Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance

Bannister, T. T.

doi:10.4319/lo.1992.37.4.0773

Cited by 40 publications

(37 citation statements)

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“…This is because the average cosine in homogeneous water does not necessarily decay monotonically with depth between the surface and large depths but instead may exhibit a maximum or minimum at a certain depth (e.g. see Bannister 1992). A mathematical justification for such behavior follows from consideration of the eigenvalue spectrum of the radiative transfer equation (McCormick 1992).…”

Section: Resultsmentioning

confidence: 99%

“…The rate of approach of the average cosine to its asymptotic value in an optically homogeneous ocean has been examined by Zaneveld (1989), who modeled G(z)-l as an exponentially decaying function with depth. Bannister (1992) used Monte Carlo simulations of radiative transfer to develop a model of the average cosine for various sun angles, for various ratios of scattering to absorption, and for typical volume scattering functions for natural seawaters. More recently, Francisco and McCormick (1994) investigated the angular behavior of radiance at great depths through asymptotic eigenfunctions of the radiative transfer equation for differing concentrations of Chl-containing particles in water.…”

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confidence: 99%

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Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field

Berwald

Stramski

Mobley

et al. 1995

Limnology & Oceanography

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The average cosine of the underwater light field (i) is a simple quantity that describes the angular distribution of radiance at a given point. A model of the rate of vertical change of ji in the ocean was developed in order to examine the influences of light absorption and scattering. We made calculations of radiative transfer based on invariant imbedding theory assuming an optically homogeneous ocean with a typical scattering phase function and the simple boundary conditions of the sun overhead in a black sky and a flat ocean surface. Under such conditions, the decrease of ji throughout the water column is well approximated by a single exponential function. The dependence of the parameter P7, which describes the rate of change of ji with optical depth, on the single-scattering albedo wo, is well approximated by a quadratic function. By applying a linearization technique to the P, vs. w. relationship, we identified the contributions of absorption and scattering to P,. Our results indicate that scattering is the more important process, contributing >50% to P, for typical situations when w. > 0.1. Absorption dominates P, when w. < 0.1, which occurs only in very clear oceanic water at long wavelengths (> 6 50 nm). Our analysis of the effect of scattering phase function shows that the scattering into the middle angles, approximately between 20" and 45", largely determines the magnitude of P,. Using spectral bio-optical models with several Chl concentrations, we also examined the rate of change in ji with geometric depth P, for various water types with realistic values of the absorption and scattering coefficients. This analysis shows large variations in both the magnitude and the spectral behavior of P, with varying Chl concentration.The average cosine of the light field (fi) is a simple and convenient quantity that describes the angular distribution of the underwater radiance at a given point. This quantity is defined as Acknowledgments

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Section: Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field

Berwald

Stramski

Mobley

et al. 1995

Limnology & Oceanography

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“…This result is supported by theory. Kirk [1994] and Bannister [1992] show with Monte Carlo simulations that the asymptotic m d increases as the ratio of scattering, b(l) (m À1 ), to total absorption, a(l) (m À1 ), decreases, and approaches 1 as b(l)/a(l) approaches 0 for vertically incident light. The ratio b(l)/a(l) must be lower for UV than for visible radiation: absorption increases exponentially (proportional to el)with decreasing wavelength, while scattering only increases (with decreasing wavelength) proportionally to wavelength to the power of 0 -1 [Gordon et al, 1988] or 2 [Sathyendranath et al, 1989].…”

Section: Discussionmentioning

confidence: 99%

“…The ratio b(l)/a(l) must be lower for UV than for visible radiation: absorption increases exponentially (proportional to el)with decreasing wavelength, while scattering only increases (with decreasing wavelength) proportionally to wavelength to the power of 0 -1 [Gordon et al, 1988] or 2 [Sathyendranath et al, 1989]. From Bannister's [1992] . Slope coefficient for CDOM absorption spectra (nm À1 ) in the Georgia Bight, calculated from SeaWiFS normalized water-leaving radiance data, binned to 9 km Â 9 km, monthly resolution: (a) January 1999 and (b) July 1999. the absorption and/or K d measurements, possibly due to wave focusing [e.g., Zaneveld et al, 2001].…”

Section: Discussionmentioning

confidence: 99%

Calculation of UV attenuation and colored dissolved organic matter absorption spectra from measurements of ocean color

2003

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[1] The absorption of ultraviolet and visible radiation by colored or chromophoric dissolved organic matter (CDOM) drives much of marine photochemistry. It also affects the penetration of ultraviolet radiation (UV) into the water column and can confound remote estimates of chlorophyll concentration. Measurements of ocean color from satellites can be used to predict UV attenuation and CDOM absorption spectra from relationships between visible reflectance, UV attenuation, and absorption by CDOM. Samples were taken from the Bering Sea and from the Mid-Atlantic Bight, and water types ranged from turbid, inshore waters to the Gulf Stream. We determined the following relationships between in situ visible radiance reflectance, L u /E d (l) (sr À1 ), and diffuse attenuation of UV,. Consistent with published observations, these empirical relationships predict that the spectral slope coefficient of CDOM absorption increases as diffuse attenuation of UV decreases. Excluding samples from turbid bays, the ratio of the CDOM absorption coefficient to K d is 0.90 at 323 nm, 0.86 at 338 nm, and 0.97 at 380 nm. We applied these relationships to SeaWiFS images of normalized water-leaving radiance to calculate the CDOM absorption and UV attenuation in the Mid-Atlantic Bight in May, July, and August 1998. The images showed a decrease in UV attenuation from May to August of approximately 50%. We also produced images of the areal distribution of the spectral slope coefficient of CDOM absorption in the Georgia Bight. The spectral slope coefficient increased offshore and changed with season.

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“…It is an important optical property that can be used to determine absorption coefficient using a relationship by Gershun 1939. Average cosine depends on the proportionality of absorption and scattering in water (Bannister 1992, Kirk 1981. Thus value of μ(λ) is comparatively higher in absorption dominated waters such as open ocean than in coastal waters where scattering dominates over absorption.…”

Section: Introductionmentioning

confidence: 99%

Empirical algorithm to estimate the average cosine of underwater light field at 490 nm

Talaulikar

Thayapurath

Desa

et al. 2011

Remote Sensing Letters

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The average cosine of the underwater light field µ(λ), where λ is wavelength, is an apparent optical property that describes the angular distribution of radiance at a given point in water. Here we present a simple algorithm to determine the average cosine at 490 nm, μ(490), which was developed using the measured optical parameters from the eastern Arabian Sea and coastal waters off Goa. The algorithm is validated using measured optical parameters. This algorithm, based on a single optical parameter, performed better compared to other empirical algorithms to determine average cosine of underwater light field. The absorption coefficient at 490 nm, derived as an application of μ(490), compared well with the synthetic optical data and optical data measured from other regions.

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Model of the mean cosine of underwater radiance and estimation of underwater scalar irradiance

Cited by 40 publications

References 10 publications

Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field

Influences of absorption and scattering on vertical changes in the average cosine of the underwater light field

Calculation of UV attenuation and colored dissolved organic matter absorption spectra from measurements of ocean color

Empirical algorithm to estimate the average cosine of underwater light field at 490 nm

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