Estimating pixel-level uncertainty in ocean color retrievals from MODIS

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.

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.