Radiative Equilibrium State Research Articles

ПАРНИКОВЫЙ ЭФФЕКТ И СОВРЕМЕННЫЙ КЛИМАТ

The concept of the greenhouse effect for the state of radiative equilibrium of the atmosphere-Earth’s surface system is discussed. The similarities and differences of modern long-term trends and intra-annual (inter-monthly) fluctuations in the concentration of CO2, CH4, N2O in the atmosphere are analyzed. The method of calculating the anthropogenic enhancement of the greenhouse effect using a one-dimensional horizontally homogeneous radiative model using modern spectroscopic data is discussed. Differences in the estimates of the greenhouse efficiency of CO2, CH4, N2O obtained using the radiative model are shown. The study explains the common mistake concerning the role of the anthropogenic enhancement of the greenhouse effect in modern climate change (it is sometimes arises from the simultaneous analysis of observational data on greenhouse gas concentrations and temperature in the near-surface layer).

Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary–lattice Boltzmann method

The Immersed Boundary–lattice Boltzmann method (IB-LBM) is developed to analyze radiative heat transfer in two-dimensional (2D) irregular geometries. Lattice Boltzmann method (LBM) has been adopted to discretize the radiative heat transfer equation in an absorbing and emitting media, and the immersed boundary method (IBM) is used to model the boundaries of irregular geometries. Due to the mismatch between boundary and computational nodes in the Immersed Boundary method, a radiative density term based on the difference of radiation intensity is added to the lattice Boltzmann equation to satisfy the boundary condition. Radiative heat flux distribution is obtained for several irregular geometries which are maintained at an isothermal media or radiative equilibrium condition in the enclosure. The results are successfully validated by comparing the results obtained from other methods of irregular geometries analysis, such as the blocked-off domain, embedded boundary, and body-fitted grid method. According to the obtained results, their accuracy, and numerical cost, the combined IB-LBM benefits from the unique and worthy advantages of both IBM and LBM in solving the complicated analysis of 2D radiative heat transfer problems. Compared to the traditional methods used for the radiative analysis of irregular geometries, the immersed boundary method can solve the complexities of modeling curved boundaries effortlessly. It should be pointed that for optically thin media, the proposed model shows poor performance.

Radiation spectra of warm and optically thick coronae in AGNs

A soft X-ray excess above the 2–10 keV power-law extrapolation is generally observed in the X-ray spectra of active galactic nuclei. The origin of this excess is still not well understood. Presently there are two competitive models: blurred ionized reflection and warm Comptonization. In the case of warm Comptonization, observations suggest a corona temperature in the range 0.1–2 keV and a corona optical depth of about 10–20. Moreover, radiative constraints from spectral fits with Comptonization models suggest that most of the accretion power should be released in the warm corona and the disk below is basically non-dissipative, radiating only the reprocessed emission from the corona. However, the true radiative properties of such a warm and optically thick plasma are not well known. For instance, the importance of the Comptonization process, the potential presence of strong absorption and/or emission features, and the spectral shape of the output spectrum have been studied only very recently. Here, we present simulations of warm and optically thick coronae using the TITAN radiative transfer code coupled with the NOAR Monte-Carlo code, the latter fully accounting for Compton scattering of continuum and lines. Illumination from above by hard X-ray emission and from below by an optically thick accretion disk are taken into account, as well as (uniform) internal heating. Our simulations show that for a large part of the parameter space, the warm corona with sufficient internal mechanical heating is dominated by Compton cooling and neither strong absorption nor emission lines are present in the outgoing spectra. In a smaller part of the parameter space, the calculated emission agrees with the spectral shape of the observed soft X-ray excess. Remarkably, this also corresponds to the conditions of radiative equilibrium of an extended warm corona covering a non-dissipative accretion disk almost entirely. These results confirm that warm Comptonization is a valuable model that can explain the origin of the soft X-ray excess.

