Thin cadmium sulphide film for radiative cooling application

The present work reports the possibility of a specific shield (CdS) to provide passive cooling for the purpose of reducing the use of classical active method. The ideal radiation shield would completely block solar radiation, but allow complete transmission in the “atmospheric-window” region.Chemical solution deposition of the thin film CdS (1 mm) for radiative cooling is described and optical properties of the thin film were measured by an OL-750 Spectroradiometer. The radiative properties of the shield improved optical properties of cooling purposes; which indicates that it has very low IR band reflectance and is transparent across the full 8-13 μm.     

Infrared radiative transfer in planetary atmospheres—I. Effects of computational and spectroscopic economies on thermal heating/cooling rates

The availability of accurate spectroscopic data and improved knowledge of continuum absorption characteristics has required a further detailed study of i.r. radiative transfer. A sophisticated radiative transfer scheme based upon the Mayer-Goody random band model is developed and the derived transmissivities for H₂O, CO₂ and O₃ are calibrated against laboratory measurements. This calibrated scheme is used to assess the effects on calculated heating/cooling rate profiles of introducing computational and spectroscopic economies.     

Multiple size group analysis for transient radiative heating of particle polydispersions

The transient radiative heating of particle polydispersions initially at uniform temperature is numerically analyzed. Due to the different radiative heating characteristics between particles, the temperature evolution of particle changes with particle diameter. To take local thermal nonequilibrium between particles into consideration, the particles are discretized into several size groups. The radiative transfer equation in particle polydispersions and the transient energy equation for each particle group are solved by the discrete ordinates method and an implicit finite difference method, respectively. The effects of the standard deviation of particle diameter and the emissivity of particle surface on the thermal evolution of particle polydispersions are analyzed. The results show that, omitting thermal nonequilibrium of particles will result in significant errors in the calculation of radiative heat transfer, especially when the nonuniformity of particle diameter is large.     

Atmospheric weighting functions and surface partial derivatives for remote sensing of scattering planetary atmospheres in thermal spectral region: general adjoint approach

An approach to formulation of inversion algorithms for remote sensing in the thermal spectral region in the case of a scattering planetary atmosphere, based on the adjoint equation of radiative transfer (Ustinov (JQSRT 68 (2001) 195; JQSRT 73 (2002) 29); referred to as Papers 1 and 2, respectively, in the main text), is applied to the general case of retrievals of atmospheric and surface parameters for the scattering atmosphere with nadir viewing geometry. Analytic expressions for corresponding weighting functions for atmospheric parameters and partial derivatives for surface parameters are derived. The case of pure atmospheric absorption with a scattering underlying surface is considered and convergence to results obtained for the non-scattering atmospheres (Ustinov (JQSRT 74 (2002) 683), referred to as Paper 3 in the main text) is demonstrated.     

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.     

The NEMESIS planetary atmosphere radiative transfer and retrieval tool

With the exception of in situ atmospheric probes, the most useful way to study the atmospheres of other planets is to observe their electromagnetic spectra through remote observations, either from ground-based telescopes or from spacecraft. Atmospheric properties most consistent with these observed spectra are then derived with retrieval models. All retrieval models attempt to extract the maximum amount of atmospheric information from finite sets of data, but while the problem to be solved is fundamentally the same for any planetary atmosphere, until now all such models have been assembled ad hoc to address data from individual missions.In this paper, we describe a new general-purpose retrieval model, Non-linear Optimal Estimator for MultivariatE Spectral analySIS (NEMESIS), which was originally developed to interpret observations of Saturn and Titan from the composite infrared spectrometer on board the NASA Cassini spacecraft. NEMESIS has been constructed to be generally applicable to any planetary atmosphere and can be applied from the visible/near-infrared right out to microwave wavelengths, modelling both reflected sunlight and thermal emission in either scattering or non-scattering conditions. NEMESIS has now been successfully applied to the analysis of data from many planetary missions and also ground-based observations.     

Linearization of radiative transfer with respect to surface properties

The linearization of radiative transfer with respect to surface properties in the UV and visible part of the solar spectrum is presented. The proposed method is a rigorous extension of the radiative perturbation theory with respect to surface properties. Given the forward and adjoint intensity field, analytical expressions are provided for the linearization of any observable related to the radiation field with respect to surface properties characterized by Minnaert's and Lambertian bidirectional reflection distribution function. For the considered surface reflection characteristics, we also discuss an extension of the reduction approach of Chandrasekhar as an alternative linearization method. The suitability of both approaches for the combined retrieval of trace gas and surface properties from the backscattered sunlight in the UV and visible part of the spectrum is discussed. The authors come to the conclusion that the perturbation theory, for this purpose, represents the superior method because of its general applicability to any parameter characterizing the optical properties of the atmosphere and the underlying surface.     

A retrospective view on “algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation” by Teruyuki Nakajima and Masayuki Tanaka (1988)

I explain the motivation behind our paper “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation” (JQSRT 1988;40:51-69) and discuss our results in a broader historical context.     

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.     

