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.

In this paper, we present a characterization of all linear fractional order partial differential operators with complex-valued coefficients that are associated to the generalized fractional Cauchy-Riemann operator in the Riemann-Liouville sense. To achieve our goal, we make use of the technique of an associated differential operator applied to the fractional case.

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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 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.

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