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

PUBLICATIONS Water Resources Research RESEARCH ARTICLE 10.1002/2014WR016805 Key Points: Stationarity paradigm is revisited using diagnostic model evaluation with DREAM (ABC) Nonstationarity is not readily apparent from statistical analysis Nonstationarity is evident from analysis of summary metrics Correspondence to: J. A. Vrugt, jasper@uci.edu Citation: Sadegh, M., J. A. Vrugt, C. Xu, and E. Volpi (2015), The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM (ABC) , Water Resour. Res., 51, 9207–9231, doi:10.1002/ 2014WR016805. Received 19 DEC 2014 Accepted 9 SEP 2015 Accepted article online 21 SEP 2015 Published online 28 NOV 2015 The stationarity paradigm revisited: Hypothesis testing using diagnostics, summary metrics, and DREAM (ABC) Mojtaba Sadegh 1 , Jasper A. Vrugt 1,2 , Chonggang Xu 3 , and Elena Volpi 4 Department of Civil and Environmental Engineering, University of California, Irvine, California, USA, 2 Department of Earth System Science, University of California, Irvine, California, USA, 3 Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA, 4 Department of Engineering, University of Roma Tre, Rome, Italy Abstract 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 (multi- variate) statistical and nonlinear optimization methods for inference of the (temporally fixed) model param- eters. 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 statis- tics 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 under- gone significant changes in land use, urbanization, and/or hydroclimatic conditions, and thus are deemed nonstationary. 1. Introduction The flow of water through watersheds is an incredibly complex process controlled by physical characteris- tics of the basin and a myriad of highly interrelated, spatially distributed, water, energy, and vegetation processes. As available measurements lack the resolution and information content required to warrant a detailed characterization of watershed structure, properties, and processes, relatively simple models are used to describe (among others) soil moisture flow, groundwater recharge, surface runoff, preferential flow, root water uptake, and river discharge at different spatial and temporal scales. This includes prediction in space (interpolation/extrapolation) and prediction in time (forecasting). These models describe spatially dis- tributed vegetation and subsurface properties with much simpler homogeneous units using transfer func- tions that describe the flow of water within and between different storage compartments. C 2015. American Geophysical Union. V All Rights Reserved. SADEGH ET AL. 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. As a consequence, the watershed behavior as measured in hydrologic states and fluxes (jointly called varia- bles) is assumed to vary around some constant mean value with fixed variance and serial correlation struc- ture [Clarke, 2007]. This assumption is rather convenient and opens up the wide arsenal of (multivariate) statistical and nonlinear optimization methods for inference of the (temporally fixed) model parameters. Notwithstanding the progress made, several contributions to the hydrologic literature have brought into question the continued usefulness of this stationary paradigm for hydrologic modeling [Westmacott and Burn, 1997; Karl and Knight, 1998; Strupczewski et al., 2001; McCabe and Wolock, 2002; Groisman et al., 2004; Fu et al., 2004; Lins and Slack, 2005; Svensson et al., 2005; Alexander et al., 2006; Hodgkins and Dudley, 2006; Xu et al., 2006; Leclerc and Ouarda, 2007; Milly et al., 2008; Villarini et al., 2009; Kundzewicz, 2011; Stedinger and Griffis, 2011; Vogel et al., 2011; Waage and Kaatz, 2011; Ishak et al., 2013; Salas and Obeysekera, 2014]. For example, Strupczewski et al. [2001] showed evidence of nonstationarity in the annual maximum flows of 39 Polish rivers during the period of 1921–1990. Villarini et al. [2009] examined annual peak discharges from REVISITING SATIONARITY PARADIGM