Ocean color measured from satellites provides daily global, synoptic views of spectral waterleaving reflectances that can be used to generate estimates of marine inherent optical properties (IOPs). These reflectances, namely the ratio of spectral upwelled radiances to spectral downwelled irradiances, describe the light exiting a water mass that defines its color. IOPs are the spectral absorption and scattering characteristics of ocean water and its dissolved and particulate constituents. Because of their dependence on the concentration and composition of marine constituents, IOPs can be used to describe the contents of the upper ocean mixed layer. This information is critical to further our scientific understanding of biogeochemical oceanic processes, such as organic carbon production and export, phytoplankton dynamics, and responses to climatic disturbances. Given their importance, the international ocean color community has invested significant effort in improving the quality of satellite-derived IOP products, both regionally and globally. Recognizing the current influx of data products into the community and the need to improve current algorithms in anticipation of new satellite instruments (e.g., the global, hyperspectral spectroradiometer of the NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission), we present a synopsis of the current state of the art in the retrieval of these core optical properties. Contemporary approaches for obtaining IOPs from satellite ocean color are reviewed and, for clarity, separated based their inversion methodology or the type of IOPs sought. Summaries of known uncertainties associated with each approach are provided, as well as common performance metrics used to evaluate them. We discuss current knowledge gaps and make recommendations for future investment for upcoming missions whose instrument characteristics diverge sufficiently from heritage and existing sensors to warrant reassessing current approaches.

Spectroradiometric satellite observations of the ocean are commonly referred to as “ocean color” remote sensing. NASA has continuously collected, processed, and distributed ocean color datasets since the launch of the Sea-viewing Wide-field-of-view Sensor (SeaWiFS) in 1997. While numerous ocean color algorithms have been developed in the past two decades that derive geophysical data products from sensor-observed radiometry, few papers have clearly demonstrated how to estimate measurement uncertainty in derived data products. As the uptake of ocean color data products continues to grow with the launch of new and advanced sensors, it is critical that pixel-by-pixel data product uncertainties are estimated during routine data processing. Knowledge of uncertainties can be used when studying long-term climate records, or to assist in the development and performance appraisal of bio-optical algorithms. In this methods paper we provide a comprehensive overview of how to formulate first-order first-moment (FOFM) calculus for propagating radiometric uncertainties through a selection of bio-optical models. We demonstrate FOFM uncertainty formulations for the following NASA ocean color data products: chlorophyll-a pigment concentration (Chl), the diffuse attenuation coefficient at 490 nm (K_d,490), particulate organic carbon (POC), normalized fluorescent line height (nflh), and inherent optical properties (IOPs). Using a quality-controlled in situ hyperspectral remote sensing reflectance (R_rs,i) dataset, we show how computationally inexpensive, yet algebraically complex, FOFM calculations may be evaluated for correctness using the more computationally expensive Monte Carlo approach. We compare bio-optical product uncertainties derived using our test R_rs dataset assuming spectrally-flat, uncorrelated relative uncertainties of 1, 5, and 10%. We also consider spectrally dependent, uncorrelated relative uncertainties in R_rs. The importance of considering spectral covariances in R_rs, where practicable, in the FOFM methodology is highlighted with an example SeaWiFS image. We also present a brief case study of two POC algorithms to illustrate how FOFM formulations may be used to construct measurement uncertainty budgets for ecologically-relevant data products. Such knowledge, even if rudimentary, may provide useful information to end-users when selecting data products or when developing their own algorithms.

We explored how algorithm (model) and in situ measurement (observation) uncertainties can effectively be incorporated into empirical ocean color model development and assessment. In this study we focused on methods for deriving the particulate backscattering coefficient at 555 nm, b_bp(555) (m⁻¹). We developed a simple empirical algorithm for deriving b_bp(555) as a function of a remote sensing reflectance line height (LH) metric. Model training was performed using a high‐quality bio‐optical dataset that contains coincident in situ measurements of the spectral remote sensing reflectances, R_rs(λ) (sr⁻¹), and the spectral particulate backscattering coefficients, b_bp(λ). The LH metric used is defined as the magnitude of R_rs(555) relative to a linear baseline drawn between R_rs(490) and R_rs(670). Using an independent validation dataset, we compared the skill of the LH‐based model with two other models. We used contemporary validation metrics, including bias and mean absolute error (MAE), that were corrected for model and observation uncertainties. The results demonstrated that measurement uncertainties do indeed impact contemporary validation metrics such as mean bias and MAE. Zeta‐scores and z‐tests for overlapping confidence intervals were also explored as potential methods for assessing model skill.

