Statistical estimation and interpretation of trends in water quality time series

Zetterqvist, Lena

doi:10.1029/91wr00478

Cited by 64 publications

(31 citation statements)

References 23 publications

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“…ven Belle & Hughes, 1984;Cailas et al, 1986;Hipel et al, 1988;Hipel & McLeod, 1994;Taylor & Loftis, 1989;Demarée & Nicolis, 1990;Zetterqvist, 1991;Chiew & McMahon, 1993;Yu et al, 1993;Hirsch et al, 1993;Lettenmaier et al, 1994;Burn, 1994;Yulianti & Burn, 1998;Gan, 1998;Lins & Slack, 1999;Douglas et al, 2000;Yue et al, 2003; and others). Another rank-based nonparametric test, the Spearman's rho (SR) test (Lehmann, 1975;Sneyers, 1990), has sometimes been applied to detect trends in hydrological data (e.g.…”

Section: Introductionmentioning

confidence: 99%

A comparison of the power of thettest, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des teststde Student, de Mann-Kendall et du bootstrap pour la détection de tendance

Yue

Pilon

2004

Hydrological Sciences Journal

337

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PO Box 5050, Burlington, Ontario L7R 4A6, Canada Abstract Monte Carlo simulation is applied to compare the power of the statistical tests: the parametric t test, the non-parametric Mann-Kendall (MK), bootstrap-based slope (BS-slope), and bootstrap-based MK (BS-MK) tests to assess the significance of monotonic (linear and nonlinear) trends. Simulation results indicate that (a) the t test and the BS-slope test, which are slope-based tests, have the same power; (b) the MK and BS-based MK tests, which are rank-based tests, have the same power; (c) for normally-distributed data, the power of the slope-based tests is slightly higher than that of the rank-based tests; and (d) for non-normally distributed series such as time series with the Pearson type III (P3), Gumbel, extreme value type II (EV2), or Weibull distributions, the power of the rank-based tests is higher than that of the slope-based tests. The power of the tests is slightly sensitive to the shape of trend. Practical assessment of the significance of trends in the annual maximum daily flows of 30 Canadian pristine river basins demonstrates a similar tendency to that obtained in the simulation studies. (BS-MK). Les résultats de simulation indiquent que (a) les tests t de Student et BS-pente, basés sur la pente, ont la même puissance; (b) les tests MK et BS-MK, basés sur le rang, ont la même puissance; (c) pour des données présentant une distribution normale, la puissance des tests basés sur la pente est légèrement supérieure à celle des tests basés sur le rang; et (d) pour des séries présentant une distribution non-normale, comme une distribution de Pearson III, de Gumbel, de valeur extrême type II, ou de Weibull, la puissance des tests basés sur le rang est supérieure à celle des tests basés sur la pente. La puissance des tests est légèrement sensible à la forme de la tendance. L'estimation pratique de la signification des tendances est similaire pour les études par simulation et pour l'analyse des données de maxima annuels de débits journaliers de 30 bassins vierges canadiens. Mots clefs détection de tendance; test t de Student; test de Mann-Kendall; test bootstrap; puissance d'un test; valeur de P; forme de tendance; analyse statistique Key words INTRODUCTIONThe rank-based nonparametric Mann-Kendall (MK) test (Mann, 1945;Kendall, 1975) has been commonly used to assess the significance of monotonic trends in hydroSheng Yue & Paul Pilon 22 meteorological time series (e.g. ven Belle & Hughes, 1984;Cailas et al., 1986;Hipel et al., 1988;Hipel & McLeod, 1994;Taylor & Loftis, 1989;Demarée & Nicolis, 1990;Zetterqvist, 1991;Chiew & McMahon, 1993;Yu et al., 1993;Hirsch et al., 1993;Lettenmaier et al., 1994;Burn, 1994;Yulianti & Burn, 1998;Gan, 1998;Lins & Slack, 1999;Douglas et al., 2000;Yue et al., 2003; and others). Another rank-based nonparametric test, the Spearman's rho (SR) test (Lehmann, 1975;Sneyers, 1990), has sometimes been applied to detect trends in hydrological data (e.g. Lettenmaier, 1976;El-Shaarawi et al., 1983;Pilon et al., 1985;McLeod et al....

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Section: Introductionmentioning

confidence: 99%

A comparison of the power of thettest, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des teststde Student, de Mann-Kendall et du bootstrap pour la détection de tendance

Yue

Pilon

2004

Hydrological Sciences Journal

337

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“…Such detrending treatment can certainly affect the estimated value of β and hence the validity of (or confidence in) any inference made regarding the statistical significance of temporal trends in the time series. This somewhat circular issue is beyond the scope of our current work -it has been previously discussed in the context of short-term memory (Zetterqvist, 1991;Darken et al, 2002;Yue et al, 2002;Noguchi et al, 2011;Clarke, 2013;Sang et al, 2014), but it is not well understood in the context of fractal scaling (or long-term memory) and hence presents an important area for future research.…”

Section: Motivation and Objective Of This Workmentioning

confidence: 84%

“…B4 and B5 were implemented using the na.locf function in the zoo R package (Zeileis and Grothendieck, 2005). B7-B11 were implemented using the loess function in the stats R package (R Development Core Team, 2014).…”

Section: Summary Of Estimation Methodsmentioning

confidence: 99%

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Zhang

Harman

Kirchner

2018

Hydrol. Earth Syst. Sci.

