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The research frontiers of radiative transfer RT in coupled atmosphere-ocean systems are explored to enable new science and specifically to support the upcoming Plankton, Aerosol, Cloud ocean Ecosystem PACE satellite mission. Instead, we focus on both theoretical and experimental studies of RT topics important to the science threshold and goal questions of the PACE mission and the measurement capabilities of its instruments.

Our topics cover 1 the ocean i. We provide for each topic a summary of past relevant heritage work, followed by a discussion for unresolved questions and RT updates. It is scheduled for launch in into a Sun synchronous, The science goals for this mission are NASA, a : 1 to extend past and current key systematic ocean color, aerosol, and cloud data records for Earth system and climate studies; and 2 to address new and emerging oceanic and atmospheric science questions using advanced instruments.

At the same time, the advanced remote sensing capabilities that these instruments offer places also require stringent requirements for forward and inverse radiative transfer RT modeling of light reflected by atmosphere-ocean systems.

The width of an OCI image will be 2, km which leads to a two-day ocean color coverage of the globe , and the spatial resolution will be 1 km for nadir viewing pixels. OCI will make single-view, hyperspectral radiance measurements for each pixel at a spectral resolution of 5 nm that cover the ultraviolet UV regime between and nm, the visible VIS between and nm, and the near infrared NIR regime between and nm.

In addition, OCI will obtain single-view, narrow-band radiance measurements for each pixel in the short-wave infrared SWIR regime at nine wavelengths , , , , , , and nm. However, it is well established that the addition of bands and increase in SNR when compared to past ocean color missions should improve the retrievals relative to the current state of the art.

The ultimate evaluation the IOP retrieval performance will take place by comparing with co-located independent IOP measurement sets. Furthermore, both polarimeter instruments will look at each of their own pixels from multiple directions and will therefore capture angular features in the total and linearly polarized radiance.

On the other hand, HARP2 will provide measurements of the total and linearly polarized radiance in discrete narrow-bands 10—40 nm resolution at four wavelengths in the VIS-NIR regime , , , and nm.

Accurate calculations of the transport of solar radiant energy entering the Earth atmosphere are important for remote sensing of ocean color, aerosols, and clouds.

They are needed to simulate the signal measured by an optical sensor, which may be carried onboard a satellite or deployed at any level in the ocean or atmosphere, to estimate the radiant contributions by various components in atmosphere-ocean systems, to characterize the properties angular, spectral, and polarized of the light field, and to develop inverse methods to retrieve the types and concentrations of optically active constituents. Diverse processes are involved and interact in various ways e.

Realistic, precise, and reliable simulations depend on the proper treatment of the various processes and their interactions, all at the required spectral resolution hyper-spectral in the case of PACE and taking into account spatial heterogeneity.

The complexity of this work becomes apparent when listing some of the properties that have to be taken into account when performing RT computations in realistic AOS:.

Furthermore, there are geometric concerns that play a role such as the sphericity of the Earth, 3-dimensional variability in scattering properties such as isolated clouds and plankton blooms, azimuthal variability caused by e.

Finally, there are numerical aspects that are important to consider for remote sensing RS applications such as the speed and validation of RT computations.

The work done by our team touches upon many of these topics, the organization of which is presented as follows.

In each of these subsections, we provide a brief overview of heritage work, followed by when applicable updated work performed by our team. In what follows, we provide a brief historical overview of some of the RT studies performed on scattering of light in atmosphere-ocean systems.

The list of studies does not do justice to the vast amount of work done on this topic by numerous researchers over a time span of many decades. We provide detailed historical information in the heritage overview part of each section. Methods and models that deal with RT in the atmosphere alone are reviewed by Hansen and Travis , van de Hulst , Lenoble , and Stamnes Chandrasekhar introduced methods to study reflected light and skylight of an atmosphere above a Lambertian surface.

His methods were extended by Sekera to investigate scattering of polarized light in a Rayleigh atmosphere above a smooth ocean see also Fraser and Walker, Later, Fraser and Ahmad and Fraser used another i.

A Monte Carlo approach was developed for an atmosphere above a smooth water surface plus water body Plass and Kattawar, , , generalized later to include polarization Kattawar et al.

The method of successive orders of scattering without polarization was used by Raschke and later by Quenzel and Kaestner for RT computations in an atmosphere with aerosols and molecules above a rough ocean surface and ocean body. Chami et al. Zhai et al. The adding method van de Hulst, extended to include polarization by Hansen and Hovenier was used by Takashima , for RT computations of polarized light in an atmosphere-surface system.

This work was later updated to include an ocean body with a rough interface Takashima, ; Takashima and Masuda, ; Masuda and Takashima, , Tanaka and Nakajima applied the matrix operator method, which is a variant of the adding method, without polarization for an atmosphere above a water body with a smooth surface. This method was later generalized to include a rough ocean surface by Nakajima and Tanaka and Fischer and Grassl Polarization was included for such systems by He et al.

Dougherty used invariant imbedding techniques to study reflection without polarization by an ocean body covered by a smooth surface but no atmosphere. Mobley , included a rough ocean surface in his Hydrolight program, and recently worked on including polarization for isolated rough ocean surfaces Mobley, and ocean bodies Mobley, Mishchenko and Travis employed a similar method including polarization for an atmosphere above a rough surface but no ocean body.

Jin et al. Meanwhile Schultz et al. Other authors opted to use a combination of the above-mentioned RT methods. For example, Chowdhary et al.

