A comparative assessment of different methods for detecting inhomogeneities in Turkish temperature data set

INTERNATIONAL JOURNAL OF CLIMATOLOGY

Int. J. Climatol. 18: 561–578 (1998)

A COMPARATIVE ASSESSMENT OF DIFFERENT METHODS FORDETECTING INHOMOGENEITIES IN TURKISH TEMPERATURE

DATA SETMETE TAYANCa,*, H. NU8 ZHET DALFESb, MEHMET KARACAb and ORHAN YENIGU8 Nc

a M. U8 . Department of En6ironmental Engineering, Kuyubası, 81040 I: stanbul, Turkeyb I: stanbul Technical Uni6ersity, Eurasia Institute of Earth Sciences, 80626 Maslak, I: stanbul, Turkey

c Bogazici Uni6ersity, Institute of En6ironmental Sciences, Bebek, 80815 I: stanbul, Turkey

Recei6ed 10 December 1996Re6ised 20 August 1997

Accepted 26 August 1997

ABSTRACT

A combination of different methods is described whereby climatological time series can be tested for inhomogeneitiesusing relative homogeneity techniques. The method set includes graphical analysis, a non-parametric Kruskal–Wallishomogeneity test and a Wald–Wolfowitz runs test application to the annual mean difference temperature seriesbetween highly correlated stations. A series of Monte Carlo simulation studies was carried out, which determined theinhomogeneity detection efficiencies of these tests. The procedure is statistically rigorous and provides estimates of thetime and magnitude of change in the mean. Its application to annual mean temperature differences series for 82Turkish climate stations indicates that the method set is a valuable tool for testing time series. © 1998 RoyalMeteorological Society.

KEY WORDS: homogeneity; temperature; Kruskal–Wallis test; Wald–Wolfowitz runs test; Turkey; time series

1. INTRODUCTION

It has long been recognized that inhomogeneous climate time series may lead to biased results in studiesof climatic change (Kohler, 1949; Conrad and Pollak, 1950). Inhomogeneities that tend to offset eachother when studies are conducted by generating gridded data with grid sizes comparable to those used incurrent GCM studies are much less likely to do so when smaller station networks are used to detectregional climate change. When using large grid sizes, many stations are involved in producing the averagevalue for the grid-point, thus a station having an inhomogeneity in its series may not create a considerableerror on the final average.

The idea behind powerful relative homogeneity tests for temperature is to use difference series betweena candidate station and its neighbouring stations. Neighbouring stations that have a high correlation ofseasonal or annual anomalies of temperature and small year-to-year variances of these anomalies aresuitable for detecting inhomogeneities at the candidate station.

Many homogeneity tests are of a type that give little information about the probable date for a shiftin the mean and no information about the magnitude of the break. Examples are the Kruskal–Wallishomogeneity test and the Wald–Wolfowitz runs test, which are tested for efficiency in this study andapplied to the temperature series with the graphical relative homogeneity analysis.

* Correspondence to: M. U8 . Department of Environmental Engineering, Kuyubası, 81040 I: stanbul, Turkey. e-mail:[email protected]

Contract grant sponsor: Turkish Scientific and Technical Research Council; Contract grant number: YDABCAG-519AContract grant sponsor: Marmara University Research Fund; Contract grant number: FB DYD-2Contract grant sponsor: Bogazici University Research Fund; Contract grant number: 94 Y0005

CCC 0899–8418/98/050561–18$17.50© 1998 Royal Meteorological Society

M. TAYANC ET AL.562

The homogeneity analyses can be classified in two groups. The first group includes the analysis of astation’s climate record without explicitly considering station history information (Mitchell et al., 1966;Potter, 1981; Alexandersson, 1986; Gullett et al., 1990; Easterling and Peterson, 1992, 1995). Others usethe available station history information (Karl and Williams, 1987). The work of Easterling and Peterson(1995) is important in that the authors have undertaken a similar study looking into the efficiency ofmany methods of detecting inhomogeneities that are different from the methods used in this study.

The aim of the work is to produce a homogeneous temperature data set for Turkey with the applicationof a homogeneity analysis method set. Eighty-two stations are used in this study, which have climaterecords for a 40-year period (1951–1990). The station history information for most of those records arenot available and the few we obtained are presented in Table I. Non-parametric tests, such as theKruskal–Wallis and Wald–Wolfowitz runs, are tested for their efficiency in detecting impurities usingartificially generated time series. Finally, both tests with the graphical analysis are used in determininginhomogeneities in mean annual temperature series of Turkish stations.

2. STATION DISTRIBUTION AND DATA SET

Temperature data and station history information are obtained from the State Meteorological Office ofTurkey. Initially, the raw temperature data set consisted of three daily observations T07, T14 and T21, andmost of the stations included had shorter observation periods than 40 years. The final data set that isgoing to be used in quality control and homogeneity analysis is produced by carrying out the followingprocedure.

(i) The stations data period is taken as the 1951–1990 interval and the ones that do not fulfil thiscriterion are eliminated from the study data set.

(ii) Daily data are produced from the three daily observations with the formula (T07+T14+2T21)/4 assuggested by WMO for daily averages. Any missing observation results in the daily mean beingentered as missing.

(iii) Monthly mean is calculated from the daily means and is entered as missing when 20% or more of thedaily means are not available.

(iv) For the stations having less than 10% monthly missing data, the climatological mean of each monthis used to complete the monthly series.

