This article focuses on extreme events of high and low temperatures and precipitation and their amplitude and frequency changes over the last 50 years in Greece. Sixteen climate indices have been calculated and their trends were analysed to identify possible changes over a network of measurement stations covering the region quite homogeneously. Furthermore, the changes in the probability distribution of the indices were examined. In addition, we analyzed the temporal evolution of the amplitude and frequency of extreme events through the parameters of extreme value distribution. The temporal stability of the fitted distributions is examined and the spatial distribution of their trend as well as the changes in the 5-year return levels is investigated.
The assessment of extreme events and their predictability is one of the major challenges of the climate change community. Extreme events are by definition rare. Depending on their severity, the recovery of the local/regional climate system from an extreme event could even take several years (Ciais et al., 2005). Apart from the significant impacts on the ecological systems, the social and the economic sector undergo long-term effects as well.
Physically, the interaction of these, in most cases, low-frequency events with synoptic systems and human-induced forcing is not well understood yet. Sophisticated models of the climate system such as the Global Circulation Models (GCM) are currently the state of the art in deterministic modelling of the climate system. However, the computational resources they require limit their resolution to scales not able to represent extreme climatological processes. Simulations in finer resolution with Regional Climate Models (RCM) driven by GCMs are subject to large uncertainties resulting in a variance in the model-predicted changes in the extremes that is larger than the natural variability (Kjellström et al., 2007). In addition, currently, there does not exist a multivariate spatiotemporal theory that can model the distribution of extremes in complex systems such as our climate and answer whether they occurred randomly (representing pulse-like events, i.e. short and intense deviations from the background climate) or are due to non-stationary phenomena.
However, there exists a basic theory for extremes that can provide simple statistical analyses related to extremes. Extreme value theory (EVT) is the branch of statistics that describes the behaviour of the largest observations in a dataset. Although it was established in 1928 (Fisher and Tippett, 1928), most of its applications were in the field of finance until recently. Up to the third assessment report of the IPCC (IPCC 2001), there was only one published report with regard to the analysis of climate extremes by means of the EVT (Katz, 1999); since then, the literature is growing (Katz et al., 2002; Naveau et al., 2005; Nogaj et al., 2006).
In addition, in 2001, the climatic community (coordinated by the joint WMO Commission for Climatology and the Expert Team on Climate Change Detection, Monitoring and Indices (ETCCDMI) of theClimate Variability and Predictability (CLIVAR) project (World Climate Research Programme)), has defined indices for temperature and precipitation extremes to gain insight to changes in extremes. Twenty-seven indices were defined based on daily temperature values (minimum, maximum) or daily precipitation amount. Some indices are calculated on the basis of station-related thresholds while others are based on fixed thresholds or absolute peak values. Upon their definition in 2001, those indicators have been evaluated in global studies (Frich et al., 2002; Alexander et al., 2006) and several regional studies (Manton et al., 2001; Peterson et al., 2002; Yan et al., 2002; Klein Tank et al., 2003, 2006; Aguilar et al., 2005; Kostopoulou and Jones, 2005; Vincent et al., 2005; Zhang et al., 2005a; New et al., 2006).
The objective of this article is to provide a comprehensive analysis of observed changes in temperature and precipitation extremes over Greece, by applying both approaches for the study of extremes. The analysis is focused on the peak maximum and minimum values as well as the peaks over (below) the 95th (5th) percentile. In particular,
1.The behaviour of extreme temperatures and precipitation events is analysed and their changes are quantified with respect to the ETCCDMI indices as well as the calculated 5th and 95th percentile indices.
2.The non-stationarity of the amplitude and frequency of the extremes is modelled in terms of the EVT.
This article is organized as follows. We describe the sources of daily data in Section 2 including descriptions of data quality control. In Section 3, we give a brief outline of the climatic indices definitions and the principles of EVT followed by a detailed account for the analysis of the indices data, including trend computation and return level estimation. Results are presented in Section 4. We offer a detailed discussion of the results in Section 5.
