TIME SERIES ANALYSIS OF HYDROLOGIC DATA FOR WATER ...

J. Hydrol. Hydromech., 54, 2006, 3, 237–257TIME SERIES ANALYSIS OF HYDROLOGIC DATA FOR WATER RESOURCESPLANNING AND MANAGEMENT: A REVIEWDEEPESH MACHIWAL 1) and MADAN K. JHA 2)1) SWE Department, College of Technology and Engineering, Udaipur-313 001, India; mailto: dmachiwal@rediffmail.com;Tel.: +91-294-2470516(O)2) AgFE Department, Indian Institute of Technology, Kharagpur-721 302, India.The main intent of this paper is to present a review on the application of time series analysis techniquesin hydrology and climatology. An overview of various statistical tests for detecting and estimating thehydrologic time series characteristics (i.e., homogeneity, stationarity, trend, periodicity, and persistence) ispresented, together with their merits and demerits followed by comprehensive reviews of past studies (bothbasic and applied), and future research directions. The present review revealed that the climatologic timeseries of precipitation, air temperature, evapotranspiration and climatic change, and the hydrologic timeseries of streamflow and surface water quality have received a great deal of attention worldwide. Althoughthe application areas of time series analysis techniques are expanding with growing concerns about climatechange and global warming, their application is still very limited in groundwater hydrology as well as fornon-traditional hydrologic time series. It is also apparent from this review that the detection of trend andstationarity by parametric and/or nonparametric tests has been a major focus in the past. Multiplecomparison tests lack appreciation by the researchers for testing homogeneity in the hydrologic andclimatologic time series. Furthermore, most studies have ignored the importance of testing periodicity andpersistence in the time series, which are equally important properties of hydrologic and climatologic timeseries. Based on the comprehensive review, future research needs for time series studies in hydrology andclimatology are discussed.KEY WORDS: Time Series Analysis Techniques, Review, Climatologic Time Series, Hydrologic TimeSeries, Water Resources Planning and Management.Deepesh Machiwal a Madan K. Jha: ANALÝZA ČASOVÝCH RADOV HYDROLOGICKÝCH ÚDAJOVPRE PLÁNOVANIE A RIADENIE VODNÝCH ZDROJOV: PREHĽAD. Vodohosp. Čas., 54, 2006, 3;127 lit.Príspevok prináša prehľad aplikácií techník analýzy časových radov v hydrológii a klimatológii. Uvádzaprehľad rôznych štatistických testov na zistenie charakteristík týchto radov (napr. homogenity, stacionarity,trendov, periodicity a perzistencie), spolu s ich prednosťami a nedostatkami. Ďalej je uvedený tiež celkovýprehľad uskutočnených štúdií (základných aj aplikovaných) a smery výskumu pre budúcnosť. Súčasnýprehľad naznačuje celosvetové sústredenie pozornosti na časové súbory klimatologických dát zrážok,teploty vzduchu, evapotranspirácie a zmien klímy, a tiež hydrologických dát prietokov a kvalitypovrchových vôd. Aj keď so zvýšením záujmu o zmenu klímy a globálne otepľovanie sa oblasti použitiatechník analýzy časových radov rozširujú, ich aplikácie v oblasti hydrológie podzemných vôd a ďalších niecelkom tradičných hydrologických údajov sú veľmi obmedzené. Tento prehľad tiež uvádza, že v minulostisa vyskytli snahy o sústredenie úsilia na postihnutie trendov a stacionarity radov použitím parametrickýcha/alebo neparametrických testov. Mnohí výskumníci dostatočne neoceňujú viacnásobné porovnávacie testy(multiple comparison tests) homogenity hydrologických a klimatických časových radov. Okrem toho voväčšine štúdií sú zanedbané dôležité testy periodicity a perzistencie hydrologických radov. Tieto sú ichrovnako dôležité charakteristiky. Na základe všeobecného prehľadu príspevok tiež pojednáva o potrebeďalšieho výskumu časových radov v hydrológii a klimatológii.KĽÚČOVÉ SLOVÁ: techniky analýzy časových radov, prehľad, časové rady v hydrológii, časové radyv klimatológii, vodohospodárske plánovanie, riadenie vodného hospodárstva.237

D. Machiwal, M. K. Jha1. IntroductionThe application of statistical hydrology in earlierdays was restricted to surface water problems, especiallyfor analyzing the hydrologic extremes suchas floods and droughts. However, during past threedecades, the statistical domain of hydrology hasbroadened to encompass the problems of both surfacewater and groundwater systems. With such abroad domain, statistics has emerged as a powerfultool for analyzing hydrologic time series. The mainaim of time series analysis is to detect and describequantitatively each of the generating processes underlyinga given sequence of observations (Shahinet al., 1993). In hydrology, time series analysis isused for building mathematical models to generatesynthetic hydrologic records, to forecast hydrologicevents, to detect trends and shifts in hydrologicrecords, and to fill in missing data and extend records(Salas, 1993).Most statistical analyses of hydrologic time seriesat the usual time scale encountered in waterresources studies are based on the following fundamentalassumptions: the series is homogenous,stationary, free from trends and shifts, non-periodicwith no persistence (Adeloye and Montaseri, 2002).Homogeneity implies that the data in the seriesbelong to one population, and hence have a timeinvariant mean. Non-homogeneity arises due tochanges in the method of data collection and/or theenvironment in which it is done (Fernando andJayawardena, 1994). Stationarity, on the otherhand, implies that the statistical parameters of theseries computed from different samples do notchange except due to sampling variations. A timeseries is said to be strictly stationary if its statisticalproperties do not vary with changes of time origin.A less strict type of stationarity (called weak stationarityor second-order stationarity) is that inwhich the first- and second-order moments dependonly on time differences (Chen and Rao, 2002). Innature, strictly stationary time series does not exist,and weakly stationary time series is practicallyconsidered as stationary time series.There are many different ways in which changesin hydro-meteorological series can take place. Achange can occur abruptly (step change) or gradually(trend) or may take more complex forms. Atime series is said to have trends, if there is a significantcorrelation (positive or negative) betweenthe observations and time. Trends and shifts in hydrologictime series are usually introduced due tonatural or artificial changes (Salas, 1993). Naturalchanges in hydrologic variables are usually gradualand are caused by a global or regional climatechange, which would be a representative of changesoccurring over the study area. Changes in monitoredvariables that may not be able to be extrapolatedover a study area could be caused by a gradualurbanization of the area surrounding the monitoringsite, changes in the method of measurement at themonitoring site, or by moving the monitoring siteeven a short distance away. The artificial change(or step change) is usually noted in the overall recordat a monitoring site, but this information is notalways presented with the sites’ data series. Thus,variables that appear to have a trend may actuallyjust represent a change in climatological conditionsnear the monitoring site. In such situations, theaffected climatological data should be modified sothat the values are better representative of the studyarea as a whole (Hameed et al., 1997). A key elementin this process is the ability to demonstratewhether a change or trend is present in the climatologicalrecord and to quantify this trend, if it ispresent.Periodicities in natural time series are generallydue to astronomical cycles such as earth’s rotationaround the sun (Kite, 1989). To identify and quantifythe periodicity in the hydrologic or climatologictime series, the time scale is to be considered lessthan a year (e.g., month or six months). In an annualtime series, periodicity effect is not discernibleand hence half-annual or monthly time series normallyencountered in hydrology can be used foranalyzing the periodicity. Lastly, the phenomenonof persistence is highly relevant to hydrologic timeseries. Persistence is the tendency for the magnitudeof an event to be dependent on the magnitudeof previous event(s), a memory effect, e.g., tendencyfor low streamflows to follow low streamflowsand that for high streamflows to follow highstreamflows; it can be considered synonymous withautocorrelation (O’Connel, 1977). Hurst (1951,1957) was the first person to describe persistencecomprehensively in his studies on a reservoir design.The phenomenon was defined in terms of aparameter called “Hurst’s coefficient”, the averagevalue of which is about 0.73 for very large samples.However, its theoretical value for an independentGaussian process to which hydrologic series areassimilated is 0.5 (Capodaglio and Moisello, 1990).If the theoretical and the observed values do notcorrespond, it is known as “Hurst’s phenomenon”.238