Quantitative evaluation of the computational accuracy for the Monte Carlo calculation of radiative heat transfer

Generally, there is no common method for directly and quantitatively evaluating computational errors in the calculation of radiative transfer. A method for quantitatively evaluating the accuracy in calculation of radiative transfer using the Monte Carlo method (MCM) is proposed, which is based on setting a radiative transfer enclosure in an isothermal and radiative equilibrium state, i.e. a state that equates exactly to a blackbody. For a gray emitting, absorbing, isotropically scattering, cubic enclosure bounded with diffusely emitting and reflecting surfaces, the computational accuracy and efficiency of the MCM are examined under fixed, constant surface emissivity of 0.5 and medium scattering albedo of 0.5. The concept of Mean Optical Thickness per Element (MOTE), that is the product of the absorption coefficient and the average length of three coordinate directions of the discrete space elements, is proposed to serve as a key scaling parameter to evaluate the calculation errors. When the MOTE is less than around 0.1, the errors for the surface elements reach a minimum level, even if the mesh density continues to increase. Scaling laws have been set up to relate the minimum errors for both the surface elements and space elements with the variation in the number of energy bundles (NEB). A desirable calculation error level is set as 1.0% for radiative heat transfer with an acceptable cost, for which the minimum NEBs are 3000 and 750 for the surface and space elements, respectively. For the surface elements, a scaling law relating the NEB and the maximum MOTE has been obtained that will enable the desirable error not to be exceeded; for the space elements, achieving the desirable error is dominated by the NEB, not the MOTE. It is stated that the cases studied in the paper have many limitations, and additional research should be done in the future to address the real cases of interest.

Decay rates of solutions to a P1-approximation model arising from radiation hydrodynamics

This paper is concerned with the global existence and large time behavior of solutions to Cauchy problem for a P1-approximation radiation hydrodynamics model. The global-in-time existence result is established in the small perturbation framework around a stable radiative equilibrium states in Sobolev space H4(R3). Moreover, when the initial perturbation is also bounded in L1(R3), the L2-decay rates of the solution and its derivatives are achieved accordingly. The proofs are based on the Littlewood–Paley decomposition techniques and elaborate energy estimates in different frequency regimes.

The Role of Eddy Diffusivity on a Poleward Jet Shift

Abstract The authors use a quasigeostrophic (QG) two-layer model to examine how eddies modify the meridional asymmetry of a zonal jet. The initial asymmetry is introduced in the model’s “radiative equilibrium state” and is intended to mimic a radiatively forced poleward jet shift simulated by climate models. The calculations show that the initial “poleward” jet shift in the two-layer model is amplified by eddy potential vorticity fluxes. This eddy-accentuation effect is greater as the baroclinicity of the equilibrium state is reduced, suggesting that seasonal variations in baroclinicity may help explain observed and modeled jet-shift sensitivity to season. The eddy-accentuated jet shift from the corresponding radiative equilibrium state is more clearly visible in the slowly varying, eddy-free reference state of Nakamura and Zhu. This reference state formally responds only to nonadvective, nonconservative processes, but ultimately arises from the advective eddy fluxes. The implication is that fast eddies are capable of driving a slowly varying jet shift, which may be balanced by nonconservative processes such as radiative heating/cooling.

Effects of Surface-Catalysis Efficiency on Aeroheating Characteristics in Hypersonic Flow

AbstractIn this paper, effects of the surface-catalysis efficiency on aeroheating characteristics are studied. The Navier–Stokes solver with a cell-centered finite-volume scheme, including the finite-rate chemistry and two-temperature thermal nonequilibrium models, is implemented in this work. The ELECTRE flight trajectory at 53 km is used for validating the developed solver. Several cases with different catalytic recombination coefficients are studied to investigate the effects of catalysis efficiency under the condition of radiative equilibrium for the C series of Radio Attenuation Measurement project II flight trajectory at 71 km. It is revealed that distributions of heat flux and wall temperature have the similar tendency for all cases except for the Stewart model. Heat flux and wall temperature do not grow endlessly as the catalytic recombination coefficients are increased. It is the gradient of species density rather than gradient of temperature that leads to the significant differences of heat flux...

Photophoresis on particles hotter/colder than the ambient gas for the entire range of pressures

Small, illuminated aerosol particles embedded in a gas experience a photophoretic force. Most approximations assume the mean particle surface temperature to be effectively the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field strongly differs from the gas temperature (optically thin gases), given approximations for the free molecule regime overestimate the photophoretic force by an order of magnitude on average and for individual configurations up to three magnitudes. We apply the radiative equilibrium condition from the previous paper (Paper 1) – where photophoresis in the free molecular flow regime was treated – to the slip flow regime. The slip-flow model accounts for thermal creep, frictional and thermal stress gas slippage and temperature jump at the gas–particle interface. In the limiting case for vanishing Knudsen numbers – the continuum limit – our derived formula has a mean error of only 4% compared to numerical values. Eventually, we propose an equation for photophoretic forces for all Knudsen numbers following the basic idea from Rohatschek by interpolating between the free molecular flow and the continuum limit.

