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
We have investigated the effect of Raman scattering on the average cosine of underwater irradiance, ,%, the diffuse attenuation coefficient of irradiance, K, and the Raman scattering source coefficient, P*, throughout the water column and into the asymptotic field. The Raman scattering source coefficient is the fractional gain in the scalar irradiance from local Raman scattering at a given depth, and it can be found from the Gershun equation with a Raman source term. In particular, by using calculations from a radiative transfer model (Hydrolight 3.0), we compare ,%, K, and P* from simulations that include and that omit Raman scattering. These simulations are performed at wavelengths between 355 and 665 nm in a vertically homogeneous ocean with inherent optical properties (IOPs) determined from case 1 bio-optical models for three different chlorophyll concentrations (0.05, 0.5, and 5 mg m-j). We also investigated several two-layered oceans that assumed different inherent optical properties in the surface and deep layers. Our calculations showed that when Raman scattering is present, there may exist strong vertical gradients in the average cosine and the diffuse attenuation coefficient, especially at long wavelengths for low chlorophyll concentrations. In addition, a quasi-asymptotic field may be a feature of the vertical profiles of the average cosine and the diffuse attenuation coefficient. In the asymptotic field, there is no effect of Raman scattering at shorter wavelengths, there is a strong effect of Raman scattering at longer wavelengths and between these two spectral regions, and there is a transition that increases from 500 to 590 nm as the concentration of chlorophyll increases from 0.05 to 5 mg m-2. Over a broad range of IOPs, the asymptotic parameters pm*, K,*, and P*, are related by a quadratic relationship. Neither the magnitude or angular distribution of surface light nor changes in the absorption and scattering coefficients in the surface layer of a two-layered ocean have auy effect on the values of ,%=*, K,*, and P*,; the values of these parameters depend only upon the IOPs in the deepest layer.
The numeric concentration of procaryotic and eucaryotic cells that form the planktonic microbial community decreases monotonically and rapidly with increasing size. This size distribution has been interpreted to be the result of allometric control of growth and respiration rates, but we propose an alternative "random encounter" hypothesis to explain such a distribution. According to this hypothesis, the size distribution of cells that range from 0.3 to 100 pm results from sizeselective predation by protozoans. A phagotrophic population will swim randomly through the water encountering both prey and predators. At steady state, such a population must ingest smaller prey at a sufficient rate to balance its rate of loss to larger predators. The size distribution of cells must, therefore, satisfy this condition. In particular, a mathematical statement of the hypothesis is based on the following relationships: volume of a cell varies as the cube of its diameter; clearance rate (L3T-I) by a predator varies as the square of its diameter; and, for a given population, its range of possible prey sizes varies with its prey diameter at the same time that the range of predator sizes able to capture the given population varies with its predator diameter.Measurements at sea of the distribution of particle sizes by electronic detection (Sheldon et al. 1972(Sheldon et al. , 1973 and by phase contrast microscopy have shown that there is a characteristic distribution for particles in the size range between 2 and 100 pm. Samples collected from diverse regions of the open ocean are all characterized by a steep and continuous decrease in the particle concentration with increasing particle size. This size distribution has been mathematically characterized as a hyperbolic distribution in which the the concentration of particles decreases as roughly the 4th power of the particle's size (e.g. McCave 1975).
The behavior of real scattering surfaces is often specified by measuring the bidirectional reflectance factor (BRF), defined as the ratio of the flux scattered into a given direction by a surface under given conditions of illumination to the flux scattered in the same direction by a Lamberüan scatterer under identical conditions. The utility of this factor is that measurements on surfaces can be related to known standards (e.g. Spectralon), which have a BRF greater than 99% for a broad range of wavelengths. In addition to the incidence angle and spectral features of the incident flux, the reflectance properties of a surface are affected by the intrinsic composition and roughness properties of the surface. Therefore, the spectral reflectance of different targets will generally yield spectral reflectance curves of different shapes, forming the basis for identification of materials. For example, optical principles developed for the determination of reflectance properties of marine particles facilitate the determination of the BRF of oceanic samples.We have recently developed and implemented a system for determining the BRF composed of a Zeiss photomicroscope equipped with a reflective system. In this system, excitation is provided over a large field of view while reflection collection is acquired over a slightly smaller solid angle. Multi-wavelength measurements allow the determination of the effect of the excitation wavelength on both the reflectance and fluorescence properties of the sample, whereas monochromatic measurements exclude fluorescence effects. This new technique provides the advantages of determination of the BRF for different types of individual and bulk particulates transferred onto an optical embedding medium or collected on an Anopore filter. Abundance and other optical properties (e.g. absorption) of dominant particle types can also be determined by individual particle analysis on the same sample.
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