Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths

Radiative Transfer Modeling of Phytoplankton Fluorescence Quenching Processes

We report the first radiative transfer model that is able to simulate phytoplankton fluorescence with both photochemical and non-photochemical quenching included. The fluorescence source term in the inelastic radiative transfer equation is proportional to both the quantum yield and scalar irradiance at excitation wavelengths. The photochemical and nonphotochemical quenching processes change the quantum yield based on the photosynthetic active radiation. A sensitivity study was performed to demonstrate the dependence of the fluorescence signal on chlorophyll a concentration, aerosol optical depths and solar zenith angles. This work enables us to better model the phytoplankton fluorescence, which can be used in the design of new space-based sensors that can provide sufficient sensitivity to detect the phytoplankton fluorescence signal. It could also lead to more accurate remote sensing algorithms for the study of phytoplankton physiology.

Progress in Forward-Inverse Modeling Based on Radiative Transfer Tools for Coupled Atmosphere-Snow/Ice-Ocean Systems: A Review and Description of the AccuRT Model

A tutorial review is provided of forward and inverse radiative transfer in coupled atmosphere-snow/ice-water systems. The coupled system is assumed to consist of two adjacent horizontal slabs separated by an interface across which the refractive index changes abruptly from its value in air to that in ice/water. A comprehensive review is provided of the inherent optical properties of air and water (including snow and ice). The radiative transfer equation for unpolarized as well as polarized radiation is described and solutions are outlined. Several examples of how to formulate and solve inverse problems encountered in environmental optics involving coupled atmosphere-water systems are discussed in some detail to illustrate how the solutions to the radiative transfer equation can be used as a forward model to solve practical inverse problems.

Characterization of the Light Field and Apparent Optical Properties in the Ocean Euphotic Layer Based on Hyperspectral Measurements of Irradiance Quartet

Although the light fields and apparent optical properties (AOPs) within the ocean euphotic layer have been studied for many decades through extensive measurements and theoretical modeling, there is virtually a lack of simultaneous high spectral resolution measurements of plane and scalar downwelling and upwelling irradiances (the so-called irradiance quartet). We describe a unique dataset of hyperspectral irradiance quartet, which was acquired under a broad range of environmental conditions within the water column from the near-surface depths to about 80 m in the Gulf of California. This dataset enabled the characterization of a comprehensive suite of AOPs for realistic non-uniform vertical distributions of seawater inherent optical properties (IOPs) and chlorophyll-a concentration (Chl) in the common presence of inelastic radiative processes within the water column, in particular Raman scattering by water molecules and chlorophyll-a fluorescence. In the blue and green spectral regions, the vertical patterns of AOPs are driven primarily by IOPs of seawater with weak or no discernible effects of inelastic processes. In the red, the light field and AOPs are strongly affected or totally dominated by inelastic processes of Raman scattering by water molecules, and additionally by chlorophyll-a fluorescence within the fluorescence emission band. The strongest effects occur in the chlorophyll-a fluorescence band within the chlorophyll-a maximum layer, where the average cosines of the light field approach the values of uniform light field, irradiance reflectance is exceptionally high approaching 1, and the diffuse attenuation coefficients for various irradiances are exceptionally low, including the negative values for the attenuation of upwelling plane and scalar irradiances. We established the empirical relationships describing the vertical patterns of some AOPs in the red spectral region as well as the relationships between some AOPs which can be useful in common experimental situations when only the downwelling plane irradiance measurements are available. We also demonstrated the applicability of irradiance quartet data in conjunction with Gershun’s equation for estimating the absorption coefficient of seawater in the blue-green spectral region, in which the effects of inelastic processes are weak or negligible.