(v) The seasonal and annual mean temperature data are estimated from the monthly and seasonal data,respectively.

Finally, 82 temperature series are obtained after the application of the above criteria, and these shouldundergo homogeneity analysis. Figure 1 shows the distribution of 82 Turkish climate stations.

3. METHODS FOR DETECTING INHOMOGENEITIES

An important problem encountered is how to form station pairs so that relative homogeneity comparisonscan be made easily with high confidence level. It is intuitively clear that an inhomogeneous series can bedetected with the highest possibility when the neighbouring stations are closer to (or rather with largestcorrelation to and minimum year-to-year variability to) the actual test site (candidate). Thus, Pearsoncorrelation matrices between those stations are formed and for each station the highest correlated ones aretaken as reference.

The main difficulties encountered in homogeneity analysis are:

(i) The fact that no series is perfect is always valid and there may be minor inhomogeneities that werenot documented and cannot be detected by the statistical tests;

© 1998 Royal Meteorological Society Int. J. Climatol. 18: 561–578 (1998)

TESTING TURKISH TEMPERATURE INHOMOGENEITIES 563

Table I. Available station history information of 30 stations

WMO Station Dates Height (m) Latitude (N) Longitude (E)number

1951–1970 44 — —17030 Samsun1971–1990 4 41.28 36.331951–1960 37 41 39.4317038 Trabzon1961–1970 30 — —1970–1990 31 41 39.721951–1990 48 41.67Edirne 26.57170501951–1970 34 40.59 28.4817058 Florya1971–1990 36 40.98 28.81951–1980 40 — —17062 Goztepe1981–1990 33 40.97 29.081951–1990 742 40.73 31.617070 Bolu1951–1990 799 41.37Kastamonu 33.77170741951–1960 730 40.36 33.3717080 Cankırı1961–1990 751 40.6 33.621951–1970 1285 39.45 37.0217090 Sivas1971–1990 1285 39.75 37.021951–1960 1213 39.44 39.317091 Erzincan1961–1970 1215 — —1971–1990 — 39.7 39.51951–1960 1893 —Erzurum —170961961–1970 1869 — —1971–1990 — 39.32 41.271951–1970 3 40.08 26.2417112 Canakkale1971–1990 6 40.13 26.41951–1990 100 40.18 29.0717116 Bursa1951–1960 902 —Ankara —171301961–1970 894 — —1971–1990 890 39.95 32.88

Kırsehir 1951–1970 985 39.08 34.1171601971–1990 1007 39.13 34.171951–1960 1732 38.28 43.2117170 Van1961–1990 1725 38.47 43.351951–1960 1020 38.45 30.3217190 Afyon1961–1990 1034 38.75 30.531951–1960 1071 38.43 35.2917196 Kayseri1961–1990 1068 38.6 35.51951–1960 977 38.21 38.1817200 Malatya1961–1990 998 38.35 38.31951–1970 1105 38.4 39.317202 Elazıg1971–1990 991 38.67 39.221951–1990 896 37.93 41.9317210 Siirt1951–1990 25 38.4I: zmir 27.17172201951–1960 1052 37.45 30.3317240 Isparta1961–1990 997 37.75 30.55

Konya 1951–1960 1026 37.52 32.3172441961–1970 1029 — —1971–1990 1026 37.87 32.51951–1960 1430 37.33Ulukısla 34.29172501961–1990 1451 37.55 34.481951–1960 840 39.05Gaziantep 37.22172601961–1970 855 — —1971–1990 — 39.08 37.37

Urfa 1951–1990 549 37.17 38.77172701951–1960 677 —Diyarbakır —172801961–1970 676 — —1971–1990 677 37.92 40.2

Mugla 1951–1990 646 37.2 28.35172921951–1990 20 36.98 35.3Adana17350


M. TAYANC ET AL.564

Figure 1. Distribution of the 82 Turkish meteorological stations providing temperature data

(ii) Ambiguous conclusions are possible when several neighbouring stations do have inhomogeneitiesthemselves.

In order to overcome or reduce the effect of these problems one must identify and use as many of thecandidate station’s nearest neighbours as possible. The use of at least several nearby stations is verylabour intensive and requires a substantial quantity of computer compatible data, particularly for caseswhere station inhomogeneities are not well documented, as it is in Turkey.

3.1. Graphical analysis

As a preliminary step in any analysis of homogeneity, it is highly instructive to plot the series to beevaluated on a linear scale. In the particular case of temperature, the most useful procedure, as suggestedby Mitchell et al. (1966), is to compute the year-to-year differences between the series to be evaluated andeach of the other sites (the ones having highest correlation and minimum variation with the candidatestation), and to plot the resulting series of differences. This method provides a rather clear indication ofthe intercomparability of the records at the selected stations, by suppressing the relatively wide interan-nual variability of temperature itself that is common to all stations. Moreover, if any of the temperaturevalues in the series being evaluated contain sizeable errors, this form of graphical analysis will reveal themby introducing ‘jumps’ on the same date in all (or at least most) of the series plotted. Although graphicalcomparisons can be very helpful in giving the analyst some perspective, they cannot be relied upon todistinguish the hidden discontinuity effects.

