Optimizing retrieval spaces of bio-optical models for remote sensing of ocean color.

We investigated the optimal number of independent parameters required to accurately represent spectral remote sensing reflectances (R rs) by performing principal component analysis on quality controlled in situ and synthetic R rs data. We found that retrieval algorithms should be able to retrieve no more than four free parameters from R rs spectra for most ocean waters. In addition, we evaluated the performance of five different bio-optical models with different numbers of free parameters for the direct inversion of in-water inherent optical properties (IOPs) from in situ and synthetic R rs data. The multi-parameter models showed similar performances regardless of the number of parameters. Considering the computational cost associated with larger parameter spaces, we recommend bio-optical models with three free parameters for the use of IOP or joint retrieval algorithms.

Instantaneous photosynthetically available radiation models for ocean waters using neural networks.

Instantaneous photosynthetically available radiation (IPAR) at the ocean surface and its vertical profile below the surface play a critical role in models to calculate net primary productivity of marine phytoplankton. In this work, we report two IPAR prediction models based on the neural network (NN) approach, one for open ocean and the other for coastal waters. These models are trained, validated, and tested using a large volume of synthetic datasets for open ocean and coastal waters simulated by a radiative transfer model. Our NN models are designed to predict IPAR under a large range of atmospheric and oceanic conditions. The NN models can compute the subsurface IPAR profile very accurately up to the euphotic zone depth. The root mean square errors associated with the diffuse attenuation coefficient of IPAR are less than 0.011m-1 and 0.036m-1 for open ocean and coastal waters, respectively. The performance of the NN models is better than presently available semi-analytical models, with significant superiority in coastal waters.

Atmospheric correction over the ocean for hyperspectral radiometers using multi-angle polarimetric retrievals.

We developed a fast and accurate polynomial based atmospheric correction (POLYAC) algorithm for hyperspectral radiometric measurements, which parameterizes the atmospheric path radiances using aerosol properties retrieved from co-located multi-wavelength multi-angle polarimeter (MAP) measurements. This algorithm has been applied to co-located spectrometer for planetary exploration (SPEX) airborne and research scanning polarimeter (RSP) measurements, where SPEX airborne was used as a proxy of hyperspectral radiometers, and RSP as the MAP. The hyperspectral remote sensing reflectance obtained from POLYAC is accurate when compared to Aerosol Robotic Network (AERONET), and Visible Infrared Imaging Radiometer Suite (VIIRS) ocean color products. POLYAC provides a robust alternative atmospheric correction algorithm for hyperspectral or multi-spectral radiometric measurements for scenes involving coastal oceans and/or absorbing aerosols, where traditional atmospheric correction algorithms are less reliable.

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era.

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will carry into space the Ocean Color Instrument (OCI), a spectrometer measuring at 5nm spectral resolution in the ultraviolet (UV) to near infrared (NIR) with additional spectral bands in the shortwave infrared (SWIR), and two multi-angle polarimeters that will overlap the OCI spectral range and spatial coverage, i. e., the Spectrometer for Planetary Exploration (SPEXone) and the Hyper-Angular Rainbow Polarimeter (HARP2). These instruments, especially when used in synergy, have great potential for improving estimates of water reflectance in the post Earth Observing System (EOS) era. Extending the top-of-atmosphere (TOA) observations to the UV, where aerosol absorption is effective, adding spectral bands in the SWIR, where even the most turbid waters are black and sensitivity to the aerosol coarse mode is higher than at shorter wavelengths, and measuring in the oxygen A-band to estimate aerosol altitude will enable greater accuracy in atmospheric correction for ocean color science. The multi-angular and polarized measurements, sensitive to aerosol properties (e.g., size distribution, index of refraction), can further help to identify or constrain the aerosol model, or to retrieve directly water reflectance. Algorithms that exploit the new capabilities are presented, and their ability to improve accuracy is discussed. They embrace a modern, adapted heritage two-step algorithm and alternative schemes (deterministic, statistical) that aim at inverting the TOA signal in a single step. These schemes, by the nature of their construction, their robustness, their generalization properties, and their ability to associate uncertainties, are expected to become the new standard in the future. A strategy for atmospheric correction is presented that ensures continuity and consistency with past and present ocean-color missions while enabling full exploitation of the new dimensions and possibilities. Despite the major improvements anticipated with the PACE instruments, gaps/issues remain to be filled/tackled. They include dealing properly with whitecaps, taking into account Earth-curvature effects, correcting for adjacency effects, accounting for the coupling between scattering and absorption, modeling accurately water reflectance, and acquiring a sufficiently representative dataset of water reflectance in the UV to SWIR. Dedicated efforts, experimental and theoretical, are in order to gather the necessary information and rectify inadequacies. Ideas and solutions are put forward to address the unresolved issues. Thanks to its design and characteristics, the PACE mission will mark the beginning of a new era of unprecedented accuracy in ocean-color radiometry from space.

