Solar Radiative Transfer Research Articles

Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium

Abstract We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and...

Radiation transfer in plant canopies: Transmission of direct solar radiation and the role of leaf orientation

Understanding the details of the interaction between the radiation field and plant structures is important climatically because of the influence of vegetation on the surface water and energy balance, but also biologically, since solar radiation provides the energy necessary for photosynthesis. The problem is complex because of the extreme variety of vegetation forms in space and time, as well as within and across plant species. This one‐dimensional vertical multilayer model describes the transfer of direct solar radiation through a leaf canopy, accounting explicitly for the vertical inhomogeneities of a plant stand and leaf orientation, as well as heliotropic plant behavior. This model reproduces observational results on homogeneous canopies, but it is also well adapted to describe vertically inhomogeneous canopies. Some of the implications of leaf orientation and plant structure as far as light collection is concerned are briefly reviewed.

TEMPERATURE DISTRIBUTION IN CONCRETE WALL UNDER SOLAR RADIATION

The temperature distribution in concrete wall is calculated as an one-dimensional problem of heat conduction. The flux of heat from the wall surface is considered to be three components, i. e. solar radiation and heat transfer of convection and emission. The results are compared with the observed temperature in a model tank and three real water tanks. Fairly good agreement independent of place, date, direction and inclination confirm the propriety of the calculating process.Some information on the highest surface temperature are obtained referring to the direction of the wall, the absorption coefficient of solar radiation and the correction factor to atmospheric transmissivity.

Theoretical study of a composite Trombe-Michel wall solar collector system

In this study, the transfer of solar radiation in a composite Trombe-Michel wall solar collector system is studied theoretically. The composite system consists of a glazing, a massive wall, and an insulating wall put together without a convection channel between glazing and wall and with one between massive and insulating walls. It is an improvement over the simple nonconvective Trombe-Michel wall solar collector system with a relatively low thermal resistance, which is taken as a reference. The theoretical results indicate that the composite system can indeed perform better in cold and/or cloudy climates than the reference system and that optimum geometrical parameters can be determined depending on the dwelling type and climatic conditions of the area. The new system has a reduced massive wall thickness that is a desirable feature for lightweight constructions.

Design and performance analysis of a solar pond power plant

This paper reports on a study for the design and performance analysis of a solar pond power plant for a site of known geographical and atmospheric conditions. Modelling and thermal analysis of the pond are carried out, including treatment of solar radiation transfer. The factors affecting selection of the optimum ORC power loop are also discussed, and overall system performance analysis is carried out under varying load conditions.

Matrix formulations for the transfer of solar radiation in a plane-parallel scattering atmosphere

Matrix formulations are presented for the discrete-ordinate and the matrix-operator methods of solving the transfer of solar radiation in a plane-parallel scattering atmosphere. Eigenspace transformations of symmetric matrices are introduced into the method of Stamnes and Swanson instead of using the decomposition of an asymmetric matrix. The computational stability is considerably improved by this algorithm, especially for single-precision calculations. Representations of the reflection and transmission matrices in the matrix-operator method are also given, in terms of the indicated formulations, by considering a boundary-value problem of the discrete-ordinate method. The solutions of the discrete-ordinate method for inhomogeneous atmospheres are given by combining discrete-ordinate solutions for respective homogeneous sublayers through the addition technique of the matrix-operator method.

