Homogenization of Temperature Time Series of Western Greece Kolokythas K.V., Argiriou A.A. Laboratory of Atmsopheric Physics, University of Patras, University Campus, GR-265 00, Patras, Greece *corresponding author e-mail:
[email protected]
Abstract Time series of climatic data are the basis in research on climate behavior and climate change. Climatic time series have to be as complete as possible and also as homogeneous as possible, in the sense that their variations should reflect changes in climate and not changes due to other reasons. Nevertheless, there are a number of factors that affect measurements of climatic parameters which may have as impacts abrupt or smother shifts and trends in the corresponding time series. Several methods have been developed in order to detect and correct these non-homogeneities. In this paper the Multiple Analysis of Series for Homogenization (MASH) method is applied to monthly mean temperature time series from a network of meteorological stations in Western Greece aiming at indentifying probable break-points, outliers and trends, and adjusting them in order to have a quality controlled and homogenized temperature time series for the specific area.
1 Introduction A time series of a climatic variable (air temperature, humidity, pressure, wind speed and direction, etc.) is considered homogeneous if its variability is due only to changes of the regional weather and climate. However, collection of climatic data is often exposed to artificial influences such as relocation of weather stations, replacement of observers and / or instruments, changes in the environment or even changes in the observation rules. As recognized and widely accepted that long and reliable observation series are required to address climate change issues and impact studies, the knowledge of any inhomogeneity existing in climatic time series is vital (Aguilar E. et al., 2003). Different statistical tests can be used for the detection of artificial changes – inhomogeneities – of the statistical properties of climatic variables such as longterm averages, trends or standard deviations. Homogenization methods can be
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classified into two groups: absolute and relative ones (Pandžic, K., T. Likso, 2010). In this paper the Multiple Analysis of Series for Homogenization (MASH) method (Szentimrey 2008) – a relative method – is used for the examination of a network consist of 8 WMO weather stations of Western Greece, for the period 1955 – 2003. The aim is to test the homogeneity of the time series, detect probable breakpoints, outliers and trends and correct them in order to obtain a set of temperature data series for the region for a relatively long period (49 years) as precise as possible, without artificial shifts and/or biases, that would give us a more reliable outline of the climate and its provoked changes in Western Greece.
2 Method The MASH method is a relative homogeneity test that does not assume the reference series as homogeneous. Its mathematical principle relies on difference time series which are constructed by subtracting the candidate time series from the weighted reference time series. Since all difference time series are calculated with respect to the candidate series, the breakpoints detected simultaneously in all time series can be attributed to the candidate one. This is achieved by multiple comparisons of a set of optimal difference time series take place each time. This set is presented below:
Z j (t ) X j (t ) i X i (t ) IH j (t ) i IH i (t ) z j (t ) ( j 1, 2, N) (1) i j
i j
In the eq. (1) Ζj are the optimal difference time series, Χj the candidate time series and i X i (t ) the sums of reference series built for the candidate Xj(t). The i j
best weighting factor λi is defined the one which eliminates the variance of difference time series (reduces the noise εΖj(t)) resulting in increasing of the effectiveness of test statistics, and is a vector of the following shape:
1 c c ,ref i Cref
1 1 C T
1 ref c , ref
T
1 ref
c
1C 1
1 (2)
with cc ,ref a covariance vector of candidate and reference time series, and Cref covariance matrix of reference series. The detection of breakpoints is based on the examination of hypothesis for a significance level, taking into account both type one (false detected inhomogeneity) and type two (existence of a real break point that we could not detect) errors.
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3 Stations network and tested time series The MASH method is applied on time series of mean ambient temperatures measured in 8 WMO weather stations (Table 1) of Western Greece belonging to the Hellenic National Meteorological Service (H.N.M.S.), for the period 1955 – 2003. All stations belong to the same climatic type defined as humid Mediterranean (Flokas 1992). Table 1. Description of the characteristics of the meteorological stations Station
WMO Code
Latitude Longitude Ε
Station altitude (m)
Begin End
Years with missing data
Kerkyra (KR)
16641
39°5Ν
19°8
4
1955
2003 -
Aktio (PZ)
16643
38°9Ν
20°7Ε
4
1971
2003 17
Agrinio (AG)
16672
38°6Ν
21°3Ε
47
1956
1968
1970
2003
1970
1987
1989
2003
1957
1957
1959
1965 6
1969
2003
Kefalonia (KF) 16685
Zakynthos (ZA) 16710
38°1Ν
37°7Ν
20°4Ε
20°8Ε
22
3
2
17
16687
38°1Ν
21°3Ε
15
1955
2003 -
Andravida (AD) 16682
37°5Ν
21°3Ε
12
1959
2002 5
8
1956
2003 1
Araxos (RX)
Kalamata (KL)
16726
37°Ν
Ε
21°9
In this work a modified version of the MASH method was applied. The homogenization procedure is divided in two parts. First the parts of the time series with no or very few missing values (1970 – 2003) are homogenized. Then those homogenized parts are merged with the remaining parts of time series (1955 – 1969) where larger data gaps exist. Finally the homogenization procedure is applied on the merged time series, resulting to their overall homogenization. At the beginning, correlation coefficients for all time series are computed based on mean monthly temperatures before homogenization. As shown, time series have in general very good cross correlation, with a mean correlation coefficient equal to 0.87. An exception is the time series of Zakynthos, which doesn’t show so good correlation with those of Kerkyra and Aktio. Therefore, during homogenization procedure Kerkyra and Aktio time series were not considered as reference series for the time series of Zakynthos. Similarly the series of Zakynthos was not considered as reference for the series of Kerkyra and Aktio as well. During the whole procedure, the defined significance level for the test statistics is 0.05. The length of the time series is 49 years (≈50), corresponding to a critical value for test statistics before homogenization (TSB) and after homogenization
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(TSA) of 20.86 (scores over that critical value mean that the tested time series are inhomogeneous, while equal or bellow that value the time series consider homogeneous).