Ota et al. Xu et al. Polarization was taken into account in all of these combined RT methods. The RT methods and AOS models listed above show a gradual trend from scalar computations for oceans with a smooth surface toward including polarization of light and considering rough ocean surfaces. However, most current RT methods still ignore inelastic radiative processes in the ocean, and most current AOS models still assume the atmosphere and ocean to be plane-parallel and horizontally homogeneous.

In addition, most current RT methods apply if not ignore altogether simplified corrections for whitecaps, shadowing effects, and multiple scattering in rough ocean surfaces. Furthermore, much work still needs to be done in linking robust RT computations for realistic atmosphere-ocean systems to bio-optical modeling of ocean color.

This requires among others more flexible bio-optical models that can also be applied to UV radiance, more realistic scattering matrices for marine particulates, better estimates of in elastic scattering and absorption by pure sea water, and less assumptions made for AOS models. Finally, there are no extended, peer-reviewed and accurate tabulated RT bench-mark results for fully coupled atmosphere-ocean models to validate any of the above-mentioned methods to accuracies consistent with PACE measurements.

The next section provides a summary of work done by the — PACE Science Team that touches upon many of these topics. Radiative transfer models describing the angular distribution of the total and polarized radiance that is singly scattered by marine particulates can be classified into A those derived from measurements, B those computed for predefined particulates, and C those approximated with analytical expressions.

Among the most widely used RT models belonging to class A are the early tabulated normalized scattering function data provided by Petzold , and the early tabulated normalized scattering matrix data provided by Voss and Fry Such models have the clear advantage of producing realistic bidirectional reflectance distribution functions BRDFs for water-leaving radiance in multiple scattering computations. The work by Sullivan and Twardowski represents another example of Class A models.

Here, the focus is placed on approximating the shape of the scattering function in the backscattering hemisphere based on extensive field measurements. Note that their results agree with the analytical Fournier-Forand scattering functions discussed below for Class C models. Furthermore they typically assume such particles to be homogeneous with real refractives index m that can be grouped into two or more classes Gordon and Brown, ; Zaneveld et al.

However, the goodness of RT and retrieval results obtained with class B models depends on the shape and internal structure assumed for marine particulates Stramski et al. For example assuming spherical shapes for phytoplankton can create significant biases in the backscattering direction Clavano et al.

Recently, Twardowski et al. Other efforts to account for particle non-sphericity in RT simulations of underwater light are described by Gordon et al. In addition, Organelli et al. Radiative transfer models belonging to class C use simple analytical expressions, instead of rigorous computations, to obtain scattering functions for marine particulates. Among the earliest and simplest models belonging to this class are linear combinations of Henyey-Greenstein functions Henyey and Greenstein, These functions can be parameterized Plass et al.

Another, more widely used model belonging to this class is the Fournier-Forand scattering function Fournier and Forand, ; Fournier and Jonasz, ; Mobley et al.

Mobley et al. Fournier-Forand phase functions are exceptionally accurate for a broad range of particle types. Sullivan and Twardowski showed a remarkably consistent shape for the particulate fraction in volume scattering function measurements collected in ten disparate field sites around the globe, including both Case I and II type waters. The observed phase function shape was consistent with analytical Fournier-Forand phase function shapes when the Mobley et al.

The Sullivan and Twardowski phase functions shape has recently been shown to be applicable even in massive cyanobacterial blooms in Lake Erie Moore et al. This is consistent with previous works showing the BRDF for ocean color remote sensing is, to first order, controlled by the shape of scattering in the backward direction Morel and Gentili, , ; Gordon, ; Zaneveld, ; Morel et al.

Finally, there are hybrid RT models that use the scattering matrices of class A models except for first normalizing them by their scattering function, and then multiplying them by the parameterized functions of class C models e. Such hybrid models combine the advantages of class A for realistic scattering matrices and of class C models for variations in the scattering function. However, they still lack variability for the other scattering matrix elements.

A potential solution to mitigate this problem is to adopt the parameterization provided by Kokhanovsky for the other scattering matrix elements. In this approach, taken by Zhai et al. To investigate the relative importance of plankton shapes and internal structures in INV RT studies of underwater light scattering, computations were initialized to compare the scattering matrices for four classes of particles: I homogeneous and spherical; II homogeneous and non-spherical; III inhomogeneous and spherical; and IV inhomogeneous and non-spherical Chowdhary, Liu et al.

It has been suggested that this plays a role in explaining the so-called missing backscattering enigma in underwater light scattering computations for micrometer-sized marine particles when compared to underwater light measurements Stramski and Kiefer, ; Stramski et al.

Details of the four classes of particles considered thus far are illustrated in Figure 1A. In this panel, chloro , cyto , mito , nucl , and vac stand for chloroplast, cytoplasma, mitochondria, nucleus, and vacuole, respectively. The diameter of the organelles varies between 0. Also shown are scattering matrix examples in Figure 1B that were computed for some of these particles for a wavelength of 0.

These initial computations show that i internal structures increase the radiance scattered in the backward direction by several factors compared to variations in particle shape; and ii only variations in particle shape can create the magnitude of deviations from unity in the 2,2 scattering matrix element seen by Voss and Fry Observation i is consistent with the scattering matrix analyses by Quinby-Hunt et al. Emerging particle characterization methods such as in situ holographic imaging Talapatra et al.

Figure 1. A Particulate classes considered for plankton particles. The lower white curve marks the physical ocean bottom. Fournier-Forand phase functions can be least-squares fit directly to these measured VSFs. This underestimation was also recently noted by Harmel et al. The systematic nature of the bias indicated there may be the possibility of invoking a fitting method that may yet enhance accuracy.

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