3.2. Test-based relati6e homogeneity analyses

In the past, objective statistical evaluation of the homogeneity of climatic time series has been confinedlargely to the evaluation of relative homogeneity of two or more series, considered one pair at a time(Conrad, 1925; Conrad and Pollak, 1950) and the application of a randomness test. Today a wider arrayof suitable statistical tests are available, such as the distribution free Kruskal–Wallis homogeneity testand the Wald–Wolfowitz runs test.

3.2.1. Kruskal–Wallis homogeneity test. This test is proposed by Sneyers (1990). The observations ofeach series are replaced by the rank that these observations occupy in the total ordered sample. If k is thenumber if independent series, nj, j=1, 2, . . ., k, is the sample size of the series j, and if rij is the rankoccupied in the total ordered sample by the observation i of the series j, the statistic is



X=� 12

n(n+1)%j

Rj2

nj

−3(n+1)�I:

1−%T

n3−n

;where the denominator is the correction factor in case of indeterminate rank raised from the equality ofcertain values, T= t3− t, with t being the number of equal values in one group of equal values and thesum � T being extended to all groups of equal values, and

Rj=%i

rij and n=%j

nj

With the null hypothesis of homogeneous means, the statistic X has approximately a x2 distribution with(k−1) degrees of freedom.

3.2.2. Wald–Wolfowitz runs test. The test statistic is the quantity

R=% number of sign changes

in the xi series, where i=1, 2, . . ., n when xi is replaced by

+1, if xi\median or −1, if xiBmedian

The method is explained in detail by Sneyers (1990). The statistic has an approximately normaldistribution of mean and variance.

E(R)=2n1n2

n+1and var R=

2n1n2(2n1n2−n)n2(n−1)

where n1 and n2 denote the number of +1 and −1 elements, respectively, in the series and n=n1+n2.

3.3. Analysing the efficiencies of the Kruskal–Wallis homogeneity test and the Wald–Wolfowitz runs test

The most important attributes of any scheme to detect station inhomogeneities is its ability to correctlydetect the discontinuities sought even in the presence of high variability. In this regard, Monte Carlosimulations are carried out to access the detection power of the Kruskal–Wallis homogeneity test and theWald–Wolfowitz runs test for any inhomogeneity of the time series.

3.3.1. Generating artificial time series. Series production can be accomplished using the following twosteps.

(i) Forming series by generating ‘good’ random numbers. For the sake of the testing scheme, the ‘good’random numbers generated by a computer program must be entirely free from any sequentialcorrelations and must be entirely unpredictable. A ‘portable’ random number generator (which can beprogrammed in a high-level language, and which will generate the same random sequence from agiven seed on all machines) given by Press et al. (1986) is used to obtain uniform pseudo-randomdeviates between 0 and 1. The constants used in the program give a period of accepted maximumlength and pass Knuth (1981) spectral test for dimensions between 2 and 6.

(ii) Transforming uniform deviates to obtain Gaussian distributed deviates; the much used Box–Mullermethod is applied to transform uniform deviates to a normal distribution with zero mean and unitvariance.

3.3.2. Analysing Kruskal–Wallis efficiency with 12 generated time series. Sneyers (1990) found that theestimates considered become more accurate as the sample size n is increased. In order to get highlyaccurate results, 12 series are formed with each containing 62 Gaussian distributed random deviates whichmay correspond to 62 years period of data. Some Turkish climate stations have a data period of1929–1990. In order to be representative of 1929–1990, 62 years of data is used in the simulations. Afterthat, inhomogeneities in the form of ‘jumps’ are introduced into the series by modifying the mean (m=0at initial) and the standard deviation (s=1 at initial).


M. TAYANC ET AL.566

By using mean and standard deviation, a parameter, U, that will provide information about themagnitude of the inhomogeneities is introduced as follows.

U=ms

Figure 2. Kruskal–Wallis homogeneity test statistics with 12 generated time series for (a) different number of series having jumpperiods of 8, 10, 14, and 18 years with U=10, (b) different U levels and different jump periods in six series, and (c) different trend

properties in the form of U reaching certain values and different trend periods in six series (C.L., confidence level)



U is the reciprocal of the coefficient of variation, which is 1/CV, where CV is s/m. Figure 2(a) shows theKruskal–Wallis statistics that are obtained by introducing a specific period of jump with U=m/s=10into the homogeneous series, starting with the first series (column) and increasing the number of seriesthat have inhomogeneities in themselves step by step. This same procedure is applied for different jumpperiods such as 8, 10, 14 and 18 years, and the curve obtained from each is illustrated in Figure 2(a). Avalue for U equal to 10 is used to obtain the Kruskal–Wallis statistics of Figure 2(a) because at this level(U=10) Kruskal–Wallis statistics are saturated, i.e. increasing the magnitude of U will not have anyeffect on the results and on the slopes of the curves in this figure. It can be seen that the highestKruskal–Wallis statistic which also enables the detection of the inhomogeneity for the series having a10-year jump period as the 95% confidence level, is obtained at point 6 (six of the series havinginhomogeneities and the other six remaining unchanged). Some fluctuations in the graphics may be theresults of the slight differences between the generated random number distributions.

Secondly, we wanted to determine the Kruskal–Wallis test performance against different jump periodsand we conducted a series of simulations. The test statistics obtained for different U values and fordifferent jump periods can be seen in Figure 2(b). It is obvious that all the lines, which correspond todifferent jump periods, reach a saturation Kruskal–Wallis statistic at about U values of 6 or 7; the greaterthe jump period, the greater is the test statistic at saturation point. This property of Kruskal–Wallis ofreaching a saturation point and not allowing further quality control analysis is due to the fact that ranksare used instead of the real values of the time series. Another problem encountered here is the detectionsensitivity of the Kruskal–Wallis homogeneity test starts at a 10-year jump period, causing all the othersmaller jump periods that may be important in the homogeneity analysis to be undetected.