Retrieval of aerosol properties and water-leaving reflectance from multi-angular polarimetric measurements over coastal waters.

Ocean color remote sensing is an important tool to monitor water quality and biogeochemical conditions of ocean. Atmospheric correction, which obtains water-leaving radiance from the total radiance measured by satellite-borne or airborne sensors, remains a challenging task for coastal waters due to the complex optical properties of aerosols and ocean waters. In this paper, we report a research algorithm on aerosol and ocean color retrieval with emphasis on coastal waters, which uses coupled atmosphere and ocean radiative transfer model to fit polarized radiance measurements at multiple viewing angles and multiple wavelengths. Ocean optical properties are characterized by a generalized bio-optical model with direct accounting for the absorption and scattering of phytoplankton, colored dissolved organic matter (CDOM) and non-algal particles (NAP). Our retrieval algorithm can accurately determine the water-leaving radiance and aerosol properties for coastal waters, and may be used to improve the atmospheric correction when apply to a hyperspectral ocean color instrument.

Single scattering properties of non-spherical hydrosols modeled by spheroids.

The single scattering properties of hydrosols play an important role in the study of ocean optics, ocean color remote sensing, and ocean biogeochemistry research. Measurements show that hydrosols can be of various sizes and shapes, suggesting general non-spherical models should be considered for the study of single scattering properties of hydrosols. In this work, light scattering by non-spherical hydrosols are modeled by randomly oriented spheroids with the Amsterdam discrete dipole approximation (ADDA) code. We have defined two new parameters to quantify the degree of optical non-sphericity (DONS) and investigated the dependence of DONS on refractive index, size, and aspect ratio. For particles with non-unitary aspect ratios, the magnitude of DONS increases as the refractive index and particle size increase. The dependence of the backscattering fraction on the non-sphericity, size, and refractive index of hydrosols is also studied. It is found that the backscattering fraction is larger for smaller particles as well as for particles with higher refractive indices. Absorptive hydrosols generally have a lower backscattering fraction than non-absorptive hydrosols. This study of light scattering by non-spherical hydrosols would lead to better radiative transfer models in ocean waters and new remote sensing techniques of hydrosol compositions.

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.

Equivalence of internal and external mixture schemes of single scattering properties in vector radiative transfer.

Polarized radiation fields in a turbid medium are influenced by single-scattering properties of scatterers. It is common that media contain two or more types of scatterers, which makes it essential to properly mix single-scattering properties of different types of scatterers in the vector radiative transfer theory. The vector radiative transfer solvers can be divided into two basic categories: the stochastic and deterministic methods. The stochastic method is basically the Monte Carlo method, which can handle scatterers with different scattering properties explicitly. This mixture scheme is called the external mixture scheme in this paper. The deterministic methods, however, can only deal with a single set of scattering properties in the smallest discretized spatial volume. The single-scattering properties of different types of scatterers have to be averaged before they are input to deterministic solvers. This second scheme is called the internal mixture scheme. The equivalence of these two different mixture schemes of scattering properties has not been demonstrated so far. In this paper, polarized radiation fields for several scattering media are solved using the Monte Carlo and successive order of scattering (SOS) methods and scattering media contain two types of scatterers: Rayleigh scatterers (molecules) and Mie scatterers (aerosols). The Monte Carlo and SOS methods employ external and internal mixture schemes of scatterers, respectively. It is found that the percentage differences between radiances solved by these two methods with different mixture schemes are of the order of 0.1%. The differences of Q/I, U/I, and V/I are of the order of 10-5∼10-4, where I, Q, U, and V are the Stokes parameters. Therefore, the equivalence between these two mixture schemes is confirmed to the accuracy level of the radiative transfer numerical benchmarks. This result provides important guidelines for many radiative transfer applications that involve the mixture of different scattering and absorptive particles.

