Approach for Propagating Radiometric Data Uncertainties Through NASA Ocean Color Algorithms

Spectral correlation in MODIS water-leaving reflectance retrieval uncertainty

Spectral remote sensing reflectance, Rrs(λ) (sr-1), is the fundamental quantity used to derive a host of bio-optical and biogeochemical properties of the water column from satellite ocean color measurements. Estimation of uncertainty in those derived geophysical products is therefore dependent on knowledge of the uncertainty in satellite-retrieved Rrs. Furthermore, since the associated algorithms require Rrs at multiple spectral bands, the spectral (i.e., band-to-band) error covariance in Rrs is needed to accurately estimate the uncertainty in those derived properties. This study establishes a derivative-based approach for propagating instrument random noise, instrument systematic uncertainty, and forward model uncertainty into Rrs, as retrieved using NASA's multiple-scattering epsilon (MSEPS) atmospheric correction algorithm, to generate pixel-level error covariance in Rrs. The approach is applied to measurements from Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite and verified using Monte Carlo (MC) analysis. We also make use of this full spectral error covariance in Rrs to calculate uncertainty in phytoplankton pigment chlorophyll-a concentration (chla, mg/m3) and diffuse attenuation coefficient of downwelling irradiance at 490 nm (Kd(490), m-1). Accounting for the error covariance in Rrs generally reduces the estimated relative uncertainty in chla by ∼1-2% (absolute value) in waters with chla < 0.25 mg/m3 where the color index (CI) algorithm is used. The reduction is ∼5-10% in waters with chla > 0.35 mg/m3 where the blue-green ratio (OCX) algorithm is used. Such reduction can be higher than 30% in some regions. For Kd(490), the reduction by error covariance is generally ∼2%, but can be higher than 20% in some regions. The error covariance in Rrs is further verified through forward-calculating chla from MODIS-retrieved and in situ Rrs and comparing estimated uncertainty with observed differences. An 8-day global composite of propagated uncertainty shows that the goal of 35% uncertainty in chla can be achieved over deep ocean waters (chla ≤ 0.1 mg/m3). While the derivative-based approach generates reasonable error covariance in Rrs, some assumptions should be updated as our knowledge improves. These include the inter-band error correlation in top-of-atmosphere reflectance, and uncertainties in the calibration of MODIS 869 nm band, in ancillary data, and in the in situ data used for system vicarious calibration.

Extending aquatic spectral information with the first radiometric IR-B field observations

Planetary radiometric observations enable remote sensing of biogeochemical parameters to describe spatiotemporal variability in aquatic ecosystems. For approximately the last half century, the science of aquatic radiometry has established a knowledge base using primarily, but not exclusively, visible wavelengths. Scientific subdisciplines supporting aquatic radiometry have evolved hardware, software, and procedures to maximize competency for exploiting visible wavelength information. This perspective culminates with the science requirement that visible spectral resolution must be continually increased to extract more information. Other sources of information, meanwhile, remain underexploited, particularly information from nonvisible wavelengths. Herein, absolute radiometry is used to evaluate spectral limits for deriving and exploiting aquatic data products, specifically the normalized water-leaving radiance, Γ ( λ ) , and its derivative products. Radiometric observations presented herein are quality assured for individual wavebands, and spectral verification is conducted by analyzing celestial radiometric results, comparing agreement of above- and in-water observations at applicable wavelengths, and evaluating consistency with bio-optical models and optical theory. The results presented include the first absolute radiometric field observations of Γ ( λ ) within the IR-B spectral domain (i.e. spanning 1400-3000 nm), which indicate that IR-B signals confer greater and more variable flux than formerly ascribed. Black-pixel processing, a routine correction in satellite and in situ aquatic radiometry wherein a spectrum is offset corrected relative to a nonvisible waveband (often IR-B or a shorter legacy waveband) set to a null value, is shown to degrade aquatic spectra and derived biogeochemical parameters.

Bayesian approach to a generalized inherent optical property model

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.

Derivation of uncertainty budgets for continuous above-water radiometric measurements along an Atlantic Meridional Transect

Fiducial reference measurements are in-situ data traceable to metrology standards, with associated uncertainties. This paper presents the methodology used to derive the uncertainty budget for underway, above-water measurements from the Seabird Hyperspectral Surface Acquisition System deployed on an Atlantic Meridional Transect in 2018. The average uncertainty of remote sensing reflectance for clear sky days was ∼ 6% at wavelengths < 490 nm and ∼ 12% at wavelengths > 550 nm. The environmental variability such as sun position, wind speed and skylight distribution caused the greatest uncertainty. The different components of the uncertainty budget are critically assessed to indicate how the measurement procedure could be improved through reducing the principal uncertainty sources.

Optimal estimation framework for ocean color atmospheric correction and pixel-level uncertainty quantification

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_rs(λ);sr^-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_rs(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_rs(λ) estimates relative to the NASA standard operational algorithm by improving all statistical metrics at 443, 555, and 667 nm. Unphysical negative R_rs(λ), which often appears in complex water conditions, was reduced by a factor of 3. The OE-derived pixel-level R_rs(λ) uncertainty estimates were also assessed relative to in-situ data and were shown to have skill.

Development and Validation of an Empirical Ocean Color Algorithm with Uncertainties: A Case Study with the Particulate Backscattering Coefficient

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.

Bayesian retrieval of optically relevant properties from hyperspectral water-leaving reflectances

Current methods to retrieve optically relevant properties from ocean color observations do not explicitly make use of prior knowledge about property distributions. Here we implement a simplified Bayesian approach that takes into account prior probability distributions on two sets of five optically relevant parameters, and conduct a retrieval of these parameters using hyperspectral simulated water-leaving reflectances. We focus specifically on the ability of the model to distinguish between two optically similar phytoplankton taxa, diatoms and Noctiluca scintillans. The inversion retrieval gives most-likely concentrations and uncertainty estimates, and we find that the model is able to probabilistically predict the occurrence of Noctiluca scintillans blooms using these metrics. We discuss how this method can be expanded to include a priori covariances between different parameters, and show the effect of varying measurement uncertainty and spectral resolution on Noctiluca scintillans bloom predictions.