiative transfer model, and for the ocean surface. The sensitivity of the results on the solar zenith angle, aerosol optical depth, and aerosol absorption is also investigated. The aerosol radiative forcing at the surface shows a very small dependency on the aerosol vertical profile. At the top of the atmosphere, the radiative forcing is weakly dependent on the vertical profile (up to 10% variation on the daily average forcing) for low absorbing particles; conversely, it shows a strong dependency (the daily radiative forcing may vary up to 100%) for absorbing particles. The top of the atmosphere visible radiative forcing efficiency produced by dust having single scattering albedo <0.7 is higher by 4 W m⁻² when the observed vertical profile instead of the standard profile is used in the calculations (i.e. it produces a lower cooling). For values of the single scattering albedo around 0.67, the sign of the forcing depends on the vertical profile. The influence of the vertical distribution on the radiative forcing is largest at small values of the solar zenith angle, and at short wavelengths.     

Temperature field of radiative equilibrium in a two-dimensional graded index medium with gray boundaries

In this paper, a numerical method is presented for the study of the radiative transfer in a two-dimensional graded index semitransparent medium with diffuse gray boundaries. The numerical method is a combination of the linear refractive index bar model, the discrete curved ray-tracing technique and the pseudo source adding method (LRIB-CRTP). In the traditional ray-tracing technique, it is difficult to deal with the diffuse gray boundary while solving the radiative transfer. Using the pseudo source adding method, the diffuse gray boundary of the medium can be treated as a black boundary. We have also studied the radiative equilibrium temperature field of the medium and analyzed the influence of some parameters involved. The results show that the directional discrete number is important for the medium having a large absorption coefficient. The results also show that the refractive index distribution greatly influences the temperature field, whereas the linear absorption coefficient distribution has little influence on the temperature field.     

Adjoint sensitivity analysis of radiative transfer equation: 2. Applications to retrievals of temperature in scattering atmospheres in thermal IR

An approach to formulation of inversion algorithms for thermal sounding in the case of scattering atmosphere based on the adjoint equation of radiative transfer (Ustinov, JQSRT 68 (2001) 195, referred to as Paper 1 in the main text) is applied to temperature retrievals in the scattering atmosphere for the nadir viewing geometry. Analytical expressions for the weighting functions involving the integration of the source function are derived. Temperature weighting functions for a simple model of the atmosphere with scattering are evaluated and convergence to the case of pure atmospheric absorption is demonstrated. The numerical experiments on temperature retrievals are carried out to demonstrate the validity of the expressions obtained.     

Analytic evaluation of the weighting functions for remote sensing of blackbody planetary atmospheres: a general linearization approach

An analytic approach is proposed for the evaluation of weighting functions for remote sensing of a blackbody planetary atmosphere based on straightforward, general linearization. In the present paper, this approach is applied to the case of remote sensing with the nadir (down-looking) geometry. Expressions for weighting functions for various atmospheric parameters are derived. It is demonstrated that in a realistic case of temperature-dependent atmospheric absorption, an additional term appears in the expression for the temperature weighting function which contains the temperature derivative of the atmospheric absorption coefficient. The approach is applied to the case of a semi-infinite atmosphere and then, to the atmosphere of a finite optical depth with the underlying surface. In this, latter case, the expressions are also obtained for partial derivatives of observed radiances with respect to surface parameters: surface pressure, temperature and emissivity.     

超光谱大气CO_2监测仪光谱定标误差修正

超光谱大气CO_2探测需对遥感器进行精确表征及定标,其中光谱定标工作最为基础。针对传统实验室定标方法获取的波长定标系数不确定度高等特点,开展基于气体吸收法原理的光谱定标误差修正研究,该方法与仪器使用状态一致,提高了定标系数实用性。首先利用辐射传输进行了理论光谱及误差因素模拟计算,并基于大气环境模拟定标仓开展了大气XO_2吸收光谱测量实验,最后采用LM算法进行光谱误差修正迭代优化。光谱定标误差修正结果表明:光谱偏差均值由修正前的0.03 cm~(-1)下降到修正后0.008 cm~(-1),且系统性与突变性误差得以剔除,大大提高了地面光谱定标精度,为后续温室气体反演奠定了基础。     

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.     

Deviations from LTE in a stellar atmosphere

Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section α_ν grows with frequency ν faster than ν²; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of α_ν. Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.     

Metal fluorescence lidar (light detection and ranging) and the middle atmosphere

Metal fluorescence lidar (light detection and ranging) has come of age as a tool for exploring the middle atmosphere. The Colorado State University sodium lidar system exemplifies these lidar systems, using a number of interesting techniques to achieve measurements of temperature and wind speed in the middle atmosphere. This and other fluorescence lidar systems have illuminated a number of interesting properties of the mesopause region (within the middle atmosphere). This paper reviews both the laboratory physics necessary to construct fluorescence lidar systems, and the advances in atmospheric science that have resulted from the data collected.     

