Analysis of underwater radiance observations: Apparent optical properties and analytic functions describing the angular radiance distribution

Abstract

Abstract. A primary data set consisting of 70 series of angular radiance distributions observed in clear blue western Mediterranean water and a secondary set of 12 series from the more green and turbid Lake Pend Oreille, Idaho, have been analyzed. The results demonstrate that the main variation of the shape of the downward radiance distribution occurs within the Snell cone. Outside the cone the variation of the shape decreases with increasing zenith angle. The most important shape changes of the upward radiance appear within the zenith angle range 90ø-130 ø . The variation in shape reaches its minimum around nadir, where an almost constant upward radiance distribution implies that a flat sea surface acts like a Lambert emitter within _+8% in the zenith angle interval 140ø-180 ø in air. The ratio Q of upward irradiance and nadir radiance, as well as the average cosines /•a and/•, for downward and upward radiance, respectively, have rather small standard deviations, _<10%, within the local water type. In contrast, the irradiance reflectance R has been observed to change up to 400% with depth in the western Mediterranean, while the maximum observed change of Q with depth is only 40%. The dependence of Q on the solar elevation for blue light at 5 m depth in the Mediterranean coincides with observations from the central Atlantic as well as with model computations. The corresponding dependence of/•a shows that diffuse light may have a significant influence on its value. Two simple functions describing the observed angular radiance distributions are proposed, and both functions can be determined by two field observations as input parameters. The e function approximates the azimuthal means of downward radiance with an average error _<7% and of upward radiance with an error of-1%. The a function describes the zenith angle dependence of the azimuthal means of upward radiance with an average error _<7% in clear ocean water, increasing to _<20% in turbid lake water. The a function suggests that the range of variation for/•, falls between 0 and 1/2, and for Q it is between rr and 2rr. The limits of both ranges are confirmed by observations. By combining the e and • functions, a complete angular description of the upward radiance field is achieved. IntroductionRadiance is the single most important quantity from which various irradiances and vertical attenuation coefficients can be derived. In addition, irradiance distribution functions, the light absorption coefficient, and, in principle (by inverse methods), the light-scattering function can be determined for a completely specified radiance field. The total radiance field gives us all the pertinent inherent and apparent parameters describing the optical characteristics of natural waters. Underwater measurements of angular radiance distributions are generally very few. Except for one recent example [Voss, 1988], it is noteworthy that one has to go 20 years or more back in time in order to find such distributions from lakes, fjords, and ocean waters [Jerlov, 1951[Jerlov, , 1976

Detailed validation of the bidirectional effect in various Case 1 waters for application to ocean color imagery

“…Aas and Hojerslev (1999), using a parameterization based on a dataset from relatively clear Mediterranean waters, predicted that Q nadir , at blue (465-475 nm) wavelengths, should follow either:…”

Secchi depth in the Oslofjord–Skagerrak area: theory, experiments and relationships to other quantities

“…Vertical profiles of the upward radiance L and the downward and upward irradiances E d and E u were recorded. According to the radiance model of Aas and Højerslev (1999), the quantity Q = L/E u should obtain values in the interval from π to 2π only, and a few stations where Q lay outside this range have been omitted. Immersion coefficients determined by the manufacturer and self-shading effects (Gordon and Ding, 1992;Zibordi and Ferrari, 1995;Aas and Korsbø, 1997) were taken into account.…”

Estimates of radiance reflected towards the zenith at the surface of the sea

“…The data were stored as graphs on paper rolls from printers. Through the years the recordings were read off and tabulated (Lundgren 1971;, and analyses were made Aas and Højerslev, 1999;Adams et al, 2002 ).…”