A total number of forty ground-based meteorological stations covering Greece were initially examined in this study. A data quality control was carried out for inhomogeneity (Peterson et al., 1998); in addition, we posed the requirement of at least 30 years of data per station. This reduced the number of available stations to twenty-three (Figure 1). In 19 of them, there were no missing data for daily temperature and precipitation values for the examined period (1955–2002). The missing data for the remaining four stations ranged between 3 and 10%.
3.1. Analysis with indices of extremes
The ETCCDMI indices (http://cccma.seos.uvic.ca/ETCCDMI/list_27_indices.shtml) are derived from daily temperature (maximum and minimum) and precipitation data. As stated in Alexander et al. (2006), The indices were chosen primarily for assessment of the many aspects of a changing global climate which include changes in intensity, frequency and duration of temperature and precipitation events. They represent events that occur several times per season or year giving them more robust statistical properties than measures of extremes which are far enough into the tails of the distribution so as not to be observed during some years. The indices (Table I) can be clustered as follows (the five non ETCCDMI indices calculated are given in italics):
1.Indices based on station-related thresholds: cold nights (TN05p), warm nights (TN95p), cold days (TX05p), warm days (TX95p) and very wet days (R95p).
2.Indices based on fixed thresholds: summer days (SU25), tropical nights (TR20) and number of heavy precipitation days (R10 mm).
3.Non-threshold indices: maximum daily maximum temperature (TXx), maximum daily minimum temperature (TNx), minimum daily maximum temperature (TXn), minimum daily minimum temperature (TNn), maximum 1-day precipitation amount (RX1day), annual precipitation total (PRCPTOT), diurnal temperature range (DTR) and annual contribution from very wet days (R95pTOT).
Table I. Definition of indices for temperature and precipitation extremes
Annual total precipitation when RR > 95th percentile
Max 1-day precipitation amount
Monthly maximum 1-day precipitation
Number of heavy precipitation days
Annual count of days when RR ≥ 10 mm
Annual total wet-day precipitation
Annual total precipitation in wet days (RR ≥ 1 mm)
Precipitation fraction due to R95p
Quotient of amount on R95p days and total amount
The ETCCDMI indices analyzed in this paper were computed with the RClimDex software (http://cccma.seos.uvic.ca/ETCCDMI/RClimDex/rclimdex.r; Zhang et al., 2005b). The percentile indices Tn05p, Tn95p, Tx05p and Tx95p were calculated with a modified version of the RClimDex while R95pTOT, defined as 100 × R95p/PRCPTOT, as well as all the analysis have been carried out with scripts written in Matlab.
The sixteen calculated indices were then analyzed in terms of their trend and their statistical distribution. In the present analysis of the climatological time series, we seek to detect climatic changes from one averaging period to another. In terms of detection and interpretation, this is straightforward when using linear trend analysis. In addition, the results could be directly compared with similar global and regional studies. Hence, the trend of each of the extreme indicator time series is tested for statistical significance through a nonparametric Mann–Kendall tau test (Sen, 1968) for each station separately. Then, the full period 1955–2002 is divided into two sub-periods (1956–1978, 1979–2002) and the probability density functions (pdfs) are calculated for each indicator and sub-period. A two-tailed Kolmogorov–Smirnov test was applied to test whether the pdfs are significantly different. Finally, we calculated the aggregated anomaly index (with reference to the base period 1961–1990) over the domain for each indicator and we present the results only for the regionally averaged anomaly indices that exhibit a significant linear trend (through a Mann–Kendall test). The relationship between the annual indices and selected monthly global climate indices, corresponding to documented teleconnections, is then investigated by means of lag-correlation analysis. The significance of the calculated correlations on the detrended time series is examined with a t-test using the effective degrees of freedom (i.e. corrected for the presence of autocorrelation in the time series).
3.2. Analysis with EVT
In this section, we model the tail of the distribution of precipitation and temperature extremes for each station separately. Annual maximum temperature and precipitation are modelled through the three-parameter GEV distribution while peaks over threshold (POT) are modelled through the two-parameter GPD distribution.