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Abstract. River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scalingin the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) -are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-meansquared error among all methods for a wide range of prescribed β values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating β in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling.

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“…A benefit of this test is that no assumptions about the probability distribution of the data are needed. It has been widely used in the hydro-climatological literature; therefore, details of its calculation are not presented in this study, but can be found in Hipel et al (1988), Zetterqvist (1991), Chiew and McMahon (1993), Burn (1994), Yulianti and Burn (1998), Lins and Slack (1999), Douglas et al (2000), Yue and Wang (2004), Yue and Pilon (2004), Burn et al (2008), Drapela (2011) and Mondal et al (2012). In the same sense, to estimate the true slope of an existing trend as change per year, the Sen nonparametric method was calculated (Theil 1950, Sen 1968.…”

Section: General Analysis Of the Historic Streamflowsmentioning

confidence: 99%

Multi-decadal variations in annual maximum peak flows in semi-arid and temperate regions of Chile

Pizarro¹,

Vera²,

Valdés³

et al. 2013

Hydrological Sciences Journal

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Editor D. Koutsoyiannis; Associate editor H. Lins Citation Pizarro, R., Vera, M., Valdés, R., Helwig, B., and Olivares, C., 2013. Multi-decadal variations in annual maximum peak flows in semi-arid and temperate regions of Chile. Hydrological Sciences Journal, 59 (2), 300-311.Abstract In determining the possible influence of climate change, it is important to understand the temporal and spatial variability in streamflow response for diverse climate zones. Thus, the aim of this study was to determine the presence of changes in annual maximum peak flow for two climate zones in Chile over the past few decades. A general analysis, a flood frequency analysis and a trend analysis were used to study such changes between 1975 and 2008 for a semi-arid (29°S-32°S) and a temperate (36°S-38°S) climatic zone. The historic annual maxima, minima and mean flows, as well as decadal mean peak flow, were compared over the period of record. The Gumbel distribution was selected to compare the 30-year flood values of two ±15-year intervals, which showed that streamflow decreased by an average of 19.5% in the semi-arid stations and increased by an average of 22.6% in the temperate stations. The Mann-Kendall test was used to investigate the temporal changes in streamflows, with negative trends being observed in 87% of the stations analysed in the semi-arid zone, and positive trends in 57% of those analysed in the temperate zone. These differences in streamflow response between climate zones could be related to recent documented increases in altitude of the zero-degree isotherm in the Andes Mountains of Chile, since most of the significant positive and negative changes were detected in first-order rivers located closer to this mountain range.Key words climate change influence; flood frequency analysis; probability distribution functions; Mann-Kendall test; peak flows; zero-degree isotherm; semi-arid climate; temperate climate Variations multidécennales des débits de pointe maximaux annuels dans les régions semi-arides et tempérées du ChiliRésumé Pour déterminer l'influence possible du changement climatique, il est important de comprendre la variabilité temporelle et spatiale de la réponse en débits pour diverses zones climatiques. Ainsi, l'objet de cette étude était de déterminer l'existence de changements dans le débit de pointe maximum annuel de deux zones climatiques du Chili au cours des dernières décennies. Une analyse générale, une analyse de la fréquence des crues et une analyse de tendances ont été utilisées pour étudier les changements des valeurs du débit de pointe maximal annuel entre 1975 et 2008 pour la zone semi-aride (29°S à 32°S) et la zone tempérée (36°S à 38°S). Les maximums, minimums et moyennes historiques annuels, ainsi que le débit de pointe décennal ont été comparés sur la période d'observation. Nous avons choisi la distribution de Gumbel pour estimer les valeurs des crues tricennales (30 ans) de deux intervalles de 15 ans, ce qui a montré que la valeur de ce débit a diminué en moyenne de 19,5% dans les stations se...

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Statistical estimation and interpretation of trends in water quality time series

Cited by 64 publications

References 23 publications

A comparison of the power of thettest, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des teststde Student, de Mann-Kendall et du bootstrap pour la détection de tendance

A comparison of the power of thettest, Mann-Kendall and bootstrap tests for trend detection / Une comparaison de la puissance des teststde Student, de Mann-Kendall et du bootstrap pour la détection de tendance

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Multi-decadal variations in annual maximum peak flows in semi-arid and temperate regions of Chile

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