Water-leaving contribution to polarized radiation field over ocean

The top-of-atmosphere (TOA) radiation field from a coupled atmosphere-ocean system (CAOS) includes contributions from the atmosphere, surface, and water body. Atmospheric correction of ocean color imagery is to retrieve water-leaving radiance from the TOA measurement, from which ocean bio-optical properties can be obtained. Knowledge of the absolute and relative magnitudes of water-leaving signal in the TOA radiation field is important for designing new atmospheric correction algorithms and developing retrieval algorithms for new ocean biogeochemical parameters. In this paper we present a systematic sensitivity study of water-leaving contribution to the TOA radiation field, from 340 nm to 865 nm, with polarization included. Ocean water inherent optical properties are derived from bio-optical models for two kinds of waters, one dominated by phytoplankton (PDW) and the other by non-algae particles (NDW). In addition to elastic scattering, Raman scattering and fluorescence from dissolved organic matter in ocean waters are included. Our sensitivity study shows that the polarized reflectance is minimized for both CAOS and ocean signals in the backscattering half plane, which leads to numerical instability when calculating water leaving relative contribution, the ratio between polarized water leaving and CAOS signals. If the backscattering plane is excluded, the water-leaving polarized signal contributes less than 9% to the TOA polarized reflectance for PDW in the whole spectra. For NDW, the polarized water leaving contribution can be as much as 20% in the wavelength range from 470 to 670 nm. For wavelengths shorter than 452 nm or longer than 865 nm, the water leaving contribution to the TOA polarized reflectance is in general smaller than 5% for NDW. For the TOA total reflectance, the water-leaving contribution has maximum values ranging from 7% to 16% at variable wavelengths from 400 nm to 550 nm from PDW. The water leaving contribution to the TOA total reflectance can be as large as 35% for NDW, which is in general peaked at 550 nm. Both the total and polarized reflectances from water-leaving contributions approach zero in the ultraviolet and near infrared bands. These facts can be used as constraints or guidelines when estimating the water leaving contribution to the TOA reflectance for new atmospheric correction algorithms for ocean color imagery.

Vector radiative transfer model for coupled atmosphere and ocean systems including inelastic sources in ocean waters

Inelastic scattering plays an important role in ocean optics. The main inelastic scattering mechanisms include Raman scattering, fluorescence by colored dissolved organic matter (FDOM), and fluorescence by chlorophyll. This paper reports an implementation of all three inelastic scattering mechanisms in the exact vector radiative transfer model for coupled atmosphere and ocean Systems (CAOS). Simulation shows that FDOM contributes to the water radiation field in the broad visible spectral region, while chlorophyll fluorescence is limited in a narrow band centered at 685 nm. This is consistent with previous findings in the literature. The fluorescence distribution as a function of depth and viewing angle is presented. The impacts of fluorescence to the degree of linear polarization (DoLP) and orientation of the polarization ellipse (OPE) are studied. The DoLP is strongly influenced by inelastic scattering at wavelengths with strong inelastic scattering contribution. The OPE is less affected by inelastic scattering but it has a noticeable impact, in terms of the angular region of positive polarization, in the backward direction. This effect is more apparent for deeper water depth.

Contribution of Raman scattering to polarized radiation field in ocean waters

We have implemented Raman scattering in a vector radiative transfer model for coupled atmosphere and ocean systems. A sensitivity study shows that the Raman scattering contribution is greatest in clear waters and at longer wavelengths. The Raman scattering contribution may surpass the elastic scattering contribution by several orders of magnitude at depth. The degree of linear polarization in water is smaller when Raman scattering is included. The orientation of the polarization ellipse shows similar patterns for both elastic and inelastic scattering contributions. As polarimeters and multipolarization-state lidars are planned for future Earth observing missions, our model can serve as a valuable tool for the simulation and interpretation of these planned observations.

Influence of Raman scattering on the light field in natural waters: a simple assessment

A simple, surprisingly accurate, method for estimating the influence of Raman scattering on the upwelling light field in natural waters is developed. The method is based on the single (or quasi-single) scattering solution of the radiative transfer equation with the Raman source function. Given the light field at the excitation wavelength, accurate estimates (~1-10%) of the contribution of Raman scattering to the light field at the emission wavelength are obtained. The accuracy is only slightly degraded when typically measured aspects of the light field at the excitation are available.