3.2.1. Generalized extreme value distribution
The family of extreme value distributions is the one to study the limiting distributions of the sample maxima, similar to the normal distribution that is the important limiting distribution for sample sums or averages as summarized in the central limit theorem. This family can be presented under a single parameterization known as the generalized extreme value distribution (GEV).
The theorem of Fisher and Tippett (1928) is in the core of the EVT. The Fisher–Tippett theorem suggests that the asymptotic distribution of the maxima belongs to a Fréchet, Weibull, or Gumbel distribution, regardless of the original distribution of the observed data. Therefore, the tail behaviour of the data series can be estimated from one of these three distributions. The flexibility of the GEV to describe all three types of tail behaviour makes it a universal tool for modelling block (e.g. annual) maxima, which converge to:
The parameter µ represents the location parameter while σ is the scale parameter. The shape parameter ξ describes the tail behaviour of the maximum distribution. If ξ is negative (Weibull), the upper tail is bounded. If ξ is zero, this corresponds to the Gumbel case (all moments are finite). If ξ is positive (Frechet), the upper tail is still unbounded but higher moments eventually become infinite. These three cases are termed ‘bounded’, ‘light-tailed’, and ‘heavy-tailed’, respectively (the larger the shape parameter, the more heavy-tailed the distribution).
3.2.2. Generalized Pareto distribution
In an extreme value context, data points are by nature scarce. This means that the uncertainty is large. Hence, any approach that reduces this uncertainty is very valuable. From the mathematical point of view, such a strategy involves modeling exceedances above a large threshold instead of working with maxima. From the climatological point of view, we are not only interested in the maxima of observations, but also in the behaviour of large observations that exceed a high threshold. Indeed, the modelling of only annual maxima is a wasteful approach to extreme value analysis if all the samples are available.
The definition of ‘large exceedances’ is clarified in terms of a probability theorem. The theorem by Balkema and de Haan (1974) and Pickands (1975) shows that for sufficiently high threshold u, the distribution function of the excess (i.e. the distribution of large exceedances above some threshold u) is not arbitrary but it may be asymptotically approximated by the generalized Pareto distribution (GPD) such that, as the threshold gets large, the excess distribution Fu(y) converges to the GPD which is:
where the random variable x now represents the exceedance above u and the parameter σ can be defined in function of the GEV parameters (µ, σ, ξ) as σ = σ+ ξ(u − µ). Practically, this means that one may find a threshold u such that the exceedances follow approximately a GPD (the criteria to choose u are based on selection methods such as the mean excess function, the thresholds versus parameters plot, etc.). Comparing Equations (1) and (2), we note that ξ is the same shape parameter and has the same interpretation for the GPD and GEV distributions. Only the scale parameter σ is different.
The GPD embeds a number of other distributions. When ξ> 0, it takes the form of the ordinary Pareto distribution (heavy tailed). When ξ = 0, the GPD corresponds to exponential distribution and it is known as a Pareto II type distribution for ξ< 0.
The model parameters for GEV and GPD were obtained by implementing a maximum likelihood estimation procedure. The analysis of extremes with EVT has been performed with scripts written in Matlab, utilising the EVIM toolbox in several cases (Gençay et al., 2001).
3.2.3. Local climate sensitivity coefficients
Local climate sensitivity coefficients are calculated with reference to the return values of the fitted EVT distribution. Mathematically, rl is the return level associated with the return period T whenever the level rl is expected to exceed on an average once in every T years. Return levels are easily calculated after estimating the GEV/GPD parameters. In this article, T is chosen to be equal to 5 years. Hence, the 5-year return level is the value that has less than 20% probability of occurrence in any year. An increase in the 5-year return value (rare extreme) between present and past climate reveals that the present day 5-year return value corresponds to extremes with a return period n > 5 years under past climate.
Initially, we present trend analyses for the temperature and precipitation indices, including changes in the probability distribution of the indices. Subsequently, we model the tail of the distribution of temperature and precipitation and investigate the changes in the return values of extreme events.