Time series analysis of hydrologic data for water resources planning and management: a reviewAll the stochastic models proposed to representhydrologic time series have attempted to reproduceor incorporate the persistence phenomenon; however,with the time series records commonly availablein hydrology, it is virtually impossible to identifyany long-term persistence in the data (Capodaglioand Moisello, 1990).Although some researchers have presented reviewson trend detection and estimation techniquesin the past (Esterby, 1996; Hess et al., 2001), acomprehensive review encompassing the applicationpotential of time series analysis techniques inhydrology and climatology is lacking. Esterby(1996) reviewed some parametric and nonparametrictrend detection methods by confining their applicationto water-quality time series, while Hess etal. (2001) presented an overview of six linear trenddetection methods used for environmental timeseries. Thus, the earlier reviews focused on a singlecharacteristic (i.e., trend) of the time series, with anemphasis on some favored techniques only. At thedawn of 21st century, there is a need to highlightthe role of time series analysis in water resourcesplanning and management amidst emerging newissues of sustainable water management. Therefore,in the present study, an attempt has been made topresent a review of the application of time seriesanalysis techniques in hydrology and climatology.There has been a dramatic increase in the applicationof time series analysis in hydrology during pastfour or five decades. However, the present reviewmainly includes the research findings reported duringpast ten years bearing in mind the size of a reviewpaper.2. Overview of the tests for determining varioustime series characteristics2.1 Homogeneity or consistencyAs mentioned earlier, homogeneity implies thatall the collected data belong to the same statisticalpopulation having a time invariant mean. Therefore,the tests to check the homogeneity of dataseries are based on evaluating the significance ofchanges in the mean value. The features of threehomogeneity tests viz., the von Neumann Test,Cumulative Deviations, and the Bayesian Test arediscussed in Buishand (1982) and Jayawardena andLau (1990). In these studies, all the three tests havebeen used as test statistics.Buishand (1982, 1984) presents detailed methodologyfor the above-mentioned three homogeneitytests, which serves as major guidelines for thesetests. Kanji (2001) in his excellent collection of 100statistical tests, have reported various homogeneitytests for multiple comparisons (e.g., Tukey, Link-Wallace, Dunnett, Bartlett, and Hartley tests).However, it has major drawbacks that the objectivesof tests are not clear and that original referencesare missing. On the other hand, some researchers(e.g., Radziejewski et al., 2002) have consideredonly a few homogeneity tests in the list oftrend detection tests. Such a reference may createconfusion about the general perception of homogeneityand trend for the researchers having no accessto other references. In the hydrologic time seriesanalysis, multiple comparison tests are still contemporary,while these tests are considered classical inthe geotechnical field (e.g., Phoon et al., 2003).2.2 StationarityA time series is said to be strictly stationary, ifits statistical properties do not vary with changes oftime origin. That is, if two non-overlapping timeintervals are selected from a given time series, thenthe two subseries will look almost the same. In fact,both the subseries will differ from one another, butwill be scattered around the same mean value.Therefore, a stationary time series cannot have anytrend or periodic component. This is the reason thatsometimes trend and periodicity tests are used tocheck the stationarity of hydrologic time series.There are two general approaches for testing stationarity:parametric and nonparametric. A detailedreview of the literature indicated that the parametricapproach is usually used by the researchers workingin the time domain, such as economists, who makecertain assumptions about the nature of their data.On the other hand, the nonparametric approach ismore commonly used by the researchers working inthe frequency domain, such as electrical engineers,who often treat the system as a "black box" andcannot make any basic assumptions about the natureof the system. In hydrology, however, bothparametric and nonparametric approaches are used.Furthermore, nonparametric tests are not based onthe knowledge or assumption that the population isnormally distributed (Bethea and Rhinehart, 1991).Therefore, the nonparametric tests are more widelyapplicable than parametric tests. However the nonparametrictests are reported to be less powerfulthan parametric tests. To arrive at the same conclusionwith the same confidence level, the nonpara-239

D. Machiwal, M. K. Jhametric tests require 5 to 35% more data than parametrictests (Bethea and Rhinehart, 1991).Very few studies are reported wherein t-test hasbeen used to examine the stationarity of hydrologictime series (e.g., Jayawardena and Lai, 1989). TheMann-Whitney Test for detecting a shift in themean or median of hydrological time series hasbeen applied by McCuen and James (1972), Lazaro(1976), Lettenmaier (1976), Helsel and Hirsch(1988), Kiely (1999), Kiely et al. (1998), Yue andWang (2002). Also, stationary stochastic modelssuch as AR (Auto Regressive), MA (Moving Average),or ARMA (Auto Regressive Moving Average)models are frequently used to characterize thestandardized time series (Hipel and McLeod, 1994).However, the standardization procedure does notensure stationarity in the transformed series (Salas,1993). Moreover, some researchers (Appel andBrandt, 1983; Lovell and Boashash, 1987; Imbergerand Ivey, 1991; Chen and Rao, 2002) have developedsegmentation algorithms to determine stationarysegments and to estimate the parameterscharacterizing each segment in order to establishpiecewise stationary time series models.2.3 TrendThere can be a variety of situations that wouldresult in the measured value of some climatologicalvariables changing over time, which in turn cause alinear or nonlinear trend in the time series of theclimatological variable. The trend in a time seriescan be expressed by a suitable linear or nonlinearmodel; the linear model is widely used in hydrology(Shahin et al., 1993). The simplest of lineartrend detection models is Student’s t-test (Hameedet al., 1997), which requires that the series undertesting should be normally distributed. Thus,whether or not the sample data follow a normaldistribution has to be examined prior in order toapplying the Student’s t-test to assess the statisticalsignificance of these two types of trends (Hoel,1954). Unfortunately, some researchers ignore thisimportant check (e.g., Fanta et al., 2001). If normalityis violated, the nonparametric test such asthe Mann-Kendall Test (Mann, 1945; Kendall,1975) is commonly applied to assess the statisticalsignificance of trends. This test detects a monotonictrend in the mean or median of a time series. Asmentioned earlier, the nonparametric tests are moresuitable for non-normal data and censored datacompared to the parametric t-test (Helsel andHirsch, 1988; Hirsch and Slack, 1984). The applicationof the nonparametric Mann-Kendall Test fordetecting monotonic trends in hydrological timeseries is reported by Hirsch et al. (1982), Hirschand Slack (1984), Burn (1994), Burn and Elnur(2002), Lettenmaier et al. (1994), Gan (1992,1998), Lins and Slack (1999), Douglas et al. (2000),Zhang et al. (2001), Yue et al. (2003), and others.Another important trend test is the Spearman RankOrder Correlation Test, which has been applied byKhan (2001) and Adeloye and Montaseri (2002).However, in some hydrologic studies, the Kendall’sRank Correlation Test has been preferred (Jayawardenaand Lai, 1989; Zipper et al., 1998;Kumar, 2003).Most of the tests (Turning Point, Kendall’sPhase, Wald-Wolfowitz Total Number of Runs,Sum of Square Lengths, Adjacency, DifferenceSign, Run Test on Successive Differences, Wilcoxon-Mann-Whitney,and Inversions tests) describedin Shahin et al. (1993) have not attractedthe attention of hydrologists, may be because of theavailability of some sound statistical trend detectiontests. Esterby (1996) and Hess et al. (2001) presentan excellent overview of the statistical methods fortrend detection and estimation in environmentaltime series (e.g., water quality and atmosphericdeposition monitoring data). Hess et al. (2001)evaluated six methods for trend detection usingreal-life data and provided recommendations basedon a simulation study. The t-test adjusted for theseasonality and the Seasonal Kendall tests are reportedto be more powerful than the remaining fourtests viz., the Spearman Partial Rank CorrelationTest, Ordinary Least Square Regression, GeneralizedLeast Square Regression, and the Kolmogorov-ZurbenkoTest. However, Hess et al. (2001)did not consider all the available trend detectiontests, which are sound and widely employed in thehydrologic time series analysis. Some more statisticaltests can be found in Mahé et al. (2001).2.4 PeriodicityPeriodicity in the hydrologic time series can bedetected if the time series are defined at time intervalsless than a year. In most cases, a periodicity of6 and 12 months is very common. The Fourier serieshas been primarily used for the detection ofperiodic components in the hydrologic time series(e.g., Maidment and Parzen, 1984; Kite, 1989; Jayawardenaand Lai, 1989; Fernando and Jayawardena,1994; Pugacheva et al., 2003). However,some researchers (e.g., Hurd and Gerr, 1991; Vec-240