Relationships between the absorption and backscattering coefficients of marine optical constituents and ocean color, or remote sensing reflectances R _rs (λ), can be used to predict the concentrations of these constituents in the upper water column. Standard inverse modeling techniques that minimize error between the modeled and observed R _rs (λ) break down when the number of products retrieved becomes similar to, or greater than, the number of different ocean color wavelengths measured. Furthermore, most conventional ocean reflectance inversion approaches, such as the default configuration of NASA’s Generalized Inherent Optical Properties algorithm framework (GIOP-DC), require a priori definitions of absorption and backscattering spectral shapes. A Bayesian approach to GIOP is implemented here to address these limitations, where the retrieval algorithm minimizes both the error in retrieved ocean color and the deviation from prior knowledge, calculated using output from a mixture of empirically-derived and best-fit values. The Bayesian approach offers potential to produce an expanded range of parameters related to the spectral shape of absorption and backscattering spectra.

We demonstrate a simple, spectrally resolved ocean color remote sensing model to estimate benthic photosynthetically active radiation (bPAR) for the waters of the Great Barrier Reef (GBR), Australia. For coastal marine environments and coral reefs, the underwater light field is critical to ecosystem health, but data on bPAR rarely exist at ecologically relevant spatio-temporal scales. The bPAR model presented here is based on Lambert-Beer’s Law and uses: (i) sea surface values of the downwelling solar irradiance, E_s(λ); (ii) high-resolution seafloor bathymetry data; and (iii) spectral estimates of the diffuse attenuation coefficient, K_d(λ), calculated from GBR-specific spectral inherent optical properties (IOPs). We first derive estimates of instantaneous bPAR. Assuming clear skies, these instantaneous values were then used to obtain daily integrated benthic PAR values. Matchup comparisons between concurrent satellite-derived bPAR and in situ values recorded at four optically varying test sites indicated strong agreement, small bias, and low mean absolute error. Overall, the matchup results suggest that our benthic irradiance model was robust to spatial variation in optical properties, typical of complex shallow coastal waters such as the GBR. We demonstrated the bPAR model for a small test region in the central GBR, with the results revealing strong patterns of temporal variability. The model will provide baseline datasets to assess changes in bPAR and its external drivers and may form the basis for a future GBR water-quality index. This model may also be applicable to other coastal waters for which spectral IOP and high-resolution bathymetry data exist.

Ocean color (OC) remote sensing requires compensation for atmospheric scattering and absorption (aerosol, Rayleigh, and trace gases), referred to as atmospheric correction (AC). AC allows inference of parameters such as spectrally resolved remote sensing reflectance ( R r s ( λ ) ; s r − 1 ) at the ocean surface from the top-of-atmosphere reflectance. Often the uncertainty of this process is not fully explored. Bayesian inference techniques provide a simultaneous AC and uncertainty assessment via a full posterior distribution of the relevant variables, given the prior distribution of those variables and the radiative transfer (RT) likelihood function. Given uncertainties in the algorithm inputs, the Bayesian framework enables better constraints on the AC process by using the complete spectral information compared to traditional approaches that use only a subset of bands for AC. This paper investigates a Bayesian inference research method (optimal estimation [OE]) for OC AC by simultaneously retrieving atmospheric and ocean properties using all visible and near-infrared spectral bands. The OE algorithm analytically approximates the posterior distribution of parameters based on normality assumptions and provides a potentially viable operational algorithm with a reduced computational expense. We developed a neural network RT forward model look-up table-based emulator to increase algorithm efficiency further and thus speed up the likelihood computations. We then applied the OE algorithm to synthetic data and observations from the moderate resolution imaging spectroradiometer (MODIS) on NASA’s Aqua spacecraft. We compared the R r s ( λ ) retrieval and its uncertainty estimates from the OE method with in-situ validation data from the SeaWiFS bio-optical archive and storage system (SeaBASS) and aerosol robotic network for ocean color (AERONET-OC) datasets. The OE algorithm improved R r s ( λ ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative R r s ( λ ) , which often appears in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level R r s ( λ ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.