4.1. Changes in the indices of extremes
The results are presented in Figures 2–5. Figure 2 shows the trend of each examined index per station for the period 1956–2001, with the filled circles indicating significant linear trend (type I error = 0.05). Figure 3 shows the annual probability distribution functions for the indices presented in Figure 2. Changes in the probability distributions of each index are examined for two 23-year periods, i.e. 1956–1978 and 1979–2002. Figure 4 shows the trend of the regionally averaged anomaly (relative to the 1961–1990 value) index for the indices that demonstrate a significant linear trend while Figure 5 presents their relationship with global climatic indices through lag-correlation analysis. A summary of the results is given in Table II.
Table II. Summary results for the indices of extremes showing: (a) the time of the peak lag correlations with the large scale climate indices (0:current year, − 1:previous year), (b) the percentage of stations with significant annual trends, (c) the regional trend, (d) whether the probability distributions differ between 1956–1978 and 1979–2002
Correlation with Global Scale Climate Indices
All trends are statistically significant at 95% level of significance. The values in bold are statistically significant at 99% level of significance.
% + ve
% − ve
Diurnal temperature range
Very wet days
− 1.0 mm/year
Max 1-day precipitation amount
Number of heavy precipitation days
Annual total wet-day precipitation
Precipitation fraction due to R95p
4.1.1. Local trend and probability distributions
The PRCPTOT has decreased significantly at almost 44% of the stations as shown in Figure 2 and the results are presented in Table II. Locally (at the station scale), there have been significant decreases of nearly 10 mm per year at many sites. In terms of the probability distributions (Figure 3), the total annual precipitation has shifted (i.e. mainly change in the mean) towards drier conditions. Similarly, there have been significant decreases in 44% of the stations of up to 3.5 days per decade in the number of days in a year with heavy precipitation (R10mm). Analogous patterns occur also for very heavy precipitation days (R20mm) and extremely heavy precipitation days (R25 mm) (not shown in Figure 3). The largest significant negative trends for PRCPTOT and R10mm are found for western Greece, which receives the highest totals of annual precipitation. Similar to PRCPTOT, the observed reduction in R10mm is also due to a shift in its pdf. The reduction in the total precipitation is linked to a rising trend in the hemispheric circulation modes of the North Atlantic oscillation (NAO) (Feidas et al., 2007) that results in fewer rain days due to an increase in the frequency and persistence of anticyclones over the Mediterranean (Maheras et al., 1999; Alpert et al., 2002; Feidas et al., 2004).
The PRCPTOT from very wet days (R95P) indicates decreased precipitation between 1955 and 2003. The generally downward trend locally reaches values of 4 mm per year at some stations. Furthermore, a well-identified reduction in the upper bound of the R95P distribution is observed. Negative trends also appear for the extremely wet days (R99P, not shown). Unlike R95P, the percentage contribution from very wet days to the annual precipitation total (R95pTOT) exhibits increased variability; it is significant only at two of the stations exhibiting positive trend (including Athens). The warming observed in the next section coupled with the finding that mainly in Athens we find increases in heavy precipitation could be attributed to the urban heat island effect (Nastos and Zerefos, 2007).
The peak annual precipitation (RX1D) is negative at the two thirds of the stations; however, it is locally significant only at 13% of the stations. This lack of significance is due to the large amount of interannual variability as was already seen for R95pTOT. Comparing the differences in the distributions of RX1D for the two periods, we find an asymmetry in the changes of the tails and the most probable value of the distribution. Specifically, we find a small decrease in the intensity of the most probable value coupled with an increase in its frequency in the second period. In addition, both tails of the distribution shifted towards larger values in the second period. Similar to R95P and R95pTOT, the station of Athens has observed an increased number of extreme precipitation events.
Mixed temperature indices
The diurnal temperature range (DTR) demonstrates a decrease at the majority of the stations, being significant at almost 40% of the cases (Table II). A notable shift exists for the distribution of the DTR coupled with a small decrease in its variance.
