A test sensitive to extreme hidden periodicities

A modified version of the widely used Kolmogorov-Smirnov (K-S) test of null hypothesis is constructed, that a given time series is Gaussian white noise, against the alternative hypothesis that the time series contains an added or multiplicative deterministic-periodic component of unspecified frequency. The usual KS test is treated as a special case. The proposed test is more powerful than the ordinary K-S test in detecting extreme (low or high) hidden periodicities. Computational procedure necessary for implementation are also given.     

Generalized Rydelek-Sacks test for distinguishing between periodic and random patterns in seismicity

For distinguishing the periodicity of strong earthquakes on the time scale of decades, we generalized the Rydelek-Sacks test (Rydelek, Sacks, 1989) to explore whether a time series is modulated by a periodic process or not. The test is conducted by comparing the total phasor of seismicity with that produced by a random Brownian motion. The phase angle is defined by the origin time of earthquakes relative to a reference time scale. Using this method we tested two hypotheses in geodynamics and earthquake prediction study. One is the hypothesis of Romanowicz (1993) who proposed that the great earthquakes alternate in a predictable fashion between strike-slip and thrusting mechanisms on a 20-30 years cycle. The other hypothesis is that the strong earthquakes in and around China have an active period of about ten years. The test obtains a negative conclusion for the former hypothesis and a positive conclusion for the latter at the 95% confidence level.     

Power of the Mann–Whitney test for detecting a shift in median or mean of hydro-meteorological data

 The non-parametric Mann–Whitney (MW) statistic test has been popularly used to assess the significance of a shift in median or mean of hydro-meteorological time series. It has been considered that the test is more suitable for non-normally distributed data and it may be not sensitive to the distribution type of sample data. However, no evidence has been provided to demonstrate these. This study investigates the power of the test in various circumstances by means of Monte Carlo simulation. Simulation results demonstrate that the power of the test is very sensitive to various properties of sample data. The power depends on the pre-assigned significance level, magnitude of a shift, sample size, and its occurrence position within a time series; and it is also strongly affected by the variation, skewness, and distribution type of a time series. The bigger the magnitude of a shift, the more powerful the test is; the larger the sample size, the more powerful the test is; and the bigger the variation within a time series, the less power the test has. The test has the highest power if a shift occurs at the midpoint of a time series. For the samples with different distribution types, the power of the test is dramatically different. The test has the highest power for time series with the extreme value type III (EV3) distribution while it indicates the lowest power for time series with the lognormal distribution.     

A simulation study to examine the sensitivity of the Pettitt test to detect abrupt changes in mean

Abstract

The Pettitt test is a non-parametric test that has been used in a number of hydroclimatological studies to detect abrupt changes in the mean of the distribution of the variable of interest. This test is based on the Mann-Whitney two-sample test (rank-based test), and allows the detection of a single shift at an unknown point in time. This test is often used to detect shifts in extremes because of the lack of distributional assumptions. However, the downside of not specifying a distribution is that the Pettitt test may be inefficient in detecting breaks when dealing with extremes. Here we adopt a Monte Carlo approach to examine the sensitivity of the Pettitt test in detecting shifts in the mean under different conditions (location of the break within the series, magnitude of the shift, record length, level of variability in the data, extreme vs non-extreme records, and pre-assigned significance level). These simulation results show that the sensitivity of this test in detecting abrupt changes increases with the increase in the magnitude of the shift and record length. The number of detections is higher when the time series represents the central part of the distribution (e.g. changes in the time series of medians), while the skill decreases as we move toward either low or high extremes (e.g. changes in the time series of maxima). Furthermore, the number of detections decreases as the variability in the data increases. Finally, abrupt changes are more easily detected when they occur toward the center of the time series.

