Water Resources Management

, Volume 28, Issue 1, pp 227–240 | Cite as

Temporal Change Analysis Based on Data Characteristics and Nonparametric Test

  • Dingfang Li
  • Huantian Xie
  • Lihua Xiong


Based on data characteristics and nonparametric test, a new statistical temporal change analysis approach is proposed. The new approach consists of data characteristics analysis, temporal change analysis (including both change point and trend analysis), and result interpretation. Data characteristics are firstly investigated, especially with respect to the assumptions of independence and normality. Then proper nonparametric methods are chosen based on the detected characteristics of the observed data to analyze change points and monotonous linear trend for each of the segments divided by the change points. To avoid shortcoming of the traditional approach of carrying out the trend analysis before change point analysis, it is proposed in this paper that change point detection be performed before trend analysis. At last, statistical analysis results are interpreted according to the physical mechanism of observations. As a study case, the proposed approach has been carried out on three annual discharge series of the Yangtze River at the Yichang hydrological station. The investigations of data characteristics show that the observed data do not meet the assumptions of being independent and identically Gaussian-distributed. So the nonparametric Pettitt’s test was adopted to detect abrupt changes in the mean levels, followed by trend analysis using the nonparametric Mann-Kendall (MK) test. Results indicate the proposed approach is both reliable and reasonable for the temporal change analysis.


Data characteristics Nonparametric test Change point analysis Trend analysis Annual discharge series 



This research was supported by the National Natural Science Foundation of China (51190094, 61271337 and 11301252). The authors are very grateful to the associate editor and two anonymous reviewers for their helpful suggestions and constructive comments in the improvement of this manuscript.


