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

Abstract. 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 estimate such source uncertainty only sound methods for two and three sources. We expand these methods developing an 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 with an example from hydrology, where we use a large tracer set from four water sources contributing to streamflow in a tropical, high-elevation catchment. However, our uncertainty estimation method can be generalized to any number of tracers across a range of disciplines.