Time series analysis of hydrologic data for water resources planning and management: a reviewchia and Ballerini, 1991) have suggested differentmethods for testing the periodically correlated timeseries.2.5 Persistence/non-randomnessIn few hydrologic time series studies, no distinctionis made between persistence and randomness.Therefore, the tests to examine the randomness of ahydrologic time series are used for detecting bothtrend and persistence. Generally, randomness ornon-persistence is defined as the independenceamong data in a hydrological time series. On thecontrary, the series is called persistent if the data inthe series are dependent on each other. Practically,persistence is a tendency of the successive values ofa climatological series to ‘remember’ their antecedentvalues, and to be influenced by them (Gilesand Flocas, 1984). Mathematically, persistence isdefined as the correlational dependency of order kbetween each i th element and the (i–k) th element ofthe series (Kendall, 1973), and is measured byautocorrelation (i.e., a correlation between the twoterms of the same time series). Here, ‘k’ is usuallycalled time lag. The detection of persistence can bemade by autocorrelation technique (time domain)and/or spectral technique (frequency domain).However, the autocorrelation technique has beenapplied in several studies such as Mirza et al.(1998), Maidment and Parzen (1984), Schwankl etal. (2000), etc. Here it is worth mentioning thatsome researchers (e.g., Jayawardena and Lai,1989) have used the autocorrelation technique fortesting the periodicity in time series. Such a misconceptionis quite common in the hydrologic timeseries analysis.3. Salient merits and demeritsof the time series tests(i) Cumulative Deviations Test is superior to theclassical von Neuman Test for a model with onlyone change in the mean (Buishand, 1982).(ii) The major limitation with all the multiple comparisontests of homogeneity (i.e., Tukey, Link-Wallace, Dunnett, Bartlett and Hartley tests) is therequirement that populations should be normallydistributed with equal variances, which makes thetests parametric in nature. Though the Link-Wallace Test, the Dunnett’s Test and the Hartley’sTest can be employed for the same purpose as theTukey’s Test, the former two tests have the limitationthat the sample size of all populations must beequal, while the Hartley’s Test is applicable to approximatelyequal sample size.(iii) Of the three stationarity tests, both the t-testsare parametric and the Mann-Whitney Test is nonparametricin nature.(iv) Among the trend tests, although the linearmodel (i.e., Regression Test) is most commonlyused, it has a demerit that it does not distinguishbetween trend and persistence. The test can also bemisleading if seasonal cycles are present, the dataare not normally distributed, and/or the data areserially correlated.(v) The Spearman Rank Order Correlation Testovercomes the problem associated with the linearmodel. Another advantage of this test is its nearlyuniform power for detecting linear as well as nonlineartrends (WMO, 1966; Dahmen and Hall,1990).(vi) The Turning Point Test is easy to apply, especiallywhen the time series is plotted graphically. Itis an effective test for randomness against systematicoscillation. However, if the turning points tendto bunch together, the Kendall’s Phase Test is morerelevant (Shahin et al., 1993). Here, the difficulty isthat a comparison of observed and theoretical numbersof phases by the usual chi-square test is invalidateddue to the fact that the lengths of phases arenot independent. Also, the distribution of phaselengths does not tend to be normal for large lengthsof a series, but the number of phases follows anormal distribution (Kendall, 1973).(vii) Among the trend tests, the superiority of oneover other is mainly associated with the extent ofadaptability of a chosen test to the structure of thetime series to be tested. The Turning Points andNumber of Phases tests are practically out-dateddue to the availability of much more powerful tests(Shahin et al., 1993).(viii) The Wald-Wolfowitz Test does not take intoaccount the length of runs and considerable informationis ignored. Hence, this test is not very powerfulnor efficient, but can be used to determinewhether observations of a random variable are independent(if they are, and there is no trend). TheSum of Squared Lengths Test is a more powerfultest (Himmelblau, 1969).(ix) The limitation of the Adjacency Test is thebasic assumptions that the observations are obtainedindependently and under similar conditions(Kanji, 2001).(x) The Difference Sign Test is applied with theassumptions that the number of observations is241

D. Machiwal, M. K. Jhalarge and that they have been obtained under similarconditions.(xi) The necessary condition for applying the RunTest on Successive Differences is that the observationsin the sample should be obtained under similarconditions.(xii) The Wilcoxon-Mann-Whitney Test is a nonparametrictest (i.e., distribution-free) and is applicableonly when the observations are random andindependent.(xiii) The Kendall’s Rank Correlation Test is themost popular test for trend detection in the hydrologictime series.(xiv) The Mann-Kendall Test is a nonparametrictest for trend detection in a time series withoutspecifying whether the trend is linear or nonlinear.Existence of serial correlation in a time series willaffect the ability of the Mann-Kendall Test to assessthe site significance of a trend, and the presenceof cross correlation among sites in a networkwill influence the ability of the test to evaluate thefield significance of trends over the network (Yue etal., 2003).(xv) In general, the parametric methods to assesssignificance of trend employ pre-specified modelsand associated tests, whereas the nonparametricmethods generally apply rank tests to the data. Neitherapproach is suitable for exploratory analysis(Ramesh and Davison, 2000).(xvi) The assumptions of the classical parametrictests viz., normality, linearity, and independenceare usually not met by the hydrological time seriesdata, especially in case of surface water qualitydata. Therefore, recently some nonparametric testshave been proposed to determine the trend in surfacewater quality time series (Kalayci and Kahya,1998). At the same time, the statistical tests fortrend detection in surface water quality time seriesare normally confounded by one or more of thefollowing problems: missing values, censored data,flow relatedness, and seasonality.4. Theoretical research on time seriesanalysis techniquesHamed and Rao (1998) studied the effects ofautocorrelation on the variance of the Mann-Kendall trend test-statistic. A theoretical relationshipwas derived to calculate the variance of theMann- Kendall test statistic for autocorrelated data.The special cases of AR(1) and MA(1) dependencewere discussed as examples. Based on the modifiedvalue of the variance of the Mann-Kendall trendtest statistic, a modified nonparametric trend testsuitable for the autocorrelated data is proposed. Themodified test was applied to rainfall and streamflowdata to demonstrate its performance compared tothe original Mann-Kendall Trend Test. The accuracyof the modified test was found to be superiorto that of the original Mann-Kendall Trend Testwithout any loss of power.Tsakalias and Koutsoyiannis (1999) developed anew approach for the computer-aided explorationand analysis of hydrologic time series with a focuson identification of multiple stage-discharge relationshipsin a river section, analyses for homogeneityand temporal consistency, detection of outliers,shifts and trends. To demonstrate the developedmethodology, initially a mathematical representationwas proposed based on the set theory. It wasdemonstrated that an exhaustive search of all candidatesolutions is intractable. Therefore, a heuristicalgorithm is proposed, which emulates the exploratorydata analysis of the human expert. This algorithmencodes a number of search strategies in apattern directed computer program, and results inan automatic determination of a satisfactory solution.Yue et al. (2002a) investigated the interaction betweena linear trend and a lag-one autoregressive[AR(1)] model using Monte Carlo simulation.Simulation analysis indicated that the existence ofserial correlation alters the variance of the Mann-Kendall (MK) statistic estimate, and the presence ofa trend alters the magnitude of serial correlation.Furthermore, it was found that the commonly usedpre-whitening procedure for eliminating the effectof serial correlation on the MK Test leads to inaccurateassessments of the significance of a trend.Therefore, it was suggested that firstly trend shouldbe removed prior to ascertaining the magnitude ofserial correlation. Both the suggested approach andthe existing approach were employed to assess thesignificance of a trend in the serially correlatedannual mean and annual minimum streamflow dataof some pristine river basins in Ontario, Canada. Itwas concluded that the researchers might have incorrectlyidentified the possibility of significanttrends by using the already existing approach.Yue et al. (2002b) studied the efficacy of the twononparametric rank-based statistical tests (theMann-Kendall Test and Spearman's Rho Test) byMonte Carlo simulation. These two tests were usedto assess the significance of trends in annual maximumstreamflow data of 20 pristine basins in Ontario,Canada. The results indicated that their effec-242

