Two-Stream Approximations to Radiative Transfer in Planetary Atmospheres: A Unified Description of Existing Methods and a New Improvement

Meador, W. E.; Weaver, W. R.

doi:10.1175/1520-0469(1980)037<0630:tsatrt>2.0.co;2

Cited by 513 publications

(378 citation statements)

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“…mi l t-, of Tho, Wit IMAL PAGE IS OP POOR QUALITY delta-two-stream (Schaller, 1979) and hybrid (Meador and Weaver, 1980) approximations. The results are shown in Figure 4.3.…”

Section: Spectral Reflectance Of Snowmentioning

confidence: 99%

“…Note that inclusion of the surface reflection in the delta-Eddingtro, approximation essentially brings out this relation. Ti)e hybrid approximation, however, has been found to give inaccurate angular variation of albede for thick perfect scattering media (see figure 4 in Meador and Weaver, 1980). In the visible region snow is an almost pure scattering medium.…”

Section: Spectral Reflectance Of Snowmentioning

confidence: 99%

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The albedo of snow for partially cloudy skies

Choudhury

Chang

1981

Boundary-Layer Meteorol

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“…mi l t-, of Tho, Wit IMAL PAGE IS OP POOR QUALITY delta-two-stream (Schaller, 1979) and hybrid (Meador and Weaver, 1980) approximations. The results are shown in Figure 4.3.…”

Section: Spectral Reflectance Of Snowmentioning

confidence: 99%

Section: Spectral Reflectance Of Snowmentioning

confidence: 99%

The albedo of snow for partially cloudy skies

Choudhury

Chang

1981

Boundary-Layer Meteorol

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“…(6.14)]; furthermore, as the only intensity I * (T, *) determines the fluxes, the relevant equation [Liou, 1980, Eq. (6.22)] constitutes the azimuthally averaged form of RTE and is the starting point for a variety of approximate methods, which by use of simple expressions for P(cos *) mainly determine radiative fluxes (Wiscombe and Joseph, 1977;Joseph et al, 1976;Liou, 1974;Schaller, 1979;Meador and Weaver, 1980). The moments xn always enter the various expressions assumed by the phase function within these forms of RTE.…”

Section: Computationsmentioning

confidence: 99%

“…(2) taken for N=1, that is, as PE (cos *)=1+3g cos *. A unified approach to these methods and to their various related forms, was developed by Meador and Weaver (1980). Furthermore, g characterizes P(cos *) in the Heney-Greenstein phase function, which approximates rather well the actual phase function and may be simply expanded in Legendre polynomials as for it xn*gn.…”

Section: Computationsmentioning

confidence: 99%

Phase Function Mean Properties at Visible and Infrared Wavelengths within a Sample of 239 Fog Spectra

Tonna¹,

Tomasi²

1992

Journal of the Meteorological Society of Japan

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The mean characteristics of the phase function and of the coefficients of its Legendre series expansion were studied within a sample of 239 observed fog droplet size spectra, by computing their mean value, dispersion coefficient, skewness and kurtosis, at 86 wavelengths in the *=0.35-90 *m spectral interval. The results showed that the mean spectral behavior of the above quantities retains all the features pertaining to single spectra, and that the values of the optical quantities obtained for the different spectra are widely dispersed about their mean values. In particular, the dispersion for the phase function, at visible wavelengths, has a minimum close to zero (disp=l.3 %) around 40*, surrounded by a wide interval (15-55*) of low dispersion; for the asymmetry parameter the dispersion increases with wavelength from 1.7 % at *=0.35 im *p to 48 % at *=90 *m. The data produced can serve as reference values for both experimental and theoretical needs.

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“…If the leaves can be assumed randomly oriented then the optical depth of the layer is equal to half the leaf area index (LAI). Meador and Weaver (1980) provided an analytic solution to these equations that is still used in a number of state-of-the-art surface energy exchange schemes (e.g. Best et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Fast matrix treatment of 3-D radiative transfer in vegetation canopies: SPARTACUS-Vegetation 1.1

2018

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Abstract. A fast scheme is described to compute the 3-D interaction of solar radiation with vegetation canopies. The canopy is split in the horizontal plane into one clear region and one or more vegetated regions, and the two-stream equations are used for each, but with additional terms representing lateral exchange of radiation between regions that are proportional to the area of the interface between them. The resulting coupled set of ordinary differential equations is solved using the matrix-exponential method. The scheme is compared to solar Monte Carlo calculations for idealized scenes from the "RAMI4PILPS" intercomparison project, for open forest canopies and shrublands both with and without snow on the ground. Agreement is good in both the visible and infrared: for the cases compared, the root-mean-squared difference in reflectance, transmittance and canopy absorptance is 0.020, 0.038 and 0.033, respectively. The technique has potential application to weather and climate modelling.

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Two-Stream Approximations to Radiative Transfer in Planetary Atmospheres: A Unified Description of Existing Methods and a New Improvement

Cited by 513 publications

References 0 publications

The albedo of snow for partially cloudy skies

The albedo of snow for partially cloudy skies

Phase Function Mean Properties at Visible and Infrared Wavelengths within a Sample of 239 Fog Spectra

Fast matrix treatment of 3-D radiative transfer in vegetation canopies: SPARTACUS-Vegetation 1.1

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