4 Conclusions 1. The total number of the detected breakpoints in all time series varies among stations for the different time scales (monthly, seasonal, and annual). Considering the results of test statistics performed at the final stage of homogenization (TSAs), the examined time series at the end of the procedure appear to be homogeneous. Fig. 1 shows the annual time series of all stations before (top) and after homogenization (down). 2. The majority of time series show a decreasing mean temperature after homogenization. Furthermore the linear trend of the mean temperature of the annual time series of all stations for the period 1955 – 2003 is slightly declining but with a lower slope than before homogenization (Fig. 2). On Fig. 2 are also illustrated the linear regression lines of the total mean temperature before and after homogenization and the corresponding regression equations.
Fig. 1. Top graph: annual time series before homogenization. Down graph: annual time series after homogenization.
3. Examining the time series in relation to the total mean, the period 1955 – 2003 can be divided into three parts. In the first part, from 1955 till the beginning of 1970, the mean temperature of all stations is higher than the total mean. In the
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second one (early 1970 to middle 1990) – which differs among stations – the mean temperature is lower than the total mean, while in the last part (common for all stations) the temperature has a constantly increasing trend. This division is also represented by the two dashed lines in Fig. 2.
Fig. 2. Variation of the mean temperature (mean of the means of all time series) for the period 1955 – 2003. Dotted line presents the variation of total mean before homogenization and solid line after homogenization. Also the corresponding linear regression lines with their equations are shown. 4. In Fig. 3 there are four graphs representing the anomalies of mean temperature
of the complete network for each season together with the anomalies of the annual mean. From these graphs it appears clearly that the mean temperature of the summer time series has almost the same variability as the annual mean. This fact reveals that the influence of the summer temperature on the total mean temperature may account for the total temperature fluctuation.
Fig. 3. Anomalies of the total mean temperature (black dashed line) and of the mean temperatures of all time series per season for the period 1955 – 2003.
Based on these results, it is estimated that the explicit and constant increasing trend of summer temperature as well as the lack of another trend (of the same magnitude) in the three other seasons, are the main reasons causing the abrupt in-
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crease of the annual mean temperature from the beginning of 1990s, in all time series. This is also supported by a number of scientific works studying the temperature variation in Greece for the last 100 years (Proedrou et al. 1997, Feidas et al. 2004, Akilas et al. 2005).
5 Discussion The correction of time series of climatic data may be a difficult and demanding work. However, taking into account the inhomogeneities these time series probably have, this work is considered to be of major importance regarding research on climate change. The homogenization of climatic time series, except for the detection and adjustment of inhomogeneities, leads in the filling of missing values, either sparse or systematic. So, the completed and homogenized series may be used for the better and more reliable studying of the climate of a significant region, as reference time series for the homogenization of other series, or even for comparing homogenization results with those of previous or future works. Acknowledgments The authors would like to thank T. Szentimrey and M. Lakatos of the Hungarian Meteorological Service for their helpful and useful comments for better understanding and operating of M.A.S.H. used in this work and E. Anadranistakis and A. Mamara of the Hellenic National Meteorological Service for providing all the necessary data.
References Aguilar E, Auer I, Brunet M, Peterson TC, Wieringa J (2003) Guidelines on climate metadata and homogenization. World Meteorological Organization WMO/TD No. 1186. Akilas Ε, Likoudis S, Lalas D (2005) Climatic change in Greek region. Analysis of observations: trend of the late 100 years. Observatory Climatic Changes, National Observatory of Athens, Chapter. 5, p. 23-38. Flokas A (1992) Meteorology and Climatology, Zitis Publishers, Thessaloniki, Greece, 1992. Feidas H, Makrogiannis T, Bora-Senta E (2004) Trend analysis of air temperature time series in Greece and their relationship with circulation using surface and satellite data: 1955-2001, Theor Appl Climatol 79, 185-208. doi:10.1007/s00704-004-0064-5 Pandžic, K., T. Likso (2010), Homogeneity of annual air temperature time series for Croatia, Int. J. Climatol. 30: 1215-1225, DOI: 10.1002/joc.1922. Proedrou M, Theoharatos G, Cartalis C (1997): Variations and Trends in Annual and Seasonal Air Temperature in Greece Determined from Ground and Satellite Measurements. Theor Appl Climatol 57. doi:10.1007/BF00867977 Szentimrey T (2008) Multiple Analysis of Series for Homogenization (M A S H v3.02).