Time series analysis of hydrologic data for water resources planning and management: a reviewtiveness depends on the pre-assigned significancelevel, magnitude of trend, sample size, and theamount of variation within a time series. Thus, thebigger the absolute magnitude of trend or larger thesample size, the more powerful are the tests; but asthe amount of variation in a time series increases,the power of the tests decreases. When a trend ispresent, the power is also dependent on the distributiontype and skewness of the time series. It wasalso found that these two tests have practicallysimilar power in detecting a trend.Clarke (2002) described a model in which theGumbel distribution has a (possibly) time-variantmean. The time-trend in mean value was determinedby a single parameter β estimated by MaximumLikelihood (ML). The large-sample varianceof the ML estimate was compared with the varianceof the trend calculated by linear regression; thelatter was found to be 64% greater. The simulatedsamples from a standard Gumbel distribution weregiven superimposed linear trends of different magnitudes,and the efficacy of three trend-testingmethods viz., Maximum Likelihood, Linear Regression,and the nonparametric Mann-Kendall Testwas compared. The ML Test was found alwaysmore powerful than the Linear Regression orMann-Kendall Test regardless of the value (positive)of the trend β; the MK Test was found leastpowerful for all the values of β.Ducré-Robitaille et al. (2003) evaluated eighthomogenization techniques for the detection ofdiscontinuities in the temperature series using simulateddatasets reproducing a vast range of possiblesituations. The simulated data represented homogeneousseries and the series having one or moresteps. Although the majority of the techniques consideredin this study performed very well, twomethods are reported to work slightly better thanthe others: the standard normal homogeneity testwithout trend, and the multiple linear regressiontechnique.Yue and Wang (2004) proposed effective samplesize (ESS) to modify the MK statistic for eliminatingthe effect of serial correlation on the MK Test.The Monte Carlo simulation indicated that when notrend exists within time series, ESS can effectivelylimit the effect of serial correlation on the MK Test.When trend exists within time series, the existenceof trend will contaminate the estimate of the magnitudeof sample serial correlation, and the ESS computedfrom the contaminated serial correlation cannotproperly eliminate the effect of serial correlationon the MK Test. However, if the ESS is computedfrom the sample serial correlation that is estimatedfrom detrended series, the ESS can stilleffectively reduce the influence of serial correlationon the MK Test.5. Application of time series analysisin climatology5.1 Precipitation/precipitation with other dataFortuniak (1995) used the daily precipitation totalsand mean daily temperature for the period 1956– 1990 from 10 Polish meteorological stations(Gdansk, Szczecin, Suwalki, Poznan, Lódz, Warszawa,Wroclaw, Kraków, Przemysl, Zakopane) totest their periodicity. The annual course of temperaturewas removed by subtracting the 35th Fourierharmonic. The classical Blackman and Tukey Testwas used to detect the cyclic behaviour of the analysedseries. The power spectrum of temperaturefor each station exhibited two significant peaks:around 7.4 years and 193 days. For the precipitation,the power spectra were found different foreach station and it was impossible to find a characteristiccycle for the entire region.Nieplová (1995) applied five statistical homogeneitytests (Student's, Bartlett's, Kruskal-Wallis's,Abbe Criterion, Spearman Rank Correlation Test)and the Craddock's Relative Homogeneity Test tothe annual and monthly air temperature means,precipitation totals and relative air humidity meansof 40 years and longer series. It was found thatmost of inhomogeneities were caused by changedobservation terms and by the relocation of measuringstations. These results were used for selectingstations for long-term monitoring of climate changein Slovakia.Walanus-Gliwice (1995) analyzed the periodicityby using the Fast Fourier Transform (FFT). Thewater stages of Vistula River at Szczucin, dischargesof Warta (Poland) and Tisa (Hungary) Rivers,Dnieper River (Ukraina), precipitation fromWarsaw, Cracow, Wroclaw and other towns, airtemperature, dendroclimatological curves and thethickness of yearly strata (warws) from GosciazLake (Central Poland) were analyzed. The 3.5-year(3.5±0.15 yr) periodicity of unknown origin in theriver discharge and the precipitation was confirmed.For rivers, the 3.5-yr signal was found much less inSzczucin, but it was visible. For the precipitation,the signal was still less, especially in comparison tothe more dominant seasonal periodicity. The perio-243

D. Machiwal, M. K. Jhadicity in rivers’ discharges was of higher amplitudethan that in the precipitation. Finally, a detailedanalysis revealed that the 3.5-yr peak in frequencydomain should be treated as a random event.Aulenbach et al. (1996) evaluated the trends inprecipitation and surface water quality at a networkof 15 small watersheds (

