The Delta-Eddington Approximation for Radiative Flux Transfer

Joseph, Joachim H.; Wiscombe, W. J.; Weinman, J. A.

doi:10.1175/1520-0469(1976)033<2452:tdeafr>2.0.co;2

Cited by 1,004 publications

(538 citation statements)

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“…The delta-Lddington approximation of the radiative transfer equation (Joseph et al 1976), which is designed for strongly asymmetric scattering medium, gives the scattering transmission coefficient as _r*64…”

Section: Parameterization Fc)uationsmentioning

confidence: 99%

The albedo of snow for partially cloudy skies

Choudhury

Chang

1981

Boundary-Layer Meteorol

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Section: Parameterization Fc)uationsmentioning

confidence: 99%

The albedo of snow for partially cloudy skies

Choudhury

Chang

1981

Boundary-Layer Meteorol

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“…This approximation is valid for a medium that shows strong forward scattering [13]. For large particle diameter-to-wavelength ratios of over I00 (as is the case here), asymptotic approximations yield accurate results with minimal computational complexity [14].…”

Section: A Near-infrared Reflectancementioning

confidence: 99%

“…The directional hemispherical reflectance, R, is then calculated at a specific angle of incidence, θ, from [13] …”

Section: A Near-infrared Reflectancementioning

confidence: 99%

Estimation of surface snow properties using combined millimeter-wave backscatter and near-infrared reflectance measurements

Narayanan

Jackson

1997

Int J Infrared Milli Waves

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Knowledge of surficial snow properties such as grain size, surface roughness, and free-water content provides clues to the metamorphic state of snow on the ground, which in turn yields information on weathering processes and climatic activity. Remote sensing techniques using combined concurrent measurements of near-infrared passive reflectance and millimeter-wave radar backscatter show promise in estimating the above snow parameters. Near-infrared reflectance is strongly dependent on snow grain size and free-water content, while millimeter-wave backscatter is primarily dependent on free-water content and, to some extent, on the surface roughness. A neural-network based inversion algorithm has been developed that optimally combines near-infrared and millimeter-wave measurements for accurate estimation of the relevant snow properties. The algorithm uses reflectances at wavelengths of 1160 nm, 1260 nm and 1360 nm, as well as co-polarized and cross-polarized backscatter at a frequency of 95 GHz. The inversion algorithm has been tested using simulated data, and is seen to perform well under noise-free conditions. Under noise-added conditions, a signal-to-noise ratio of 32 dB or greater ensures acceptable errors in snow parameter estimation.

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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%

“…The Eddington and the Two-Stream methods have been improved by the Delta-Eddington (Joseph et al, 1976) and the Delta-Two-Stream (Schaller, 1979) methods by making use of the *-approximation to the phase function, which combines a delta function expressing the contribution of the forward peak with two terms depending on *. An extension of the *-approximation is the *-M approximation (Wiscombe, 1977), which expresses the phase function as a delta function plus 2M terms depending on * (for M=1 one gets the above *-approximation) ; an example of using this approximation in connection with the spherical harmonics method, leading to the the Delta-Spherical Harmonics method, can be found in Kondratyev et al (1981).…”

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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The Delta-Eddington Approximation for Radiative Flux Transfer

Cited by 1,004 publications

References 0 publications

The albedo of snow for partially cloudy skies

The albedo of snow for partially cloudy skies

Estimation of surface snow properties using combined millimeter-wave backscatter and near-infrared reflectance measurements

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

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