The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation

Shettle, E. P.; Weinman, J. A.

doi:10.1175/1520-0469(1970)027<1048:ttosit>2.0.co;2

Cited by 163 publications

(68 citation statements)

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“…The coefficients A n and B n are determined by solving the system, which allows explicit calculation of the diffuse irradiance at any depth. The two-stream method has been extensively described (Shettle and Weinman, 1970;Wiscombe, 1977;Toon et al, 1989). The total irradiance is obtained by summing the The Cryosphere, 7, 1803-1818, 2013…”

Section: Extension To a Multi-layer Snowpack Using The Eddington Apprmentioning

confidence: 99%

Influence of grain shape on light penetration in snow

Libois

Picard²,

France³

et al. 2013

The Cryosphere

193

284

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Abstract. The energy budget and the photochemistry of a snowpack depend greatly on the penetration of solar radiation in snow. Below the snow surface, spectral irradiance decreases exponentially with depth with a decay constant called the asymptotic flux extinction coefficient. As with the albedo of the snowpack, the asymptotic flux extinction coefficient depends on snow grain shape. While representing snow by a collection of spherical particles has been successful in the numerical computation of albedo, such a description poorly explains the decrease of irradiance in snow with depth. Here we explore the limits of the spherical representation. Under the assumption of geometric optics and weak absorption by snow, the grain shape can be simply described by two parameters: the absorption enhancement parameter B and the geometric asymmetry factor g G . Theoretical calculations show that the albedo depends on the ratio B/(1−g G ) and the asymptotic flux extinction coefficient depends on the product B(1 − g G ). To understand the influence of grain shape, the values of B and g G are calculated for a variety of simple geometric shapes using ray tracing simulations. The results show that B and (1 − g G ) generally covary so that the asymptotic flux extinction coefficient exhibits larger sensitivity to the grain shape than albedo. In particular it is found that spherical grains propagate light deeper than any other investigated shape. In a second step, we developed a method to estimate B from optical measurements in snow. A multi-layer, two-stream, radiative transfer model, with explicit grain shape dependence, is used to retrieve values of the B parameter of snow by comparing the model to joint measurements of reflectance and irradiance profiles. Such measurements were performed in Antarctica and in the Alps yielding estimates of B between 0.8 and 2.0. In addition, values of B were estimated from various measurements found in the literature, leading to a wider range of values (1.0-9.9) which may be partially explained by the limited accuracy of the data. This work highlights the large variety of snow microstructure and experimentally demonstrates that spherical grains, with B = 1.25, are inappropriate to model irradiance profiles in snow, an important result that should be considered in further studies dedicated to subsurface absorption of short-wave radiation and snow photochemistry.

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Section: Extension To a Multi-layer Snowpack Using The Eddington Apprmentioning

confidence: 99%

Influence of grain shape on light penetration in snow

Libois

Picard²,

France³

et al. 2013

The Cryosphere

193

284

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“…For constant ω 0 and g the delta-Eddington equation can be solved analytically (Shettle and Weinman, 1970;Joseph et al, 1976):…”

Section: The Delta-eddington Model For Shortwave Radiative Transfermentioning

confidence: 99%

Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and overview of its applications

et al. 2010

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Abstract. The current version of the Dutch AtmosphericLarge-Eddy Simulation (DALES) is presented. DALES is a large-eddy simulation code designed for studies of the physics of the atmospheric boundary layer, including convective and stable boundary layers as well as cloudy boundary layers. In addition, DALES can be used for studies of more specific cases, such as flow over sloping or heterogeneous terrain, and dispersion of inert and chemically active species. This paper contains an extensive description of the physical and numerical formulation of the code, and gives an overview of its applications and accomplishments in recent years.

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“…He uses two approximate methods, two-stream and delta Eddington. The impact of clouds on the irradiance is examined by Shettle and Weinman [1970], who utilize the Eddington approximation. We will discuss a more accurate method for calculating the actinic flux and irradiance in a vertically inhomogeneous atmosphere with anisotropic, nonconservative scatterers.…”

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confidence: 99%

Enhancement of atmospheric radiation by an aerosol layer

Michelangeli¹,

Allen²,

Yung³

et al. 1992

J. Geophys. Res.

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The presence of a stratospheric haze layer may produce increases in both the actinic flux and the irradiance below this layer. Such haze layers result from the injection of aerosol-forming material into the stratosphere byvolcanic eruptions. Simple heuristic arguments show that the increase in flux below the haze layer, relative to a clear sky case, is a consequence of "photon trapping. Consider a stratospheric H2SO4 aerosol layer formed by a volcanic eruption. This can be modeled as a nearly conservatively scattering layer in a Rayleigh-scattering atmosphere (layer B in Figure 1). Intuition suggests that the introduction of the scattering would lead to an increase in the actinic flux above the aerosol layer (region A in Figure 1) due to back scattering, or within the aerosol layer (region B) due to multiple scattering. However, we might not expect increases in the actinic flux beneath the aerosol layer (region C), for the following reasons. In region C there is additional actinic flux due to multiple scattering by the aerosol layer B, but we can argue that this flux is originally in the direct solar beam. It has been removed by layer B, which redistributes the radiation into the backward direction (region A) and the forward direction (region C). Therefore it follows that the sum of the attenuated direct solar flux and the diffuse actinic flux in region C should not exceed the original actinic flux when the aerosol layer is absent. We might also anticipate that the absolute value of the irradiance would decrease at the surface with the introduction of the aerosol layer, reflecting the loss to space of backscattered photons. (In this paper, variation of the irradiance or its components will be discussed always with regard to absolute values.)We will show, however, that under certain circumstances the actinic flux below the aerosol layer can increase without violating conservation of photons and under special conditions the irradiance also can increase below the aerosol layer, with respect to the clear sky situation. Our new radiative transfer model is described and utilized to explore the effects of aerosols.

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The Transfer of Solar Irradiance Through Inhomogeneous Turbid Atmospheres Evaluated by Eddington's Approximation

Cited by 163 publications

References 0 publications

Influence of grain shape on light penetration in snow

Influence of grain shape on light penetration in snow

Formulation of the Dutch Atmospheric Large-Eddy Simulation (DALES) and overview of its applications

Enhancement of atmospheric radiation by an aerosol layer

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