Time series analysis of hydrologic data for water resources planning and management: a reviewwas found to cause a significant positive trend inthe total precipitation contributed by heavy precipitationevents (i.e., daily precipitations >25 mm and>50 mm). Furthermore, the trend was mainlycaused by past 60–80 years, and was particularlyevident during the periods of 1930 – 1945 and 1975– 1995.Molénat et al. (2000) analyzed the hydrologicaland hydrochemical behaviour of three agriculturalcatchments located in different regions of France(Kervidy, Melarchez and Mercube). The time serieswere considered as input or output data and thespectral analysis was performed. The input data forhydrology and chemistry were respectively rainfalland nitrate leaching, and the output data werestreamflow and nitrate concentration in the stream.It appears that nitrate concentrations measured atthe outlet of the three catchments exhibit a strongand unique one-year periodicity. This periodicity isdue to the hydrological regime and the time distributionof the nitrate availability in the soil. Moreover,a cross-spectral analysis was performed betweenthe input and output data for each catchmentand the major processes that govern water and nitratetransfer and the characteristic time scale ofthese processes were identified. It was concludedthat the spectral and cross-spectral methods arevaluable techniques for identifying the main transferprocesses operating in different catchments.Brunetti et al. (2001) analyzed the seasonal andannual precipitations and the number of rainy daysin northeastern Italy during 1920 – 1998. The precipitationintensity was analyzed by using both themean precipitation amount per wet day and dividingthe precipitation into heavy and non-heavyclasses. In addition, the return period of extremeevents was calculated for the 30-years and its variationswere examined. The results indicated a negativetrend in the number of wet days associated withan increase in the contribution of heavy rainfallevents to the total precipitation. This finding is inagreement with the reality (i.e., a reduction in thereturn period of extreme events since 1920).Kripalani and Kulkarni (2001) prepared regionalrainfall anomaly time series using the 118-year(1881 to 1998) data of three regions, India, northernChina and southern Japan. All the three series (India,China, and Japan) were subjected to selectedstatistical tests. The analysis of the results revealedthat though there are year-to-year fluctuations inrainfalls, the Mann-Kendall Rank statistic suggestedno significant long-term trends. However,the application of the Cramer's statistic to study theshort-term climate variability depicts decadal variabilitywith certain epochs of above and belownormal rainfall over each region. The epochs tendto last for about three decades over India andChina, and about five decades over Japan. The turningpoints for China follow those of India afterabout a decade.Adamowski and Bougadis (2003) estimatedtrends for different durations of annual extremerainfall by using the regional average Mann-Kendall S Trend Test. The method of L-momentswas employed to delineate homogeneous regions.The trend test was modified to account for the observedautocorrelation, and the bootstrap methodwas used to account for the observed spatial correlation.Numerical analysis was performed for 44rainfall stations in Ontario, Canada for a 20-yeartime frame using the data from homogeneous regions.Depending on the rainfall durations, four andfive homogeneous regions were delineated. At the5% significance level, approximately 23% of theregions tested had a significant trend, predominantlyfor short-duration storms. The serial dependencywas observed in 2-3% of datasets and the spatialcorrelation was found in 18% of the regions.The presence of serial and spatial correlation wasfound to have significant impacts on trend determination.Xu et al. (2003) detected long-term trends in thespatially averaged Japanese precipitation time seriesby applying the parametric t-test and the nonparametricMann-Kendall and Mann-Whitney tests.The results indicated that despite several stepchanges in the Japanese precipitation, the time seriesdid not exhibit significant evidence of monotonictrend during the past century. Further, it wasfound that if the magnitude of the step changereaches one or two times of its standard deviation,the previous 50-year records together with 5 yearsor more new data will be available for detecting thepossible trend. This finding is useful for the detectionof step changes in the regions where the precipitationhas near-normal distributions.5.2 Air and water temperatureEsteban-Parra and Castro-Diez (1995) analyzedthe longest annual and seasonal series of maximum,minimum and average temperatures of some localitiesin Spain. The homogeneity was checked byusing the Thom and Bartlett tests. These methodsare reported to yield different results in some cases.The analysis was performed to explore how the245

D. Machiwal, M. K. Jhaexistence of actual trends and/or discontinuities inthe series affects the sensitivity and have a repercussionon the results of the tests. This analysissuggested an adequate confidence level and theneed of the use of relative homogeneity tests.Webb (1996) analyzed the future trends in watertemperatures from different parts of the world. Thepotential causes of trends in the thermal regimes ofstreams and rivers are many, but the existing databaseof water temperature was found inadequate toprovide a global perspective on changes during therecent past. The data from Europe suggested that anincrease of up to 1°C in the mean river-water temperatureshas occurred during the 20 th century.However, this trend was not found continuous andcorrelated with simple hydro-meteorological factors;rather it was found to be distorted by extremehydrological events influenced by a variety of humanactivities. Predictive studies indicated that anaccelerated rise in stream and river water temperatureswill occur during the next century because ofglobal warming. However, the forecasts are tentativebecause future climatic conditions are uncertain,and the interactions between climate and hydrologicaland vegetation changes are complex.Tayanç and Toros (1997) studied the daily maximumtemperature and temperature difference series(1951 – 1990) of four urban stations and theirneighboring rural stations in Turkey. The resultsindicated that there is a shift towards the warmerside in the frequency distributions of both the series,which is an indication of urban heat island.The seasonal analysis of individual 21.00 hr temperatureseries suggested that the regional warmingis the strongest in spring and the weakest in autumnand winter. Urban warming is detected to be moreor less equally distributed over the year with aslight increase in autumn. Using the Mann-KendallTrend Test for the temperature difference series, theurban heat island effect was found to be significantat all urban sites. On the other hand, no significanturban effects on the precipitation were found.Keiser and Griffiths (1998) used a homogeneitytest developed by Alexandersson (1986, 1995) andapplied it to the mean monthly maximum, minimum,and mean temperature data from 22 stationsin the northern Great Plains of USA. One of thesestations, Valentine, is a first-order station and isused as the reference station. When Valentine stationwas adjusted for a possible inhomogeneity dueto its move, it was found that the Valentine's adjustmentshave a distinct seasonal pattern. The testingof other stations against Valentine revealed thatthe position of a significant discontinuity in a station'smonthly mean or annual temperature series isnot always the same as in the correspondingmonthly maximum and minimum series. In addition,a seasonal pattern similar to that of Valentinestation was found in every station's adjustment values.Tayanç et al. (1998) presented a combination ofdifferent methods (i.e., graphical analysis, nonparametricKruskal-Wallis Homogeneity Test andWald-Wolfowitz Runs Test) to test climatologicaltime series for inhomogeneities. These methodswere applied to the annual mean difference temperatureseries of 82 Turkish weather stations, andthe inhomogeneity detection efficiencies of thesetests were determined by a series of Monte Carlosimulation studies. It was concluded that the procedureis statistically rigorous, provides estimates ofthe time and magnitude of change in the mean, andis a valuable tool for testing time series.Serra et al. (2001) used the entropy concept andspectral power analysis to analyze the homogeneity,randomness, trends and their statistical significance,and time irregularities in the daily maximum andminimum temperature series (1917 to 1998) recordedat Fabra Observatory, Barcelona. The homogeneity,randomness and the statistical significanceof trends in the time series were tested byusing the adaptive Kolmogorov-Zurbenko Filter,the von Neumann Ratio Test, and the Spearman andMann-Kendall tests, respectively. The periodicitiesobtained from spectral power analyses werechecked with the hypothesis of white-noise andMarkov’s red-noise stochastic processes. The mostnotable features, common to maximum and minimumtemperatures, were the lack of randomness inthe series and the different trends obtained for theperiods 1917 – 1980 and 1917 – 1998, which wereconfirmed by the Spearman and Sequential Mann-Kendall tests. Nevertheless, the maximum andminimum temperature series showed a very differentbehavior based on the time irregularities interms of entropy and periodicities.Astatkie et al. (2003) used the daily average temperaturedata of 15 locations spatially distributedacross Canada to test the presence of trend in variability(measured by the range, standard deviationand IQR) by using a bootstrap method. The lengthof the temperature series at these sites ranged from30 to 151 years. The analysis was undertaken forthe monthly, seasonal, and annual data. For calculatingstandard deviations, estimates of the annualmean temperatures were used to make the results246

