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Stepánek P.1,   Brázdil R.1,   Kveton V.2
1 Department of Geography, Masaryk University, Kotlárská 2, 611 37 Brno, Czech Republic
2 Czech Hydrometeorological Institute, Na Sabatce 17, 143 06 Praha, Czech Republic


Monthly, seasonal and annual air temperature series from 95 climatological stations in the Czech Republic during the period 1961-1999 were tested for relative homogeneity using the Standard Normal Homogeneity Test by Alexandersson and the Bivariate Test of Maronna and Yohai. Reference series were created by means of averaging all the series. Inhomogeneities detected were adjusted only in those cases where they have been documented by metadata from the individual stations or in case of "undoubted" inhomogeneities (i.e. inhomogeneities not documented by station metadata, but following clearly from the homogeneity tests). From 93 homogenized series, a mean temperature series for the Czech Republic was calculated and further analyzed. The present state of homogenization of air temperature series from before 1961 was described as well. AnClim software for testing homogeneity and time series analysis is presented.


An investigation of climatic change must be based on a homogeneous climatological time series. A series is defined to be homogeneous "if its variations are caused only by variations in weather and climate" (Conrad and Pollak, 1962). It is well known that long climatological series can also be influenced by non-climatic factors. They are connected with station relocation, changes in observational procedures, instruments etc. A variety of tests have been developed for detecting and adjusting inhomogeneities in climatic time series. Almost all of these tests are based on testing relative homogeneity. A series is defined to be "relatively homogeneous with respect to a synchronous series at another place if the differences (ratios) of the pairs of homologous averages represent a series of random numbers, which satisfies the normal law of errors" (Conrad and Pollak, 1962).
This paper presents results and experience with homogenization of selected air temperature series from the Czech Republic during the period in question.


Mean monthly air temperatures from 95 climatological stations (Fig. 1) in the Czech Hydrometeorological Institute database for the period 1961-1999 were selected for homogenization and subsequent analysis of temperature patterns across the Czech Republic. The condition for selecting individual stations was that the number of missing monthly values for a particular station did not exceed 16 (i.e. less than 1.5 year). Missing monthly temperatures (0.45% of all monthly values) were interpolated according to a reference series, which was created as a simple arithmetic mean from all series. The mean value of correlation coefficients between the series of individual stations and the reference series was 0.964 (a maximum value of 0.997 and a minimum value of 0.814).

Figure 1:
Climatological stations (circles) selected for homogenization of temperature series in the Czech Republic from 1961-1999