Role of Debris Cover in the Thermal Physics of Glaciers

AbstractA mathematical model is presented of non-stationary melting processes of ice including particles of morainic material. The problem is treated as a Stephen-type one with the phase boundary of ice melting being located under the debris cover. The main terms of the heat-balance equation for a glacier surface are solar radiation and convective heat transfer. The quantitative relationships characterizing the effect of glacier run-off augmentation from under a thin layer of debris cover are obtained for different bulk moraine concentrations inside the ice. The concept of equivalent time is introduced. It is defined as the time elapsed until the moment the sub-moraine ice-ablation rate becomes equal to the ablation rate of clean ice. This moment signifies the beginning of the shielding stage. Thus, a glacier can be considered as a self-controlling system with respect to its summer run-off. A series of numerical tests for Djankuat glacier, Central Caucasus, has been carried out. The dynamics of moraine-cover growth and alterations of seasonal ablation rate under debris show perfect agreement between the computed data and the results of 14 years of direct observations. Some practical recommendations concerning artificial blackening of a glacier surface for augmentation of liquid run-off are presented. Conditions promoting increase of run-off are: relatively high albedo, relatively low summer air temperature, and relatively small convective heat transfer between the air and the ice surface. The method of artificially blackening a glacier surface is by means of a durable thin dark polymer film. In conclusion, some further aspects of the problem are discussed.

Role of Debris Cover in the Thermal Physics of Glaciers

AbstractA mathematical model is presented of non-stationary melting processes of ice including particles of morainic material. The problem is treated as a Stephen-type one with the phase boundary of ice melting being located under the debris cover. The main terms of the heat-balance equation for a glacier surface are solar radiation and convective heat transfer. The quantitative relationships characterizing the effect of glacier run-off augmentation from under a thin layer of debris cover are obtained for different bulk moraine concentrations inside the ice. The concept of equivalent time is introduced. It is defined as the time elapsed until the moment the sub-moraine ice-ablation rate becomes equal to the ablation rate of clean ice. This moment signifies the beginning of the shielding stage. Thus, a glacier can be considered as a self-controlling system with respect to its summer run-off. A series of numerical tests for Djankuat glacier, Central Caucasus, has been carried out. The dynamics of moraine-cover growth and alterations of seasonal ablation rate under debris show perfect agreement between the computed data and the results of 14 years of direct observations. Some practical recommendations concerning artificial blackening of a glacier surface for augmentation of liquid run-off are presented. Conditions promoting increase of run-off are: relatively high albedo, relatively low summer air temperature, and relatively small convective heat transfer between the air and the ice surface. The method of artificially blackening a glacier surface is by means of a durable thin dark polymer film. In conclusion, some further aspects of the problem are discussed.

Optical properties of soda lime silica glasses

A comprehensive set of optical constants and a partial set of bulk optical properties are listed for clear, absorbing, and low-iron glasses used for windows. The measurements extend from the near ultraviolet to the far infrared, covering the range of interest for calculating solar and thermal radiative transfer through windows. This information is also needed to calculate the properties of thin-film coatings on glass substrates. Large variations in solar absorption are observed among these glasses, whereas the far-infrared properties are almost constant for all glass types. An important quantity, the hemispherical total emissivity, is 0.837 at 20°C, as determined from reflectance data measured with an IBM Fourier-transform spectrometer. Solar properties are determined from conventional transmission and reflection measurements.

Coupled atmosphere/canopy model for remote sensing of plant reflectance features

Solar radiative transfer through a coupled system of atmosphere and plant canopy is modeled as a multiple-scattering problem through a layered medium of random scatterers. The radiative transfer equation is solved by the discrete-ordinates finite-element method. Analytic expressions are derived that allow the calculation of scattering and absorption cross sections for any plant canopy layer from measurable biophysical parameters such as the leaf area index, leaf angle distribution, and individual leaf reflectance and transmittance data. An expression for a canopy scattering phase function is also given. Computational results are in good agreement with spectral reflectance measurements directly above a soybean canopy, and the concept of greenness- and brightness-transforms of Landsat MSS data is reconfirmed with our computed results. A sensitivity analysis with the coupled atmosphere/canopy model quantifies how satellite-sensed spectral radiances are affected by increased atmospheric aerosols, by varying leaf area index, by anisotropic leaf scattering, and by non-Lambertian soil boundary conditions. Possible extensions to a 2-D model are also discussed.

