|Authors||Brewer, M.J., Tetzlaff, D., Malcolm, I.A. and Soulsby, C.|
|Publication details||Environmetrics 22, 921-932.|
|Keywords||compositional analysis; hierarchical Bayesian model; MCMC; WinBUGS; chemical tracers|
End-member mixing (EMM) 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, and is often recorded as 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.