Technical note: Uncertainty in multi-source partitioning using large tracer data sets

The availability of large tracer data sets opened up the opportunity to investigate multiple source contributions to a mixture. However, the source contributions may be uncertain and, apart from Bayesian approaches, to date there are only solid methods to estimate such uncertainties for two and three sources. We introduce an alternative uncertainty estimation method for four sources based on multiple tracers as input data. Taylor series approximation is used to solve the set of linear mass balance equations. We illustrate the method to compute individual uncertainties in the calculation of source contributions to a mixture, with an example from hydrology, using a 14-tracer set from water sources and streamflow from a tropical, high-elevation catchment. Moreover, this method has the potential to be generalized to any number of tracers across a range of disciplines.