The occurrence of cold nights (TN05p) and warm nights (TN95p), i.e. the percentile-based indices, is examined now. Approximately, 74% (26%) of the stations shows a significant increase (decrease) in the annual occurrence of warm nights (cold nights) (Table II). A direct comparison of TN05P and TN95P trend for each station separately shows that the increase (decrease) in TN95P is accompanied with a decrease (increase) in TN05P, indicating a shift in minimum temperature towards warmer conditions for the majority of the stations. This shift in minimum temperature is clearly observed in Figure 3, especially for TN95P. The presence of cold nights shows decreased frequency and intensity while warm nights can be associated with a warmer climate. This warming occurs in summer and is physically linked to the weakening of the Etesian winds because of the less frequent expansion of the low over the southeastern Mediterranean (Feidas et al., 2004).
The absolute temperature index TNX (maximum daily minimum temperature) exhibit a similar pattern to TN95P. Approximately 56% (39%) of the stations shows a significant increase in the maximum (minimum) daily minimum temperature (Table II). The distribution of TNX does not show a simple shift in the distribution like TN95P, but it also demonstrates an increase in the variance of the peak minimum temperature affecting particularly the upper limit of TNX for the most recent 23-year period.
An even more coherent pattern is evident for the threshold index TR20 (annual number of tropical nights) that possess significant positive trend at 65% of the stations, resulting in a notable increase of the upper bound of its distribution.
The summer day counts (SU25) show an increase over the domain that is locally significant at 35% of the stations. This increase is observed as a shift in the distribution of summer days.
Results from TX05P (cold days) and TX95P (warm days) have generally lower significance in comparison with TN05P and TN95P. Small differences between the distributions for the occurrence of warm days (Figure 3) are seen in the kurtosis that is increased in the latter period indicating that mostly the variance is due to infrequent extreme deviations. There is also an indication for an increase in the number of cold days. According to Maheras et al. (2000) and Feidas et al. (2004), the continuing cooling during the winter is due to an increase in the frequency and duration of high-pressure systems over the central Mediterranean and the Balkans.
Following TX05P and TX95P, the observed trends for TXN and TXX (minimum/maximum daily maximum temperature) are insignificant. In terms of the TXX, we observe a shift in the lower tail of the distribution [TXX is greater than 32 °C (30 °C) in the second (first) period] accompanied with a decrease in its variance. Comparing the distributions of TNX and TXX, we see that warming affected the lower tail of TXX and particularly the upper tail of TNX.
4.1.2. Regional trend and global climatic indices
Four out of the eleven temperature indices demonstrate significant regional changes over the 1956–2002 period, namely, TN95p, TNX, DTR and TR20. A clear and coherent increase in minimum temperature (Figure 4) is evident over the domain especially after the mid 1980s, in agreement with previous regional studies (Kostopoulou and Jones, 2005) as well as global studies (Alexander et al., 2006). Trends in the maximum temperature are of lower significance and magnitude (due to generally fewer stations having significant changes), making inferences more difficult.
Regionally, the annual number of warm nights (TN95p) has increased by about 5 days since 1955. Both TN95p and TN05p (not shown) indices reach critical values around the mid 1970s, which corresponds to changes in mean global temperature (Jones et al., 1999; Folland et al., 2001; Jones and Moberg, 2003) and in mean regional (Greece, Eastern Mediterranean) temperature (Repapis and Philandras, 1988). Repapis and Philandras (1988) showed that eastern Mediterranean air temperature time series follow the Northern Hemisphere secular trend from the late nineteenth century to the 1970s. Nevertheless, the warming trend of the last 30 years that is well documented for the Northern Hemisphere and the global average appears only since the early 1990s in the eastern Mediterranean region and Greece in particular (Saaroni et al., 2003; Feidas et al., 2004; Repapis et al., 2007). In fact, only positive anomalies occur for the annual occurrence of warm nights since 1985.