Homogeneity testing was performed for the monthly, seasonal and annual series of the selected stations. All series were tested for relative homogeneity using both the Standard Normal Homogeneity Test for single shift (SNHT - Alexandersson, 1986) and the Bivariate Test (BT - Maronna and Yohai, 1978) using the "AnClim" software package (Stepánek, 2000). The arithmetic mean of temperatures of all stations was used as the homogeneous reference series.
The results of the two tests differ in only a few cases. At the significance level a = 0.05, inhomogeneities were found in 31% (SNHT) or 33% (BT) of the 114 months analyzed. For the 475 seasons and years analyzed, inhomogeneities were found in 50 or 51% of the cases, respectively. From the distribution of inhomogeneities, within individual months, it follows that they appear mostly during the summer months. The lowest occurrence of inhomogeneities was found in the winter months (four times less often than in the summer months).
Adjustment was made for those temperature series in which years of statistically significant inhomogeneities, as indicated by the tests, were clearly related to station metadata (such as relocation). Metadata, however, seldom includes all the changes taking place at a given station. So adjustment was also carried out for cases of clearly "undoubted" inhomogeneities, which, although not evident in the metadata, were unambiguously indicated by the results of tests and were physically justified (see Brázdil and Stepánek, 1998). For example, if an inhomogeneity year of the candidate station was indicated for the major part of the monthly as well as seasonal and annual series, additional correlations were taken into account between the candidate and reference series, as well as fluctuations in differences between these two series. Complementary information was provided by the SNHT for double shift (Moberg and Alexandersson, 1996) and the two-phase regression test (Easterling and Peterson, 1995).
For further analysis, two stations were excluded: Prague-Klementinum, which is strongly influenced by the intensification of the urban heat island (see Brázdil and Budíková, 1999), and Svetlá Hora, where the observations appeared to be of lower quality.
Twenty-four stations were involved in the homogenization. Despite adjustments (which were performed only in the above mentioned cases), 20% (SNHT) or 21.5% (BT) months remained uncorrected (in the case of seasonal or annual means, the figures were 38 or 40% respectively of seasons and years uncorrected). These homogeneous series were used for the calculation of a mean temperature series for the Czech Republic.
An open question in homogenization remains what is the possible effect of the transition to automatic temperature measurements, which since 1997 has been gradually implemented in the Czech Republic. Namely, in almost all cases manual observations were replaced by automatic ones without any comparative measurements studying the impact of such a change. At the present, it is too early to judge the impact of this replacement because the series are still too brief.
As was pointed out, the proportion of uncorrected inhomogeneities in these series, even after the adjustment, is still very large. But complete adjustment of temperature series based on the test results and without recourse to metadata, cannot be accepted. To estimate possible error resulting from this fact, a new hypothetical "totally homogeneous" mean series for the Czech Republic was calculated from 93 temperature series, in which all adjustments based on the homogeneity tests were performed. This series was subsequently compared with the mean temperature series calculated only from partly adjusted series. The two series differ for individual years by a maximum of 0.09şC in April and September (Fig. 2b), for the other months, however, mostly by 0.05şC. The differences between two mean annual temperature series (Fig. 2a) were also negligible (maximum 0.03şC). This analysis shows that since 1961, temperature fluctuations throughout the Czech Republic were essentially the same in the partially-and the fully-homogeneous series. It confirms the fact that series averaged from partly-homogenized series can be regarded as homogeneous. It seems that the homogenization has a relatively smaller effect when working with averages from so many stations.

Figure 2:
Differences (°C) between averaged temperature series calculated from original and partly-homogenized series for annual values (a) and for April and September monthly values (b).


From the partly homogenized temperature series of 93 stations, a series for the Czech Republic was calculated a) by averaging the data of all 93 stations, and, b) by averaging temperatures to 21 grid points with a step of 1° longitude and 0.5° latitude. Temperatures at the grid points were calculated using the weighted mean from station data within a radius of 50 km from the grid point, using reciprocals of the distance as weights. Differences between the two calculated mean series are negligible (for the mean annual temperatures, they do not exceed 0.04°C in individual years). For further analysis only the first, simple series was used.
Figure 3 shows the fluctuations of seasonal and annual mean temperature series for the Czech Republic during the period 1961-1999. The mean series exhibits statistically significant increases for January, May, July, August, all seasons (except autumn) and the year (Table 1). Further, the air temperature series of the Czech Republic were compared with the series for the Northern Hemisphere. A maximum entropy spectral analysis was also performed (statistically significant eight-year and 2.7-year cycles). Consequently, a multiple linear regression model was applied to study possible natural (solar output changes, volcanic activity, ocean-atmosphere interactions) and anthropogenic (increasing greenhouse gases and sulfate aerosols, ozone depletion) forces within the temperature series (for more details see Brázdil et al., 2000a, b).

Figure 3:
Fluctuations of air temperature anomalies (°C; reference period 1961-1990) and the linear trend (dotted line, numbers in the graph - values of the trend in °C/decade, bold - significant for a=0.05) for the seasons and the year in the Czech Republic in the period 1961-1999. All series smoothed by a 10-year low-pass Gaussian filter (Brázdil et al., 2000b).


A database of stations with long-term air temperature series for the Czech Republic was developed at the Department of Geography, Masaryk University, Brno. The aim of this project was to collect long-term air temperature series, homogenize them and study temperature fluctuations within the Czech Republic as well as the influence of various forces in temperature series during the period under study.
The number of climatological stations, which were available through the climatological yearbooks released by the Czech Hydrometeorological Institute (before 1918, the Central Institute for Meteorology and Geodynamics, Vienna, after 1918, the National Meteorological Institute, Prague and the Hydrometeorological Institute after 1954), is shown in Fig. 4. The number of stations varies significantly as the result of several reorganizations of meteorological services, political changes, world wars etc. Hydrological stations were not included in this summary even if the air temperature data were used from their records when they had long-term measurements. From Fig. 4, it follows that about 100 climatological stations were available from the last decade of the nineteenth century through World War I, when the number of stations dropped to fifty. Beginning in the 1920s, there was an increase. During the 1940s and 1950s, there was a sudden shift to a higher number of stations (with a gap at the end of the World War II). Since 1961 the number of stations has been more or less the same - about 200.

