Practical aspects of providing pixel-level spectral Rrs error covariance in satellite ocean color products

Abstract

We previously established a derivative-based approach to generate a pixel-level spectral error covariance matrix in satellite-retrieved remote sensing reflectance, ∑Rᵣₛ. However, one practical issue is the delivery of the products without increasing the file size by an order of magnitude or more, considering that for N sensor spectral bands, there are N × (N+1)/2 covariance matrix elements to be specified at each pixel. The issue becomes more pertinent for hyperspectral imaging spectroradiometers such as the Ocean Color Instrument (OCI) on NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem mission (PACE), which has 286 bands, resulting in ∼40,000 unique elements in ∑Rᵣₛ per pixel that would lead to a ∼60 GB Level-2 file for one 5-min granule. As a first step to tackle the issue, we took OCI and Moderate Resolution Imaging Spectroradiometer (MODIS) data to explore the possibility of approximating ∑Rᵣₛ using a third-degree polynomial, thereby decreasing the memory overhead to 4×N numbers. We found that ∑Rᵣₛ derived from the polynomial fitting matches well with the original value, with the difference smaller than 5%. We then compared the relative uncertainty in two derived ocean color data products (chlₐ and K<subscript d>(490)) calculated using the original fully computed ∑Rᵣₛ and then using the polynomial model approximation for ∑Rᵣₛ, finding the absolute difference between the two approaches to be smaller than 0.5%. These evaluations suggest the polynomial approximation of ∑Rᵣₛ is suitable without degrading the scientific quality. By including the coefficients derived from polynomial fitting instead of the full error covariance matrix, a typical 5-min Level-2 file for OCI decreases from ∼60 GB to a more practical ∼1.7 GB.