Time series analysis of hydrologic data for water resources planning and management: a reviewinvariant to the presence of trend in mean. Themonthly and seasonal analysis revealed the presenceof either increasing or decreasing variabilityfor some months and some seasons. The results ofthe annual data analysis did not reveal appreciablevariability, especially at sites where some monthshave an increasing trend while others have a decreasingtrend. The results across sites did not exhibita clear geographic pattern. However, consistentlyincreasing trends in the variability werefound in Toronto and St. John’s during nonsummermonths, and mostly decreasing trend inEdmonton. The significance of trend in the variabilitymeasured by the range and standard deviationwere consistent in less than 30% of the time acrosssites and across the monthly, seasonal and annualaggregations. There was not much agreement betweenthe standard deviation and the IQR, whichshows the importance of the choice for measuringvariability.5.3 Climatic changeBurn (1994) examined the impact of climaticchange on the timing of spring runoff by using anonparametric statistical trend test applied to thedatasets of 84 natural rivers from the west-centralregion of Canada. The results indicated that agreater number of rivers exhibit earlier spring runoffthan can be attributed to the chance occurrence.The impacts on the timing of spring runoff werefound more prevalent in the recent portion of therecords, which is consistent with what one wouldexpect if the impacts are due to the greenhouse gasinducedclimatic change.Westmacott and Burn (1997) evaluated the possibleeffects of climate change on four hydrologicvariables pertaining to the magnitude and timing ofhydrologic events in the Churchill-Nelson RiverBasin of west-central Canada. By using the Mann-Kendall Trend Test, and a regionalization procedure,the severity of climatic effects within the riverbasin was quantified, which was then used to createawareness about future consequences of water resourcesystems planning and management strategies.It was found that the magnitude of hydrologicevents decreased during the study period, while thesnowmelt runoff events occurred earlier. The onlyexceptions to this behavior were the spring meanmonthly streamflows, which exhibited increasingtrends due to the potential for snow melting duringthe study period. The timing of a hydrologic eventwas greatly influenced by the changes in temperature.Further, the decreasing trends were found tobe concentrated in the southern regions of the basinwhereas the increasing trends were found primarilyin northern regions.Lubes-Niel et al. (1998) investigated the powerand the robustness of some widely-used climaticvariability tests with the help of simulation. In eachcase, 100 samples of fifty elements were generatedbased on the main characteristics of natural rainfallseries. A shift in the mean was used to represent apossible climatic variation. The Rank CorrelationTest, Pettitt's Test, Buishand's Test, Lee andHeghinian's Bayesian Method, and the Hubert andCarbonnel's Segmentation Method were used forhydrometeorological series. Each simulation of 100samples were used to assess the performance ofdifferent methods considering a specific characteristicof the series, viz., normality or non-normality,autocorrelation, trend, and shift in the variance. TheRank Correlation Test, Pettitt's Test, Buishand'sTest and the Segmentation Method with a significancelevel of 1% (significance level of Scheffé'sTest) rejected heterogeneity in less than 10 seriesover 100 homogeneous simulated series. On theother hand, the Lee and Heghinian's BayesianMethod rejected about 40% of the series. This findingsuggests that the latter method should be appliedonly under the hypothesis of heterogeneity.Independent series were simulated by normal, lognormaland Pearson distributions to compare theperformance of the methods requiring normality.The results indicated that the normality has no significantimpacts on the performance of the methodsused. However, the simulation results indicated thatthe condition of independence of the successiveelements of the series is essential to keep theperformance constant. Otherwise a trend in theseries makes the methods inefficient, except for theRank Correlation Test for which the alternative is atrend. None of the method were found to be robustagainst both negative and positive autoregressivedependencies.Burn and Elnur (2002) analyzed 18 hydrologicvariables for a network of 248 Canadian catchmentsreflecting natural conditions. The Mann-KendallTest was used to detect trends and a permutationapproach was used to estimate the test distribution.The catchments having trends in hydrologic variableswere further studied to examine trends inmeteorological variables and explore the relationshipbetween hydrologic and meteorological responsesto climatic change. It is concluded that agreater number of trends were detected than are247

D. Machiwal, M. K. Jhaexpected to occur by chance. There were differencesin the geographic location of significanttrends in the hydrologic variables, which indicatedthat the climatic impacts were not spatially uniform.Yu et al. (2002) investigated the impact of climatechange on the water resources of the Kao-PenCreek Basin in southern Taiwan. The historicaltrends of salient meteorological variables (i.e.,mean daily temperature, mean daily precipitationon wet days, monthly wet days, and the transitionprobabilities of daily precipitation occurrence ineach month) were detected using the nonparametricMann-Kendall Test. The trends of these meteorologicalvariables were then employed to generaterunoff under future climatic conditions using a continuousrainfall-runoff model. The results indicatedthat the transition probabilities of daily precipitationoccurrence significantly influence the precipitationgeneration, and the generated runoff underfuture climatic conditions was found to increaseduring the wet season and decrease during the dryseason.5.4 EvapotranspirationZaninovic and Gajic-Capka (2000) analyzed thevariations and trends in some water balance componentsviz., soil water content, evaporation lossesfrom the surface and subsurface soil layers, transpiration,groundwater recharge, and runoff. Thesecomponents were calculated by the Palmer methodusing the 1900 – 1995 data from Osijek, Croatia.Besides the meteorological inputs necessary for thewater balance calculation (i.e., precipitation, temperatureand relative humidity), the pedologicalcharacteristics of this area was also taken into account.Fluctuations were accounted for by considering11-year binomial filtered series and the lineartrends were tested by the Mann-Kendall Rank Test.A progressive analysis of the time series was alsoperformed to obtain better insights into the trendsof water balance components. The results suggesteda significant increase in the potential evapotranspirationand evapotranspiration, but a decrease in therunoff and soil-water content during the twentiethcentury.Hobbins et al. (2001) analyzed the annual andseasonal trends in a monthly time series of actualevapotranspiration using the Mann-Kendall Testwithin the context of the complementary relationshipon a regional basis to establish that regionaltrends can be determined to originate in either theenergy budget or the water budget, or both. Themonthly time series of 27 years at a 5-km resolutionover the conterminous United States was created byusing a regional, seasonal Advection-Ariditymodel, which provided a tool for studies on climatechange and variability based on comparison of intra-annualtrend results with results from anotherstudy.6. Application of time series analysisin surface water hydrology6.1 StreamflowLye and Lin (1994) analyzed the peak flow seriesfrom 90 Canadian rivers to examine stationarity.The results suggested that although short-term dependenceis practically absent for most peak flowseries, significant long-term dependence is presentfor a large number of peak flow series tested. It wasdemonstrated that the most statistical tests of independenceor stationarity are designed to detect onlyshort-term serial correlation. They were found insensitiveto the long-term serial correlation structureof flood records, which can be far more important.Lins and Slack (1999) determined secular trendsin the streamflows of 395 climate-sensitivestreamgaging stations in the conterminous UnitedStates by the nonparametric Mann-Kendall Test.Trends were calculated for the selected quantiles ofdischarge [0 th ] to [100 th percentiles] to evaluate thedifferences between low-, medium-, and high-flowregimes during the twentieth century. Two generalpatterns emerged: (i) trends are most prevalent inthe annual minimum (Q 0 ) to median (Q 50 ) flowcategories and least prevalent in the annual maximum(Q 100 ) category; and (ii) at all but the highestquantiles, streamflow has increased across broadsections of the United States. The decrease instreamflow was found only in parts of the PacificNorthwest and Southeast. Systematic patterns wereless apparent in the Q 100 flow. Hydrologically, theseresults imply that the conterminous U.S. is gettingwetter.Douglas et al. (2000) evaluated trends in theflood and low streamflows of the US by using aregional average Kendall's S Trend Test at twospatial scales and over two timeframes. The fieldsignificance was assessed following a bootstrapmethodology to account for the regional crosscorrelationof streamflows. The flood flow series wasfound trend-free at 5% level of significance, but248

