Abstract
Measured streamflow and flood series of 43 gauging stations from 25 west flowing rivers in Kerala, India, were analysed for their descriptive characteristics to study their spatial and temporal variation. The spatial and temporal variations in streamflow are influenced by many factors including climatic and basin characteristics. Streamflow data from each station (length varies from 14 to 43 years) is analysed for their internal characteristics such as trend, stationarity, homogeneity, noise and periodicity to incorporate it in hydrological models, so that their predictions would be more accurate. The internal characteristics were studied along with the statistical analysis. For analysing each internal characteristic, more than one method of analysis has been used to have reliable result. The trend characteristic was analysed using Mann-Kendall (MK) test, Sen’s slope test, Spearman’s rank correlation coefficient and Pearson correlation coefficient methods. Stationarity characteristics have been tested using augmented Dickey-Fuller test (ADF), Phillips-Perron test and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. For identifying homogeneous nature, Pettitt test, standard normal homogeneity (SNH) test, Buishand test and von Neumann tests were used. Noise in the streamflow was verified using Box-Peirce, Ljung-Box and McLeod-Li tests. From the study, it is found that the daily series is non-homogeneous, stationary data with white noise, whereas flood series shows mixed characteristics. Based on the variations in the time series, the daily streamflow and flood series are classified into different categories such as high, average, moderate, minor and no variation stations. In most of the river basins, daily flow shows average variation. Flood series shows average variation in 44% of stations and moderate variation in 28% of stations.
Similar content being viewed by others
References
Abghari H, Tabari H, Hosseinzadeh Talaee P (2013) River flow trends in the west of Iran during the past 40years: impact of precipitation variability. Glob Planet Change 101:52–60. https://doi.org/10.1016/j.gloplacha.2012.12.003
Ahmad NH, Deni SM (2013) Homogeneity test on daily rainfall series for Malaysia. Matematika 29:141–150
Akinsanola AA, Ogunjobi KO (2017) Recent homogeneity analysis and long-term spatio-temporal rainfall trends in Nigeria. Theor Appl Climatol 128:275–289. https://doi.org/10.1007/s00704-015-1701-x
Alexandersson H, Moberg A (1997) Homogenization of Swedish temperature data. Part I: homogeneity test for linear trends. Int J Climatol 17:25–34. https://doi.org/10.1002/(SICI)1097-0088(199701)17:1<25::AID-JOC103>3.0.CO;2-J
Ampitiyawatta A, Guo S (2010) Precipitation trends in the Kalu ganga basin in Sri Lanka. J Agric Sci 4:10–18. https://doi.org/10.4038/jas.v4i1.1641
Barrett KR, Salis W (2017) Prevalence and Magnitude of Trends in Peak Annual Flow and 5- , 10- , and 20-Year Flows in the Northeastern United States. J Hydrol Eng 2:1–9. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001474
Birsan MV, Molnar P, Burlando P, Pfaundler M (2005) Streamflow trends in Switzerland. J Hydrol 314:312–329. https://doi.org/10.1016/j.jhydrol.2005.06.008
Bisht DS, Chatterjee C, Raghuwanshi NS, Sridhar V (2017) Spatio-temporal trends of rainfall across Indian river basins. Theor Appl Climatol 132:1–18. https://doi.org/10.1007/s00704-017-2095-8
Box GEP, Pierce DA (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average Tim published by : Americane series models author ( s ): statistical association stable URL : http://www.jstor.org/stable/2284333. J Am Stat Assoc 65:1509–1526
Buishand TA, de Haan L, Zhou C (2008) On spatial extremes: with application to a rainfall problem. Ann Appl Stat 2:624–642. https://doi.org/10.1214/08-AOAS159
Chandniha SK, Meshram SG, Adamowski JF, Meshram C (2017) Trend analysis of precipitation in Jharkhand state, India: investigating precipitation variability in Jharkhand state. Theor Appl Climatol 130:261–274. https://doi.org/10.1007/s00704-016-1875-x
Chatfield C (2000) Time-series forecasting. Chapman &C Hall/CRC, Boca Raton London New York Washington, D.C.
