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Water Resources Research
Volume 38, Issue 6
Free Access

Applicability of prewhitening to eliminate the influence of serial correlation on the Mann‐Kendall test

Sheng Yue

Meteorological Services of Canada, Ontario Region, Environment Canada, Burlington, Ontario, Canada

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Chun Yuan Wang

Development Research Center, Water Resources Ministry of China, Beijing, China

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First published: 04 June 2002
https://doi.org/10.1029/2001WR000861
Citations: 300

Abstract

[1] Prewhitening has been used to eliminate the influence of serial correlation on the Mann‐Kendall (MK) test in trend‐detection studies of hydrological time series. However, its ability to accomplish such a task has not been well documented. This study investigates this issue by Monte Carlo simulation. Simulated time series consist of a linear trend and a lag 1 autoregressive (AR(1)) process with a noise. Simulation results demonstrate that when trend exists in a time series, the effect of positive/negative serial correlation on the MK test is dependent upon sample size, magnitude of serial correlation, and magnitude of trend. When sample size and magnitude of trend are large enough, serial correlation no longer significantly affects the MK test statistics. Removal of positive AR(1) from time series by prewhitening will remove a portion of trend and hence reduces the possibility of rejecting the null hypothesis while it might be false. Contrarily, removal of negative AR(1) by prewhitening will inflate trend and leads to an increase in the possibility of rejecting the null hypothesis while it might be true. Therefore, prewhitening is not suitable for eliminating the effect of serial correlation on the MK test when trend exists within a time series.

1. Introduction

[2] In the past three decades, increased public concern over environmental degradation has led to the popular use of the nonparametric Mann‐Kendall (MK) statistical test [Mann, 1945; Kendall, 1975] to assess significant trends in water quality indicators [e.g., Hirsch et al., 1982; van Belle and Hughes, 1984; Cailas et al., 1986; Hipel et al., 1988; Taylor and Loftis, 1989; Zetterqvist, 1991; Yu et al., 1993]. Recently, great interests in the implications of greenhouse gases or global warming on the environment have led to a number of studies of applying the MK test to identify whether or not significant trends exist in hydrometeorological time series such as streamflow, precipitation, and temperature series. Examples include the works by Hirsch and Slack [1984], Demaree and Nicolis [1990], Gan [1998], Chiew and McMahon [1993], Lettenmaier et al. [1994], Burn [1994], Lins and Slack [1999], Douglas et al. [2000], Zhang et al. [2000, 2001], and Hamilton et al. [2001]. Most trend‐detection studies using the MK test have assumed that sample data are serially independent, even though certain hydrological time series such as water quality series and annual mean and annual minimum streamflows may frequently display statistically significant serial correlation. von Storch [1995] documented that the existence of positive serial correlation increases the probability that the MK test detects trend when no trend exists. This could lead to a rejection of the null hypothesis of no trend, while the null hypothesis is actually true.

[3] To eliminate the influence of serial correlation on the MK test, von Storch [1995] proposed to remove a serial correlation component such as a lag 1 autoregressive (AR(1)) process from time series prior to applying the MK test to assess the significance of trend. This treatment is called as “prewhitening.” The MK test is then used to detect trend in the residual (or prewhitened) series. Douglas et al. [2000] tried to reduce the influence of serial correlation on the MK test by prewhitening in the trend‐detection study of the low flows in the United States. They found that the number of significant trends after prewhitening was less than that before prewhitening. In the trend analyses of Canadian temperature and rainfall data by Zhang et al. [2000] and Hamilton et al. [2001], prewhitening was applied to eliminate the effect of serial correlation on the MK test without any proof of the ability of prewhitening to fulfill such a task. Similarly, Zhang et al. [2001] and Burn and Hag Elnur [2001] employed this approach in streamflow trend analyses of Canada. It seems that prewhitening has been becoming popularly used to limit the effect of serial correlation on the MK test in trend analyses of hydrometeorological time series. Prewhitening has also been proposed to remove an AR process from a time series in the bootstrap postblackening approach [e.g., Davison and Hinkley, 1997; Srinivas and Srinivasan, 2000]. In the case that time series only consist of an AR(1) process with a noise, von Storch [1995] demonstrated that prewhitening can remove the AR(1) process from a time series and eliminate its influence on the MK test. The purpose of trend analyses by the MK test is to assess whether or not a significant trend exists in a tested series. In the case that a trend does exist in a time series, should prewhitening work, it relies on the fact that prewhitening could remove an AR process from a time series without affecting the existing trend. However, no evidence has been provided to certify this.

[4] The previous study of Yue et al. [2002] explored the influence of prewhitening on the prewhitened series only in the case that time series consist of an upward trend and a positive AR(1) process. It demonstrated that removal of positive serial correlation by prewhitening removes a portion of trend. This study extends the work of Yue et al. [2002] and is to further investigate this issue by Monte Carlo simulation. Time series with four kinds of combinations between linear trends (Tt = βt) and AR(1) processes (At = μA + ρ1(At−1 − μA) + εt) are examined: (1) positive AR(1) and upward trend (PAR‐UT), (2) positive AR(1) and downward trend (PAR‐DT); (3) negative AR(1) and upward trend (NAR‐UT), and (4) negative AR(1) and downward trend (NAR‐DT).

