Simplified model of spectral absorption by non-algal particles and dissolved organic materials in aquatic environments

Absorption by non-algal particles (NAP, ad) and colored dissolved organic matter (CDOM, ag) are frequently modeled by exponential functions of wavelength, either separately or as a sum. We present a new representation of NAP-plus-CDOM absorption adg based on the stretched exponential function adg(λ) = A exp{−[s(λ − λo)]β}, whose parameter β can be considered a measure of optical heterogeneity. A double exponential representation of adg can be fit extremely well by a stretched exponential for all plausible parameter combinations, despite having one fewer free parameter than a double exponential. Fitting two published compilations of in situ adg data – one at low spectral resolution (n = 5, λ = 412–555 nm) and one at high spectral resolution (n = 201, λ = 300–700 nm) – the stretched exponential outperforms the single exponential, double exponential, and a power law. We thereby conclude that the stretched exponential is the preferred model for adg absorption in circumstances when NAP and CDOM cannot be separated, such as in remote sensing inversions.