Time series analysis of hydrologic data for water resources planning and management: a reviewlow streamflows showed upward trends with significanttemporal persistence. After removing serialcorrelation from the series, significant trends in lowflows were apparent but were less in numbers. Theignorance of regional cross-correlation resulted instatistically significant trends in all but two of thelow flow analyses and in two-thirds of the floodflow analyses. In addition, it was found that thecross-correlation of streamflow records dramaticallyreduces the effective number of samples requiredfor trend assessment.Alemaw and Chaoka (2002) investigated possibletrends in the annual riverflow of 502 rivers (datafrom early 1950s to late 1990s) in the region ofSouth Africa by visualization technique. The rescaledadjusted partial sums (RAPS) were usedinstead of the actual time series plots of runoff. Asimulation experiment of the technique was conductedto demonstrate how the plot of RAPS offersa reasonable visualization of the readily apparentmode of underlying trend, which may be hidden inthe standard time series plots. The dominantly visualizedtrends were linear and declining. A subsequentlinear trend test by fitting a linear trendmodel to the annual river discharge series revealeda dominant negative slope ranging from –6.8 to –0.2%; it suggests the existence of declining trendsin some rivers of the South African Region. Of the502 time series, 137 time series had statisticallysignificant decreasing trend, 96 series had significantincreasing trend, and the remaining 269 serieshad no trend at all.Birsan et al. (2002) analyzed the mean daily runoffdata from undisturbed and independent watershedsin Switzerland for detecting trends by theMann-Kendall Trend Test. Based on the seasonalanalyses of streamflow quantiles, it was found that:(i) the streamflow has increased in the winter period,especially the winter annual maximum, atabout 60% of the stations; and (ii) the streamflowhas decreased in the summer period, particularlythe low streamflow quantiles. The trends werefound to be statistically significant, which indicatea substantial change in the streamflow regime.Adeloye and Montaseri (2002) described threetests for determining consistency, trend, and randomnessin hydrological data series. The tests werethen applied to monthly streamflow data recordsfrom seven sites – three in Iran and four in Yorkshire,England. All hydrological series were foundconsistent, trend-free and random. Furthermore,few goodness-of-fit tests (i.e., Chisquare, Kolmogorov-Smirnov,Probability Plot Correlation Coefficientand Moment Ratio Diagram) for probabilitydistribution are discussed. Based on the results,Probability Plot Correlation Coefficient Test wasfound simple to use and this test can be employedeven if critical test-statistic values are not known.Beighley and Moglen (2002) analyzed the trendsof non-stationary discharge corresponding to theperiods of urbanization by employing three statisticaltests: one parametric t-test and two nonparametrictests (Kendall’s Tau and Spearman Rank Correlationtests) using the annual maximum dischargeand annual maximum discharge-precipitation ratiosseries. It was concluded that the ratios are moreeffective than the discharges alone for identifyingnon-stationarity resulting from urbanization. Inaddition, the relationships between measures ofurbanization and the presence/absence of significanttrends in the discharge series are presented.Kahya and Kalayci (2004) presented a trendanalysis of 31-year monthly streamflows obtainedfrom 26 basins of Turkey. Four non-parametrictrend tests (i.e., Sen's T, Spearman's Rho, Mann-Kendall, and Seasonal Kendall) which are popularfor detecting linear trends in a hydrological timeseries were used. The Van Belle and Hughes' basinwidetrend test was also included in the analysis.Homogeneity of trends in monthly streamflows wastested following the method developed by VanBelle and Hughes. Thus, this study presents a completeapplication of both the Van Belle and Hughes'tests for homogeneity of trends and basin-widetrend tests (originally developed for trend detectionin water quality data) in a hydro-climatic variable.The results revealed that the basins located in westernTurkey, in general, exhibit downward trend (at0.05 or lower level of significance), whereas thebasins of eastern Turkey have no trends. In mostcases, the first four trend tests were found to yieldthe same conclusion about the trend existence. Furthermore,based on the Van Belle and Hughes' basin-widetrend test, some basins located in southernTurkey were found to exhibit a global trend, whichsuggests the homogeneity of trends both in seasonsand in stations.Yurekli et al. (2004) analyzed daily maximumstreamflow data of each month from three gaugestations on Cekerek Stream in Turkey for simulationusing stochastic approaches. Initially nonparametricMann-Kendall (MK) Test was used to identifythe trend during the study period. Two approachesof stochastic modeling viz., ARIMA andThomas-Fiering models were used to simulatemonthly maximum data. The error estimates of249

D. Machiwal, M. K. Jhapredictions from both approaches were compared toidentify the most suitable approach for reliablesimulation. The MK Test suggested no linear trendin monthly maximum data sequences of each mentionedgauge station. Though the error estimatesindicated that the ARIMA model is slightly betterthan the Thomas-Fiering model, both the approachesare recommended for simulating the dailymaximum streamflow of Cekerek Stream.6.2 Surface water qualityHarned and Davenport (1990) analyzed trends inthe water quality data of 1945 – 1988 from majorstreams flowing into the Albemarle-Pamlico estuarinesystem. The nonparametric Seasonal KendallTest indicated a change in the water quality dataduring the 1945 to 1988 period. The evaluation ofwater-quality data and more than 50 basin variablesindicated 121 significant correlations between 11basin characteristics and 12 water-quality constituentsat 21 estuary locations and 7 National StreamQuality Accounting Network stations.Yu et al. (1993) analyzed the surface water qualitydata of the Arkansas, Verdigris, Neosho, andWalnut River Basins, Kansas to examine trends in17 major constituents by using four different nonparametricmethods. The results indicated that theconcentrations of specific conductance, total dissolvedsolids, calcium, hardness, sodium, potassium,alkalinity, sulfate, chloride, total phosphorus,ammonia plus organic nitrogen, and suspendedsediment generally have downward trends. Some ofthe downward trends were related to the increase indischarge, while the others were attributed to thedecrease in pollution sources. The homogeneitytests suggested that both the station-wide trends andbasin-wide trends are non-homogeneous.Robson and Neal (1996) examined the trend often years upland stream and bulk deposition waterquality data from Plynlimon, mid-Wales by applyingthe Seasonal Kendall Test. The plotted data ontime scale showed long-term cycles, which relate tothe fluctuations in weather patterns at Plynlimonand thus violate the assumptions of common statisticaltrend tests. Even though the Seasonal KendallTest was significant for some determinands, thegraphs suggested that many of these trends areunlikely to continue. There was no indication ofchanging acid deposition inputs or changing aciditywithin the runoff, despite a decline in the UK sulphurdioxide emissions. The stream water dissolvedorganic carbon showed an increase over time, butthere was not corresponding decrease in pH asmight be expected from the acidification theory.There were cyclic variations in bulk precipitationand in stream water quality, which indicated thattrends cannot be established even with 10 years ofdata. Therefore, it was strongly recommended thatlong-term monitoring program should continue forseveral decades. It was also emphasized thatgraphical analysis greatly enhances data interpretation,and should be considered as an essential componentfor trend investigation.Kalayci and Kahya (1998) detected linear trendsin the surface water quality of rivers in the SusurlukBasin by employing four nonparametric trend testsviz., the Sen's T Test, Spearman's Rho Test, Mann-Kendall Test and the Seasonal Kendall Test. Thelinear slopes (change per unit time) of trends werecalculated by using a nonparametric estimator. Inaddition, the homogeneity in monthly trends wastested by the Van Belle and Hughes method. Theresults of the nonparametric tests indicated that thedischarge and sediment concentration have downwardtrends, while the temperature, EC and theconcentrations of sodium, potassium, calcium +magnesium, bicarbonate and chloride have upwardtrends. In contrast, the concentrations of carbonate,pH, sulfate, organic matter, and boron have notrends.Harned and McMohan (1997) examined themonotonically increasing or decreasing temporaltrends in riverine water quality including the suspendedsediment, solids, and nutrients for six stationsof the Contentnea Creek Basin by using SeasonalKendall Test. The variation in water qualitybecause of the variation in streamflow was alsoaccounted for in cases where streamflow data wereavailable. The results indicated that the nutrientconcentrations for Contentnea Creek at Hookertonhave declined since 1980. Total nitrogen, nitrate+nitrite,and nitrate concentrations have a significantdeclined trend, with the greatest reductionsoccurring from 1980 to 1992. Total ammonia andorganic nitrogen concentrations, which were increasingduring the 1980's, have declined sincearound 1990. Furthermore, the total phosphorus,dissolved phosphorus and orthophosphorus, whichincreased during the 1980, have shown a significantdecline since 1988 – the first year of the legislatedphosphate detergent ban.Antonopoulos et al. (2001) analyzed the time seriesof water quality parameters and the dischargeof Strymon River in Greece for the 1980 – 1997period. The nonparametric Spearman’s criterion250

