How many independent quantities can be extracted from ocean color?

Products derived from remote sensing reflectances (R-rs(lambda)), for example, chlorophyll, phytoplankton carbon, euphotic depth, or particle size, are widely used in oceanography. Problematically, R-rs(lambda) may have fewer degrees of freedom (DoF) than measured wavebands or derived products. Here, we show that a global sea surface hyperspectral R-rs(lambda) dataset has DoF = 4. MODIS-like multispectral equivalent in situ data also have DoF = 4, while their SeaWiFS equivalent has DoF = 3. Both multispectral-equivalent datasets predict individual hyperspectral wavelengths' R-rs(lambda) within nominal uncertainties. Remotely sensed climatological multispectral R-rs(lambda) have DoF = 2, as information is lost by atmospheric correction, shifting to larger spatiotemporal scales, and/or more open-ocean measurements, but suites of R-rs(lambda )-derived products have DoF = 1. These results suggest that remote sensing products based on existing satellites' R-rs(lambda ) are not independent and should not be treated as such, that existing R-rs(lambda) measurements hold unutilized information, and that future multi-or especially hyper-spectral algorithms must rigorously consider correlations between R-rs(lambda ) wavebands.