In defence of stationarity (invited talk)

D. Koutsoyiannis, In defence of stationarity (invited talk), IAHS - IAPSO - IASPEI Joint Assembly, Gothenburg, Sweden, doi:10.13140/RG.2.2.18211.66083, International Association of Hydrological Sciences, International Association for the Physical Sciences of the Oceans, International Association of Seismology and Physics of the Earth's Interior, 2013.



As long as “steady flow” describes a flow, a “stationary process” describes a process. It is then a tautology to say that in a process there is change. Even a stationary process describes a system changing in time, rather than a static one which keeps a constant state all the time. However, this is often missed, which has led to misusing the term “nonstationarity” as a synonymous to “change”. A simple rule to avoid such misuse is to answer the question: can the change be predicted in deterministic terms? If the answer is positive, then it is legitimate to invoke nonstationarity. Otherwise a stationary model should be sought. In addition, we should have in mind that models are made to simulate the future rather than to describe the past, which is better to try to observe than simulate. In this respect, in studying the above question we must assess whether or not future changes are deterministically predictable. Usually they are not and thus the models should, on the one hand, be stationary and, on the other hand, describe in stochastic terms the full variability, originating from all agents of change. Even if the past evolution of the process of interest contains changes explainable in deterministic terms (e.g. urbanization), again it is better to describe the future conditions in stationary terms, after “stationarizing” the past observations, i.e. adapting them to represent the future conditions. An exception in which nonstationary models are justified is the case of planned and controllable future changes (e.g. catchment modification by construction of hydraulic infrastructures, water abstractions), which indeed allow prediction in deterministic terms.

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