I'm trying to understand the best way to calculate the spectral slope from absorbance data on dissolved organic matter (DOM). The following formula can be seen in a lot of articles (e.g. Helms (2008)):

1 ) aλ = aλref e−S (λ−λref)

where aλ is the Napierian absorption coefficient, λ the wavelength, λref the reference wavelength and S the spectral slope that has to be calculated. Different wavelength subsets are used for different slopes (e.g. λ300 : λ700, λ275 : λ295 or λ350 : λ400), however none of the articles mention what reference wavelength is used for the calculation.

I'm in the process of building a bunch of Matlab functions to calculate the most used fluorescence and absorbance indices, but when I test the Sλ300 : λ700 my results differ on the λref I used for the fitting of the function. I started by using 410 nm, since it might be that this reference is used in Twardowski (2004) - an article that is often cited. However, I tried using 300 nm as λref - thinking that using the lowest wavelength of the subset used for fitting might be a good reference as well - and came to different slopes in this way.

Am I missing anything? Is λref even a constant that can be chosen, or should it be dynamic (e.g. in a λ-1 kind of way, but then again, why is this not noted in this manner?). If the λref influences the slopes - should some kind of agreement be made as to what the reference should be? Unless I am mis-understanding, it seems an unnecessary source of variance.

I know there's some other formulas as well (see Twardowski 2004) and could resort to using the simplified:

2 ) aλ = A e−S (λ)

where A is a constant (amplitude) that could serve as a proxy for DOM concentration - however, in my experience adding a constant like this can result in pretty big model variances of both the amplitude and the slope constants. I'd rather make formula 1) work - if only to see the difference between the options.

Helms (2008) Absorption spectral slopes and slope ratios as indicators of molecular weight, source, and photobleaching of chromophoric dissolved organic matter

https://doi.org/10.4319/lo.2008.53.3.0955

Twardowski (2004) Modeling the spectral shape of absorption by chromophoric dissolved organic matter

Article Modeling the Spectral Shape of Absorbing Chromophoric Dissol...