  1. Anderson RL (1942) Distribution of the serial correlation coefficient. Annals of Math Stat 13(1):1–13CrossRefGoogle Scholar
  2. Bartels R (1982) The rank version of von Neumann’s ratio test for randomness. J Am Stat Assoc 77(377):40–46CrossRefGoogle Scholar
  3. Brillinger DR (2001) Time series: data analysis and theory. Society for industrial and applied mathematics, PhiladelphiaCrossRefGoogle Scholar
  4. Buishand TA (1984) Tests for detecting a shift in the mean of hydrological time series. J Hydrol 73(1):51–69CrossRefGoogle Scholar
  5. Burn DH, Hag Elnur MA (2002) Detection of hydrologic trends and variability. J Hydrol 255(1):107–122CrossRefGoogle Scholar
  6. Clarke RT (1973) Mathematical models in hydrology. FAO, RomeGoogle Scholar
  7. Cox DR, Stuart A (1955) Some quick sign tests for trend in location and dispersion. Biometrika 42(1–2):80–95Google Scholar
  8. Douglas EM, Vogel RM, Kroll CN (2000) Trends in floods and low flows in the United States: impact of spatial correlation. J Hydrol 240(1):90–105CrossRefGoogle Scholar
  9. Hirsch RM, Slack JR, Smith RA (1982) Techniques of trend analysis for monthly water quality data. Water Resour Res 18(1):107–121CrossRefGoogle Scholar
  10. Kahya E, Kalayci S (2004) Trend analysis of streamflow in Turkey. J Hydrol 289:128–144CrossRefGoogle Scholar
  11. Kalra A, Piechota TC, Davies R, Tootle GA (2008) Changes in US streamflow and western US snowpack. J Hydrol Eng 13(3):156–163CrossRefGoogle Scholar
  12. Kendall MG (1938) A new measure of rank correlation. Biometrika 30(1–2):81–93Google Scholar
  13. Kendall MG (1975) Rank correlation methods. Charles Griffin, LondonGoogle Scholar
  14. Koutsoyiannis D (2006) Nonstationarity versus scaling in hydrology. J Hydrol 324(1):239–254CrossRefGoogle Scholar
  15. Kulkarni A, von Storch H (1995) Monte Carlo experiments on the effect of serial correlation on the Mann-Kendall test of trend. Meteorol Z 4(2):82–85Google Scholar
  16. Li S, Xiong LH, Dong LH, Zhang J (2012) Effects of the Three Gorges Reservoir on the hydrological droughts at the downstream Yichang station during 2003–2011. Hydrol Process. doi: 10.1002/hyp.9541 Google Scholar
  17. Lins HF, Slack JR (1999) Streamflow trends in the United States. Geophys Res Lett 26(2):227–230CrossRefGoogle Scholar
  18. Mann HB (1945) Non-parametric tests against trend. Econometrica 13:245–259CrossRefGoogle Scholar
  19. Matalas NC (1997) Stochastic hydrology in the context of climate change. Clim Chang 37:89–101CrossRefGoogle Scholar
  20. McCabe GJ, Wolock DM (2002) A step increase in streamflow in the conterminous United States. Geophys Res Lett 29(24):2185CrossRefGoogle Scholar
  21. Perreault L, Haché M, Slivitzky M, Bobée B (1999) Detection of changes in precipitation and runoff over eastern Canada and US using a Bayesian approach. Stoch Env Res Risk A 13:201–216CrossRefGoogle Scholar
  22. Perreault L, Bernier J, Bobée B, Parent E (2000a) Bayesian change point analysis in hydrometerological time series. Part 1: The normal model revisited. J Hydrol 235:221–241CrossRefGoogle Scholar
  23. Perreault L, Bernier J, Bobée B, Parent E (2000b) Bayesian change point analysis in hydrometerological time series. Part 2: Comparison of change point models and forecasting. J Hydrol 235:242–263CrossRefGoogle Scholar
  24. Pettitt AN (1979) A non-parametric approach to the change point problem. Appl Statist 28(2):126–135CrossRefGoogle Scholar
  25. Rougé C, Ge Y, Cai X (2013) Detecting gradual and abrupt changes in hydrological records. Adv Water Resour 53:33–44CrossRefGoogle Scholar
  26. Salas JD (1993) Analysis and modeling of hydrologic time series. In: Maidment D (ed) Handbook of hydrology. McGraw Hill, NewYork, pp 19.1–19.72Google Scholar
  27. Salas JD, Delleur JW, Yevjevich V, Lane WL (1980) Applied modelling of hydrologic time series. Water Resources Publications, LittletonGoogle Scholar
  28. Sen PK (1968) Estimates of the regression coefficient based on Kendall’s tau. J Am Stat Assoc 63(324):1379–1389CrossRefGoogle Scholar
  29. Theil H (1950) A rank-invariant method of linear and polynomial regression analysis, I, II, III. Nederl Akad Wetensch Proc 53:386–392, 512–525, 1397–1412Google Scholar
  30. Villarini G, Smith JA (2010) Flood peak distributions for the eastern United States. Water Resour Res 46, W06504. doi: 10.1029/2009WR008395 Google Scholar
  31. Villarini G, Serinaldi F, Smith JA, Krajewski WF (2009) On the stationarity of annual flood peaks in the continental United States during the 20th century. Water Resour Res 45, W08417. doi: 10.1029/2008WR007645 Google Scholar
  32. Villarini G, Smith JA, Baeck ML, Krajewski WF (2011a) Examining flood frequency distributions in the Midwest US 1. J Am Water Resour As 47(3):447–463CrossRefGoogle Scholar
  33. Villarini G, Smith JA, Serinaldi F, Ntelekos AA (2011b) Analyses of seasonal and annual maximum daily discharge records for central Europe. J Hydrol 399(3–4):299–312CrossRefGoogle Scholar
  34. Von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Annals of Math Stat 13:367–395CrossRefGoogle Scholar
  35. Xie HT, Li DF, Xiong LH (2013) Exploring the ability of the Pettitt method for detecting change point by Monte Carlo simulation. Stoch Environ Res Risk Assess. doi: 10.1007/s00477-013-0814-y Google Scholar
  36. Xiong LH, Guo SL (2004) Trend test and change point detection for the annual discharge series of the Yangtze River at the Yichang hydrological station. Hydrol Sci J 49(1):99–112CrossRefGoogle Scholar
  37. Yue S, Wang CY (2004) The Mann-Kendall test modified by effective sample size to detect trend in serially correlated hydrological series. Water Resour Manage 18(3):201–218CrossRefGoogle Scholar
  38. Yue S, Pilon P, Phinney B, Cavadias G (2002) The influence of autocorrelation on the ability to detect trend in hydrological series. Hydrol Process 16:1807–1829CrossRefGoogle Scholar
  39. Yue S, Pilon P, Phinney B (2003) Canadian streamflow trend detection: impacts of serial and cross-correlation. Hydrol Sci J 48(1):51–63CrossRefGoogle Scholar
  40. Zhang Q, Jiang T, Gemmer M, Becker S (2005) Precipitation, temperature and discharge analysis from 1951 to 2002 in the Yangtze catchment, China. Hydrol Sci J 50(1):65–80Google Scholar
  41. Zhang Q, Liu CL, Xu CY, Xu YP, Jiang T (2006) Observed trends of annual maximum water level and streamflow during past 130 years in the Yangtze River basin, China. J Hydrol 324:255–265CrossRefGoogle Scholar
  42. Zhang Q, Xu CY, Yang T (2009) Variability of water resource in the Yellow River basin of past 50 years, China. Water Resour Manage 23(6):1157–1170CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanPeople’s Republic of China
  2. 2.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanPeople’s Republic of China
  3. 3.School of ScienceLinyi UniversityLinyiPeople’s Republic of China

Personalised recommendations