Heroic: 3D general relativistic radiative post-processor with comptonization for black hole accretion discs

We describe HEROIC, an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in the short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic MHD simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below the photosphere in the multi-dimensional HEROIC solution is nearly isothermal, quite different from previous solutions based on 1D plane parallel atmospheres. The second application is to a geometrically thick radiation-dominated accretion disc accreting at 11 times the Eddington rate. The multi-dimensional HEROIC solution shows that, for observers who are on axis and look down the polar funnel, the isotropic equivalent luminosity could be more than ten times the Eddington limit, even though the spectrum might still look thermal and show no signs of relativistic beaming.

Effects of nonlinear gradient index on radiative heat transfer in a one-dimensional medium by the DRESOR method

The DRESOR (Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface) method is applied for radiative heat transfer in a one-dimensional medium with a nonlinear gradient index and gray boundary surfaces. In this proposed method, the DRESOR values calculated by the Monte Carlo method express quantitatively the impact of scattering on radiative transfer and the radiative intensity with high directional resolution of high precision can be easily obtained. With given media characteristics and boundary conditions, the temperature and radiative flux distributions inside the medium are calculated under the condition of radiative equilibrium. It is shown, in the cases studied, that the DRESOR method has a good accuracy. The temperature distributions have a node with different kinds of sine changed gradient index distributions under the same boundary emissivity. The impact of the gradient index on the radiative heat transfer is considerable, and the same as that of the ratios of its amplitude and average index. Besides, the effects of optical thickness, boundary emissivity and scattering phase function on radiative transfer also should be paid adequate attention.

Modeling of Gray Gas Radiation With Different Shapes of Heat Source in Three-Dimensional Enclosures

This article deals with performance evaluation of the discrete ordinates method in terms of its capacity to provide accurate results in solving radiation mode problems with different complexities. The problem formulation is done keeping in view the heat transfer process in an evaporator used in a coal-based thermal power station. The hot gas mass in the evaporator is assumed to be a heat source with two different shapes, spherical and conical. The evaporator walls that are covered with a water cooling jacket are modeled with a convective boundary condition. The gas is assumed to be gray and absorbing–emitting. The solution of the radiative transport equation is carried out using the discrete ordinates method. Parametric studies are performed for a wide range of aspect ratio, extinction coefficient, and convective heat transfer coefficient. The code is validated by comparing the result of discrete ordinates method with the exact and the discrete transfer method for nonradiative as well as radiative equilibrium conditions.

Development of an Urban Multilayer Radiation Scheme and Its Application to the Urban Surface Warming Potential

To investigate how a three-dimensional structure such as an urban canyon can affect urban surface warming, we developed an urban multilayer radiation scheme. The complete consideration of multiple scattering of shortwave and longwave radiation using the radiosity method is an important feature of the present scheme. A brief description of this scheme is presented, followed by evaluations that compare its results with observations of the effective albedo and radiative temperature for urban blocks. Next, we calculate the urban surface warming potential (USWP), defined as the difference between the daily mean radiative temperature of urban surfaces (which are assumed to be black bodies), including their canyon effects and the daily mean temperature of a flat surface with the same material properties, under a radiative equilibrium state. Assuming standard material properties (albedo and emissivity of 0.4 and 0.9, respectively), we studied the sensitivity of the USWP to various aspect ratios of building heights to road widths. The results show that the temporally-averaged surface temperature of an urban area can be higher than that of a flat surface. In addition, we determined the overestimation of the effective temperature of urban surfaces induced by the overestimation of the radiation distribution to the walls when one uses a single-layer scheme for urban block arrays that have a low sky-view factor less than around 0.5.

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.

Theoretical analysis of thermal radiative equilibrium via a radiosity method

AbstractWe propose a theoretical consideration of thermal radiative equilibrium via a radiosity method. According to G. Kirchhoff's research on cavity radiation, the condition of radiative equilibrium arises in a cavity in which the internal wall temperature is uniform. Furthermore, by considering the balance of energy on the wall surfaces in the cavity, the relationship, emittance ϵ = absorptance α, is obtained. Adversely, in the present study, we developed a method to prove the conclusion of the uniformity and uniqueness of radiative equilibrium in the cavity (independent of the emittance of the interior wall surfaces) by considering the relationship ϵ = α on the wall surfaces to be a supposition. Using the concept of radiosity, we proved that the radiosities on the internal wall surfaces can be kept uniform in the enclosed system of thermal radiative equilibrium. This knowledge is advantageous for inspecting the benchmarks of various programs for radiative analysis. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20372

