The radiative transfer equation for strongly-fluctuating, continuous random media

Jin, Ya‐Qiu

doi:10.1016/0022-4073(89)90043-5

Cited by 22 publications

(34 citation statements)

References 7 publications

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“…where the phase matrix elements P (θ, φ; θ , φ ) are [5]: (10) where δ is the normalized variance of fluctuations (2). The function W α,β can be obtained by [3] …”

Section: Matrix In Strong Fluctuation Theorymentioning

confidence: 99%

“…For the non-spherical case, we consider anisotropic correlation function with azimuthal symmetry [5]:…”

Section: Matrix In Strong Fluctuation Theorymentioning

confidence: 99%

“…However, the experimental values of extinction coefficients at 18 GHz may be biased, due to the low transmission loss (mostly below 1 dB) even for thick snow samples [9]. At 90 GHz, the results of the models fit into the measured extinction coefficients for grain sizes smaller than 0.9 mm (samples [1][2][3][4][5][6][7][8]. The model derived values are larger than the measured extinction coefficients for grain sizes larger than 0.9 mm (samples 9-18).…”

Section: Comparison Of Calculated Extinction Coefficients With Datamentioning

confidence: 99%

See 2 more Smart Citations

Extinction Behavior of Dry Snow at Microwave Range up to 90 GHZ by Using Strong Fluctuation Theory

Wang

Pulliainen²,

Hallikainen³

2000

PIER

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“…where the phase matrix elements P (θ, φ; θ , φ ) are [5]: (10) where δ is the normalized variance of fluctuations (2). The function W α,β can be obtained by [3] …”

Section: Matrix In Strong Fluctuation Theorymentioning

confidence: 99%

“…For the non-spherical case, we consider anisotropic correlation function with azimuthal symmetry [5]:…”

Section: Matrix In Strong Fluctuation Theorymentioning

confidence: 99%

Section: Comparison Of Calculated Extinction Coefficients With Datamentioning

confidence: 99%

See 1 more Smart Citation

Extinction Behavior of Dry Snow at Microwave Range up to 90 GHZ by Using Strong Fluctuation Theory

Wang

Pulliainen²,

Hallikainen³

2000

PIER

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“…At VHF, UHF and microwave frequencies (10 MHz-100 GHz), the permittivity of pure and impure ice ε ice can be found in [16,17]. The scattering coefficients κ sv and κ sh are deduced from the phase matrix components P (θ, φ; θ , φ ) [7]:…”

Section: Formulationmentioning

confidence: 99%

“…To find a possible effect due to the small roughness of the surface, we simply modify the reflectivity r mnp according to [7]:…”

Section: Formulationmentioning

confidence: 99%

Application of Strong Fluctuation Theory to Microwave Emission from Dry Snow

Wang¹,

Pulliainen²,

Hallikainen³

2000

PIER

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Abstract-This study is concerned with the development of a model to describe microwave emission from dry snow cover. The model is based on the radiative transfer and the strong fluctuation theory. In the model, a spherical symmetric correlation function with an exponential form is used to describe the random permittivity fluctuations. The phase matrix and extinction coefficient of snowpack for a spherical symmetric correlation function are obtained by employing the strong fluctuation theory. The vector radiative transfer equation for a layer of a random medium is solved by using Gaussian quadrature and eigen analysis. Comparisons with brightness temperature data at 5, 10.7, 18, 37 GHz are made. It is shown that the model fits the experimental data by using physical parameters of the dry snow as obtained from ground truth measurements.

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Snow-cover environmental monitoring and assessment in Northeast China using passive microwave emission models

Song

Zhang

2007

Environ Monit Assess

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In this study, we present the application of the passive microwave emission models to snow-cover environment monitoring and assessment in Northeast China. The study employs the radiative transfer function and strong fluctuation theory to develop the models. We used the exponential form of a spherical symmetric correlation function to describe random permittivity fluctuations. From strong fluctuation, we then obtained the phase matrix and extinction coefficients of snow-packs for the spherical symmetric correlation function. We also used the vector radiative transfer formula for the layer of a random medium by solving Gaussian quadrature and eigen analysis. By comparing the brightness temperatures at 5, 10.7, 18, and 37 GHz, the modelling results agreed with experimental data of dry-snow physical parameters as measured in the fieldwork.

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The radiative transfer equation for strongly-fluctuating, continuous random media

Cited by 22 publications

References 7 publications

Extinction Behavior of Dry Snow at Microwave Range up to 90 GHZ by Using Strong Fluctuation Theory

Extinction Behavior of Dry Snow at Microwave Range up to 90 GHZ by Using Strong Fluctuation Theory

Application of Strong Fluctuation Theory to Microwave Emission from Dry Snow

Snow-cover environmental monitoring and assessment in Northeast China using passive microwave emission models

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