Source distribution modelling for end-member mixing in hydrology

M. J. Brewer, Doerthe Tetzlaff, I. A. Malcolm, C. Soulsby

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


End-member mixing is a method in hydrology for attempting to define the runoff sources in river catchments. It involves estimation of the relative proportions of water from different sources, commonly producing a time series. Given regular measurements of a chemical tracer on the target water body and, in addition, corresponding measurements for samples of known sources, it is possible to perform end-member mixing using Bayesian models taking (essentially) a random effects approach in a hierarchical framework, including covariates if appropriate. This paper considers the case where there are no separate data available for the source components, and develops a model for source distributions via nonlinear regression on the tracer/flow relationship and nonparametric density estimation. We allow these source component distributions to vary from year to year and apply the model to a data set from two streams in central Scotland, comprised of weekly or fortnightly readings over seventeen years. We conclude there is evidence of a change in source distribution over time; that corresponding to low flow conditions exhibits a gradual increase in alkalinity for both of two streams studied, whereas for high flow conditions alkalinity appeared to be rising for only one stream. Copyright (C) 2011 John Wiley & Sons, Ltd.

Original languageEnglish
Pages (from-to)921-932
Number of pages12
Issue number8
Early online date25 Mar 2011
Publication statusPublished - Dec 2011


  • compositional analysis
  • hierarchical Bayesian model
  • MCMC
  • WinBUGS
  • chemical tracers
  • multivariate receptor models
  • kernel density-estimation
  • mesoscale catchment
  • residence times
  • uncertainty
  • stream
  • water
  • chemistry
  • quality
  • salt


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