Radiation thermo-chemical models of protoplanetary discs - III. Impact of inner rims on spectral energy distributions

We study the hydrostatic density structure of the inner disc rim around HerbigAe stars using the thermo-chemical hydrostatic code ProDiMo. We compare the Spectral Energy Distributions (SEDs) and images from our hydrostatic disc models to that from prescribed density structure discs. The 2D continuum radiative transfer in ProDiMo includes isotropic scattering. The dust temperature is set by the condition of radiative equilibrium. In the thermal-decoupled case the gas temperature is governed by the balance between various heating and cooling processes. The gas and dust interact thermally via photoelectrons, radiatively, and via gas accommodation on grain surfaces. As a result, the gas is much hotter than in the thermo-coupled case, where the gas and dust temperatures are equal, reaching a few thousands K in the upper disc layers and making the inner rim higher. A physically motivated density drop at the inner radius ("soft-edge") results in rounded inner rims, which appear ring-like in near-infrared images. The combination of lower gravity pull and hot gas beyond ~1 AU results in a disc atmosphere that reaches a height over radius ratio z/r of 0.1 while this ratio is 0.2 only in the thermo-coupled case. This puffed-up disc atmosphere intercepts larger amount of stellar radiation, which translates into enhanced continuum emission in the 3- 30 micron wavelength region from hotter grains at ~500 K. We also consider the effect of disc mass and grain size distribution on the SEDs self-consistently feeding those quantities back into the gas temperature, chemistry, and hydrostatic equilibrium computation.

Regime Transitions of Steady and Time-Dependent Hadley Circulations: Comparison of Axisymmetric and Eddy-Permitting Simulations

Abstract Steady-state and time-dependent Hadley circulations are investigated with an idealized dry GCM, in which thermal forcing is represented as relaxation of temperatures toward a radiative-equilibrium state. The latitude ϕ0 of maximum radiative-equilibrium temperature is progressively displaced off the equator or varied in time to study how the Hadley circulation responds to seasonally varying forcing; axisymmetric simulations are compared with eddy-permitting simulations. In axisymmetric steady-state simulations, the Hadley circulations for all ϕ0 approach the nearly inviscid, angular-momentum-conserving limit, despite the presence of finite vertical diffusion of momentum and dry static energy. In contrast, in corresponding eddy-permitting simulations, the Hadley circulations undergo a regime transition as ϕ0 is increased, from an equinox regime (small ϕ0) in which eddy momentum fluxes strongly influence both Hadley cells to a solstice regime (large ϕ0) in which the cross-equatorial winter Hadley cell more closely approaches the angular-momentum-conserving limit. In axisymmetric time-dependent simulations, the Hadley cells undergo transitions between a linear equinox regime and a nonlinear, nearly angular-momentum-conserving solstice regime. Unlike in the eddy-permitting simulations, time tendencies of the zonal wind play a role in the dynamics of the transitions in the axisymmetric simulation. Nonetheless, the axisymmetric transitions are similar to those in the eddy-permitting simulations in that the role of the nonlinear mean momentum flux divergence in the zonal momentum budget shifts from marginal in the equinox regime to dominant in the solstice regime. As in the eddy-permitting simulations, a mean-flow feedback—involving the upper-level zonal winds, the lower-level temperature gradient, and the poleward boundary of the cross-equatorial Hadley cell—makes it possible for the circulation fields to change at the transition more rapidly than can be explained by the steady-state response to the thermal forcing. However, the regime transitions in the axisymmetric simulations are less sharp than those in the eddy-permitting simulations because eddy–mean flow feedbacks in the eddy-permitting simulations additionally sharpen the transitions.