Figure 2(c) gives the performance results of the Kruskal–Wallis test against the generated differenttrend properties. For this figure, U values starting from 0 and reaching constant values (4, 6, 8 and 10)are generated into the six series as trends, and the number of years having a trend are changed to generatedifferent trend periods. Regardless of trend strength and its accompanying slope steepness, the Kruskal–Wallis homogeneity test detected only the trends greater than 12 years with a 95% confidence level.

In this form, the Kruskal–Wallis homogeneity test can be applied to monthly series of temperature, butthe differences due to seasonal variability of temperature between the months must be eliminatedbeforehand. It must be noted that the Kruskal–Wallis homogeneity test is not so powerful as Sneyers(1990) indicates and must not be used individually in detecting inhomogeneities; some other tests mustalso be used in order to overcome the deficiencies of this test.

3.3.3. Analysing the Kruskal–Wallis and Wald–Wolfowitz runs tests with two generated time series. Tomimic our case studies, we generated pairs of artificial time series of 40 year of length. The first elementof the pair is kept the same. The second series is ‘contaminated’ with an inhomogeneity of some sort(jumps, trends, or different U levels).

These series are tested by the Kruskal–Wallis homogeneity test and the Wald–Wolfowitz runs test,each time the second series includes a different errant data property. One important property of the twoseries is that they are not composed of identical random numbers (but note that both series have 0 meanand 1 standard deviation). Thus, when the second series includes no impurities, the results of both testsare not zero, reflecting the randomized testing character of both tests. Note also that the results may varya little bit depending on the relative place of the introduced jump in the series.

The Kruskal–Wallis homogeneity test results are presented in Figure 3(a–c) and those for Wald–Wol-fowitz in Figure 4(a–c). Figure 3(a) shows the testing efficiency of the Kruskal–Wallis homogeneity testfor different U values (in other words, the second series is generated with a different U value from thestart to the end). It can be clearly said that the Kruskal–Wallis homogeneity test is highly sensitive todifferent U values, in contrast to the Wald–Wolfowitz runs test which has no sensitivity to this property(Figure 4(a)). In the Wald–Wolfowitz runs test, the difference of the two series is cut by the median, thusintroducing different U levels in the second series causes no more runs up and down.

Figure 3(b) and 4(b) represent the results obtained from both tests by introducing jumps into the secondseries and altering the value of U. The Kruskal–Wallis performance in analysing two series is more


M. TAYANC ET AL.568

Figure 3. Kruskal–Wallis homogeneity test statistics with two generated time series for (a) generated different U levels in the secondseries, (b) generated different U levels and different jump periods in the second series, and (c) generated different trend properties

in the form of U reaching certain values and different trend periods. (C.L., confidence level)

powerful than the 12 series; it can be seen that the jump period of 8 years can be detected at the 95%confidence level (in the previous analysis with 12 series, the detected jump period was a minimum of 10years), and the intersection points of the curves of different jump periods with the 95% confidence line arelocated at smaller U values in Figure 3(b) than in Figure 2(b). The Wald–Wolfowitz runs test results area little weak in power; starting to detect inhomogeneity at a jump period of 10 years and having greater



U values at the 95% confidence level. The sharp transitions in the figures are due to the characteristics ofthe Wald–Wolfowitz test arising from the number of runs up and down.

For Figure 3(c) and 4(c), U values starting from 0 and reaching to a certain level are introduced intothe second series as trends and the trend duration is determined by altering the number of years. It isobvious that U reaching 10 in 8 years is steeper in slope than U reaching 10 in 22 years. Kruskal–Wallisis again more efficient than Wald–Wolfowitz; starting to detect a trend from 8 years whereas the latter’svalue is 10 years, with Wald–Wolfowitz having lots of zig-zag features, which are easily created bychanging the property of a data value from +1 to −1 or 6ice 6ersa.

Figure 4. As in Figure 3 except for Wald–Wolfowitz runs test statistics


M. TAYANC ET AL.570

Figure 5. The location of six example stations in bold and their neighbouring stations located on Anatolia

Detection power of the two tests are not investigated for composite inhomogeneities such as multiplejumps, trends on a jump, jumps on a jump, etc., which can give more information about their behaviour.For these composite inhomogeneities, Wald–Wolfowitz runs test may yield more powerful results thanthe Kruskal–Wallis homogeneity test, as can be seen in the results section.

4. HOMOGENEITY ANALYSIS RESULTS

The combination of Kruskal–Wallis, Wald–Wolfowitz tests and graphical analysis is used to detect thediscontinuities in the Turkish temperature data set. The Wald–Wolfowitz runs test is applied to overcomethe deficiencies of the Kruskal–Wallis homogeneity test in detecting the composite inhomogeneities, andgraphical analysis is expected to provide information about the probable date of the inhomogeneity andhelp to distinguish trends from jumps. At the end of the analysis of the Turkish temperature series, theabove expectancies are largely met.

