The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM(ABC)

Many watershed models used within the hydrologic research community assume (by default) stationary conditions, that is, the key watershed properties that control water flow are considered to be time invariant. This assumption is rather convenient and pragmatic and opens up the wide arsenal of (multivariate) statistical and nonlinear optimization methods for inference of the (temporally fixed) model parameters. Several contributions to the hydrologic literature have brought into question the continued usefulness of this stationary paradigm for hydrologic modeling. This paper builds on the likelihood-free diagnostics approach of Vrugt and Sadegh (2013) and uses a diverse set of hydrologic summary metrics to test the stationary hypothesis and detect changes in the watersheds response to hydroclimatic forcing. Models with fixed parameter values cannot simulate adequately temporal variations in the summary statistics of the observed catchment data, and consequently, the DREAM(ABC) algorithm cannot find solutions that sufficiently honor the observed metrics. We demonstrate that the presented methodology is able to differentiate successfully between watersheds that are classified as stationary and those that have undergone significant changes in land use, urbanization, and/or hydroclimatic conditions, and thus are deemed nonstationary.