Cohen J (1988) Statistical power analysis for the behavioral sciences, second. Lawrence Erlbaum Associates, New York
Coscarelli R, Caloiero T (2012) Analysis of daily and monthly rainfall concentration in southern Italy (Calabria region). J Hydrol 416–417:145–156. https://doi.org/10.1016/j.jhydrol.2011.11.047
CWRDM (1995) Water atlas, Centre for Water Resources Development and Management. Kerala, Kozhikode, India
Dahmen E, Hall MJ (1990) Screening of hydrological data :tests for stationarity and relative consistency. International Institute for Land Reclamation and. Improvement/ILRI, Wageningen, Netherlands
De Lima MIP, Carvalho SCP, De Lima JLM, Coelho MFES (2010) Trends in precipitation: analysis of long annual and monthly time series from mainland Portugal. Adv Geosci 25:155–160. https://doi.org/10.5194/adgeo-25-155-2010
Dhorde AG, Zarenistanak M (2013) Three-way approach to test data homogeneity : an analysis of temperature and precipitation series over southwestern Islamic Republic of Iran. J Ind Geophys Union 17:233–242
Dickey DA, Fuller WA (1979) Distribution of the estimators for auroregressive time series with a unit root. J Am Stat Assoc 74:427–431
Diop L, Yaseen ZM, Bodian A, Djaman K, Brown L (2017) Trend analysis of streamflow with different time scales: a case study of the upper Senegal River. ISH J Hydraul Eng 5010:1–10. https://doi.org/10.1080/09715010.2017.1333045
Do HX, Westra S, Leonard M (2017) A global-scale investigation of trends in annual maximum streamflow. J Hydrol 552:28–43. https://doi.org/10.1016/j.jhydrol.2017.06.015
Elfeky MG, Aref WG, Elmagarmid AK (2005) Periodicity detection in time series databases. IEEE Trans Knowl Data Eng 17:875–887. https://doi.org/10.1109/TKDE.2005.114
Gauthier TD (2001) Detecting trends using spearman’s rank correlation coefficient. Environ Forensic 2:359–362. https://doi.org/10.1080/713848278
Gemmer M, Becker S, Jiang T (2004) Observed monthly precipitation trends in China 1951-2002. Theor Appl Climatol 77:39–45. https://doi.org/10.1007/s00704-003-0018-3
Ghasemi AR (2015) Changes and trends in maximum, minimum and mean temperature series in Iran. Atmos Sci Lett 16:366–372. https://doi.org/10.1002/asl2.569
Gilbert RO (1987) Statistical methods for environmental pollution monitoring. John Wiley and Sons. Inc., Pacific Northwest Laboratory
Guhathakurta P, Rajeevan M (2008) Trends in the rainfall pattern over India. Int J Climatol 28:1453–1469. https://doi.org/10.1002/joc.1640
Huza J, Teuling AJ, Braud I, Grazioli J, Melsen LA, Nord G, Raupach TH, Uijlenhoet R (2014) Precipitation, soil moisture and runoff variability in a small river catchment (Arde’che, France) during HyMeX special observation period 1. J Hydrol 516:330–342. https://doi.org/10.1016/j.jhydrol.2014.01.041
Irmak S, Kabenge I, Skaggs KE, Mutiibwa D (2012) Trend and magnitude of changes in climate variables and reference evapotrans- piration over 116-yr period in the Platte River Basin , central Nebraska – USA. J Hydrol 420–421:228–244. https://doi.org/10.1016/j.jhydrol.2011.12.006
James EJ (1998) Water related environmental problems of Kerala, water scenario of Kerala-a compendium of background papers on the focal theme of tenth Kerala science congress. The State Committee on Science Technology and Environment, Government of Kerala
Jain SK, Kumar V (2012) Trend analysis of rainfall and temperature data for India. Curr Sci 102:37–49
Kahya E, Kalayci S (2004) Trend analysis of streamflow in Turkey. J Hydrol 289:128–144. https://doi.org/10.1016/j.jhydrol.2003.11.006
Kang HM, Yusof F (2012) Homogeneity Tests on Daily Rainfall Series in Peninsular Malaysia. Int J Contemp Math Sciences 7:9–22
Kottegoda NT (1980) Stochastic water resources technology. The MacMillan Press Ltd., Hong Kong Retrieved from http://www.getcited.org/pub/101974066
Krishnakumar KN, Prasada Rao GSLHV, Gopakumar CS (2009) Rainfall trends in twentieth century over Kerala, India. Atmos Environ 43:1940–1944. https://doi.org/10.1016/j.atmosenv.2008.12.053