2. Simulation Study

[5] Simulation generated 5000 time series of AR(1) processes with mean of 1 and coefficient variation of 0.5 for each sample size (n = 20, 40, 50, 60, 70, and 80) with different given ρ1 = 0 (±0.1) ± 0.9. Then a trend with slope β = 0.00 (±0.001) ± 0.009 is superimposed onto each of the generated series, as given by
equation image
As β = 0.00 (±0.001) ± 0.009 (0.00, ±0.001, ±0.002, ±0.003, …, ±0.009), correspondingly, the mean (=1.0) over 100 years will increase (β × 100 × 100/1)% = 0(±10) ± 90%, i.e., increase/decrease 0 (10) 90%. The rate of rejecting the null hypothesis of no trend can be given by
equation image
where N is the total number of simulation experiments and Nrej is the number of experiments that fall in the critical region. On the basis of the null distribution of the MK test statistics S [Mann, 1945; Kendall, 1975] the critical regions of the MK statistic can be approximately given by
equation image
where α is the preselected significance level, z1−α/2 are the 1 − α/2 quantiles of the standard normal distribution, and V(S) is the sample variance of the MK statistic.

[6] The significance level α is set to be 0.05 in this study. Figure 1 shows the rejection rates, computed by equation (2), for the PAR‐UT series. Figure 1a indicates that in comparison with the series without serial correlation (ρ1 = 0.0), the existence of positive serial correlation increases the probability of rejecting the null hypothesis while it is actually true (β = 0.00). It also shows that the effect of serial correlation on the rejection rate is almost not sensitive to the sample size when no trend exists.

image
Figure 1
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Rejection rate for the PAR‐UT series (α = 0.05).

[7] Figures 1b–1j illustrate the rejection rates for the PAR‐UT series with the presence of some trend. By viewing these diagrams, it is found that the influence of serial correlation on the MK test is somewhat different from that without the existence of trend. Positive serial correlation increases the possibility of rejecting the null hypothesis for time series with short record length (say, n < 60 years). Its effect on the rejection rate tends to become weak as the magnitude of trend and sample size increase. For series with longer record length (n ≥ 70) and larger trend (say, β ≥ 0.005, i.e., increase of 50% over 100 years), the impact of serial correlation on the rejection rate is no longer significant. In the extreme cases, say n ≥ 80 and β ≥ 0.007, positive serial correlation decreases the rejection rate. For the PAR‐DT series the same observations as in the PAR‐UT case were obtained and are omitted here.

[8] Figure 2 depicts the rejection rates for the NAR‐DT series. It indicates that the presence of negative serial correlation decreases the rejection rate, while the null hypothesis may be false. When sample size and the magnitude of trend are large enough (say n ≥ 80 and |β| ≥ 0.006), negative serial correlation slightly increases the possibility of rejecting the null hypothesis. These two points are opposite to the PAR‐UT case. It can be seen that as the magnitude of trend and sample size increase, similar to the PAR‐UT case, the influence of negative serial correlation on the rejection rate tends to become weak. The rejection rates for the NAR‐UT series are also the same as shown by Figure 2 and are not presented.

image
Figure 2
Open in figure viewerPowerPoint
Rejection rate for the NAR‐DT series (α = 0.05).
[9] In order to reduce the impact of serial correlation on the MK test, prewhitening by von Storch [1995] was used to remove serial correlation from time series as
equation image
where r1 is the lag 1 serial correlation coefficient of sample data. In practice, as we do not know the true AR process in sample data. The lag 1 serial correlation coefficient r1 can only be estimated from sample data by an autocorrelation function as given in the work of Salas et al. [1980, p.38]. Equation (4) has been used to remove an AR(1) process from sample data in the trend‐detection studies of Douglas et al. [2000], Zhang et al. [2000, 2001], Hamilton et al. [2001], and Burn and Hag Elnur [2001].
[10] The rejection rates of the prewhitened series with β = 0.005, X′t, corresponding to the PAR‐UT and NAR‐DT are displayed in Figures 3a and 4a, respectively. The results corresponding to the series with other different trends are almost identical to the case with β = 0.005 and are not presented. Figure 3a indicates that removal of positive AR(1) by prewhitening greatly reduces the rejection rate or power of the test of rejecting the null hypothesis while it might be false. Figure 4a shows that removal of negative AR(1) by prewhitening dramatically increases the rejection rate or power of the test. To find the reason for these phenomena, the means of the lag 1 serial correlation coefficients of the above prewhitened series corresponding to the PAR‐UT and NAR‐DT are displayed in Figures 3b and 4, respectively. The means of the slopes of trend of the prewhitened series, estimated using the approach of Sen [1968] [also see Hirsch et al., 1982; Gan, 1998], are depicted in Figures 3c and 4c, respectively. Figures 3b and 4b shows that the AR(1) processes were almost removed from the series, except for an extreme case (|ρ1| = 0.9). Figures 3c and 4c indicates that prewhitening positive AR(1) removes a portion of trend, and prewhitening negative AR(1) inflates the magnitude of trend. These are the reason why the rejection rates of the prewhitened series are dramatically different from those without serial correlation. Theoretical interpretation is given as follows. By rewriting equation (4) as
equation image
it can be seen that the slope of the prewhitened series is β′ = (1 − r1)β, which is no longer equal to the true slope β. If r1 > 0, then β′ < β, i.e., removal of positive AR(1) by prewhitening will remove a portion of trend. If r1 < 0, then |β′| > |β|, i.e., removal of negative AR(1) by prewhitening will inflate the existing trend. Therefore, when trend does exist in a time series, prewhitening is not suitable for eliminating the influence of serial correlation on the MK test. The results for the PAR‐DT and NAR‐UT series are almost identical to those of the PAR‐UT and NAR‐DT, respectively, except for the difference in trend direction, as would be expected by symmetry alone. For brevity, these results were not presented.
image
Figure 3
Open in figure viewerPowerPoint
Prewhitened series corresponding to the PAR‐UT series. (a) Rejection rate of the prewhitened series. (b) Means of the serial correlation coefficients. (c) Means of the magnitude of slopes.
image
Figure 4
Open in figure viewerPowerPoint
Prewhitened series corresponding to the NAR‐DT series. (a) Rejection rate of the prewhitened series. (b) Means of the serial correlation coefficients. (c) Means of the magnitude of slopes.

