A novel method for analysing consistency and unravelling multiple solutions in sediment fingerprinting

Fingerprinting technique is a widely used tool to assess the sources of sediments and particle bound chemicals within a watershed, and the results obtained from unmixing models are becoming valuable data to support soil and water resources monitoring and conservation. Nowadays, numerous studies have used fingerprinting techniques to examine specific catchment management problems. Despite its shortcomings and the lack of standardization, the technique continues on an upward trend globally. This paper takes a new look at the utility of the mostly used tracer selection methods and their influence when using fingerprinting models. Furthermore, the increase in the analysis capabilities and the use of more tracers than n-1 tracers (where n is the number of sources) for unmixing leads to the possibility of mathematical inconsistency and the existence of multiple solutions in the analysis of a particular mixture, which is a possible source of errors that remains unexplored nowadays. Within the framework of these criteria, we have i) inspected if both types of models, Frequentist and Bayesian, are sensitive to tracers with erroneous information; ii) examined the most commonly used tracer selection methods; iii) tested the consistency and the existence of multiple solutions in over-determined systems and iv) devised a Consistent Tracer Selection (CTS) method to extract the solutions present in the dataset. The strength of this novel study lies in the valuable and useful tracer selection method that has been presented. Frequentist model such as FingerPro and a Bayesian model, MixSIAR, are implemented to test the method. Both models agreed on their solutions when selecting the tracers based on the new method, while both disagreed when selecting the tracers following previous methods. The new CTS method's ability to extract the multiple discriminant and consistent solutions inside fingerprinting datasets has no precedent in the literature.