Abstract
Products derived from remote sensing reflectances
($R_{rs}(\lambda)$), e.g. 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. A global sea surface hyperspectral
$R_{rs}(\lambda)$ dataset has DoF=4. MODIS-like
multispectral equivalent 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.