Evaluation of the linear mixing model in fluorescence spectroscopy

• Replicate fluorescence intensity measurements can be used to quantify sources of experimental variation. • The fluorescence intensities of a mixed water sample is approximately equal to the mixture of its endmember intensities. • Abundances of high-fluorescence endmembers can be estimated accurately using linear unmixing methods. • Abundances of low-fluorescence endmembers are highly variable across replications. Analyses of spectral data often assume a linear mixing hypothesis , which states that the spectrum of a mixed substance is approximately the mixture of the individual spectra of its constituent parts. We evaluate this hypothesis in the context of dissolved organic matter (DOM) fluorescence spectroscopy for endmember abundance recovery from mixtures of three different DOM endmembers: groundwater, stream water, and wastewater. We quantify two key sources of experimental variation, which we refer to as procedural variation and measurement variation, and statistically evaluate the linear mixing hypotheses in the context of this variation on triplicate measurements of variable mixtures of each DOM source. We find that there is not strong statistical evidence against this hypothesis for fluorescence measurements greater than 1 QSU, and that true abundances of fluorescence endmembers above this concentration are accurately recovered from the excitation-emission fluorescence spectra of mixed samples using linear methods. However, abundances of a low-fluorescence endmember (0.9 ± 0.2 QSU) are less well-estimated, in that the abundance coefficient estimates exhibit a high degree of variability across replicate experiments. It is recommended that triplicate measurements can be used to appropriately constrain this experimental variation. Thus, we conclude that linear mixing holds for samples having fluorescence values greater than 1 quinine sulfate unit (QSU) under the measurement protocols used in this study.