Transparent insulation

Efficient passive or active use of solar energy is mainly a problem of transparent insulation. The requirements are, high transmission for solar radiation and low heat transfer coefficient. This paper deals with the theoretical limits of transparent insulation and with new transparent insulating materials. We divide transparent insulation into materials with structures parallel and perpendicular to the outer and inner cover and homogeneous materials. The perpendicular structures (‘honeycomb’) have the advantage of high transmission for solar radiation. Our best already commercially fabricated material has a heat transfer coefficient k = 1 Wm −2 K −1 with a transmission higher than 65%.

Solar and terrestrial parameterizations for radiative-convective models

We present a radiative-convective modelling technique with parameterizations, for both solar and terrestrial radiation transfer, which allow the rapid computation of the mean vertical temperature profile from the ground to the thermosphere. Our method has been specifically designed for modelling the evolution of the Earth's mean vertical temperature structure due to changes in atmospheric composition, variations in the solar flux, surface albedo, cloud cover, water vapour and lapse rate, and changes in the temperature of the thermosphere which is associated with solar activity.

A Two-Dimensional Radiation-Turbulence Climate Model. I: Sensitivity to Cirrus Radiative Properties

Based on the thermodynamic energy balance between radiation and vertical plus horizontal dynamic transports, a two-dimensional radiation-turbulence climate model is developed. This model consists of a broadband solar and IR radiation transfer scheme previously presented by the authors and vertical and horizontal dynamic eddy transports utilizing the elementary turbulent theory. In the model, three kinds of feedback mechanisms are considered: the humidity feedback via the constant relative humidity assumption, the ice-albedo feedback via a preliminary correlation between the surface albedo and the surface temperature and the dynamic transport feedback through the parameterization of eddy transports and the prescribed mean wind field. A standard temperature field, which differs from the climatological data by no more than 0.1°C, is first obtained by solving the coupled thermodynamic and surface flux budget equations using climatological distributions of H2O, CO2, O3, surface albedo and cloud properties. The model-derived atmospheric radiation budget, surface energy balance and horizontal transport patterns compare reasonably well with available observational data. Further validation of the model includes sensitivity studies on the effects of doubling of CO2 and a 2% increase in the solar constant. The temperature changes relative to the standard field on these experiments agree closely with those presented by Manabe and Wetherald utilizing a general circulation model. To investigate the two-dimensional cirrus–radiation interaction, a relationship between the cirrus IR emissivity and solar reflectance (and transmittance) is established based on the parameterization equations. On the basis of a number of experiments involving various couplings and feedbacks, we find that 1) the humidity and albedo feedbacks are most active in the tropics and arctic area, respectively, 2) the dynamic transport is a negative feedback in the equatorial and polar regions but a positive one in midlatitudes and 3) the relative importance of each feedback depends only slightly on the radiative properties of cirrus. Finally, we demonstrate that slight variations in the cirrus IR emissivity lead to significant temperature perturbations in the arctic surface and tropical troposphere.

A Fast Solar Radiation Transfer Code for Application in Climate Models

A method is presented for the calculation of solar heating rates in turbid and cloudy atmospheres. In contrast to other typical two-stream procedures, the system of differential equations describing the radiative transfer is decoupled through the application of a series expansion of the flux densities resulting in a single analytical expression for each flux. The present method (PM) yields a solution for the entire atmosphere instead of individual atmospheric layers. This procedure avoids as part of the solution scheme the inversion of a rather complex matrix thus resulting in high numerical efficiency. The model includes the absorption by atmospheric gases such as water vapor, CO2, O3 and NO2. This list can be extended if desired. Moreover absorption by aerosols and cloud particles is accounted for in addition to multiple scattering. A comparison with the rather accurate and already efficient transfer code of Zdunkowski et al. [6] shows that the present method is similarly accurate but numerically even more efficient. Therefore, this radiation scheme becomes very suitable for use in some circulation models of the atmosphere, such as prediction models of radiation fog.[/p]

Effect of wind-generated waves on the transfer of solar radiation in the atmosphere-ocean system

Transfer of solar radiation in the combined atmosphere and ocean system is evaluated by the matrix operator method. Derivation of the reflection and transmission matrices required for applying the matrix method is discussed introducing the shadowing effect of light by the ocean waves. Spectral and total radiation fields just above and below the ocean surface, as well as the top of the atmosphere, are numerically calculated using several optical models of the atmosphere, ocean, and wind roughened ocean surface. Dependencies of radiance and flux reflectivity on the wind velocity and optical property of the ocean body are discussed in detail.

