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With previous NASA PACE Science Team support, Twardowski and Tonizzo (2018) (TT18) developed a new radiative transfer (RT) approximation for ocean color reflectance that includes the bidirectional reflectance distribution function (BRDF) and explicitly incorporates the volume scattering function (VSF). This model, called Zaneveld-Twardowski-Tonizzo (ZTT), has demonstrated improved performance relative to current state-of-the-art models by Morel et al. (2002) (M02) and Lee et al. (2011) that are based on simple first order approximations relating reflectance to absorption and backscattering based originally on Gordon et al. (1988). TT18 demonstrated the stronger performance was due to the greater degrees of freedom in describing the RT phenomenon relative to simple first order approximations.

The ZTT model is readily amenable to inversion within the Generalized IOP (GIOP) algorithm framework as currently implemented by NASA OBPG in SeaDAS and described in Werdell et al. (2013). Biogeochemical subcomponents of absorption and backscattering can similarly be derived. In preliminary assessments, the ZTT inversion has exhibited stronger overall performance than similar implementation configurations for GIOP. There are several additional expected advantages in application of the algorithm for the future PACE mission, as the model:

1. is natively hyperspectral (M02 is not);
2. enables direct assimilation of VSF data from concurrent PACE polarimetry measurements to potentially reduce uncertainties in IOP retrievals;
3. includes the backscattering ratio, a long sought-after product of ocean color remote sensing with valuable information on particle composition;
4. is generic to any natural water;
5. is a single analytical and invertible expression describing the RT process for all remote sensing geometries, i.e., it includes the BRDF and eliminates BRDF normalization steps;
6. retains native RT relationships directly linked to physically meaningful terms with more degrees of freedom than simple first order approximations;
7. allows the uncertainties for all parameters including the VSF to be readily characterized; and
8. can be readily enhanced by tuning one or more terms rather than developing new look-up tables from complete recomputations of full RT.

Our approach will start with characterizing uncertainties for the ZTT model for all remote sensing viewing geometries. TT18 were only able to validate the model for conventional nadir viewing radiance measurements. We will also provide a new BRDF normalization algorithm for PACE, needed for reflectance intercomparisons and mapping and will work with Marco Talone and Giuseppe Zibordi to quantify uncertainties in applying the ZTT BRDF model to the AERONET data sets.

We will assess uncertainties in applying the ZTT inversion within the GIOP framework to derive IOPs for available validation data sets and compare to current state-of-the-art inversion algorithms. We will seek to enhance the performance of ZTT inversions in GIOP by 1) compiling enhanced hyperspectral libraries of subcomponent IOPs to serve as spectral shape vectors in the algorithm and 2) by implementing a more robust, quicker, and accurate error minimization algorithm based on Particle Swarm Optimization (PSO). We will configure the ZTT inversion to incorporate concurrent VSF data from PACE polarimeters and to provide the particulate backscattering ratio as a new product. A final objective will be pursuing a polarized version of the ZTT model that may be implemented with PACE.

OUR OVERALL PROJECT GOAL: to provide IOP inversion algorithms to be implemented for the PACE mission based on the natively hyperspectral ZTT model with robustly characterized uncertainties for all IOP products.

Radiative transfer (RT) approximations form the basis of semi-analytical (SA) inversion algorithms formulated to derive IOPs and subsequently biogeochemical parameters from ocean color remote sensing. Leading SA inversion algorithms, however, have not been rigorously assessed with respect to particulate volume scattering function (VSF) variability in the ocean, as, up until very recently, the comprehensive VSF data sets required for such an assessment have not been available. It is generally recognized by the community that there is likely no larger source of uncertainty in current SA algorithms to derive IOPs than the uncertainty associated with variability in VSF shapes, as the other important parameters in the inversions have been rigorously assessed (Loisel et al. 2001; Morel et al. 2002; Gordon 2002). Through field work since 2005 supported by NASA and other sources, we now have extensive in situ IOP data sets from 18 locations that contain fully resolved VSFs in a wide range of Case I and Case II waters throughout the world (Sullivan and Twardowski 2009; Czerski et al. 2011; You et al. 2011; Twardowski et al. 2012; Gilerson et al. 2013; Randolph et al., in press). Included in these data sets are NASA ocean color validation experiments with concurrently collected IOP (including VSF) and radiometric measurements, where the technological assets employed, scope of the measurements, and attention to accuracy make these data sets special and unique. Not only are they some of the few nominally complete data sets from an RT closure perspective that we are aware of (as they include full VSFs and full radiance distributions), but the data quality is the highest possible that can be achieved at this time. With such measurements in hand, we have an exciting opportunity to evaluate the effects of varying VSF shape on retrieval uncertainties for the leading SA inversions, and to assess performance for a variety of specific environmental conditions. There is also the opportunity to reevaluate RT approximations such as a Zaneveld (1995) model that explicitly includes VSF shape information, as these models have generally been avoided due to the historical lack of representative VSF data. The specific goals of this work are to 1) assess the full range of variability in VSF shapes in the ocean using an extensive data base of custom VSF measurements collected by our lab, 2) evaluate uncertainties in leading SA inversion approaches associated with this natural VSF variability through RT modeling, and 3) to resuscitate, rework, and evaluate uncertainties in native, analytical RT approximations developed by Zaneveld (1995) and Jerlov (1976) that have received little attention to date specifically because of the fact that they included explicit VSF formulations that could not be practically applied in the past. Our approach will first involve computing remote sensing reflectances from our extensive data sets using the Hydrolight RT solution. Reflectances will then be validated using concurrently measured radiometry data to assess convolved errors in the measurements (separate from uncertainties related to inversion approximations), and to ensure the data sets are sound from a theoretical standpoint. The SA inversion algorithms will then be applied, with the retrieved absorption and backscattering compared to the original measurements to quantify uncertainties. Our overall goal is to quantify and minimize errors in inversion results when applied to a representative range of observed VSFs in the ocean, leading to recommendations in SA algorithm applications for the future PACE mission.