Figure 4:
Number of climatological stations in the Czech Republic since 1864 (according to climatological yearbooks)

From the climatological as well as hydrological stations, those with a period of air temperature measurements covering at least twenty years were selected. Figure 5 shows how the number of selected stations changed over time. There are 101 stations for Bohemia, 35 for Moravia and 40 for Silesia in the database. From the 1850s, about ten stations were available. There was then an increase in the number of stations from the 1870s to the beginning of the twentieth century. Since that time, about 70 stations were utilizable. Another increase followed World War II, reaching a total of about 120 station in the 1960s and to a maximum of over 120 stations in the 1970s. Figure 6 shows the distribution of the number of stations with respect to the length of temperature series. For instance, there are 16 stations with air temperature measurements longer than 100 years, 22 stations with measurements longer than 80 years etc.

Figure 5:
Number of collected stations in the database

Figure 6:
Number of temperature series of a given length in the database

At present the homogenization of the selected temperature series is being processed. The methodology of the homogenization of monthly air temperatures has three steps:
(i) "Raw" homogenization is performed to eliminate clear inhomogeneities from the series. In this initial step, every series is compared to several surrounding stations and the most evident shifts in the series are corrected.
(ii) Anomalies are created. All the series are normalized to the period 1961-1990. If the measurements are not available from this period, then the series is adjusted to the average of several highly correlated neighboring stations for another common thirty-year period.
(iii) A reference series is created as an arithmetic mean of all the stations. With respect to this reference series, all the series (anomalies) are tested for relative homogeneity.


For homogenization and time series analysis, the AnClim software was created by Petr Stepánek at the Department of Geography, Masaryk University, Brno (Fig. 7). The aim was to put into one software package the methods most often used for the analysis of climatological time series data. In AnClim, tools for the visualization of data, calculating basic statistical characteristics (including testing of normal distribution, randomness etc.), a variety of tests for relative homogeneity testing (Table 2), tools for correlation and spectral analyses and for the filtering of time series are all available. As for SNHT, many modifications of the test are available, such as SNHT for single shift, for double shift, for trend, for two standard deviations, as well as a tool for creating reference series from several neighboring stations (Moberg and Alexandersson, 1996).

Table 2:
Homogeneity tests included in the AnClim software and their sources

For spectral analysis, AnClim includes periodogram, the Blackman and Tukey method, Maximum Entropy Spectral Analysis (MESA) and dynamic MESA. Filters for smoothing time series - low-pass filters, band-pass filters and high-pass filters are also available. Finally, there is also a tool for study of influence of force factors, using multivariate linear regression.
The software is freely available via the internet
( or

Figure 7:
AnClim Software

Air temperature series from 95 selected stations within the Czech Republic for the period 1961-1999 were tested for relative homogeneity using SNHT by Alexandersson (1986) and the Bivariate Test of Maronna and Yohai (1978). About one-third of the monthly series was found to be inhomogeneous (in the case of seasonal and annual data, this figure was about one-half). After adjustments performed only according to metadata and in the case of an "undoubted" inhomogeneity, the number of inhomogeneities only dropped to about 20% (or 40% respectively). In any event, possible bias due to uncorrected inhomogeneities is negligible when creating a mean series for the Czech Republic from all the series. This averaged series can be regarded as truly homogeneous and can be used for further analysis.
The homogenization of the air temperature series for the Czech Republic during the period prior to 1961 is being processed at present. Results will be available in future. Only the initial tasks in this homogenization process were discussed in this paper.
Finally, the AnClim software, a powerful tool for homogenization and time series analysis, was presented.

Acknowledgement: The work of R. Brázdil and P. Stepánek was realized with the financial support of the Grant Agency of the Czech Republic in awarding Grant No. 205/98/1542.


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