Kundu S, Khare D, Mondal A (2017) Interrelationship of rainfall, temperature and reference evapotranspiration trends and their net response to the climate change in Central India. Theor Appl Climatol 130:879–900. https://doi.org/10.1007/s00704-016-1924-5
Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root how sure are we that economic time series have a unit root ? Journal of Econometrics 54:159–178
Ling H, Xu H, Fu J (2013) Temporal and spatial variation in regional climate and its impact on runoff in Xinjiang, China. Water Resour Manag 27:381–399. https://doi.org/10.1007/s11269-012-0192-0
Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–303
Lorenzo-Lacruz J, Vicente-Serrano SM, López-Moreno JI, Morán-Tejeda E, Zabalza J (2012) Recent trends in Iberian streamflows (1945-2005). J Hydrol 414–415:463–475. https://doi.org/10.1016/j.jhydrol.2011.11.023
Martinez CJ, Maleski JJ, Miller MF (2012) Trends in precipitation and temperature in Florida, USA. J Hydrol 452–453:259–281. https://doi.org/10.1016/j.jhydrol.2012.05.066
McLeod AI, Li WK (1983) Diagnostic checking ARMA time series models using squared-residual autocorrelations. The Journal of Time Series Analysis 4:269–273
Pal I, Al-Tabbaa A (2009) Trends in seasonal precipitation extremes - an indicator of “climate change” in Kerala, India. J Hydrol 367:62–69. https://doi.org/10.1016/j.jhydrol.2008.12.025
PennState (2017), STAT 510-Applied Time series analysis, PennState Eberly College of Science, The Pennsylvania State University, https://onlinecourses.science.psu.edu/stat510/node/71 (accessed on 14/12/2017)
Pettitt AN (1979) A non-parametric approach to the change-point problem. Appl Stat 28:126–135
Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75(2):335–346
Schuster A (1898) On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terr Magn 3:13–41. https://doi.org/10.1029/TM003i001p00013
Sen PK (1968) Estimates of the regression coefficient based on Kendall’s tau. J Am Stat Assoc 63:1379–1389
Shadmani M, Marofi S, Roknian M (2012) Trend analysis in reference evapotranspiration using Mann-Kendall and spearman ’ s rho tests in arid regions of Iran. 211–224 . doi: https://doi.org/10.1007/s11269-011-9913-z
Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15:72–101
Toreti A, Kuglitsch FG, Xoplaki E, Della-Marta PM, Aguilar E, Prohom M, Luterbacher J (2011) A note on the use of the standard normal homogeneity test to detect inhomogeneities in climatic time series. Int J Climatol 31:630–632. https://doi.org/10.1002/joc.2088
Tuomenvirta H (2002) Homogeneity testing and adjustment of climatic time series in Finland. Geophysica 38:15–41
Vezzoli R, Pecora S, Zenoni E, Tonelli F (2012) Data analysis to detect inhomogeneity, change points, trends in observations: an application to Po River discharge extremes. Cent euro-Mediterraneo sui Cambiamenti Climatici Res Pap RP0 138:1–15
von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann Math Stat 12:367–395
Wang W, Van Gelder PHAJM, Vrijling JK (2005) Trend and stationarity analysis for stream flow processes of rivers in Western Europe in the 20th century. In: IWA International conference on water economics, statistics, and finance. Rethymno, pp 8–10
Yue S, Pilon P, Cavadias G (2002) Power of the Mann-Kendall and Spearman’s rho tests for detecting monotonic trends in hydrological series. J Hydrol 259:254–271. https://doi.org/10.1016/S0022-1694(01)00594-7
Zhang L, Karthikeyan R, Bai Z, Wang J (2017) Spatial and temporal variability of temperature, precipitation, and streamflow in upper sang-kan basin, China. Hydrol Process 31:279–295. https://doi.org/10.1002/hyp.10983
Acknowledgements
Authors are thankful to the Central Water Commission, Government of India and Water Resources Department, Government of Kerala for sharing the discharge data.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Drissia, T.K., Jothiprakash, V. & Anitha, A.B. Statistical classification of streamflow based on flow variability in west flowing rivers of Kerala, India. Theor Appl Climatol 137, 1643–1658 (2019). https://doi.org/10.1007/s00704-018-2677-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-018-2677-0