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Janet B. Wijngaard and Albert M.G. Klein Tank
Royal Netherlands Meteorological Institute (KNMI)
PO Box 201, 3730 AE De Bilt, The Netherlands
Telephone : +31 30 2206524 Fax: +31 30 2210407


In the European Climate Assessment (ECA) the twentieth century temperature and precipitation climate is analysed for WMO region VI (Europe and Middle East). Changes in the mean, as well as changes in extremes and climate variability are considered. In particular the analysis of extremes and short term variability requires data with daily resolution (Folland et al., 2000). Already 30 countries participate and they contributed long (40-100 years) daily temperature (Figure 1) and precipitation time series.

Figure 1:
Stations for which daily temperature series are collected (August 2000) The size of the circle determines the length of the series.

In order to use these series for climate analysis it is important to have reliable data without artificial irregularities. Such inhomogeneities may mask natural trends and variability. Since in many countries different observation and quality control practices were in operation during the last century, inhomogeneities may be present in the series. Most meteorological institutes maintain an archive with information about the measuring site, instruments and techniques used. Unfortunately, this metadata information is not always available in this assessment project and, if present, not always easy to interpret without knowledge of the local situation. To obtain insight into the quality of the series of the ECA temperature data, objective statistical tests for departure of homogeneity were applied to the series of the diurnal temperature range (DTR=maximum temperature minus minimum temperature).


Testing homogeneity requires a method that distinguishes artificial from natural changes. It is very common to test homogeneity relatively by using nearby reference stations for filtering out natural changes (Peterson and Easterling, 1994). The idea behind this method is that natural changes are similar in both series, whereas artificial irregularities are site specific. The stations in the ECA data set are rather diverse; some are urban, others rural, some are mountain stations and others coastal. It appeared not to be straightforward to choose or construct homogeneous reference series for all these stations. An additional problem with relative homogeneity testing can be that entire networks undergo simultaneous instrumental changes (Parker et al., 1994). Consequently not only natural but also artificial changes will filter out (Easterling and Peterson, 1992). To gain insight into the quality of the temperature series of the ECA data set the annual DTR series were tested absolutely i.e. without reference series. Station relocations, changes in measuring techniques and circumstances appear often clearly in the DTR series (Sparks, 1972; Heino et al., 1999). Many of these artificial changes are related to radiation effects on temperature measurements. They have an opposite effect on maximum and minimum temperature and as a result become distinct in the DTR. Natural changes have mostly the same effect on minimum and maximum, only the magnitude can be rather different (Karl et al., 1993; Horton, 1995).
A wide range of methods to test homogeneity is developed (Szalai et al., 1998). Many of these tests are rather similar. Therefore, only three methods are chosen for testing the homogeneity of the annual DTR. The often used Standard Normal Homogeneity Test (SNHT) for a single shift is one of the tests applied to the DTR series (Alexandersson, 1986). Various tests based on adjusted partial sums are described by Buishand (1982), here the Range-test is used. Also the classical von Neumann Ratio is applied (Von Neumann, 1941).
To test the annual DTR series,Yi ( i is the year from 1 to n), it is supposed under the null hypothesis H0 that the Yi's have the same mean. Under the alternative hypothesis HA the SNHT assumes that a shift in the mean is present, although it is not known in advance where in the series this shift actually takes place. Tests on the adjusted partial sums are also designed for situations that jumps in the mean may occur at unknown positions. For the different tests it is further assumed that the Yi's are independent and are normally distributed. The tests are carried out for two periods. The first period ranges from 1910 until 1998 and covers the complete period the ECA focuses on, but not all stations are available for this long period. The second period, 1958-1998, has a maximal data coverage and this period is also used for analysis of climate variability and extremes within the ECA project.


Alexandersson (1986) uses a statistic T(a) to compare the mean of the first a years of the record with that of the last n-a years. T(a) will be small for all a if H0 is true. Whereas large values of T(a) make the HA hypothesis more probable. A possible shift is located at the year A, when T(a) reaches a maximum at the year a=A. The test statistic T0  is defined as:

where is the mean and s the standard deviation of the sample

The null hypothesis will be rejected if Tn is above a certain level, which is dependent on the sample size, see for critical values Alexandersson (1986) and for the 1% level Table 1.

Table 1:
1% critical values (cr) for the single shift SNHT as a function of n (calculated from the simulations done by Jarusková (1994)).

The adjusted partial sums are defined as:

When a series is homogeneous the values of S*k will fluctuate around zero, because no systematic deviations of the Yi's with respect to their mean will appear. A possible shift is present in year K, when the S*k reaches a maximum (negative shift) or minimum (positive shift) for k=K. The significance of the shift can be tested with the 'rescaled adjusted range' R. Which is the difference between the maximum and the minimum of the S*k's rescaled with the sample standard deviation:

High values of R are an indication of shifts (Wallis and O'Connell, 1973; Buishand, 1982).

Von Neumann Ratio
The von Neumann Ratio (N) is defined as the ratio of the mean square successive (year to year) difference to the variance (Von Neumann, 1941):

When the sample is homogeneous the expected value of N   is two. Does the sample contain a shift the value of N  tends to be lower than this expected value (Buishand, 1981). Samples with rapid variations in their mean may yield values that rise above two (Bingham and Nelson, 1981). This test gives no information about the location of the shift. For large n, the distribution of N  tends to a normal distribution (Buishand, 1981).


