Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology

Francesco Serinaldi,Federico Lombardo,Chris G Kilsby

doi:10.1016/j.advwatres.2017.10.015

Francesco Serinaldi, Federico Lombardo + Show 1 more

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https://doi.org/10.1016/j.advwatres.2017.10.015

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Abstract

Abstract The detection and attribution of long-term patterns in hydrological time series have been important research topics for decades. A significant portion of the literature regards such patterns as ‘deterministic components’ or ‘trends’ even though the complexity of hydrological systems does not allow easy deterministic explanations and attributions. Consequently, trend estimation techniques have been developed to make and justify statements about tendencies in the historical data, which are often used to predict future events. Testing trend hypothesis on observed time series is widespread in the hydro-meteorological literature mainly due to the interest in detecting consequences of human activities on the hydrological cycle. This analysis usually relies on the application of some null hypothesis significance tests (NHSTs) for slowly-varying and/or abrupt changes, such as Mann-Kendall, Pettitt, or similar, to summary statistics of hydrological time series (e.g., annual averages, maxima, minima, etc.). However, the reliability of this application has seldom been explored in detail. This paper discusses misuse, misinterpretation, and logical flaws of NHST for trends in the analysis of hydrological data from three different points of view: historic-logical, semantic-epistemological, and practical. Based on a review of NHST rationale, and basic statistical definitions of stationarity, nonstationarity, and ergodicity, we show that even if the empirical estimation of trends in hydrological time series is always feasible from a numerical point of view, it is uninformative and does not allow the inference of nonstationarity without assuming a priori additional information on the underlying stochastic process, according to deductive reasoning. This prevents the use of trend NHST outcomes to support nonstationary frequency analysis and modeling. We also show that the correlation structures characterizing hydrological time series might easily be underestimated, further compromising the attempt to draw conclusions about trends spanning the period of records. Moreover, even though adjusting procedures accounting for correlation have been developed, some of them are insufficient or are applied only to some tests, while some others are theoretically flawed but still widely applied. In particular, using 250 unimpacted stream flow time series across the conterminous United States (CONUS), we show that the test results can dramatically change if the sequences of annual values are reproduced starting from daily stream flow records, whose larger sizes enable a more reliable assessment of the correlation structures.

Highlights

Due to the complexity of hydrological systems, their analysis and modeling heavily rely on historical records as theoretical reasoning and deduction are often inadequate
The point (ii) is subtle but critical; the behavior of summary statistics can be strongly influenced by the nature of the underlying process; for example, processes with long range dependence (LRD) yields maximum values over blocks of observations that tend to cluster in time (e.g., Bunde et al, 2005; Eichner et al, 2011). This results in apparent trends in terms of frequency and magnitude if the analysis relies on short series of such maxima, even though these summary statistics might show no or very weak autocorrelation. Since this behavior is found in stream flow time series (Serinaldi and Kilsby, 2016c), we show in the case study that it might have a dramatic effect on trend null hypothesis statistical tests (NHSTs) outcomes
Results for iterative amplitude adjusted Fourier transformation (IAAFT)-based tests show the dramatic decrease of evidence for deterministic changes when fluctuations of seasonal/annual averages and maxima are influenced by the entire flow process at daily scale

Summary

Introduction

Due to the complexity of hydrological systems, their analysis and modeling heavily rely on historical records as theoretical reasoning and deduction are often inadequate. A change of paradigm from stationary to nonstationary can be claimed to account for human activities producing predictable changes, such as land-use and land-cover changes, and water resources exploitation, or more complex but less predictable phenomena such as the worldwide hydrologic change ascribed to anthropogenic climate change (ACC) (Milly et al, 2015). In this respect, in the last three decades, a huge number of studies have investigated possible humandriven changes in the form of slowly-varying trends or abrupt changes in time series of hydrological variables across different regions of the world. Speaking and taking for granted unavoidable differences, the aim of these studies has been to understand if these changes are detectable, what is their pattern, and to infer nonstationarity, promoting the implementation of nonstationary models to support new design and planning strategies (e.g., Ouarda and El-Adlouni, 2011; Rootzén and Katz, 2013; Cheng et al, 2014, among many others)

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