Several examples are provided that illustrate clear inhomogeneity. In these examples, some of them areso clearly inhomogeneous that shifts in the mean for individual time series can be seen by eye. The othersdo not show any signs of inhomogeneity in their individual time series, expressing the importance of arelative homogeneity analysis to reveal the inhomogeneities that are not detected directly by visualinspection. By using two or more highly correlated neighbour stations to the candidate one, relativehomogeneity analysis, which includes the graphical and test based analyses, provides such results, sojudgements about the homogeneity of the difference series can be made easily. The main idea is based onthe fact that any regional climate change or fluctuations experienced by the candidate station will showup in the nearby neighbouring stations as well, but this may not be true for the inhomogeneities.

Figure 5 shows the location of the example stations that are going to be compared with theirneighbours. The time series of mean annual temperatures at two Black Sea shore stations are presentedin Figure 6(a). Giresun is within several kilometres of the Black Sea but Artvin is located more inland.The Artvin time series, at first glance, give the impression of a cooling trend, except for the last years. TheGiresun data also has trends with warming indicated at the beginning of the series and cooling at the end.



The Giresun series shows a probable jump at about 1965. Figure 6(b) represents the graphical results ofArtvin and Giresun series differences with their highly correlated neighbours. Trabzon and Samsun arethe neighbours of Artvin, and Trabzon and Zonguldak are neighbours of Giresun. Beforehand, theseneighbouring stations are tested for homogeneity so their difference series results are reliable. Thegraphics of Artvin–Trabzon and Artvin–Samsun resemble each other as having different means betweenthe intervals of 1951–1960 and 1961–1990 and a jump in between. The Kruskal–Wallis and Wald–Wol-fowitz statistics for Artvin–Trabzon and Artvin–Samsun are 38.43, −0.95 and 45.63, −1.55, respec-tively, and can be seen in Table II. High Kruskal–Wallis values comes from the jump in difference seriesand different U levels of the two series. However, Wald–Wolfowitz runs test failed to detect inhomogene-ity, confirming the efficiency results. Figure 4(b) demonstrates that a 10-year length jump can be detectedonly at values of 2.55U without any other jump or trend. There is approximately a 1°C jump in theArtvin–Trabzon series but almost no change in the standard deviation, giving a U magnitude of 1. It alsomust be expressed that there is no significant trend or jump in either of the series broken by thediscontinuity at 1961, which may influence the results of the tests. As a result, Artvin can be classified asinhomogeneous. In the Giresun difference series a jump can be observed at 1967–1968, separating twoseries 1951–1966 and 1969–1990 with different means. Kruskal–Wallis values for Giresun–Trabzon andGiresun–Zonguldak are 6.47 and 15.84 and Wald–Wolfowitz values for the two difference series are−4.16 and −3, respectively. All of the statistics have detected the inhomogeneity in the Giresun seriesat a high significant level.

Figure 6. (a) Annual mean temperature series of Artvin and Giresun, (b) annual mean temperature difference series of Artvin–Tra-bzon, Artvin–Samsun, Giresun–Trabzon and Giresun–Zonguldak


M. TAYANC ET AL.572

Table II. Detailed homogeneity analysis information of 82 stations

WMO Station Compared ResultsbK–W W–W Remarkswith statisticnumber (on graphicalstatistic

analysis)a

17020 Sile Sarıyer 1.56 −3.84** Trend and a smalljump

Kumkoy 3.66 −4.16** Trend and a small IHjump

17022 Zonguldak Sarıyer 0.32 −0.4 —Kumkoy 1.45 −1.91 — H

17024 I: nebolu Zonguldak 5.17* −3.55** Trend and a 5 yearjump at start

Sinop 19.47** −2.88** Trend and a 5 year IHjump at start

17026 Sinop Kumkoy 3.83 −0.57 —Florya 0.06 −1.28 — H

17030 Samsun Trabzon 3.74 −0.07 —Goztepe 1.94 −3.2** —Bursa 1.35 −3.79** — H

17034 Giresun Trabzon 6.47* −4.16** JumpZonguldak 15.84** −3.00** Jump IH

17038 Trabzon Sinop 15.53** 0.64 Trend and DUZonguldak 32.8** −1.23 Trend and DU H

17040 Rize Trabzon 14.4** −4.37 Jump, trend and DUZonguldak 8.53** 0.07 Jump and trend IH

17041 Artvin Samsun 45.63** −1.55 Jump and DUTrabzon 38.43** −0.95 Jump and DU IH

17050 Edirne Sarıyer 0.75 0.39 —Tekirdag 6.59* −0.31 Trend and DU H

17052 Luluburgaz Edirne 19.45** −4.16** TrendTekirdag 36.13** −1.4 Trend and DU H

17054 Corlu — — — — M17056 Tekirdag Florya 0.9 −3.52** Trend

Sarıyer 2.88 −0.6 —Kumkoy 1.19 −0.94 — H

17058 Florya Goztepe 2.46 −1.13 —Kumkoy 3.72 −1.49 Trend H

17059 Kumkoy Sarıyer 0.57 0.43 —Zonguldak 1.45 −1.91 — H

17061 Sarıyer Zonguldak 0.32 −0.4 —Kumkoy 0.57 0.43 — H

17062 Goztepe Bandırma 0.07 −4.79** TrendFlorya 2.46 −1.13 — H

17066 Kocaeli — — — — M17068 Adapazarı — — — — M17070 Bolu Kastamonu 11.51** 1.62 Trend and DU

Erzincan 3.48 0 — H17074 Kastamonu Erzincan 19.63** −0.64 DU and weak trend

Sivas 17.43** −0.58 DU and weak trendAnkara 49.33** −1.4 DU and trend H

17080 Cankırı Bolu 33.78** 0.09 Jump and DUAnkara 8.08** −2.54** Jump and DU IH

17082 Merzifon Kastamonu 22.29** −3.84** Jump and DUBolu 33.78** −2.24 Jump, trend and DUCankırı (IH) 1.99 −3.2** Jump IH