3. Case Study

[11] Annual minimum daily streamflows of 36 pristine catchments with almost continuous observation from 1957 to 1997 are selected from the Canadian Reference Hydrometric Basin Network (RHBN) [Harvey et al., 1999]. The same data source was also used by Zhang et al. [2001]. The identifiers of the gauging stations, their locations, and their means of the annual minimum flows are given in Table 1. The lag 1 serial correlation coefficients of sample data before and after prewhitening are presented in columns 4 and 5 of Table 1, respectively. Column 5 indicates that serial correlation in most sites has been effectively removed from sample data. The estimates of the slope of the trends in sample data before and after prewhitening by Sen's approach [Sen, 1968] are given in columns 6 and 7 of Table 1, respectively. The percentage decrease/increase in the slope caused by prewhitening is listed in column 8. It is evident that the slope of sample data after prewhitening series is greatly different from that before prewhitening. Removal of positive serial correlation by prewhitening dramatically reduces the slope of the trend, and removal of negative serial correlation by prewhitening inflates the slope of the trends, as observed in the above simulation experiments.

Table 1. Comparison of Slopes Before and After Prewhitening
Station Identifier Province Mean (m3/s) Correlation Slope Decrease or increase,aa Decrease or increase is (slope before prewhitening—slope after prewhitening)/slope before prewhitening.
%
Before After Before After
01BP001 New Brunswick 5.4 0.18 −0.01 0.04648 0.02695 42
02FB007 Ontario 0.5 0.68 −0.35 0.01133 0.00313 72
02GA010 Ontario 2.1 0.51 −0.13 0.02902 0.01395 52
02HL004 Ontario 0.3 0.42 −0.01 0.00620 0.00253 59
09AA006 British Columbia 28.5 0.54 −0.11 0.20777 0.04524 78
09AC001 Yukon and Northwest Territories 9.6 0.14 −0.02 0.03783 0.01926 49
09AE003 Britsh Columbia 8.6 0.17 −0.01 0.02047 0.00592 71
09BC001 Yukon and Northwest Territories 47.4 0.33 −0.05 0.17500 0.03545 80
09CA002 Yukon and Northwest Territories 9.8 0.40 −0.05 0.12043 0.07391 39
10CB001 British Columbia 3.7 0.32 0.01 0.02647 0.01603 39
10CD001 British Columbia 15.6 0.26 −0.05 0.22105 0.14511 34
05AA023 Alberta 1.4 0.47 0.14 −0.00810 −0.00479 41
05AD003 Alberta 2.1 0.24 0.01 −0.00897 −0.00663 26
02ZF001 Newfoundland 8.9 0.16 0.04 −0.08310 −0.06903 17
02KB001 Ontario 11.3 0.28 0.00 −0.07000 −0.04939 29
08GA010 British Columbia 2.0 0.40 −0.05 −0.03789 −0.02850 25
08GD004 British Columbia 37.1 0.18 0.06 −0.20769 −0.14570 30
08HB008 British Columbia 2.8 0.24 −0.03 −0.06625 −0.05178 22
08HC002 British Columbia 1.9 0.23 −0.08 −0.04000 −0.03118 22
08JB002 British Columbia 5.0 0.30 0.01 −0.04282 −0.03869 10
08MG005 British Columbia 20.9 0.28 0.09 −0.06183 −0.05655 9
08NB005 British Columbia 25.7 0.24 −0.01 −0.20385 −0.16335 20
08NE077 British Columbia 0.5 0.25 0.09 −0.00185 −0.00163 12
08NL007 British Columbia 2.1 0.30 0.06 −0.03419 −0.02978 13
02OE027 Quebec 1.0 0.17 0.00 −0.00924 −0.00793 14
02VC001 Quebec 59.7 0.29 −0.04 −0.55000 −0.48809 11
01EC001 Nova Scotia 1.5 −0.41 −0.03 0.00222 0.00435 −96
08CE001 British Columbia 51.9 −0.16 0.03 0.22902 0.25208 −10
08KH006 British Columbia 56.0 −0.10 0.02 0.23125 0.29192 −26
02PJ007 Quebec 1.0 −0.12 0.01 0.01520 0.01734 −14
01DG003 Nova Scotia 0.1 −0.22 −0.01 −0.00066 −0.00130 −97
01EF001 Nova Scotia 2.0 −0.28 −0.02 −0.01431 −0.02461 −72
01EO001 Nova Scotia 2.4 −0.14 0.00 −0.01528 −0.03353 −119
08HA001 British Columbia 0.5 −0.21 0.03 −0.00509 −0.00738 −45
08JE001 British Columbia 41.7 −0.28 −0.01 −0.10000 −0.18264 −83
08LA001 British Columbia 35.6 −0.18 −0.04 −0.03708 −0.03842 −4
  • a Decrease or increase is (slope before prewhitening—slope after prewhitening)/slope before prewhitening.