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.

Spectral sea surface reflectance of skylight.

In examining the dependence of the sea surface reflectance of skylight ρs on sky conditions, wind speed, solar zenith angle, and viewing geometry, Mobley [Appl. Opt.38, 7442 (1999).10.1364/AO.38.007442] assumed ρs is independent of wavelength. Lee et al. [Opt. Express18, 26313 (2010).10.1364/OE.18.026313] showed experimentally that ρs does vary spectrally due to the spectral difference of sky radiance coming from different directions, which was ignored in Mobley's study. We simulated ρs from 350 nm to 1000 nm by explicitly accounting for spectral variations of skylight distribution and Fresnel reflectance. Furthermore, we separated sun glint from sky glint because of significant differences in magnitude, spectrum and polarization state between direct sun light and skylight light. The results confirm that spectral variation of ρs(λ) mainly arises from the spectral distribution of skylight and would vary from slightly blueish due to normal dispersion of the refractive index of water, to neutral and then to reddish with increasing wind speeds and decreasing solar zenith angles. Polarization moderately increases sky glint by 8 - 20% at 400 nm but only by 0 - 10% at 1000 nm. Sun glint is inherently reddish and becomes significant (>10% of sky glint) when the sun is at the zenith with moderate winds or when the sea is roughened (wind speeds > 10 m s-1) with solar zenith angles < 20°. We recommend a two-step procedure by first correcting the glint due to direct sun light, which is unpolarized, followed by removing the glint due to diffused and polarized skylight. The simulated ρs(λ) as a function of wind speeds, sun angles and aerosol concentrations for currently recommended sensor-sun geometry, i.e., zenith angle = 40° and azimuthal angle relative to the sun = 45°, is available upon request.

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.

Inherent optical properties of the coccolithophore: Emiliania huxleyi.

A realistic nonspherical model for Emiliania huxleyi (EHUX) is built, based on electron micrographs of coccolithophore cells. The Inherent Optical Properties (IOP) of the EHUX are then calculated numerically by using the discrete dipole approximation. The coccolithophore model includes a near-spherical core with the refractive index of 1.04 + m(i)j, and a carbonate shell formed by smaller coccoliths with refractive index of 1.2 + m(i)j, where m(i) = 0 or 0.01 and j(2) = -1. The reported IOP are the Mueller scattering matrix, backscattering probability, and depolarization ratio. Our calculation shows that the Mueller matrices of coccolithophores show different angular dependence from those of coccoliths.

CALIPSO lidar ratio retrieval over the ocean.

We are demonstrating on a few cases the capability of CALIPSO to retrieve the 532 nm lidar ratio over the ocean when CloudSat surface scattering cross section is used as a constraint. We are presenting the algorithm used and comparisons with the column lidar ratio retrieved by the NASA airborne high spectral resolution lidar. For the three cases presented here, the agreement is fairly good. The average CALIPSO 532 nm column lidar ratio bias is 13.7% relative to HSRL, and the relative standard deviation is 13.6%. Considering the natural variability of aerosol microphysical properties, this level of accuracy is significant since the lidar ratio is a good indicator of aerosol types. We are discussing dependencies of the accuracy of retrieved aerosol lidar ratio on atmospheric aerosol homogeneity, lidar signal to noise ratio, and errors in the optical depth retrievals. We are obtaining the best result (bias 7% and standard deviation around 6%) for a nighttime case with a relatively constant lidar ratio (in the vertical) indicative of homogeneous aerosol type.