Influence of Raman scattering on ocean color inversion models

Raman scattering can be a significant contributor to the emergent radiance spectrum from the surface ocean. Here, we present an analytical approach to directly estimate the Raman contribution to remote sensing reflectance, and evaluate its effects on optical properties estimated from two common semianalytical inversion models. For application of the method to ocean color remote sensing, spectral irradiance products in the ultraviolet from the OMI instrument are merged with MODerate-resolution Imaging Spectroradiometer (MODIS) data in the visible. The resulting global fields of Raman-corrected optical properties show significant differences from standard retrievals, particularly for the particulate backscattering coefficient, b(bp), where average errors in clear ocean waters are ~50%. Given the interest in transforming b(bp) into biogeochemical quantities, Raman scattering must be accounted for in semianalytical inversion schemes.

Accurate measurements of the Raman scattering coefficient and the depolarization ratio in liquid water

Despite a long history, the Raman scattering coefficient of water has so far only been measured with 10% uncertainty using a 95% confidence interval. In this paper, we present an experiment where we have achieved 1.5% uncertainty by using a low concentration of Rhodamine 6G in ethanol as a reference along with accurate consideration of polarization-related effects and the geometry of the experimental setup. We have found that the photon-to-photon Raman scattering coefficient of the OH stretching band of liquid water is (1.84±0.03)×10(-4) m(-1) when integrated over the spectral frequency range from 620 to 700 nm while the exciting laser operates at 532 nm. We have also accurately measured the depolarization ratio across this band.

Beam attenuation coefficient retrieval by inversion of airborne lidar-induced chromophoric dissolved organic matter fluorescence. I. Theory

It is shown that the oceanic beam attenuation coefficient can be retrieved from airborne laser-induced and depth-resolved chromophoric dissolved organic matter (CDOM) fluorescence. The radiative transfer equation (RTE) retrieval methodology does not require a laser beam spread function model since two CDOM fluorescence bands are used in conjunction with a beam attenuation spectral model, is self-normalizing since the CDOM absorption coefficient and laser beam irradiance are common to both fluorescence observational channels, and is enabled by the known isotropic phase function for CDOM fluorescence. Although this RTE analytical inversion theory is exact, the retrieval uncertainty is reduced by configuring the proposed lidar in the multiple-field-of-view beam attenuation mode to significantly diminish observation of multiple scattering. The theory can be applied over wide regions of the ocean's continental margins, estuaries, lakes, and rivers that are known to have sufficient CDOM.

Effect of inelastic scattering on underwater daylight in the ocean: model evaluation, validation, and first results

A model based on a matrix-operator theory capable of simulating underwater daylight in the ocean is presented. The main focus is on gelbstoff and chlorophyll fluorscence as well as water Raman scattering as sources of inelastic scattering and their effect on underwater daylight and relevance for the remote sensing of ocean color. Any combination of inelastic sources can be investigated, including differences in simulated underwater daylight in the absence and the presence of these sources. To our knowledge, it is the first matrix-operator model to include all these inelastic source. The model allows simulations for case 1 and case 2 waters. Calculations can be done with highly anisotropic phase functions as they are observed in the ocean, and every order of multiple scattering is considered. A detailed mathematical description of inelastic sources is given, and a special treatment of the depth dependency of these sources is presented. The model is validated by comparison with depth-dependent and spectrally resolved measurements of downward irradiance in the open ocean. The differences between measured and simulated data are within the error of the radiometric measurements. Water Raman scattering has been found to contribute significantly to water-leaving radiance. The inelastic fraction depends on the water Raman scattering coefficient, on the ratio of the total attenuation coefficient at excitation and emission wavelengths, and on the spectral course of the irradiance incident on the ocean. For clear ocean waters the inelastic fraction can reach values of more than 17% [C = 0.08 mg m(-3), a(y) (440 nm) = 0.01 m(-1)] at wavelengths relevant for the remote sensing of ocean color. The inelastic fraction of gelbstoff fluorescence can reach or even exceed the relevance of water Raman scattering atshort wavelengths. In the water column, depending on optically active substances and on actual depth, water Raman scattering can provide 100% of the light field at wavelengths greater than 580 nm. The effect of gelbstoff fluorescence on depth-dependent irradiances is less significant than the effect of water Raman scattering in all cases considered, except for near surface levels and high gelbstoff concentrations.

Irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: Raman-scattering effects

We modify an algorithm for retrieving the absorption (a) and backscattering (b(b)) coefficient profiles in natural waters by inverting profiles of downwelling and upwelling irradiance so as to include the presence of Raman scattering. For a given wavelength of interest, lambda, the light field at the appropriate Raman excitation wavelength lambda(e) is first inverted to obtain the Raman source function at lambda. Starting from estimates of the inherent optical properties at lambda, the contribution to the irradiances at lambda from Raman scattering is then estimated and subtracted from the total irradiances to obtain the elastically scattered irradiances. We then inverted the elastically scattered irradiances to find new estimates of a and b(b) using our original method [Appl. Opt. 37, 3886 (1998)]. The algorithm then operates iteratively: The new estimates are used with the Raman source function to derive a new estimate of the Raman contribution, etc. Sample results are provided that demonstrate the working of the algorithm and show that the absorption and scattering coefficients can be retrieved with accuracies similar to those in the absence of Raman scattering down to depths at which the light field is significantly perturbed by it, e.g., with approximately 90% of the upwelling light field originating from Raman scattering.

Contribution of Raman scattering to water-leaving radiance: a reexamination

We have reexamined the contribution of Raman scattering to the water-leaving radiance in case 1 waters by carrying out radiative transfer simulations that combine the latest reported measurements of the absorption coefficient of pure water with direct measurements of the spectral variation of the Raman-scattering coefficient. The resulting contribution of Raman scattering is then compared with experimental measurements of the water-leaving radiance, and the fractional contribution of radiance produced by Raman scattering to the total radiance measured at a given wavelength is determined. The results show that (1) the contribution of Raman scattering to the water-leaving radiance in an ocean of pure seawater is as much as 50-100% larger than earlier predictions, and (2) the Raman contribution does not decay as rapidly with increasing concentrations of chlorophyllouslike pigments C as predicted earlier. In fact, the Raman fraction for C <or= 1 mg/m(3) is approximately >8% at wavelengths of interest in ocean color remote sensing and therefore cannot be ignored in ocean color modeling.

Ocean optical source estimation with widely spaced irradiance measurements

A method was developed for determining the spatial distribution of a source from downward and upward irradiance measurements at a single wavelength in seawater of known optical properties. The algorithm uses measurements at two depths located an arbitrary distance apart and solves two nonlinear equations for two parameters that fit a globally exponential or linear source shape. Complex spatially dependent source shapes can be estimated from an irradiance profile by piecing together estimates from neighboring measurement pairs. Numerical tests illustrate the sensitivity of the algorithm to depth, measurement spacing, chlorophyll concentration, sensor noise, and uncertainty in the a priori assumed inherent optical properties. The algorithm works well with widely spaced measurements, moderate sensor noise, and uncertainties in the optical properties regardless of whether the assumed and true profiles are the same shape.

Raman scattering by pure water and seawater

Measurements of the magnitude and spectral distribution of the Raman-scattering coefficients of pure water (b(rw)) and seawater (b(rs)) are presented. Two independent measurements of the spectral distribution of the Raman-scattering coefficient of pure water were made for incident wavelengths ranging from 250 to 500 nm. These measurements revealed a strong dependence of b(rw) on wavelength that could be represented by a (lambda')(-5.3+/-0.3) relationship, where lambda' is the incident wavelength, or a lambda(-4.6+/-0.3) relationship, where lambda is the Raman-scattered wavelength, when normalized to units of photons. The corresponding relationships for normalization to energy are (lambda')(-5.5+/-0.4) and lambda(-4.8+/-0.3), respectively. These relationships are found to be consistent with resonance Raman theory for an absorption wavelength of 130 nm. The absolute value of b(rw) for the 3400-cm(-1) line was found to be (2.7 +/- 0.2) x 10(-4) m(-1) for an incident wavelength of 488 nm, which is consistent with a number of earlier reports. The difference between the magnitudes of the Raman-scattering coefficients for pure water and seawater was statistically insignificant.