4. Concluding Remarks

[12] The study examined the applicability of prewhitening to eliminate the influence of serial correlation on the MK test by Monte Carlo simulation. Results demonstrate that when trend exists in a time series, the impact of positive/negative serial correlation on the MK test is dependent upon sample size, magnitude of serial correlation, and magnitude of trend. For the series with short record length (say, n ≤ 50) the presence of positive serial correlation will increase the possibility of rejecting the null hypothesis, while negative serial correlation will decrease the rejection rate. When sample size and magnitude of trend are large enough, serial correlation does not significantly influence the MK test. In such a case, it is better to use the MK test on the original data rather than after prewhitening. Prewhitening will seriously distort the possibility of the test to detect trend. Removal of positive AR(1) by prewhitening will remove a portion of the trend, and removal of negative AR(1) by prewhitening will inflate the trend. In practice, for the purpose of water resources planning and management, policy makers and practitioners could be interested in the magnitude of the true trend in a series. If the slope of trend is estimated from the prewhitened series, such a slope is not the true one that a series has, as shown in Table 1. This study only addressed the case that a time series can be modeled by an AR(1) process and the ability of prewhitening to eliminate the influence of serial correlation on the MK test. If the process is not an AR(1) process but of higher order or of a different model type, even though there is no trend, the prewhitening cannot sufficiently reduce the effect of serial correlation on the MK test [von Storch, 1995].

Acknowledgments

[13] The thoughtful comments of William G. Gray and the anonymous reviewers are gratefully acknowledged.