Scaling algorithms for the calculation of solar radiative fluxes

We derived new scaling formulae based on the method of successive orders of scattering to calculate solar radiative flux. In this report, we demonstrate a multiple scaling method, in which we introduce scaling factors for each scattering order independently. The formula of radiative transfer by the method of successive orders of scattering cannot be solved rapidly except in the case of optically thin atmospheres. Then we further derived a double scaling method, which scales the ordinary radiative transfer equation by two scaling factors. We applied the double scaling method to two-stream and four-stream approximations of the discrete ordinates method. Comparing the results of the double scaling method with those of the delta-M method, we found that the double scaling method improved the accuracy of radiative fluxes at large solar zenith angles, especially in the optically thin region, and that in the region where multiple scattering dominates, its accuracy was comparable to that of the delta-M method. Once we determined the scaling factors appropriately, the double scaling method calculated radiative fluxes as rapidly as the delta-M method in the two-stream and four-stream approximations. This method, therefore, is useful for accurate computation of solar radiative fluxes in general circulation models.     

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres - except for two methods limited to narrow angle lidars - the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.     

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.     

Switching of heating and cooling modes using thermal radiation films

We study emissivity (ε)-dependent radiative heat transfer phenomena in remote and contact configurations. To demonstrate the emissivity-dependent radiative heating mode in a remote configuration, we fabricated miniature greenhouses covered with low (0.34)- and high-ε (0.86) polyethylene films and monitored temperatures on the floors, insides, and covers of the greenhouses during 24 h. The high-ε greenhouse yielded a 9-°C increase in floor temperature relative to the low-ε greenhouse at a one-sun solar irradiance because the high-ε film effectively trapped floor radiation. In contrast, the cover temperature remained lower in the high-ε greenhouse due to intensified radiation released from the high-ε film. This self-cooling effect was more evident when an emissive film was in physical contact with an object. While bare copper heated up to 55 °C, a high-ε film coated copper substrate was kept cooler by 4 and 2 °C compared with the bare and low-ε film coated copper samples, respectively.     

Generalized form of the direct and adjoint radiative transfer equations

The main goal of this paper is to give a rigorous derivation of the generalized form of the direct (also referenced as forward) and adjoint radiative transfer equations. The obtained expressions coincide with expressions derived by Ustinov [Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211]. However, in contrast to [Ustinov EA. Adjoint sensitivity analysis of radiative transfer equation: temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR. JQSRT 2001;68:195-211] we formulate the generalized form of the direct radiative transfer operator fully independent from its adjoint. To illustrate the application of the derived adjoint radiative transfer operator we consider the angular interpolation problem in the framework of the discrete ordinate method widely used to solve the radiative transfer equation. It is shown that under certain conditions the usage of the solution of the adjoint radiative transfer equation for the angular interpolation of the intensity can be computationally more efficient than the commonly used source function integration technique.     

Robust and accurate filtered spherical harmonics expansions for radiative transfer

We present a novel application of filters to the spherical harmonics (P_N) expansion for radiative transfer problems in the high-energy-density regime. The filter we use is based on non-oscillatory spherical splines and a filter strength chosen to (i) preserve the equilibrium diffusion limit and (ii) vanish as the expansion order tends to infinity. Our implementation is based on modified equations that are derived by applying the filter after every time step in a simple first-order time integration scheme. The method is readily applied to existing codes that solve the P_N equations. Numerical results demonstrate that the solution to the filtered P_N equations are (i) more robust and less oscillatory than standard P_N solutions and (ii) more accurate than discrete ordinates solutions of comparable order. In particular, the filtered P₇ solution demonstrates comparable accuracy to an implicit Monte Carlo solution for a benchmark hohlraum problem in 2D Cartesian geometry.     

Comparison of the radiative transfer equations for constant and spatially varying refraction

The radiative transfer equation for scattering media with constant refraction index (RTE) and the radiative transfer equation for scattering media with spatially varying refraction index (RTEvri) are compared by using the principle of conservation of energy. It is shown that the RTEvri, not only accounts for the spatial variations of refraction index, but also contains a term that accounts for the divergence of the rays. The latter term is missing in the RTE. A corrected RTE is proposed.     

Computation of Green's function for radiative transfer

In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented.     

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.     

A quasi-analytic solution of the radiative transfer equation for three-dimensional atmospheres

In this study, we present a new solution of the three-dimensional (3-D) radiation transfer equation (RTE). The solution employs a discretization technique to separate the independent variables involved in the 3-D RTE, and the doubling-adding method to solve the RTE explicitly and quasi-analytically. The remarkable feature of the present solution is the application of scaling-function expansion to those terms that are dependent on horizontal coordinates. Scaling-function expansion is suitable for representing irregular horizontal inhomogeneities with small-scale variations. By applying scaling-function expansion, the 3-D RTE can be formulated in the form of a vector-matrix differential equation; matrices involved in the equation are generally sparse and dominantly diagonal matrices, and this considerably reduces the labor involved in matrix calculations. We tested the performance of the present solution via radiative transfer calculations of solar radiation in horizontally inhomogeneous two-dimensional cloud models. The calculated results indicate that even if the resolution of the scaling-function expansion is too coarse in regions around small-scale variations, the influence does not spread problematically to other regions far from the variations; this illustrates the advantage of the scaling-function expansion. The present solution can be used to investigate quantitatively and to estimate the effects of cloud spatial inhomogeneity on the corresponding radiation field.