17084 Corum Kutahya 0.15 −1.6 —Nigde 1.45 −1.6 — H

17086 Tokat Sivas 53.52** −1.4 Jump, trend and DUCorum 41.25** −3.84** Jump, trend and DU IH

17090 Sivas Yozgat 0.04 −3.46** TrendVan 0.2 −0.64 — H



Table II. (Continued)

StationWMO Compared K–W ResultsbW–W Remarkswith statistic (on graphicalstatisticnumber

analysis)a

Kutahya 0.03 0.817091 —ErzincanKayseri 1.65 −1.27 — HAgrı 0.04 −1.6 —17096 HErzurum— — —Kars — M17098Konya (IH) 2.54 0.3217100 —IgdırAnkara 1.48 −1.6 — HErzurum 0.04 −1.6 —17102 HAgrıBalıkesir 6.27* −1.91Canakkale DU17112Bandırma 27.22** −2.8** Trend and DU HManisa 53.58** −0.96Bandırma Trend and DU17115Akhisar 51.19** −2.24** Trend and DUFlorya 2.58 −3.52** TrendSamsun 1.57 −1.27 — HBalıkesir 1.8 −4.23**Bursa Trend17116Bilecik 52.46** −2.23** Trend and DU HUsak 0.06 −1.6Bilecik —17122Balıkesir 52.95** −1.74 DU HKutahya 8.15** −1.49Eskisehir Weak trend and DU17124Nigde 2.84 −0.07 —Afyon 0.05 −0.42 — H

Etimesgut17129 — — — — MKonya (IH) 0.3 −3.2**Ankara Trend17130Yozgat 52.83** −2.74** Strong trend and DU HVan 0.26 −3.52Yozgat Trend17132Bolu 33.55** −2.88** Trend and DU HBursa 1.8 4.23**Balıkesir Trend17150Canakkale 6.27* −1.91 DU HNigde 0.86 0.39 —17152 KutahyaErzincan 0.03 0.8 — HYozgat 50.34** −2.23** DU and trend17160 KırsehirAnkara 7.15** −0.32 DU and trendNigde 6.01* −1.28 DU and trend HYozgat 0.26 −3.52**Van Trend17170Sivas 0.2 −0.64 — HManisa 16.24** −3.34**Dikili Trend and DU17180Akhisar 10.66** −2.2** Trend and DU HBandırma 53.58** −0.96Manisa Trend and DU17182Akhisar 33.11** −2.2** Trend and DUDikili 16.24** −3.34** DU and trend HManisa 33.11** −2.2** DU17184 AkhisarBalıkesir 46.96** −0.95 DU and trend HBilecik 0.06 −1.6 —17188 UsakKutahya 49.35** −0.78 DU HNigde 3.02 −0.9517190 —AfyonEskisehir 0.05 −0.42 — H— — — —17192 MAksehirKonya (IH) 24.94** −3.2**Kayseri DU and jump17196Erzincan 1.65 −1.74 JumpCorum 1.53 −2.48** JumpYozgat 32.76** −1.92 DU and jump IHSiirt 53.69** −0.96Malatya DU17200Elazıg 5.66* −2.3** Trend and DU HBurdur 0.88 −0.64Elazıg —17202Siirt 52.63** 2.88** DU HDiyarbakır 0.01 −1.53Siirt —17210Mardin 0.42 −2.53** — HAydın 1.42 −2.56**I: zmir Weak trend17220Dikili 53.69** −2.3** Weak trend and DU H


M. TAYANC ET AL.574

Table II. (Continued)

WMO Station Compared with ResultsbK–W W–W Remarksstatisticstatistic (on graphicalnumber

analysis)a

17222 O8 demis — — — — M17230 Nigde Erzincan 0.85 0.02 —

Kutahya 0.86 0.39 —Eskisehir 2.84 −0.07 — H

17232 Kusadası — — — — M17234 Aydın I: zmir 1.42 2.56** Jump

Manisa 25.05** −3** Jump and DU IH17236 Nazilli — — — — M17238 Burdur Usak 27.46** −1.16 Trend and DU

Isparta (IH) 34.69** −5.64** DU and trendElazıg 0.88 −0.64 — H

17240 Isparta Burdur 34.69** −5.64** DU and jumpsKonya (IH) 6.26* −4.12** JumpsAfyon 29.6** −2.41** DU and jump IH

17244 Konya Nigde 17** −2.53** DU, trend and jump in last4 years

Ankara 0.3 −3.2* Jump in last 4 yearsKırsehir 4.28* −2.53** Trend and jump in last 4 IH

years17250 Ulukısla — — — — M17260 Gaziantep Urfa 53.53** −2.55** DU

Diyarbakır 35.42** −1.91 DU and trend H17270 Urfa Mardin (IH) 24.63** −2.53** DU and weak jump