To illustrate the problems that can arise with homogeneity, a Dutch station from the ECA data set is further analysed. In figure 2 the annual series of the diurnal temperature range at station Eelde Groningen is presented. At least three changes in observation contaminate the series during the last century. The metadata give an indication for a break around 1950, caused by the introduction of a ventilated observation hut in 1948 and -more importantly- a station relocation from the city to the nearby airport in 1951. The effect of a change in sensor height from 2.2 m to 1.5 m in July 1959 can, although less clear, also be seen.

Figure 2:
Annual mean of diurnal temperature range (thin line) at station Eelde Groningen, the Netherlands. The smoothed curve (thick line) is created using the Loess smoother with a time span of 15 years (Cleveland, 1979).

The quality of the station Eelde Groningen was also studied by performing the homogeneity tests as described above. In figure 3a and 3b the results of the SNHT and Range-test are shown for the two periods. For the period 1910-1998 the SNHT gives an extreme in 1950, afterwards the test statistic decreases a little and then stays at a high level until 1960. The maximum value causes a rejection of the null hypothesis significant at the 1% level. As a result the alternative hypothesis which assumes a shift becomes likely. The same conclusion is drawn from the Range-test with a minimum around 1950. In addition the value for the von Neumann Ratio (0.55) is strongly significant which is an indication for non homogeneity.

Figure 3a (above):
Results for the SNHT applied to the DTR series for the period 1910-1998 (left) and for the period 1958-1998 (right) for the station Eelde Groningen. The statistic TA is plotted

Figure 3b (below):
Results for the Range-test applied to the DTR series for the same periods as 3a. The plotted Sk* is rescaled by the standard deviation and the square root of the sample size n.

For the shorter period 1958-1998 both the SNHT and Range-test give much lower values for their test-statistics which are not significant at the 5% level, also the von Neumann Ratio (1.85) is not significant at this level. All test results agree very well with the information obtained from the metadata. Based on the findings above, the pre-1960 part is not considered in further climate analyses within the ECA project, whereas the more recent period is still used.

Another example is given for Brussels (Uccle) in Figure 4. An indication for a break is seen around 1970. Using 1-day changes of daily temperature anomalies Moberg et al. (2000) found a minor shift in the Brussels series in 1969. This finding corresponds with the shift found in the DTR series as detected by the SNHT and Range-test (not shown). According to Moberg et al. this may be caused by the introduction of a closed screen.

Figure 4:
Annual mean of diurnal temperature range (thin line) at station Brussels, Belgium. The smoothed curve (thick line) is created using the Loess smoother with a time span of 15 years (Cleveland, 1979).

For all other stations in the ECA data set the three described homogeneity tests are applied on the annual DTR series. The different tests give similar results. In Figure 5 the summarised outcomes of the tests are presented for the periods 1910-1998 and 1958-1998. For each station the number of the applied tests which are significant at the 1% level is shown. In this way a quick overview is given of the underlying test results. In the period 1910-1998 the majority of the station series is significant at this level for one or more tests and a break seems likely. For the 1958-1998 period more stations seem reliable. The greater part of the stations is not significant for all tests applied, so the null hypothesis is not rejected at the 1% level and consequently shifts in the mean are unlikely. A minority of the stations is significant for all the tests applied. Remarkable is that many of these stations are coastal. A reason for this may be that relocations can have a rather large impact in coastal areas, as a result of the strong temperature gradients.

Figure 5:
Number of tests which are significant at the 1% level. Three tests are applied on the annual DTR series: the SNHT, the Range-test and the von Neumann Ratio.

above: For the period 1910-1998 (number of years >70). below: For 1958-1998 (number of years >30).


In this study annual means of the DTR are tested to identify breaks in the daily temperature series of the ECA data set. Moberg et al. (2000) emphasise that testing homogeneity for daily data is more complex than monthly or annual data. The three tests applied here on the annual DTR series will not account for changes in the variation on daily or monthly bases, but most severe discontinuities will be detected.

For the stations Eelde Groningen and Brussels the DTR test results agree very well with the information extracted from the metadata. For many other stations in the ECA set the metadata information is not readily available. Testing the DTR as described with the SNHT, the Range-test and the von Neumann Ratio may give a good first indication for homogeneity. However, these tests can have problems to distinguish between artificial and natural changes, especially when the latter become rather large. In general, testing homogeneity statistically will not reveal all details about the series. Therefore, to take full advantage of these data, the test results should be used in combination with metadata information. This requires that more station history will be made available for the ECA project. The interpretation of this metadata can best be done in the countries that maintain the stations and archive the series. On the other hand, the value of homogeneity tests increases when consistent methods are applied to the whole data set. For these reasons, improving the homogeneity of the ECA data set will be most successful by an ongoing co-operation between participants.


The ECA project is a joint project of 30 countries. The support of all participants is acknowledged. More information is available at:


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Bingham, C. and L.S. Nelson, 1981. An approximation for the distribution of the von Neumann ratio. Technometrics 23, 285-288.
Buishand, T.A., 1981. The analysis of homogeneity of long-term rainfall records in the Netherlands. KNMI Scientific Report WR 81-7, De Bilt, pp42.
Buishand, T.A., 1982. Some methods for testing the homogeneity of rainfall records. J. Hydrol. 58, 11-27.
Cleveland, W.S., 1979. Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc. 74, 829-836.
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COST Action 0601 
Városklíma 2011 
Climate variability and climate change 
RCM Workshop 2008 
HIRLAM / AAA Workshop 2007 
The preparation of climate atlas 
17th EGOWS Meeting 
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6th Seminar for homogenization 
5th Seminar for homogenization 
Természeti katasztrófák megelőzése, hatásainak csökkentése

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