Influence of surface waves on measured and modeled irradiance profiles.

Classical radiative transfer programs are based on the plane-parallel assumption. We show that the Gershun equation is valid if the irradiance is averaged over a sufficiently large area. We show that the equation is invalid for horizontal areas of the order of tens of meters in which horizontal gradients of irradiance in the presence of waves are much larger than vertical gradients. We calculate the distribution of irradiance beneath modeled two-dimensional surface waves. We show that many of the features typically observed in irradiance profiles can be explained by use of such models. We derive a method for determination of the diffuse attenuation coefficient that is based on the upward integration of the irradiance field beneath waves, starting at a depth at which the irradiance profile is affected only weakly by waves.

The influence of coherent waves on the remotely sensed reflectance.

Oceanic waves have been found to contribute enhanced back-scattering in the direction of the illumination source in studies that assumed the ocean surface to be a random sum of waves. Here we investigate enhanced back-scattering by coherent capillary-gravity wave trains that co-exist near the crests of short gravity waves in the ocean. We find that the enhanced back-scattering effect is intensified relative to that of a random surface and that the effect is observed at larger angles. This effect may not only affect active sensors such as lidar, which have a viewing angle close to that of the source but possibly passive sensors as well. This effect is likely to result in biases when attempting closure between radiative transfer models that do not include realistic representation of the ocean surface and observed water leaving radiance.

In situ determination of the remotely sensed reflectance and the absorption coefficient: closure and inversion.

We tested closure between in situ radiometric and absorption coefficient measurements by using a nearly backscattering-independent remote-sensing reflectance model that employs the remote-sensing reflectance at three wavelengths. We show that only a small error is introduced into the closure model when the proper functional relationships of f/Q and the backscattering is taken to be a constant when using the sea-viewing wide field-of-view sensor wavelengths 443, 490, and 555 nm. A method of inverting the model to obtain the absorption coefficient by use of simple linear spectral relationships of the absorption coefficient is provided. The results of the model show that the independent measurements of reflectance and absorption obtain closure with a high degree of accuracy.

Asymptotic light field in the presence of a bubble-layer.

We report that the submerged microbubbles are an efficient source of diffuse radiance and may contribute to a rapid transition to the diffuse asymptotic regime. In this asymptotic regime an average cosine is easily predictable and measurable.

Comparison of near-forward light scattering on oceanic turbulence and particles.

We examine and compare near-forward light scattering that is caused by turbulence and typical particulate assemblages in the ocean. The near-forward scattering by particles was calculated using Mie theory for homogeneous spheres and particle size distributions representative of natural assemblages in the ocean. Direct numerical simulations of a passive scalar with Prandtl number 7 mixed by homogeneous turbulence were used to represent temperature fluctuations and resulting inhomogeneities in the refractive index of water. Light scattering on the simulated turbulent flow was calculated using the geometrical-optics approximation. We found that the smallest temperature scales contribute the most to scattering, and that scattering on turbulence typically dominates over scattering on particles for small angles as large as 0.1 degrees . The scattering angle deviation that is due to turbulence for a light beam propagating over a 0.25-m path length in the oceanic water can be as large as 0.1 degrees . In addition, we carried out a preliminary laboratory experiment that illustrates the differences in the near-forward scattering on refractive-index inhomogeneities and particles.

Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity.

We have measured the absorption coefficient of pure and salt water at 15 wavelengths in the visible and near-infrared regions of the spectrum using WETLabs nine-wavelength absorption and attenuation meters and a three-wavelength absorption meter. The water temperature was varied between 15 and 30 degrees C, and the salinity was varied between 0 and 38 PSU to study the effects of these parameters on the absorption coefficient of liquid water. In the near-infrared portion of the spectrum the absorption coefficient of water was confirmed to be highly dependent on temperature. In the visible region the temperature dependence was found to be less than 0.001 m-1 degrees C except for a small region around 610 nm. The same results were found for the temperature dependence of a saltwater solution. After accounting for index-of-refraction effects, the salinity dependence at visible wavelengths is negligible. Salinity does appear to be important in determining the absorption coefficient of water in the near-infrared region. At 715 nm, for example, the salinity dependence was -0.00027 m-1 /PSU. Field measurements support the temperature and salinity dependencies found in the laboratory both in the near infrared and at shorter wavelengths. To make estimates of the temperature dependence in wavelength regions for which we did not make measurements we used a series of Gaussian curves that were fit to the absorption spectrum in the visible region of the spectrum. The spectral dependence on temperature was then estimated based on multiplying the Gaussians by a fitting factor.

Effect of particle size distribution and chlorophyll content on beam attenuation spectra.

The relationships between beam attenuation spectra, chlorophyll and pheophytin pigment concentrations, and particle size distributions are examined for a coastal region (Monterey Bay area) believed to have negligible concentrations of terrestrially derived dissolved organic compounds (during May 1977) but large quantities of phytoplankton and resuspended sediments. It was found that the slope of the beam attenuation spectra increases when the hyperbolic slope of the size distribution increases. The magnitude of this increase in slope was consistent with calculations based on a range of particle diameters from 0.5 to 30 microm, so that it would be possible to predict the slope of the particle size distribution if the slope of the beam attenuation spectra is known. The ratio of chlorophyll and pheophytin pigments to suspended volume concentrations affected the beam attenuation spectra to a lesser degree and in a more complex manner. Because of the strong effect of slope, it was concluded that the chlorophyll and pheophytin pigment content of suspended particles could not be efficiently predicted by means of beam attenuation measurements.

Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation.

An exact expression for the remotely sensed reflectance (RSR, upwelling radiance divided by downwelling scalar irradiance) just beneath the surface of the ocean is derived from the equation of radiative transfer. It is shown that the RSR at a given depth in the ocean depends only on the inherent optical properties, the attenuation coefficient for upwelling radiance, and two shape factors that depend on the radiance distribution and volume scattering function. The shape factors are shown to be close to unity. An exact expression for the RSR just beneath the surface as a function of the vertical structure of inherent and apparent optical properties is derived. This expression is solved for an N-layered system, which presents the possibility of inverting remotely sensed reflectance data to obtain the vertical structure of chlorophyll in the ocean.

Volume scattering function of suspended particulate matter at near-forward angles: a comparison of experimental and theoretical values.

Narrow angle light scattering measurements were made for various sizes of spherical particles suspended in water. These were compared to calculated theoretical scattering values as derived from the theory of Mie (1908). Through measurements with different particle concentrations at angles between 0.2 degrees and 0.7 degrees the effect of the unscattered main beam light was removed. Results agreed well with Mie theory for these angles.