Spectral correlation in MODIS water-leaving reflectance retrieval uncertainty

Abstract

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 (Kₔ(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 Kₔ(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.