      Number of times cited according to CrossRef: 300

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        Crossref
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        Crossref
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        Wiley Online Library
      • Mustafa Nuri Balov, Abdüsselam Altunkaynak, Spatio-temporal evaluation of various global circulation models in terms of projection of different meteorological drought indices, Environmental Earth Sciences, 10.1007/s12665-020-8881-0, 79, 6, (2020).
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      • Goutam Konapala, Ashok Mishra, Dynamics of virtual water networks: Role of national socio-economic indicators across the world, Journal of Hydrology, 10.1016/j.jhydrol.2020.125171, 589, (125171), (2020).
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        Crossref
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        Crossref
      • N. Naranjo-Fernández, C. Guardiola-Albert, H. Aguilera, C. Serrano-Hidalgo, M. Rodríguez-Rodríguez, A. Fernández-Ayuso, F. Ruiz-Bermudo, E. Montero-González, Relevance of spatio-temporal rainfall variability regarding groundwater management challenges under global change: case study in Doñana (SW Spain), Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-020-01771-7, (2020).
        Crossref
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        Crossref
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        Crossref
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        Crossref
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        Crossref
      • Guangyong You, M Altaf Arain, Shusen Wang, Shawn McKenzie, Bing Xu, Yaqian He, Dan Wu, Naifeng Lin, Jixi Gao, Xiru Jia, Inter-annual Climate Variability and Vegetation Dynamic in the Upper Amur (Heilongjiang) River Basin in Northeast Asia, Environmental Research Communications, 10.1088/2515-7620/ab9525, 2, 6, (061003), (2020).
        Crossref
      • Aminjon Gulakhmadov, Xi Chen, Nekruz Gulahmadov, Tie Liu, Rashid Davlyatov, Safarkhon Sharofiddinov, Manuchekhr Gulakhmadov, Long-Term Hydro–Climatic Trends in the Mountainous Kofarnihon River Basin in Central Asia, Water, 10.3390/w12082140, 12, 8, (2140), (2020).
        Crossref
      • Bikash Ranjan Parida, Arvind Chandra Pandey, N.R. Patel, Greening and Browning Trends of Vegetation in India and Their Responses to Climatic and Non-Climatic Drivers, Climate, 10.3390/cli8080092, 8, 8, (92), (2020).
        Crossref
      • Mariola Kędra, Regional Response to Global Warming: Water Temperature Trends in Semi-Natural Mountain River Systems, Water, 10.3390/w12010283, 12, 1, (283), (2020).
        Crossref
      • K. Alsafadi, S. A. Mohammed, B. Ayugi, M. Sharaf, E. Harsányi, Spatial–Temporal Evolution of Drought Characteristics Over Hungary Between 1961 and 2010, Pure and Applied Geophysics, 10.1007/s00024-020-02449-5, (2020).
        Crossref
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        Crossref
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        Wiley Online Library
      • Salah Basem Ajjur, Mohammed I. Riffi, Analysis of the observed trends in daily extreme precipitation indices in Gaza Strip during 1974–2016, International Journal of Climatology, 10.1002/joc.6576, 0, 0, (2020).
        Wiley Online Library
      • Francesco Serinaldi, Fateh Chebana, Chris G. Kilsby, Dissecting innovative trend analysis, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-020-01797-x, (2020).
        Crossref
      • Jenq-Tzong Shiau, Pei-Syun Wu, Nonstationary Distributional Changes of Annual Rainfall Indices in Taiwan, Asia-Pacific Journal of Atmospheric Sciences, 10.1007/s13143-020-00198-y, (2020).
        Crossref
      • Nazmus Sazib, John Bolten, Iliana Mladenova, Exploring Spatiotemporal Relations between Soil Moisture, Precipitation, and Streamflow for a Large Set of Watersheds Using Google Earth Engine, Water, 10.3390/w12051371, 12, 5, (1371), (2020).
        Crossref
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        Crossref
      • Mohammad Jafar Nazemosadat, Kokab Shahgholian, Habiballah Ghaedamini, Elham Nazemosadat, Introducing new climate indices for identifying wet/dry spells within an Madden‐Julian Oscillation phase, International Journal of Climatology, 10.1002/joc.6799, 0, 0, (2020).
        Wiley Online Library
      • Di Zhu, Yadong Mei, Yue Ben, Xinfa Xu, Inter- and intra-annual trend analysis of water level and flow in the middle and lower reaches of the Ganjiang River, China, Hydrological Sciences Journal, 10.1080/02626667.2020.1788716, (1-14), (2020).
        Crossref
      • Zichen Hu, Shuguang Liu, Guihui Zhong, Hejuan Lin, Zhengzheng Zhou, Modified Mann-Kendall trend test for hydrological time series under the scaling hypothesis and its application, Hydrological Sciences Journal, 10.1080/02626667.2020.1810253, (2020).
        Crossref
      • Haowei Sun, Haiying Hu, Zhaoli Wang, Chengguang Lai, Temporal Variability of Drought in Nine Agricultural Regions of China and the Influence of Atmospheric Circulation, Atmosphere, 10.3390/atmos11090990, 11, 9, (990), (2020).
        Crossref
      • Yangyang Xie, Saiyan Liu, Hongyuan Fang, Jingcai Wang, Global autocorrelation test based on the Monte Carlo method and impacts of eliminating nonstationary components on the global autocorrelation test, Stochastic Environmental Research and Risk Assessment, 10.1007/s00477-020-01854-5, (2020).
        Crossref
