Zhang Minwei, Ibrahim Amir, Franz Bryan A, Sayer Andrew M, Werdell P Jeremy, McKinna Lachlan I
Opt Express. 2024 Jan 15;32(2):2490-2506. doi: 10.1364/OE.502561.
Spectral remote sensing reflectance, R(λ) (sr), 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 R. Furthermore, since the associated algorithms require R at multiple spectral bands, the spectral (i.e., band-to-band) error covariance in R 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 R, as retrieved using NASA's multiple-scattering epsilon (MSEPS) atmospheric correction algorithm, to generate pixel-level error covariance in R. 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 R to calculate uncertainty in phytoplankton pigment chlorophyll-a concentration (chl, mg/m) and diffuse attenuation coefficient of downwelling irradiance at 490 nm (K(490), m). Accounting for the error covariance in R generally reduces the estimated relative uncertainty in chl by ∼1-2% (absolute value) in waters with chl< 0.25 mg/m where the color index (CI) algorithm is used. The reduction is ∼5-10% in waters with chl> 0.35 mg/m where the blue-green ratio (OCX) algorithm is used. Such reduction can be higher than 30% in some regions. For K(490), the reduction by error covariance is generally ∼2%, but can be higher than 20% in some regions. The error covariance in R is further verified through forward-calculating chl from MODIS-retrieved and in situ R and comparing estimated uncertainty with observed differences. An 8-day global composite of propagated uncertainty shows that the goal of 35% uncertainty in chl can be achieved over deep ocean waters (chl ≤ 0.1 mg/m). While the derivative-based approach generates reasonable error covariance in R, 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.
光谱遥感反射率R(λ)（sr）是用于从卫星海洋颜色测量中推导一系列水柱生物光学和生物地球化学特性的基本量。因此，这些推导的地球物理产品的不确定性估计取决于对卫星反演R的不确定性的了解。此外，由于相关算法需要多个光谱波段的R，因此需要R中的光谱（即波段间）误差协方差来准确估计这些推导特性的不确定性。本研究建立了一种基于导数的方法，将仪器随机噪声、仪器系统不确定性和正向模型不确定性传播到使用美国国家航空航天局（NASA）的多重散射ε（MSEPS）大气校正算法反演的R中，以生成R中的像素级误差协方差。该方法应用于Aqua卫星上的中分辨率成像光谱仪（MODIS）的测量数据，并通过蒙特卡罗（MC）分析进行验证。我们还利用R中的这种全光谱误差协方差来计算浮游植物色素叶绿素a浓度（chl，mg/m）和490nm处下行辐照度的漫衰减系数（K(490)，m）的不确定性。考虑R中的误差协方差通常会使使用颜色指数（CI）算法的chl<0.25mg/m的水域中估计的相对不确定性降低约1-2%（绝对值）。在使用蓝绿比（OCX）算法的chl>0.35mg/m的水域中，降低幅度约为5-10%。在某些区域，这种降低幅度可能高于30%。对于K(490)，误差协方差导致的降低幅度通常约为2%，但在某些区域可能高于20%。通过从MODIS反演的和现场的R正向计算chl，并将估计的不确定性与观测差异进行比较，进一步验证了R中的误差协方差。一个8天的全球传播不确定性合成数据表明，在深海区域（chl≤0.1mg/m）可以实现chl不确定性为35%的目标。虽然基于导数的方法在R中生成了合理的误差协方差，但随着我们知识的提高，一些假设应该更新。这些假设包括大气顶反射率的波段间误差相关性，以及MODIS 869nm波段校准、辅助数据和用于系统替代校准的现场数据中的不确定性。
