A new approach to simulating stream isotope dynamics using Markov switching autoregressive models

Christian Birkel, Roberta Paroli, Luigi Spezia, Sarah M. Dunn, Doerthe Tetzlaff, Chris Soulsby

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In this study we applied Markov switching autoregressive models (MSARMs) as a proof-of-concept to analyze the temporal dynamics and statistical characteristics of the time series of two conservative water isotopes, deuterium (d2H) and oxygen-18 (d18O), in daily stream water samples over two years in a small catchment in eastern Scotland. MSARMs enabled us to explicitly account for the identified non-linear, non-Normal and non-stationary isotope dynamics of both time series. The hidden states of the Markov chain could also be associated with meteorological and hydrological drivers identifying the short (event) and longer-term (inter-event) transport mechanisms for both isotopes. Inference was based on the Bayesian approach performed through Markov Chain Monte Carlo algorithms, which also allowed us to deal with a high rate of missing values (17%). Although it is usually assumed that both isotopes are conservative and exhibit similar dynamics, d18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but d18O demanded autoregressions of the first order, whereas d2H of the second. Moreover, both the dynamics of observations and the hidden states of the two isotopes were explained by two different sets of covariates. Consequently use of the two tracers for transit time modelling and hydrograph separation may result in different interpretations on the functioning of a catchment system.
Original languageEnglish
Pages (from-to)20-30
Number of pages11
JournalAdvances in Water Resources
Early online date14 Jun 2012
Publication statusPublished - Sept 2012


  • Bayesian inference
  • complex stochastic systems
  • Markov chains
  • non-linearity
  • stable isotopes
  • tracers


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