      • Qing Dong, Weiguang Wang, Quanxi Shao, Wanqiu Xing, Yimin Ding, Jianyu Fu, The response of reference evapotranspiration to climate change in Xinjiang, China: Historical changes, driving forces, and future projections, International Journal of Climatology, 10.1002/joc.6206, 40, 1, (235-254), (2019).
        Wiley Online Library
      • Dong Wu, Shibo Fang, Xuan Li, Di He, Yongchao Zhu, Zaiqiang Yang, Jiaxin Xu, Yingjie Wu, Spatial-temporal variation in irrigation water requirement for the winter wheat-summer maize rotation system since the 1980s on the North China Plain, Agricultural Water Management, 10.1016/j.agwat.2019.01.004, 214, (78-86), (2019).
        Crossref
      • Lei Wang, Rensheng Chen, Chuntan Han, Xiqiang Wang, Guohua Liu, Yaoxuan Song, Yong Yang, Junfeng Liu, Zhangwen Liu, Xiaojiao Liu, Shuhai Guo, Qin Zheng, Change characteristics of precipitation and temperature in the Qilian Mountains and Hexi Oasis, Northwestern China, Environmental Earth Sciences, 10.1007/s12665-019-8289-x, 78, 9, (2019).
        Crossref
      • Md. Siddiqur Rahman, Abu Reza Md. Towfiqul Islam, Are precipitation concentration and intensity changing in Bangladesh overtimes? Analysis of the possible causes of changes in precipitation systems, Science of The Total Environment, 10.1016/j.scitotenv.2019.06.529, 690, (370-387), (2019).
        Crossref
      • Xiaoyan Zhang, Baoqing Zhang, The responses of natural vegetation dynamics to drought during the growing season across China, Journal of Hydrology, 10.1016/j.jhydrol.2019.04.084, (2019).
        Crossref
      • Robin Glas, Douglas Burns, Laura Lautz, Historical changes in New York State streamflow: attribution of temporal shifts and spatial patterns from 1961-2016, Journal of Hydrology, 10.1016/j.jhydrol.2019.04.060, (2019).
        Crossref
      • John Ruprecht, Tim Sparks, Ning Liu, Bernard Dell, Richard Harper, Using reforestation to reverse salinisation in a large watershed, Journal of Hydrology, 10.1016/j.jhydrol.2019.123976, (123976), (2019).
        Crossref
      • Pooja Agarwal, Lalit Pal, Mohd. Afaq Alam, Regional Scale analysis of hydro-meteorological variables in Kesinga sub-catchment of Mahanadi Basin, India, Environmental Earth Sciences, 10.1007/s12665-019-8457-z, 78, 15, (2019).
        Crossref
      • Priyanka Sharma, Deepesh Machiwal, Madan Kumar Jha, Overview, Current Status, and Future Prospect of Stochastic Time Series Modeling in Subsurface Hydrology, GIS and Geostatistical Techniques for Groundwater Science, 10.1016/B978-0-12-815413-7.00010-9, (133-151), (2019).
        Crossref
      • Md. Hussain, Ishtiak Mahmud, pyMannKendall: a python package for non parametric Mann Kendall family of trend tests., Journal of Open Source Software, 10.21105/joss.01556, 4, 39, (1556), (2019).
        Crossref
      • Qiu-Bo Long, Impacts of Climate Variability and Human Activities on Runoff: A Case Study in the Jinghe River Basin, Sustainable Development of Water Resources and Hydraulic Engineering in China, 10.1007/978-3-319-61630-8_30, (351-366), (2019).
        Crossref
      • Ping Xie, Haiting Gu, Yan-Fang Sang, Ziyi Wu, Vijay P. Singh, Comparison of different methods for detecting change points in hydroclimatic time series, Journal of Hydrology, 10.1016/j.jhydrol.2019.123973, (123973), (2019).
        Crossref
      • Ju-Young Shin, Taereem Kim, Jun-Haeng Heo, Joon-Hak Lee, Spatial and temporal variations in rainfall erosivity and erosivity density in South Korea, CATENA, 10.1016/j.catena.2019.01.005, 176, (125-144), (2019).
        Crossref
      • Haihan Zhao, Xuebiao Pan, Ziwen Wang, Shaojie Jiang, Lizhong Liang, Xiaochen Wang, Xiaoxiao Wang, What were the changing trends of the seasonal and annual aridity indexes in northwestern China during 1961–2015?, Atmospheric Research, 10.1016/j.atmosres.2019.02.012, (2019).
        Crossref
      • ML Marston, AW Ellis, Change in the uniformity of the temporal distribution of precipitation across the MidAtlantic region of the United States, 1950-2017, Climate Research, 10.3354/cr01561, 78, 1, (69-81), (2019).
        Crossref
      • Ganeshchandra Mallya, Shivam Tripathi, Rao S. Govindaraju, Detection of Temporal Changes in Droughts Over Indiana, Trends and Changes in Hydroclimatic Variables, 10.1016/B978-0-12-810985-4.00006-2, (305-360), (2019).
        Crossref
      • Deepesh Machiwal, Adlul Islam, Trupti Kamble, Trends and probabilistic stability index for evaluating groundwater quality: The case of quaternary alluvial and quartzite aquifer system of India, Journal of Environmental Management, 10.1016/j.jenvman.2019.02.071, 237, (457-475), (2019).
        Crossref
      • Ganeshchandra Mallya, Shivam Tripathi, Rao S. Govindaraju, An Analysis of Spatio-Temporal Changes in Drought Characteristics over India, Hydrology in a Changing World, 10.1007/978-3-030-02197-9_2, (23-71), (2019).
        Crossref
      • Balbhadra Thakur, Ajay Kalra, Venkat Lakshmi, Kenneth W. Lamb, William P. Miller, Glenn Tootle, Linkage between ENSO phases and western US snow water equivalent, Atmospheric Research, 10.1016/j.atmosres.2019.104827, (104827), (2019).
        Crossref
      • Tianci Yao, Hongwei Lu, Wei Feng, Qing Yu, Evaporation abrupt changes in the Qinghai-Tibet Plateau during the last half-century, Scientific Reports, 10.1038/s41598-019-56464-1, 9, 1, (2019).
        Crossref
      • Xuhu Wang, Baitian Wang, Xianying Xu, Effects of large-scale climate anomalies on trends in seasonal precipitation over the Loess Plateau of China from 1961 to 2016, Ecological Indicators, 10.1016/j.ecolind.2019.105643, 107, (105643), (2019).