Editor D. Koutsoyiannis Associate editor K. Hamed     

Trend detection in river flow series: 1. Annual maximum flow / Détection de tendance dans des séries de débit fluvial: 1. Débit maximum annuel

Abstract

Results of a study on change detection in hydrological time series of annual maximum river flow are presented. Out of more than a thousand long time series made available by the Global Runoff Data Centre (GRDC) in Koblenz, Germany, a worldwide data set consisting of 195 long series of daily mean flow records was selected, based on such criteria as length of series, currency, lack of gaps and missing values, adequate geographical distribution, and priority to smaller catchments. The analysis of annual maximum flows does not support the hypothesis of ubiquitous growth of high flows. Although 27 cases of strong, statistically significant increase were identified by the Mann-Kendall test, there are 31 decreases as well, and most (137) time series do not show any significant changes (at the 10% level). Caution is advised in interpreting these results as flooding is a complex phenomenon, caused by a number of factors that can be associated with local, regional, and hemispheric climatic processes. Moreover, river flow has strong natural variability and exhibits long-term persistence which can confound the results of trend and significance tests.     

The influence of serial correlation on the Mann–Whitney test for detecting a shift in median

The non-parametric Mann–Whitney (MW) statistical test for assessing the significance of a shift in median or mean requires a tested series to be serially independent. However, hydrological time series such as water quality, streamflow, and others may frequently display serial correlation. In such cases, the existence of serial correlation might alter the ability of the test to detect a shift in mean. This study investigates this issue by means of the Monte Carlo simulation. Simulation results indicate that: (i) when there is no shift or a moderate shift in mean, the existence of positive serial correlation will increase the possibility to reject the null hypothesis of no shift while it might be true; and the existence of negative serial correlation will reduce the possibility to detect a shift; (ii) when a bigger shift occurs in a time series, for a series with smaller sample size, the influence of serial correlation on the test is similar to that in (i), but it is much less than that in (i); while for a series with larger sample size, the influence of serial correlation on the test is opposite to (i), i.e., positive serial correlation reduces the power of the test for detecting a shift while negative serial correlation slightly increases the power of the test for identifying a shift; and (iii) removal of serial correlation by pre-whitening can effectively remove the serial correlation and eliminate the influence of the serial correlation on the test.     

Gaussianity and linearity tests of hydrologic time series

Although the non-Gaussian nature of many hydrologic time series is well recognized and their nonlinearity is suspected, neither property is well tested. This situation has existed partly because of a lack of appropriate tests. Recently Hinich (1982) has developed a test to test the linearity of time series which is based on the bispectral characteristics of the series. This test is used in this study to investigate the linearity and non-Gaussian characteristics of annual and daily rainfall and runoff series. The annual series may be modeled by linear models with Gaussian inputs. The daily data, on the other hand, often demonstrate nonlinear characteristics and are non-Gaussian as well.     

Spectral techniques for the analysis of tidal time series

Summary Three different methods are given for the Fourier analysis of time series leading to the determination of high reliable values of frequencies, amplitudes and phases of the inherent components. For two methods the hypothesis is made that the time series is sufficiently long to separate very close components, while for the third the frequencies are supposed to be given. Two of these methods have been applied to a time series obtained by sampling an artificial tidal function.     

BIBLIOGRAPHIE

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Modarres, R. and Ouarda, T.B.M.J., 2013. Modelling heteroscedasticty of streamflow times series. Hydrological Sciences Journal, 58 (1), 1–11.     

Correlation analysis and causality test between Ludong-Huanghai block and South Japan

In this paper, we make a comparative analysis and correlation test for the seismic activities in the South Japan and the Ludong-Huanghai block (a secondary tectonic unit in the North China) and approach the relationship between the energy release processes of these two areas by using co-integration analysis and Granger causality test for the time series of random variables. The results show that the seismic activities in these two areas are correlative and synchronous to a certain extent, and their release series of cumulative strain energy are contemporaneously cor-relative. Both energy series are first-order difference stationary processes and there is secular and steady co-integration between them. We make a positive analysis on the first-order difference energy series through Granger causality test based on vector error correction (VEC) model and find there is unilateral Granger causality and prominent co-integration between the two energy release processes.     

Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region (Turkey)

The purpose of this study is to determine the possible trends in annual total precipitation series by using the non-parametric methods such as the wavelet analysis and Mann-Kendall test. The wavelet trend (W-T) analysis is for the first time presented in this study. Using discrete wavelet components of measurement series, we aimed to find which periodicities are mainly responsible for trend of the measurement series. We found that some periodic events clearly affect the trend of precipitation series. 16-yearly periodic component is the effective component on Bal?kesir annual precipitation data and is responsible for producing a real trend founded on the data. Also, global wavelet spectra and continuous wavelet transform were used for analysis to precipitation time series in order to clarify time-scale characteristics of the measured series. The effects of regional differences on W-T analysis are checked by using records of measurement stations located in different climatic areas. The data set spans from 1929 to 1993 and includes precipitation records from meteorological stations of Turkey. The trend analysis on DW components of the precipitation time series (W-T model) clearly explains the trend structure of data.     

Kinematic transformations for planar multi‐directional pseudodynamic testing

The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd.     

隔震桥梁子结构拟动力实验中加载速率的影响因素研究

本研究运用DSP高速数字信号处理器的实时信号处理与控制技术,研究了基于速度控制法、OS数值积分法和相应的实验误差控制法的子结构拟动力实验系统。该试验系统对动力加载装置采用速度控制,在加载过程中考虑了加载速率对实验结果的影响,使隔震橡胶支座的速度相关性能在试验中得到充分体现,同时采用OS数值积分法,充分地减少了试验的时滞误差,提高了试验精度。并通过不同加载速率的子结构拟动力实验研究了天然橡胶支座、高阻尼橡胶隔震支座和超高阻尼橡胶隔震支座对桥梁的隔震效果,在对实验结果进行分析对比后,定量地研究了不同的加载速率对隔震桥梁子结构拟动力实验结果的影响。     

Real-time on-line test for MDOF systems

This paper presents a test system for conducting on-line tests in a real time and a series of real-time on-line tests conducted to verify the effectiveness of the system. The proposed system is characterized by (1) use of a Digital Signal Processor (DSP) now readily available, (2) adoption of the C language to ensure easy programming, and (3) separation of response analysis and displacement signal generation to apply the system for tests with complex structures. To create displacement signals successively without being interrupted by the computation of equations of motion, extrapolation and interpolation procedures using present and past target displacements are developed. Base-isolated building models were chosen for the real-time on-line test. The effectiveness of the extrapolation and interpolation procedures was demonstrated through a series of real-time on-line tests applied to the models treated as SDOF structures. A five-storey base-isolated building model (treated as a six DOF structure) was tested for various ground motions, and it was verified that the system is able to simulate earthquake responses involving large displacements and large velocities. The number of DOFs that can be handled in the proposed system was investigated, and it was found that the system is capable of performing the test with reasonable accuracy for up to 10 DOF structures with a range of response frequency not greater than 3·0 Hz, or 12 DOF structures with a range of response frequency not greater than 2·0 Hz. Copyright © 1999 John Wiley & Sons, Ltd.     

Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log‐Pearson type 3 distribution. This paper examines the suitability of a five‐parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas. Copyright © 2014 John Wiley & Sons, Ltd.     

Temporal trends in δ18O composition of precipitation in Germany: insights from time series modelling and trend analysis

Temporal and spatial variations of stable oxygen (¹⁸O) and hydrogen (²H) isotope measurements in precipitation act as important proxies for changing hydro‐meteorological and regional and global climate patterns. Temporal trends in time series of the stable isotope composition in precipitation were rarely observed, and they are poorly understood. These might be a result of a lack of proper trend detection tools and effort for exploring trend processes. Here, we investigate temporal trends of δ¹⁸O in precipitation at 17 observation stations in Germany between 1978 and 2009. We test if significant trends in the isotope time series from different models can be observed. Mann–Kendall trend tests are applied on the isotope series, using general multiplicative seasonal autoregressive integrate moving average (ARIMA) models, which account for first and higher order serial correlations. Effects of temperature, precipitation, and geographic parameters on isotope trends are also investigated in the proposed models. To benchmark our proposed approach, the ARIMA results are compared with a trend‐free pre‐whitening procedure, the state of the art method for removing the first order autocorrelation in environmental trend studies. Moreover, we further explore whether higher order serial correlations in isotope series affects our trend results. Overall, three out of the 17 stations show significant changes when higher order autocorrelation are adjusted, and four show a significant trend when temperature and precipitation effects are considered. The significant trends in the isotope time series generally occur only at low elevation stations. Higher order autoregressive processes are shown to be important in the isotope time series analysis. Results suggest that the widely used trend analysis with only the first order autocorrelation adjustment may not adequately take account of the high order autocorrelated processes in the stable isotope series. The investigated time series analysis method including higher autocorrelation and external climate variable adjustments is shown to be a better alternative. Copyright © 2014 John Wiley & Sons, Ltd.     

