Information content of absorption spectra and implications for ocean color inversion

The increasing use of hyperspectral optical data in oceanography, both in situ and via remote sensing, holds the potential to significantly advance characterization of marine ecology and biogeochemistry because, in principle, hyperspectral data can provide much more detailed inferences of ecosystem properties via inversion. Effective inferences, however, require careful consideration of the close similarity of different signals of interest, and how these interplay with measurement error and uncertainty to reduce the degrees of freedom (DoF) of hyperspectral measurements. Here we discuss complementary approaches to quantify the DoF in hyperspectral measurements in the case of in situ particulate absorption measurements, though these approaches can also be used on other such data, e.g., ocean color remote sensing. Analyses suggest intermediate (${\sim}5 $∼5) DoF for our dataset of global hyperspectral particulate absorption spectra from the Tara Oceans expedition, meaning that these data can yield coarse community structure information. Empirically, chlorophyll is an effective first-order predictor of absorption spectra, meaning that error characteristics and the mathematics of inversion need to be carefully considered for hyperspectral data to provide information beyond that which chlorophyll provides. We also discuss other useful analytical tools that can be applied to this problem and place our results in the context of hyperspectral remote sensing.