        Crossref
      • Upaka Rathnayake, Comparison of Statistical Methods to Graphical Methods in Rainfall Trend Analysis: Case Studies from Tropical Catchments, Advances in Meteorology, 10.1155/2019/8603586, 2019, (1-10), (2019).
        Crossref
      • Chengcheng Gang, Xuerui Gao, Shouzhang Peng, Mingxun Chen, Liang Guo, Jingwei Jin, Satellite Observations of the Recovery of Forests and Grasslands in Western China, Journal of Geophysical Research: Biogeosciences, 10.1029/2019JG005198, 124, 7, (1905-1922), (2019).
        Wiley Online Library
      • Najeebullah Khan, Sahar Hadi Pour, Shamsuddin Shahid, Tarmizi Ismail, Kamal Ahmed, Eun‐Sung Chung, Nadeem Nawaz, Xiaojun Wang, Spatial distribution of secular trends in rainfall indices of Peninsular Malaysia in the presence of long‐term persistence, Meteorological Applications, 10.1002/met.1792, 26, 4, (655-670), (2019).
        Wiley Online Library
      • K. Satish Kumar, E. Venkata Rathnam, Analysis and Prediction of Groundwater Level Trends Using Four Variations of Mann Kendall Tests and ARIMA Modelling, Journal of the Geological Society of India, 10.1007/s12594-019-1308-4, 94, 3, (281-289), (2019).
        Crossref
      • Mustafa Nuri Balov, Abdüsselam Altunkaynak, Trend Analyses of Extreme Precipitation Indices Based on Downscaled Outputs of Global Circulation Models in Western Black Sea Basin, Turkey, Iranian Journal of Science and Technology, Transactions of Civil Engineering, 10.1007/s40996-019-00237-3, (2019).
        Crossref
      • Pedro Arriagada, Bastien Dieppois, Moussa Sidibe, Oscar Link, Impacts of Climate Change and Climate Variability on Hydropower Potential in Data-Scarce Regions Subjected to Multi-Decadal Variability, Energies, 10.3390/en12142747, 12, 14, (2747), (2019).
        Crossref
      • Sean Hardison, Charles T Perretti, Geret S DePiper, Andrew Beet, A simulation study of trend detection methods for integrated ecosystem assessment, ICES Journal of Marine Science, 10.1093/icesjms/fsz097, (2019).
        Crossref
      • Mohamed Salem Nashwan, Shamsuddin Shahid, Xiaojun Wang, Uncertainty in Estimated Trends Using Gridded Rainfall Data: A Case Study of Bangladesh, Water, 10.3390/w11020349, 11, 2, (349), (2019).
        Crossref
      • Hakan Tongal, Spatiotemporal analysis of precipitation and extreme indices in the Antalya Basin, Turkey, Theoretical and Applied Climatology, 10.1007/s00704-019-02927-4, (2019).
        Crossref
      • L.L. Paniagua, A. García-Martín, F.J. Moral, F.J. Rebollo, Aridity in the Iberian Peninsula (1960–2017): distribution, tendencies, and changes, Theoretical and Applied Climatology, 10.1007/s00704-019-02866-0, (2019).
        Crossref
      • Paresha M. Baria, S. M. Yadav, Investigating extreme rainfall non-stationarity of upper Tapi river basin, India, ISH Journal of Hydraulic Engineering, 10.1080/09715010.2019.1627679, (1-9), (2019).
        Crossref
      • Zhenhui Wu, Yadong Mei, Junhong Chen, Tiesong Hu, Weihua Xiao, Attribution Analysis of Dry Season Runoff in the Lhasa River Using an Extended Hydrological Sensitivity Method and a Hydrological Model, Water, 10.3390/w11061187, 11, 6, (1187), (2019).
        Crossref
      • Yédjinnavènan Ahokpossi, Analysis of the rainfall variability and change in the Republic of Benin (West Africa), Hydrological Sciences Journal, 10.1080/02626667.2018.1554286, (1-27), (2019).
        Crossref
      • Weizhi Gao, Zhaoli Wang, Guoru Huang, Spatiotemporal Variability of Actual Evapotranspiration and the Dominant Climatic Factors in the Pearl River Basin, China, Atmosphere, 10.3390/atmos10060340, 10, 6, (340), (2019).
        Crossref
      • Mike Hobbins, Gabriel Senay, Prasanna H. Gowda, Guleid Artan, Evapotranspiration and Evaporative Demand, Statistical Analysis of Hydrologic Variables, 10.1061/9780784415177, (71-143), (2019).
        Crossref
      • Guangyong You, M Altaf Arain, Shusen Wang, Shawn McKenzie, Changxin Zou, Zhi Wang, Haidong Li, Bo Liu, Xiaohua Zhang, Yangyang Gu, Jixi Gao, The spatial-temporal distributions of controlling factors on vegetation growth in Tibet Autonomous Region, Southwestern China, Environmental Research Communications, 10.1088/2515-7620/ab3d87, 1, 9, (091003), (2019).
        Crossref
      • Suzhen Dang, Manfei Yao, Xiaoyan Liu, Guotao Dong, Variations and Statistical Probability Characteristic Analysis of Extreme Precipitation in the Hekouzhen-Longmen Region of the Yellow River, China, Asia-Pacific Journal of Atmospheric Sciences, 10.1007/s13143-019-00117-w, (2019).
        Crossref
      • Isabell Haag, Philip D. Jones, Cyrus Samimi, Central Asia’s Changing Climate: How Temperature and Precipitation Have Changed across Time, Space, and Altitude, Climate, 10.3390/cli7100123, 7, 10, (123), (2019).
        Crossref
      • undefined Zhou, undefined Wang, undefined Wu, undefined Chen, undefined Zhong, undefined Li, undefined Chen, undefined Li, undefined Guo, undefined Chen, Spatiotemporal Variation of Annual Runoff and Sediment Load in the Pearl River during 1953–2017, Sustainability, 10.3390/su11185007, 11, 18, (5007), (2019).
        Crossref
      • Guangsheng Liu, An empirical research on the relationship between water quality, climate change and economic development in Jiulong River Watershed, IOP Conference Series: Earth and Environmental Science, 10.1088/1755-1315/356/1/012015, 356, (012015), (2019).
        Crossref