Lidar equation for ocean surface and subsurface.

The lidar equation for ocean at optical wavelengths including subsurface signals is revisited using the recent work of the radiative transfer and ocean color community for passive measurements. The previous form of the specular and subsurface echo term are corrected from their heritage, which originated from passive remote sensing of whitecaps, and is improved for more accurate use in future lidar research. A corrected expression for specular and subsurface lidar return is presented. The previous formalism does not correctly address angular dependency of specular lidar return and overestimates the subsurface term by a factor ranging from 89% to 194% for a nadir pointing lidar. Suggestions for future improvements to the lidar equation are also presented.

Platform effects on optical variability and prediction of underwater visibility.

We present hydrographic and optical data collected concurrently from two different platforms, the R/P FLoating Instrument Platform and the R/V Kilo Moana, located about 2km apart in the Santa Barbara Channel in California. We show that optical variability between the two platforms was due primarily to platform effects, specifically the breakdown of stratification from mixing by the hull of R/P FLIP. Modeled underwater radiance distribution differed by as much as 50% between the two platforms during stratified conditions. We determine that the observed optical variability resulted in up to 57% differences in predicted horizontal visibility of a black target.

Equivalent path lengths in an integrating cavity: comment.

The equivalent absorption path length in an integrating cavity is examined. In an otherwise excellent paper, Tranchart et al. [Appl. Opt. 35, 7070 (1996)] made an important error in obtaining the expressions for the equivalent path length in an integrating cavity. This error has been propagated through several other publications in the literature. Since the equivalent path length is the sine qua non for obtaining an accurate absorption coefficient when using an integrating cavity, it is our intent here to give the correct formulas to prevent further errors when extracting absorption coefficients.

Polarized radiance fields under a dynamic ocean surface: a three-dimensional radiative transfer solution.

The hybrid matrix operator, Monte Carlo (HMOMC) method previously reported [Appl. Opt.47, 1063-1071 (2008)] is improved by neglecting higher-order terms in the coupling of the matrix operators and by introducing a dual grid scheme. The computational efficiency for solving the vector radiative transfer equation in a full 3D coupled atmosphere-surface-ocean system is substantially improved, and, thus, large-scale simulations of the radiance distribution become feasible. The improved method is applied to the computation of the polarized radiance field under realistic surface waves simulated by the power spectral density method. To the authors' best knowledge, this is the first time that the polarized radiance field under a dynamic ocean surface and the underwater image of an object above such an ocean surface have been reported.

A vector radiative transfer model for coupled atmosphere and ocean systems based on successive order of scattering method.

A vector radiative transfer model has been developed for coupled atmosphere and ocean systems based on the Successive Order of Scattering (SOS) Method. The emphasis of this study is to make the model easy-to-use and computationally efficient. This model provides the full Stokes vector at arbitrary locations which can be conveniently specified by users. The model is capable of tracking and labeling different sources of the photons that are measured, e.g. water leaving radiances and reflected sky lights. This model also has the capability to separate florescence from multi-scattered sunlight. The delta - fit technique has been adopted to reduce computational time associated with the strongly forward-peaked scattering phase matrices. The exponential - linear approximation has been used to reduce the number of discretized vertical layers while maintaining the accuracy. This model is developed to serve the remote sensing community in harvesting physical parameters from multi-platform, multi-sensor measurements that target different components of the atmosphere-oceanic system.

Mueller matrix imaging of targets under an air-sea interface.

The Mueller matrix imaging method is a powerful tool for target detection. In this study, the effect of the air-sea interface on the detection of underwater objects is studied. A backward Monte Carlo code has been developed to study this effect. The main result is that the reflection of the diffuse sky light by the interface reduces the Mueller image contrast. If the air-sea interface is ruffled by wind, the distinction between different regions of the underwater target is smoothed out. The effect of the finite size of an active light source is also studied. The image contrast is found to be relatively insensitive to the size of the light source. The volume scattering function plays an important role on the underwater object detection. Generally, a smaller asymmetry parameter decreases the contrast of the polarimetry images.