Ocean-color model incorporating transspectral processes

Ocean color is determined by spectral variations in reflectance at the sea surface, which in turn result from both elastic and inelastic processes. We extend an elastic-scattering model of sea surface reflectance to deal with Raman scattering, which is an inelastic process. The analytic solutions are derived for a vertically homogeneous and optically deep water column. The model presented here is based on the quasi-single-scattering approximation of Gordon [Appl. Opt. 12, 2803 (1973)] and is an extension of the model of Sathyendranath and Platt [Appl. Opt. 36, 2620 (1997)]. The Raman-scattering model includes a first-order Raman-scattering term and four second-order terms. Two of the second-order terms result from a combination of an elastic and a Raman-scattering event, whereas the other two second-order terms result from two Raman-scattering events. We show that the contribution to reflectance from these last two terms is typically of the order of 1% of the first-order Raman-scattering term. Therefore these terms and higher-order terms can be neglected for most applications. Issues related to the implementation of the model are discussed, with special reference to remote-sensing applications. Results from the analytic model are compared with Monte Carlo simulations of reflectance at the sea surface.

In situ measurements of Raman scattering in clear ocean water

We have further developed and improved the prototype oceanic Fraunhofer line discriminator by using a well-protected fiber-optic-wire cable and in-water electronic housing. We conducted a series of in situ measurements in clear ocean water in the Florida Straits. By comparing the reduced data with the Monte Carlo simulation results, we verify the Raman scattering coefficient B(r) with an excitation wavelength at 488 nm to be 2.6 x 10(-4) m(-1) [Appl. Opt. 29, 71-84 (1990)], as opposed to 14.4 x 10(-4) m(-1) [Appl. Opt.14, 2116-2120 (1975)]. The wavelength dependence of the Raman scattering coefficient is found to have an insignificant effect on the in-water light field. We also discuss factors that lead to errors. This study can be used as a basis for inelastic light scattering in the radiative transfer theory and will allow other inelastic light, e.g., fluorescence, to be detected with in situ measurements.

Marine asymptotic daylight field: effects of inelastic processes

The governing equations are developed for the marine asymptotic daylight field in the scalar approximation, including the effects of inelastic processes-Raman scattering and chromophoric dissolved organic matter fluorescence. The governing equations are solved numerically and compared with Monte Carlo simulations. It is found that these solutions are the actual radiance distributions approached by the asymptotic field in the Monte Carlo simulations. Sample solutions are provided to show the sensitivity of the light field to the various parameters of the medium. For certain values of the parameters, inclusion of inelastic processes can drastically alter the radiance distribution, e.g., from a near-Dirac delta function in the absence of inelastic processes to a near-isotropic distribution in their presence. The results suggest that in a real ocean, the asymptotic (and near-asymptotic) radiance distribution will tend to become more uniform as the wavelength increases beyond ~500 nm. Finally, it is shown that even for depths far from the asymptotic regime, the radiance distribution of the inelastic component of the light field can be well approximated by the asymptotic theory developed here for inelastic processes. Two exact analytical solutions to the governing equations are also provided.

Sensitivity of radiative transfer to small-angle scattering in the ocean: Quantitative assessment

It is shown that measurements of the absorption coefficient and the volume-scattering function for scattering angles ? 15° of ocean water are sufficient for predicting the transport of irradiance in the ocean. Thus, difficult-to-measure small-angle scattering is not necessary in many applications. Furthermore, the irrelevance of small-angle scattering suggests the irrelevance of the scattering coefficient and of the routinely measured beam-attenuation coefficient in many radiative-transfer problems. Finally, these observations provide a method for determining the adequacy of instruments in which small sampling volumes (~ few cm(3)) are analyzed when predicting irradiance attenuation and diffuse reflection for large volumes (~ 10-10(4) M(3)).

Comparison of numerical models for computing underwater light fields

Seven models for computing underwater radiances and irradiances by numerical solution of the radiative transfer equation are compared. The models are applied to the solution of several problems drawn from optical oceanography. The problems include highly absorbing and highly scattering waters, scattering by molecules and by particulates, stratified water, atmospheric effects, surface-wave effects, bottom effects, and Raman scattering. The models provide consistent output, with errors (resulting from Monte Carlo statistical fluctuations) in computed irradiances that are seldom larger, and are usually smaller, than the experimental errors made in measuring irradiances when using current oceanographic instrumentation. Computed radiances display somewhat larger errors.