The annual number of tropical nights (TR20, not shown) is increasing over the domain with a rate of 3 days per decade. Furthermore, TNX increased by nearly 1.5 °C between 1955 and 2003. Those three indexes (TN95P, TNX, TR20) have similar functional form when regionally averaged and clearly indicate a change in the minimum temperature around the mid 1980s related to anthropogenic forcing (Christidis et al., 2005). DTR is also decreasing over the region at a rate of 0.16 °C per decade, consistent with the faster warming of the minimum over the maximum temperatures.
The PRCPTOT has decreased significantly over the area during the second half of the twientieth century. Regionally, the annual rainfall amount is approximately 200 mm less in comparison with 1950 as shown in Figure 4. Moreover, the discrepancy recorded after the 1980s is linked to the NAO that has remained in a positive extreme phase (Hurrell et al., 2003). A similar pattern is observed for the heavy precipitation (R10mm), with the regionally averaged decrease being 1.3 days per decade. Finally, the significant downward trend for R95p has a regional average of 1.0 mm per year (i.e. the total annual precipitation in very wet days is 50 mm less in comparison to 50 years ago).
The changes over the Atlantic Ocean are well documented as being related to changes in temperature and precipitation for the Meditteranean region (Hurrell, 1995). Moreover, links between tropical SSTs and extratropical climate have become well established in recent years (Mathieu et al., 2004; Wu et al., 2007). Figure 5 shows the existence of significant lagged correlations (smoothed with a loess filter (Cleveland, 1979)), between the indices of temperature extremes and the NINO12 index (http://www.cpc.noaa.gov/data/indices/sstoi.indices) (SST anomalies over the region 90W-80W, 10S-0). The number of cold nights in a year over the examined area (as well as the cold days, the minimum TN, the minimum TX and the summer days) is related to the SST changes over the NINO12 region in the spring of the previous year providing a simple way for their prediction of many months in advance (e.g., Nicholls et al., 2005). Similar relations are shown between PRECTOT (and R10mm) with the NAO index (http://www.cgd.ucar.edu/cas/jhurrell/indices.html) (normalized pressure difference between Azores and Iceland) (bottom row). Here the total annual precipitation, as well as the annual number of heavy precipitation days, is related to the SLP changes in February of the same year (Kioutsioukis et al., 2006).
4.2. Tail modelling through EVT
4.2.1. Temporal stability of the parameters
The estimation of the GEV parameters is straightforward. However, for the POT, one has to define a sufficiently high optimal threshold, such that the exceedances above this threshold follow asymptotically a GPD. Very large thresholds lead to estimates with high variance while too small thresholds results in biased estimates. We have examined a range of thresholds in terms of the mean excess function and the thresholds versus the estimated parameters and safely set the threshold to the 95th percentile for each station. The verification of the selected threshold was also gauged by the quality of the fitted distribution.
The estimated shape parameter is clearly negative (Table III), with 80% of the ξ values in (−0.24, − 0.06) and a median of − 0.17 ( ± 0.05), which indicates that the distribution of exceedances is bounded. Changes of both signs appear for ξ. The trend of the scale parameter is positive at the majority of the stations with the median change being 11.4%. The modelling of the peak values through the GEV distribution showed similar tail behaviour with negative shape parameter while in addition, the trend of the location parameter is clearly positive (median is 3.1%). This implies increased upper bounds for the minimum temperature for both annual maximum and POT. This tail behaviour has been confirmed in the previous section.
Table III. Parameters of the EVT distributions and their change
Location (% change)
Scale (% change)
The presented values correspond to median (10th percentile, 90th percentile). The units for the changes of the location and scale parameters are given in percentages.