D. Machiwal, M. K. Jhation of other attenuation processes (dilution or dispersion)was found increased.Kim et al. (2005) applied time series analysis toinvestigate effect of tides on groundwater quality.Continuous and regular in situ monitored data ofelectrical conductivity (EC) and groundwater level,and tide level data measured by the NationalOceanographic Research Institute were used in thisstudy. The results of time series analysis indicatedthat the EC and groundwater level conspicuouslyfluctuate with two periodicities (15.4- and 0.52-day), which is very similar to those of the tide.Also, the behavior of their fluctuations was foundto vary with the tidal period. This finding suggestedthat the groundwater quality has been mainly controlledby the tidal level, and the strength of tidaleffect on groundwater quality is different accordingto the tidal period.7.2 Groundwater flowMolénat et al. (1999) viewed the catchment as asystem that converts the rainfall to the stream dischargethrough a transfer function (TF). By comparingthe observed TF with the simulated TF, thehydrological processes and their time scales wereidentified. The simulated transfer functions weredeveloped using the Dupuit’s assumptions and linearrepresentation of the aquifer. The identificationof the TF was based on the stochastic method usinga spectral representation of the rainfall and streamflowtime series. The novelty of this work is toextend the stochastic approach to the one-ordercatchment hydrology and to develop a model,which takes into account both the aquifer dischargeand rapid flows. The proposed method was appliedto three first-order agricultural catchments locatedin different regions of France. For each site, theobtained results were in good agreement with reality.These results indicated that the streamflow isdominated by the aquifer flow, which is the fasttransfer accounting for 3 – 8% of the total dischargedepending on the catchment. The stochastic approachbased on the spectral analysis of temporalvariations in global observations proved to be usefulfor extracting significant information about thedominant processes occurring in the catchment andtheir characteristic time scales.8. Application of time series analysisto irrigation water managementGupta and Chauhan (1986) studied the stochasticstructure of weekly irrigation requirements of acrop by considering the irrigation requirement timeseries as an additive model with trend, periodicityand stochasticity as its components. Each componentwas identified and, if found, removed from theoriginal series. The Turning Point Test and theKendall’s Rank Correlation Test were applied fordetecting trends, whereas the correlogram techniquewas used to detect the periodicity. The harmonicanalysis was done for identifying significantharmonics. The series was then tested for stationarityand the dependent part of the stochastic componentwas found to be expressed well by the secondorderautoregressive model. Therefore, the developedmodel superimposed a periodic-deterministicprocess and a stochastic component. The adequacyof fit was judged by the insignificant correlationand the normal distribution of obtained residuals. Itwas concluded that the developed periodicstochasticmodel can be used for representing thetime-based structure of the irrigation requirementtime series for paddy crops.9. Future research directionsIt is apparent from the comprehensive reviewsthat time series analysis techniques have a vastapplication in hydrology and climatology, withincreased use of these techniques in the recent past.Detection of trend and stationarity is a major focusof past hydrologic and climatologic time seriesanalyses with a wide application of Regressionand/or Kendall’s Rank Correlation tests. However,some other trend tests (e.g., SROC and Mann-Kendall tests) which are equally important andmore powerful than the Regression and Kendall’stests have been employed in a few recent studiesonly. Therefore, there is a need to use efficient andpowerful trend detection tests (e.g., Mann-KendallTest) in future hydrologic time series analyses.The present review also revealed that very fewstudies have dealt with the homogeneity detection,and mainly the classical von Neumann, CumulativeDeviations and Bayesian tests have been used. Themultiple comparisons tests for homogeneity such asthe Bartlett, Dunnett, Link-Wallace, Tukey, andHartley tests are lacking in hydrologic time seriesanalyses. These tests are, however, considered asclassical in the field of soil science. Future studies252

Time series analysis of hydrologic data for water resources planning and management: a reviewin this direction should also consider contemporarymultiple comparison tests in addition to the commonlyused tests for checking homogeneity in thehydrologic time series.In several studies, a hydrologic time series is declaredstationary based on the randomness andtrend tests only. Specific stationarity tests such asparametric t-tests and nonparametric Mann-Whitney Test have not been employed. Furthermore,the detection of periodicity and persistence isignored in most studies involving hydrologic timeseries analyses. As every time series characteristicis very important for water resources planning andmanagement, future studies should fulfill this gap.During last two-three decades, time series analyseshave been applied for the impact assessment ofclimatic change and variability by several researchersworldwide. Hydrological research strongly suggeststhat the well-known ‘greenhouse effect’ willalter the timing and magnitude of runoff and soilmoisture, change lake levels, and affect water quality.Such changes raise the possibility of environmentaland socioeconomic dislocations, and theyhave important implications for the planning andmanagement of water resources in the future(Gleick, 1989; IPCC, 1996). Moreover, with presentglobal warming perspective, many researchershave used time series analysis techniques to assessthe impacts of El Nino and La Nina (e.g., Cimino etal., 1999). Future research should address the applicationsof time series analysis techniques in theseexciting areas in order to make these applicationsrobust and widely acceptable. To this end, the qualityof hydrological or climatological data will playa central role in proving these techniques useful andreliable.The pre-processing of time series is sometimesrequired as per the nature and state of records, but itis often neglected. For example, the extension ofthe data for their proper use and the filling of missingdata in the series; these are often true in practicefor natural time series records (Nawaj and Adeloye,1999). Future time series studies should take intoaccount all the pre-processing requirements in thetime series prior to applying the techniques of timeseries analysis. The methodologies for the extensionof time series data are described in Hirsch etal. (1993), whereas Salas (1993) presents the proceduresfor both data filling and extension.It is also obvious from the review that severalgroundwater-level time series have been used in thepast without prior time series analyses. Hence, thereis an urgent need for introducing the time seriesanalysis in this important area. In fact, time seriesof each component in the water cycle (e.g., evaporation,transpiration, infiltration, interflow, quickflow,baseflow, streamflow, spring flow, percolation,groundwater discharge, etc.) must be tested forthe validity of the basic assumptions associatedwith different statistical analyses. Unfortunately,the most time series of these hydrologic variablesare used without time series analyses. Thus, there isan urgent need to promote awareness about theimportance of time series analysis in handling nontraditionalhydrologic time series.10. ConclusionsTime series analysis has been applied in a varietyof fields in the past such as hydrology, climatology,geology, oceanography, seismology, etc. In thispaper, a review on the application of time seriesanalysis techniques in hydrology and climatology ispresented. Based on the comprehensive review, it isapparent that precipitation and streamflow are themajor hydrologic variables followed by temperatureand surface water quality, which attracted the attentionof worldwide researchers for applying timeseries analysis techniques. The use of standard statisticaltests and the performance evaluation ofsome statistical tests have been a major focus ofapplied research. On the other hand, less number ofstudies on the development of a novel approach/methodologyor the modification of existingapproaches for time series analysis is reported inthe literature. Furthermore, not a single study isreported to date covering all aspects (i.e., all basicproperties) of the hydrologic time series analysis.Most researchers have used the Kendall Test or theSeasonal Kendall Test for detecting tends, and theremaining trend detection tests as well as otherproperties of the time series (i.e., stationarity, homogeneity,periodicity and persistence) have beenignored. The main reason behind this ignorance isprobably the lack of awareness about these timeseries analysis techniques and/or the negligence byresearchers. Therefore, future studies should bedirected towards fulfilling these shortcomings.Based on the reviews presented, the needs for futuretime series-based research in the fields of hydrologyand climatology have been identified thatcan serve as guidelines for both researchers andpracticing water resources engineers or scientists.Acknowledgement. The authors gratefully acknowledgethe financial support provided by the Indian253

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