Gaziantep 53.53** −2.55** DU H17280 Diyarbakır Mardin (IH) 0.31 −2.56** Trend

Gaziantep 35.42** −1.91 DU H17282 Mardin Urfa 24.63** −2.53** DU and weak jump

Diyarbakır 0.31 −2.56** Trend IH17290 Bodrum Mugla 53.74** −0.95 DU

Adana 1.14 −2.88** TrendAlanya 2 −0.93 — H

17292 Mugla Adana 53.73** −3.52** DU and trendCanakkale 0.08 −0.32 — H

17296 Fethiye Adana 19.39** −3.5** Jump, trend and DUAntalya (IH) 3.11 −3.82** JumpBodrum 16.15** −4.52** Jump and DU IH

17300 Antalya Bodrum 8.76** −1.23 JumpAdana 13.2** −2.88** Jump, trend and DU IH

17320 Anamur Alanya 9.67** −3.82** JumpIslahiye 53.54** −2.2** Jump and DU IH

17330 Silifke — — — — M17340 Mersin Antalya (IH) 0.66 −4.16** Jump

Adana 10.37** −4.74** Jump, trend and DU IH17350 Adana Bodrum 1.14 −2.88** Trend

Alanya 5.63* −4.17** Trend H17360 Dortyol Adana 3.85* −3.41** Jump

I: skenderun (IH) 45.54** −4.16** Jump and DU IH17370 I: skenderun Antakya 53.01** −3.2** DU and jump

Adana 42.94** −5.44** DU and jump IH17378 Antakya Adana 31.56** −3.46** DU and trend

Bodrum 26.47** −1.92 DU H17380 Islahiye Adana 53.55** −2.88** DU and trend

Antakya 46.16** −0.26 DU H17609 Alanya Bodrum 2 −0.93 —

Adana 5.63* −4.17** Trend H17612 Alpullu S.F. — — — — M17620 Bahcekoy Sarıyer 30.02** −2.23** Jumps and DU

Kumkoy 33.97** −4.81** Jumps and DU IH

* Significant at the 95% level.** Significant at the 99% level.a DU, different U levels between two series.b H, homogeneous; IH, inhomogeneous; M, having more than 10% missing data.



Figure 7. As in Figure 6(a) except for Konya and Cankırı. (b). As in Figure 6(b) but for Konya–Nigde, Konya–Kırsehir,Konya–Ankara, Cankırı–Bolu and Cankırı–Ankara

Konya and Cankırı are inland Anatolian stations located on a high plateau. They have documentedstation history information that enabled us to compare the results obtained in this study with thosedocumented. The annual mean temperature series of both those stations do not reveal any informationabout the inhomogeneities they may contain (Figure 7(a)). In Figure 7(b) Konya’s difference series withits neighbours do not show any significant jump in 1960 when the station was moved to another location,however, in the Konya–Nigde and Konya-Kırsehir series, a small 6-year jump period is detected between1957–1963 which cannot be seen in the Konya–Ankara series. A main problem is encountered in the last4 years of the Konya series; a large jump towards cooling in all the difference series. The documentedchange, which has no date, most probably occurred in 1986. From Table II, the test statistics suitable tothe situation of Konya can be seen; making Konya another inhomogeneous station. Cankırı is well suitedwith its history information, having a jump period between years 1951–1960 in its difference series withBolu and Ankara. One important feature is the increase of the variability of the Cankırı–Bolu series in


M. TAYANC ET AL.576

Figure 8. (a) As in Figure 6(a) except for Fethiye and Mersin. (b) As in Figure 6(b) except for Fethiye–Bodrum and Mersin–Adana

recent years, which probably is due to the urbanization effects in Bolu. Urbanization may lead to highervalues of temperature and reduction in the variability of the series.

Fethiye and Mersin are among the southernmost stations of Turkey and in close proximity to theMediterranean Sea. In Figure 8(a) the individual time series of Fethiye shows a very clear jump in the1962–1963 years. Figure 8(b) confirms the behaviour of Fethiye annual mean temperature series. Thestatistics in Table II affirm the alternative hypothesis at the 99% significant level. The time series ofMersin provides clues about two discontinuities that it may contain. In fact, Mersin–Adana differenceseries exhibits two jumps; one occurring in 1960 and the other in 1978–1979, producing three serieshaving different means (Figure 8(b)). Both of the statistics detected the inhomogeneity in the Mersinseries.

Table II is prepared using data for 82 stations and carrying out the following procedure: by using theannual mean temperatures, individual time series of all stations are plotted and a correlation matrixbetween them established, difference series between the highly correlated stations are plotted, and theKruskal–Wallis and the Wald–Wolfowitz runs tests are applied to the stations. In general, moreintercomparisons were made than are listed. Only a few stations, which supplied the highest Pearsoncoefficient with the candidate one, have been included in Table II. Although there are some inconsisten-cies between the analysis results and available documented station history information, in most cases theresults are in harmony with the history information.

In the case of composite inhomogeneities and coinciding analysis results, additional neighbour stationsare used in order to determine the classification of the candidate station. One of the labour intensive tasksis the removal of the inhomogeneous stations used in the comparisons and choosing another highlycorrelated station for the analysis of the candidate one.

5. SUMMARY AND CONCLUSIONS

A scheme has been produced that detects the climatological time series of temperature for inhomogeneitiesdue to factors explained in detail by Bradley and Jones (1985). The Kruskal–Wallis homogeneity test andthe Wald–Wolfowitz runs test and graphical analysis are the main pillars of this scheme.