光学的に非等方性の氷晶雲における太陽放射伝達

光学的に非等方性の氷晶雲における太陽放射伝達

A multi-fluid model of an H2O-dominated dusty cometary atmosphere

A self-consistent multi-fluid solution of the dynamical and thermal structure of an H2O-dominated, two-phase dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy, together with the transfer of solar radiation in streams responsible for the major photolytic processes and the heating of the nucleus. The validity of this model, as in the earlier single-fluid ones, is restricted to the collision-dominated region where all the heavy species (ions and neutrals) are assumed to achieve a common temperature and velocity. However, recognizing that the photo-produced hydrogen is rather inefficient in exchanging energy with the heavier species we treat the hydrogen separately: it is assumed to be composed of a thermalized component (the second fluid) and a pre-thermal component.

Effects of aerosols on photosynthesis

Air pollution can cause various problems to agriculture through its direct or indirect effects on plants1,2. The net effects of air pollution on agricultural crop yields are very difficult to estimate quantitatively, and are generally considered secondary to the effects of fertilizers or chemical disease control measures. However, continually increasing air pollution may represent a persistent and largely irreversible threat to agriculture in the future. Here we have examined only one indirect aerosol effect on agricultural plant life—the reduction in photosynthetically active radiation (PAR) reaching the ground in the presence of significant air pollution. This effect can be quantified confidently from results of detailed model calculations of the transfer of solar radiation through the atmosphere with varying levels of air pollution. For the biologically effective wavelength region between 0.35 and 0.72 µm, the reductions in PAR due to increasing tropospheric aerosol loads have been determined for rural and urban pollution scenarios. For example, for the northeastern United States during the summer months, a reduction in PAR of about 20% and 33% was obtained when the visual range due to rural and urbtn aerosols, respectively, was decreased from clear air conditions to 10 km.

The photochemistry and dynamics of a dusty cometary atmosphere

A self-consistent solution of the dynamical and thermal structure of an H2O-dominated, two-phase, dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy together with the transfer of solar radiation in the streams responsible for the major photolytic processes and the heating of the nucleus. The validity of the model is restricted to the collision-dominated region where all the gas species are assumed to attain a common velocity and common temperature. Two models are considered for the transfer of solar radiation through the circum-nuclear dust halo. In the first only the direct extinction by the dust is considered. In the second, the finding of some recent models, that the diffuse radiation field due to multiple scattering by the dust halo more or less compensates for radiation removed by direct absorption when the optical depth is near unity, is approximated by neglecting the attenuation of the radiation by the dust altogether.

The effects of isotropic multiple scattering and surface albedo on the photochemistry of the troposphere

A recent paper (Anderson and Meier, 1979) critically evaluated the treatment of the transfer of incoming solar radiation into and through the cloudless troposphere in most photochemical models of the troposphere. They concluded that the one- and two-stream approximations used in these models are poor representations of the radiation field. A one-dimensional global photochemical model of the troposphere has been coupled to a radiative transfer model that includes the effects of isotropic multiple scattering, pure absorption and ground albedo on the transfer of incoming solar radiation through the cloudless troposphere. The results obtained using the more realistic treatment of the radiation field are compared with results using the Leighton approximation, a one-stream approximation used in tropospheric photochemical models. Significant differences in the vertical profiles of several key tropospheric species were found. The tropospheric profiles of excited oxygen atom, O( 1D) and the hydroxyl radical, OH, were found to increase by about a factor of three when multiple scattering was included and a ground albedo of 0.25 was used. Even higher values of these species were found for higher ground albedos. The vertical distribution of ozone photolysis frequency calculated with the multiple scattering code are compared to some recent measurements.