Apparent breakdown of reciprocity in reflected solar radiances

Girolamo, Larry Di; Várnai, Tamás; Davies, Roger

doi:10.1029/98jd00345

Cited by 27 publications

(13 citation statements)

References 17 publications

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“…This violation of reciprocity is a desirable attribute of stochastic RT modeling at least in atmospheric applications. It is indeed consistent with realworld satellite observations of reciprocity violation uncovered by DiGirolamo et al [61] in spatially variable cloud scenes inside a relatively broad field of view, and readily replicated with numerical Monte Carlo simulations. These findings were soon explained theoretically by Leroy [62].…”

Section: Single Scattering In D = 3: Violation Of Angular Reciprocitysupporting

confidence: 87%

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

Davis

2014

Journal of Computational and Theoretical Transport

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We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance r(s), for fixed physical distance s, thus becomes (1 + r(s)/a)~", with standard exponential decay re covered when a -*■ oo. Atmospheric turbulence phenomenology for fluctuating optical properties rationalizes this switch. Foundational equations for this generalized trans port model are stated in integral form for d = 1,2,3 spatial dimensions. A deterministic numerical solution is developed in d = 1 using Markov Chain formalism, verified with Monte Carlo, and used to investigate internal radiation fields. Standard two-stream theory, where diffusion is exact, is recovered when a = oo. Differential diffusion equa tions are not presently known when a < oo, nor is the integro-differential form of the generalized transport equation. Monte Carlo simulations are performed in d = 2, as a model for transport on random surfaces, to explore scaling behavior of transmit tance T when transport optical thickness rt » 1. Random walk theory correctly predicts T a rt ĩm,I',1,a/2) in the absence of absorption. Finally, single scattering theory in d = 3 highlights the model's violation of angular reciprocity when a < oo, a desirable prop erty at least in atmospheric applications. This violation is traced back to a key trait of generalized transport theory, namely, that we must distinguish more carefully between two kinds of propagation: one that ends in a virtual or actual detection and the other in a transition from one position to another in the medium.

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Section: Single Scattering In D = 3: Violation Of Angular Reciprocitysupporting

confidence: 87%

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

Davis

2014

Journal of Computational and Theoretical Transport

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“…an out of focus image) the scene appears to behave more like a plane parallel one. Analogous resolutiondependent effects were noted earlier by Di Girolamo et al [1998] and by Oreopoulos and Davies [1998].…”

Section: Discussionsupporting

confidence: 84%

Anisotropy of water cloud reflectance: A comparison of measurements and 1D theory

Horváth

Davies

2004

Geophysical Research Letters

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[1] Bi-directional reflectances of marine liquid water clouds, as measured by the Multiangle Imaging SpectroRadiometer (MISR), are compared with planeparallel radiative transfer model calculations. We define an angular consistency test that requires measured and modeled radiances to agree within ±5% for all chosen view angles for the observations to be classified as planeparallel. When all nine MISR angles are used at the full 275 m resolution, 1 in 6 pixels (17%) pass the test. There is a slight dependence on effective radius R e , with R e = 8 mm resulting in the highest pass rate. As the resolution is degraded, clouds appear more plane-parallel, and the passing rate increases to 38% at the coarsest 17.6 km scale. The passing rate quickly decreases as the number of angles used in the angular test increases. Requiring a match at only the nadir and two near-nadir angles immediately eliminates half of the full resolution pixels.

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“…In conclusion, this paper presents a theoretical framework for understanding and quantifying deviations from directional reciprocity. The predictions of (14) agree a posteriori with the results of Monte Carlo simulations [Di Girolamo et al, 1998], which showed that the deviations from reciprocity (1) increase with scene heterogeneity, (2) increase as the view direction gets farther from the illumination direction, (3) decrease as the sensor pixel size increases. The scaling derived from the theory permits to determine whether angular models should be considered as reciprocal or not, depending on the characteristics of photon mean free path, sensor resolution, and scene heterogeneity of the physical problem to be studied.…”

Section: Discussionsupporting

confidence: 72%

Deviation from reciprocity in bidirectional reflectance

Leroy¹

2001

J. Geophys. Res.

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Abstract. The subject of the paper is to discuss and quantify deviations from reciprocity of the bidirectional reflectance distribution function (BRDF), i.e., the difference of BRDF obtained when inverting illumination and viewing directions. Directional reciprocity is not valid in general, because when the illumination beam has a spatial extension larger than the viewed area (as is most often the case for BRDF measurements), some of the scatterers building up the observed radiance are located at different places in reciprocal measurements. The physical systems under consideration in the two experiments are different, hence the breakdown of reciprocity. The paper develops a theory aiming at a quantitative estimation of deviations from directional reciprocity due to this factor. The theory is based on integral forms of the radiative transfer equation in a horizontal slab of heterogeneous absorbing and scattering media. The observed scene radiance is expanded in a series of scattering orders. Integral expressions of the single-and multiple-scattering radiance are derived and put in a form suitable for the analysis of the reciprocity problem. IntroductionThe principle of reciprocity, also referred to as Helmoltz reciprocity, is widely accepted in various branches of physics. Its modern and most general form [Van der Hulst, 1980] states that "in any linear physical system, the channels which lead from a cause at one point to an effect at another point can be equally well traversed in the opposite direction. Let the cause be first placed at P and the effect measured at Q; and in a second experiment, carried out in the same physical system, let the cause be at Q and the effect at P. The reciprocity principle is then expressed by the proportionality: effect at Q/cause at P = effect at P/cause at Q.

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Apparent breakdown of reciprocity in reflected solar radiances

Cited by 27 publications

References 17 publications

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

Anisotropy of water cloud reflectance: A comparison of measurements and 1D theory

Deviation from reciprocity in bidirectional reflectance

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