Influence of complex component and particle polydispersity on radiative properties of soot aggregate in atmosphere

The effects of morphological structure, water coating, dust mixing and primary particle size distribution on the radiative properties of soot fractal aggregates in atmosphere are investigated using T-matrix method. These fractal aggregates are numerically generated using a combination of the particle-cluster and cluster-cluster aggregation algorithms with fractal parameters representing soot aggregate in atmosphere. The radiative properties of compact aggregate notably deviate from that of the branched one, and the effect of morphology changes on the radiative properties in wet air cannot be neglected. However it is reasonable to use realization-averaged radiative properties to represent that of the aggregates with certain morphology. In wet air, the scattering, absorption and extinction cross-section and symmetry parameter of soot aggregates coated with water notably increase with water shell thickness. The mixing structures of dust have little effect on radiative properties of aggregates, but the volume fraction of dust has an obvious effect on extinction, scattering and absorption cross-section of aggregates when the size parameters are above the Rayleigh limit. Although the primary particle size distribution of soot aggregate has mild effect on the scattering albedo and asymmetry parameter, the deviations of the extinction, scattering, absorption cross-section among the three size distributions are significant in this study. The size distribution has a significant effect on forward scattering of phase function, while the effect can be neglected as the size parameter approaches to the Rayleigh limit.     

Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere

The propagation properties of flattened Gaussian beam with a misaligned circular aperture in turbulent atmosphere have been studied by using the extended Huygens-Fresnel formula. From the study and numerical calculation, the effects of aperture parameters on the propagation properties of flattened Gaussian beams in turbulent atmosphere have been illuminated. The results show that angle misalignments and lateral displacements of aperture create unsymmetrical average intensity distribution at any cross section. The intensity distributions are much more sensitive to the lateral displacement than to the angle misalignments. And the propagation properties of different flattened Gaussian beams in turbulent atmosphere are also compared.     

Sensitivity of trace gas abundances retrievals from infrared limb emission spectra to simplifying approximations in radiative transfer modelling

The accuracy of trace gas abundances retrieved from spectrally resolved infrared limb emission measurements relies, among other things, on the appropriate modelling of radiative transfer through the actual atmosphere. We quantify the mapping of several commonly applied simplifications in radiative transfer modelling on the trace gas abundances retrieval error at the example of the Michelson interferometer for passive atmospheric sounding (MIPAS)/environmental satellite (ENVISAT) space borne Fourier transform infra-red limb emission experiment. The Karlsruhe optimized and precise radiative transfer algorithm (KOPRA) which was used as a tool for this study will be introduced. KOPRA supports accurate modelling of the particular instrument requirements of MIPAS and the observation scenarios during the ENVISAT mission, in particular with respect to its viewing direction and its altitude coverage of the atmosphere. We show that disregarding of horizontal temperature inhomogeneities and non-local thermodynamic equilibrium effects, insufficient accuracy in modelling of field-of-view and apodisation effects, and disregarding individual profiles of isotopic species play the key roles in radiative transfer modelling and lead to systematic retrieval errors which can by far exceed the expected random retrieval error caused by measurement noise.     

Visualization of three-dimensional temperature distributions in a large-scale furnace via regularized reconstruction from radiative energy images: numerical studies

In this paper, the possibility of visualization of three-dimensional (3-D) temperature distributions in large-scale boiler furnaces from radiative energy images captured by multiple charge-coupled device (CCD) cameras mounted around the furnace is studied numerically. For the calculation of the radiative energy image formation, a fast algorithm proposed by the authors for pinhole imaging is used in this paper, which is based on the Monte Carlo method and combined with a concept of angular factor effective for image formation. This algorithm is applicable for the emitting, absorbing, and isotropic scattering medium. For the inversion of the 3-D temperature distributions which is an ill-posed problem, a modified Tikhonov regularization method is improved, where the finite difference regularizer is defined and can be used in 3-D cases, and the optimal regularization parameter is suggested to be selected by using a post-treatment method. For a 3-D unimodal temperature distribution, the numerical simulation results show that the reconstruction errors for the 3-D temperature distribution can be maintained at levels similar to the measurement error and the visualization quality of the temperature distribution is satisfactory. For a kind of bimodal temperature distribution, the reconstruction errors are higher than those for the unimodal distribution, but the bimodal feature of the temperature distribution can also be reproduced clearly.     

Spatial coherence of laser light passed through rotating ground glass

The ensemble-averaged spatial coherence of quasi-thermal light, produced by passing a focused laser beam through a rotating ground glass plate, is studied as a function of the illuminated area, the fineness of the glass used, the speed of rotation of the glass, and the laser mode selected as a primary source. It becomes clear that the ensemble-averaged spatial coherence depends strongly upon the illuminated area and on the fineness of the rotating ground glass, and also on the laser mode chosen but not on the speed of rotation of the glass.