A Wave Amplitude Transition in a Quasi-Linear Model with Radiative Forcing and Surface Drag

Abstract A quasi-linear two-layer quasigeostrophic β-plane model of the interaction between a baroclinic jet and a single zonal wavenumber perturbation is used to study the mechanics leading to a wave amplitude bifurcation—in particular, the role of the critical surfaces in the upper-tropospheric jet flanks. The jet is forced by Newtonian heating toward a radiative equilibrium state, and Ekman damping is applied at the surface. When the typical horizontal scale is approximately the Rossby radius of deformation, the waves equilibrate at a finite amplitude that is comparable to the mean flow. This state is obtained as a result of a wave-induced temporary destabilization of the mean flow, during which the waves grow to their finite-equilibrium amplitude. When the typical horizontal scale is wider, the model also supports a state in which the waves equilibrate at negligible amplitudes. The transition from small to finite-amplitude waves, which occurs at weak instabilities, is abrupt as the parameters of the system are gradually varied, and in a certain range of parameter values both equilibrated states are supported. The simple two-layer quasi-linear setting of the model allows a detailed examination of the temporary destabilization process inherent in the large-amplitude equilibration. As the waves grow they reduce the baroclinic growth by reducing the vertical shear of the mean flow, and reduce the barotropic decay by reducing the mean potential vorticity gradient at the inner sides of the upper-layer critical levels. Temporary destabilization occurs when the reduction in barotropic decay is larger than the reduction in baroclinic growth, leading to a larger total growth rate. Ekman friction and radiative damping are found to play a major role in sustaining the vertical shear of the mean flow and enabling the baroclinic growth to continue. By controlling the mean flow potential vorticity gradient near the critical level, the model evolution can be changed from one type of equilibration to the other.

A CODE FOR CALCULATING STATIC MODEL STELLAR ATMOSPHERES

In this paper we present an independent FORTRAN code for calculating LTE-plane-parallel model atmospheres. The transfer equation has been solved using Avrett and Loeser method. It is shown that, using an approximate non-gray temperature distribution together with the iteration factors method (Simonneau and Crivellari) for correcting the temperature distribution reduce the number of iteration required to achieve the condition of radiative equilibrium. Preliminary results for pure helium model atmospheres are presented.

Upper thermal boundary layer of planetary atmosphere: An attempt of developing a general model

In any planetary atmosphere there is an uppermost layer in which the molecular thermal conduction is a significant mechanism of forming the thermal structure of the atmosphere. In this paper, the similarity approach is first used to develop the 1-D general model of aforementioned layer. The main concepts of the model are (i) the radiative equilibrium condition at the lower boundary of the layer and (ii) taking into account a single rovibrational band for radiative cooling of the layer. Five dimensionless parameters of the model characterize both “strengths” and altitudinal distributions of heat sources and sinks in the layer, including an effect of the atmosphere under the layer. By fitting the modeled temperature profile to the mean empirical profile, both the magnitudes of the parameters and the relations between them have been determined for the Earth and Mars. Distinctions between these planets in both the parameter magnitudes and relationships can be accounted for by distinction in composition of their atmospheres. For both planets the model shows weak sensitivity of the modeled temperature profile to significant changes in the state of the underlying atmosphere. The model demonstrates some prognostic capabilities. Namely, the fitting reveals presence of O in the martian thermosphere. (However, the fractional O abundance is overestimated.) From drag deceleration of the MGS orbiter the mean temperature profile of the martian thermosphere between 115 and 170 km has been derived for the solar zenith angle of 45°–70°, the solar longitude of 30°–80°, and the latitude range from −10° to 60°at a moderate level of solar activity.

Energy transport, overshoot, and mixing in the atmospheres of M-type main- and pre-main-sequence objects

We constructed hydrodynamical model atmospheres for mid M-type main-, as well as pre-main-sequence (PMS) objects. Despite the complex chemistry encountered in these cool atmospheres a reasonably accurate representation of the radiative transfer is possible, even in the context of time-dependent and three-dimensional models. The models provide detailed information about the morphology of M-type granulation and statistical properties of the convective surface flows. In particular, we determined the efficiency of the convective energy transport, and the efficiency of mixing by convective overshoot. The convective transport efficiency was expressed in terms of an equivalent mixing-length parameter alpha in the formulation of mixing-length theory (MLT) given by Mihalas (1978). Alpha amounts to values around 2 for matching the entropy of the deep, adiabatically stratified regions of the convective envelope, and lies between 2.5 and 3.0 for matching the thermal structure of the deep photosphere. For current spectral analysis of PMS objects this implies that MLT models based on alpha=2.0 overestimate the effective temperature by 100 K and surface gravities by 0.25 dex. The average thermal structure of the formally convectively stable layers is little affected by convective overshoot and wave heating, i.e., stays close to radiative equilibrium conditions. Our models suggest that the rate of mixing by convective overshoot declines exponentially with geometrical distance to the Schwarzschild stability boundary. It increases at given effective temperature with decreasing gravitational acceleration.