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

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 (δ2Hδ2H) and oxygen-18 (δ18Oδ18O), 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, δ18Oδ18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but δ18Oδ18O demanded autoregressions of the first order, whereas δ2Hδ2H 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.

► MSARMs demonstrated the non-linear, non-Normal and non-stationary characteristics of stream isotope dynamics.
► The statistical model is capable of reproducing event and inter-event dynamical states.
► Adding explanatory covariates allowed inferences about the catchment functioning.
► The conservative tracers deuterium and oxygen-18 showed slightly different characteristics.