The tests have been assessed for their performance in detecting inhomogeneities in time series bysimulation. The results indicate that the Kruskal–Wallis homogeneity test is sensitive to (a) jump, (b)trend and (c) different U values. The sensitivities of Wald–Wolfowitz runs test are (a) jump and (b) trend.Both tests are not powerful enough to be used individually in the relative homogeneity analysis. They



Figure 9. Distribution of 50 stations having homogeneous temperature records

must be used in conjunction with graphical analysis to increase the power of overall analysis and to obtaininformation about the probable date of shift and the magnitude of the inhomogeneity. By includinggraphical analysis it is also possible to distinguish between jumps and trends; the former may be noise andthe latter may be signal, as in the case of our study. This criterion is qualitative and depends on the natureof the study. Thus the three tests together produce a homogeneity analysis set. Although the detectionpower of these tests are not studied for complex time series behaviour, the set appears to be a promisingtool for screening time series for homogeneity.

The tests applied by Maronna and Yohai (1978), Alexandersson (1986), Gullett et al. (1990), Easterlingand Peterson (1995) have been used previously and are suggested as reliable homogeneity testing methodsin climate time series. Because the method used here also has large capabilities it is recommended by theauthors, but the required labour intensive tasks must also be taken into account. It is better to have allhistory information for all stations before applying the above procedure, but in the absence of suchknowledge this set can still produce reliable results. The method can be applied to temperature time seriesfor the detection of inhomogeneities.

Station records that indicated inhomogeneities are not correlated and are flagged as unusable insubsequent analyses. A future study that will try to correct the errant data will be very useful.

After the application of the analyses, 50 stations remained homogeneous, which at the same time haveless than 10% missing data. No statistically significant outliers are encountered in any of the annual meantemperature series. The final distribution of the stations can be seen from Figure 9. Although there aregaps in the final distribution of the stations, the temperature records can be used reliably to study regionalurbanization or climatic change effects, or it can also be included in a global data base to carry out studiesof large-scale climatic changes.

ACKNOWLEDGEMENTS

The authors thank Huseyin Toros for his valuable assistance. This study is a part of projects YDABCAG-519A, FB DYD-2 and 94 Y0005, which are financially supported by the Turkish Scientific and TechnicalResearch Council (TU8 BI: TAK), the Marmara University Research Fund and the Bogazici UniversityFund, respectively.

REFERENCES

Alexandersson, H. 1986. ‘A homogeneity test applied to precipitation data’, J. Climatol., 6, 661–675.Bradley, R.S. and Jones, P.D. 1985. Data Bases for Detecting CO2-induced Climatic Change, US Department of Energy State of the

Art Report on the Detection of Climatic Change, Carbon Dioxide Research Division, US Department of Energy, WashingtonDC.


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Conrad, V. 1925. ‘Homogeneitats-bestimmung meteorlologischer Beobachtungsreihen’, Meteorol. Z., 42, 482.Conrad, V. and Pollak, L.W. 1950. Methods in Climatology, Harvard University Press, 459 pp.Easterling, D.R. and Peterson, T.C. 1992. ‘Techniques for detecting and adjusting for artificial discontinuities in climatological time

series: a review’, Preprints, Fifth International Meeting on Statistical Climatology, 22–26 June 1992, Toronto, pp. J28–J32.Easterling, D.R. and Peterson, T.C. 1995. ‘A new method for detecting undocumented discontinuities in climatological time series,

Int. J. Climatol., 15, 369–377.Gullett, D.W., Vincent, L. and Sajecki, P.J.F. 1990. Testing for Homogeneity in Temperature Time Series at Canadian Climate

Stations, Publication of the Canadian Climate Program, 43 pp.Karl, T.R. and Williams, C.N., Jr. 1987. ‘An approach to adjusting climatological time series for discontinuous inhomogeneities’,

J. Clim. Appl. Meteorol., 26, 1745–1761.Knuth, D.E. 1981. Seminumerical Algorithms, 2nd edn, Vol. 2, The Art of Computer Programming, Chapter 3. Addison-Wesley,

Reading, MA.Kohler, M.A. 1949. ‘Double-mass analysis for testing the consistency of record and for making adjustments’, Bull. Am. Meteorol.

Soc., 30, 188–189.Maronna, R. and Yohai, V.J. 1978. ‘A bivariate test for the detection of systematic change in mean’, J. Am. Stat. Assoc., 73,

640–645.Mitchell, J.M., Jr., Dzerdeevskii, B., Flahn, H., Hofmeyr, W.L., Lamb, H.H., Rao, K.N. and Wallen, C.C. 1966. Climatic Change.

WMO Technical Note 79, World Meteorological Organization, Genera, 79 pp.Potter, K.E. 1981. ‘Illustration of a new test for detection of a shift in mean in precipitation series’, Mon. Wea. Re6., 109,

2040–2045.Press, W.H., Flannery, B.P. Teukolsky, S.A. and Vetterling, W.T. 1986. Numerical Recipes in Fortran, the Art of Scientific

Computing, Cambridge University Press, Cambridge, 735 pp.Sneyers, R. 1990. On the Statistical Analysis of Series of Obser6ations, WMO Technical Note 143, World Meteorological

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A comparative assessment of different methods for detecting inhomogeneities in Turkish temperature data set