Trends in hydrological and climatic variables affected by four variations of the Mann-Kendall approach in Urmia Lake basin,Iran

ABSTRACT

The trends in hydrological and climatic time series data of Urmia Lake basin in Iran were examined using the four different versions of the Mann-Kendall (MK) approach: (i) the original MK test; (ii) the MK test considering the effect of lag-1 autocorrelation; (iii) the MK test considering the effect of all autocorrelation or sample size; and (iv) the MK test considering the Hurst coefficient. Identification of hydrological and climatic data trends was carried out at monthly and annual time scales for 25 temperature, 35 precipitation and 35 streamflow gauging stations selected from the Urmia Lake basin. Mann-Kendall and Pearson tests were also applied to explore the relationships between temperature, precipitation and streamflow trends. The results show statistically significant upward and downward trends in the annual and monthly hydrological and climatic variables. The upward trends in temperature, unlike streamflow, are much more pronounced than the downward trends, but for precipitation the behaviour of trend is different on monthly and annual time scales. Furthermore, the trend results were affected by the different approaches. Specifically, the number of stations showing trends in hydrological and climatic variables decreased significantly (up to 50%) when the fourth test was considered instead of the first and the absolute value of the Z statistic for most of the time series was reduced. The results of correlations between streamflow and climatic variables showed that the streamflow in Urmia Lake basin is more sensitive to changes in temperature than those of precipitation. The observed decreases in streamflow and increases in temperature in the Urmia Lake basin in recent decades may thus have serious implications for water resources management under the warming climate with the expected population growth and increased freshwater consumption in this region.

Editor Z. W. Kundzewicz; Associate editor Q. Zhang     

Hastening of occurrences of earthquakes due to dynamic triggering: The observation at Matsushiro, central Japan

Dynamic stress/strain changes associated with the passage of seismic waves perturb the state of stress of a fault.We hypothesize that this perturbation increases the instability of the fault and that it hastens the occurrence of an earthquake that would otherwise occur somewhat later.To test this hypothesis, we investigate a time interval defined as a time difference between the occurrence of a dynamic strain change and the origin time of the first subsequent earthquake.If the occurrence of an earthquake is hastened by the strain change, the time interval would be shortened, compared with a case of a random occurrence.Here we used two datasets: 1) origin times of earthquakes at Matsushiro, Nagano Prefecture, central Japan, with magnitudes of 1.6 or greater, between November 1984 and December 1994; and 2) strainmeter records of remote earthquakes at the Matsushiro Seismological Observatory over the same period.We applied a statistical test to the distribution of the observed time intervals between dynamic strain changes due to remote earthquakes and the first earthquakes at Matsushiro subsequent to the strain changes, in order to compare it to the distribution of expected time intervals generated by a random (Monte Carlo) simulation.Because of limitations of the statistical test, we could not establish the quantitative relationship between the degree of hastening and the amplitude of the strain changes, but we found a statistically significant decrease of the observed time intervals.We also investigated the number of the earthquakes before and after the strain changes, and found that dynamic triggering has little significant impact on the occurrences of earthquakes at Matsushiro.Therefore, we conclude that dynamic triggering at Matsushiro is weaker than those reported in previous studies and that the time interval might be an important parameter for a statistical study of weak dynamic triggering.     

Investigation into the automatic recognition of time series precursor of earthquakes

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The influence of autocorrelation on the ability to detect trend in hydrological series

This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag‐one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre‐whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre‐whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre‐whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright © Environment Canada. Published by John Wiley & Sons, Ltd.