      • Yao Fu, Zhibin Ren, Qiuyan Yu, Xingyuan He, Lu Xiao, Qiong Wang, Chang Liu, Long-term dynamics of urban thermal comfort in China’s four major capital cities across different climate zones, PeerJ, 10.7717/peerj.8026, 7, (e8026), (2019).
        Crossref
      • Chunyu Liu, Yungang Li, Xuan Ji, Xian Luo, Mengtao Zhu, Observed Changes in Temperature and Precipitation Extremes Over the Yarlung Tsangpo River Basin during 1970–2017, Atmosphere, 10.3390/atmos10120815, 10, 12, (815), (2019).
        Crossref
      • Chen Chen, Tiejian Li, Bellie Sivakumar, Jiaye Li, Guangqian Wang, Attribution of growing season vegetation activity to climate change and human activities in the Three-River Headwaters Region, China, Journal of Hydroinformatics, 10.2166/hydro.2019.003, (2019).
        Crossref
      • Sanim Bissenbayeva, Jilili Abuduwaili, Dana Shokparova, Asel Saparova, Variation in Runoff of the Arys River and Keles River Watersheds (Kazakhstan), as Influenced by Climate Variation and Human Activity, Sustainability, 10.3390/su11174788, 11, 17, (4788), (2019).
        Crossref
      • Cansu Beşel, Emine Tanır Kayıkçı, Serisel Korelasyonun Toplam Zenit Gecikmesi Zaman Serilerinde Parametrik Olmayan Trend Belirleme Üzerindeki Etkisi, Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 10.17714/gumusfenbil.417853, (2019).
        Crossref
      • Deepesh Machiwal, P. C. Moharana, Sanjay Kumar, Vandita Srivastava, Subhash L. Bhandari, Exploring temporal dynamics of spatially-distributed groundwater levels by integrating time series modeling with geographic information system, Geocarto International, 10.1080/10106049.2019.1648561, (1-21), (2019).
        Crossref
      • Pauline Rivoire, Yves Tramblay, Luc Neppel, Elke Hertig, Sergio M. Vicente-Serrano, Impact of the dry-day definition on Mediterranean extreme dry-spell analysis, Natural Hazards and Earth System Sciences, 10.5194/nhess-19-1629-2019, 19, 8, (1629-1638), (2019).
        Crossref
      • Fan Song, Xiaohua Yang, Feifei Wu, Catastrophe progression method based on M-K test and correlation analysis for assessing water resources carrying capacity in Hubei province, Journal of Water and Climate Change, 10.2166/wcc.2018.114, 11, 2, (556-567), (2018).
        Crossref
      • V. Baldasso, A. Soncini, R. S. Azzoni, G. Diolaiuti, C. Smiraglia, D. Bocchiola, Recent evolution of glaciers in Western Asia in response to global warming: the case study of Mount Ararat, Turkey, Theoretical and Applied Climatology, 10.1007/s00704-018-2581-7, 137, 1-2, (45-59), (2018).
        Crossref
      • Jinlin Zha, Jian Wu, Deming Zhao, Jianping Tang, A possible recovery of the near-surface wind speed in Eastern China during winter after 2000 and the potential causes, Theoretical and Applied Climatology, 10.1007/s00704-018-2471-z, 136, 1-2, (119-134), (2018).
        Crossref
      • Babatunde Adeniyi Osunmadewa, Worku Zewdie Gebrehiwot, Elmar Csaplovics, Olabinjo Clement Adeofun, Spatio-temporal monitoring of vegetation phenology in the dry sub-humid region of Nigeria using time series of AVHRR NDVI and TAMSAT datasets, Open Geosciences, 10.1515/geo-2018-0001, 10, 1, (1-11), (2018).
        Crossref
      • Guangyao Gao, Bojie Fu, Jianjun Zhang, Ying Ma, Murugesu Sivapalan, Multiscale temporal variability of flow-sediment relationships during the 1950s–2014 in the Loess Plateau, China, Journal of Hydrology, 10.1016/j.jhydrol.2018.06.044, 563, (609-619), (2018).
        Crossref
      • Hang-Tak Jeon, Se-Yeong Hamm, Jae-Yeol Cheong, Cheol-Woo Lee, Jong-Tae Lee, Woo-Ri Lim, Analysis of long-term water level change of Dongrae hot spring using time series methods, Journal of the Geological Society of Korea, 10.14770/jgsk.2018.54.5.529, 54, 5, (529-544), (2018).
        Crossref
      • Saman Razavi, Richard Vogel, Prewhitening of hydroclimatic time series? Implications for inferred change and variability across time scales, Journal of Hydrology, 10.1016/j.jhydrol.2017.11.053, 557, (109-115), (2018).
        Crossref
      • Francesco Serinaldi, Chris G. Kilsby, Federico Lombardo, Untenable nonstationarity: An assessment of the fitness for purpose of trend tests in hydrology, Advances in Water Resources, 10.1016/j.advwatres.2017.10.015, 111, (132-155), (2018).
        Crossref
      • Sadık Alashan, An improved version of innovative trend analyses, Arabian Journal of Geosciences, 10.1007/s12517-018-3393-x, 11, 3, (2018).
        Crossref
      • Archana Sarkar, Vaibhav Garg, Study of Climate Change in Uttarakhand Himalayas: Changing Patterns of Historical Rainfall, Climate Change Impacts, 10.1007/978-981-10-5714-4_14, (165-179), (2018).
        Crossref
      • Rengui Jiang, Yinping Wang, Jiancang Xie, Yong Zhao, Fawen Li, Xiaojie Wang, Assessment of extreme precipitation events and their teleconnections to El Niño Southern Oscillation, a case study in the Wei River Basin of China, Atmospheric Research, 10.1016/j.atmosres.2018.12.015, (2018).
        Crossref
      • Meixian Liu, Xianli Xu, Alexander Y. Sun, New drought index indicates that land surface changes might have enhanced drying tendencies over the Loess Plateau, Ecological Indicators, 10.1016/j.ecolind.2018.02.003, 89, (716-724), (2018).
        Crossref
      • Wei Zhang, Yu Cao, Yuliang Zhu, Jinhai Zheng, Xiaomei Ji, Yanwen Xu, Yao Wu, A.J.F. Hoitink, Unravelling the causes of tidal asymmetry in deltas, Journal of Hydrology, 10.1016/j.jhydrol.2018.07.023, 564, (588-604), (2018).
        Crossref
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