46 (33, 59)
− 8 (−33, 10)
15 (12, 21)
− 7 (−55, 34)
0.1 (−0.04, 0.24)
0.1 (−0.3, 0.3)
24 (20, 27)
3.1 (−1.4, 6.8)
1.3 (1.0, 2.0)
1.1 (−30, 20)
− 0.13 (−0.31, − 0.05)
0.1 (−0.3, 0.5)
36 (34, 39)
1.0 (−2.2, 3.2)
1.9 (1.5, 2.4)
− 17 (−33, 35)
− 0.22 (−0.34, − 0.05)
0.2 (−0.1, 0.5)
13 (8, 16)
− 0.2 (−33, 21)
0.16 (0, 0.2)
0 (−0.2, 0.2)
1.5 (1.3, 2.1)
11 (−13, 44)
− 0.17 (−0.24, − 0.06)
0 (−0.2, 0.1)
2.0 (1.8, 2.5)
4 (−17, 14)
− 0.13 (−0.22, − 0.08)
0 (−0.0, 0.1)
The behaviour of the peak maximum temperature has a smaller magnitude of change when compared to the peak minimum temperature. Here, 80% of the ξ values are in (−0.22, − 0.08) with a median of − 0.13 ( ± 0.04) with a clear positive trend observed at the majority of the stations.
The modelling of the peak annual precipitation though the GEV distribution revealed a negative trend (∼8%) for the location parameter (amplitude of extremes), a negative trend for the scale (variability of extremes) and variations of both signs for the positive shape (bound of extremes) parameter (Table III). In terms of the POT, the estimated shape parameter for precipitation is predominanly positive. We find that 80% of the ξ values are in (0.0, 0.2) with the median ξ to be equal to 0.16 (with a standard error of 0.04), which indicates that the distribution of exceedances is heavy tailed. At many stations, the changes in the scale and shape parameter are of opposite sign (not shown). Reductions in the scale parameter and increases in the shape and location parameter identify the stations with increased intensity of extreme events.
To summarize, in terms of the POT, we found the following representative values of the parameters over the region for future impact studies:
1.Shape: Positive shape parameter for the precipitation (PREC) (0.16 ± 0.04) and negative shape parameter for the minimum (TMIN) (−0.17 ± 0.05) and maximum (TMAX) temperature (−0.13 ± 0.04). Variability of both signs for the shape parameter (−0.2, 0.2), with the highest amplitude for PREC and TMIN and the lowest for TMAX.
2.Scale: Variability of both signs for PREC (−33%, 21%) and TMAX (−17%, 14%) and predominantly positive for TMIN (−13%, 44%).
The scale parameter was found to be the most variable. This points out that the most influenced factor is the variability of the extremes. The same range of variation was also seen for the location parameter of the annual peak precipitation.
Moreover, the changes in the scale parameter are generally higher in the GEV fit in comparison to the GPD fit. This is mainly attributed to the higher changes in the width of the distribution for the peak values versus the POT values, as can be seen from the pdfs of TN95P versus TNX (Figure 3) (similarly for TX95P and TXX). In addition, the limited length of the timeseries in the GEV fit together with the presence of large peak values has implications for the stability of fitted parameters. This testifies to the fact that more than 23 years of data are required to give stable estimates for GEV versus GPD analyses.
4.2.2. Return values
Figure 6 displays the estimated 5-year return levels for the full period and their computed difference for the two sub-periods, for the annual temperature and precipitation maxima and peaks over threshold. The top row is dedicated to the analysis of daily extreme precipitation. The median 5-year return value is 49 mm for the peaks over the 95th percentile and 70 mm for the peak precipitation. The change in the 5-year return values for the peak annual precipitation varied between − 24 and 20% (median = − 7.3%) and varied between − 13 and 7% (median = 0%) for the POT of PREC. Although the regional change is a small negative number, the pattern of change is different between the eastern part of the domain (drier climate) where a decrease is observed using both methods, and the continental part of the domain (mixed pattern). The domain mean 5-year return value for PRECMAX (POT of PREC) under present climate (1979–2001) is equal to the 4-(5-)year return value under past climate (1956–1978); however, there is large spread in those values (an increase in the 5-year return value is only evident at the eastern part of the domain). As stated in the previous section, those changes can be explained by changes in the probability distributions of the regimes of atmospheric circulation. Extreme precipitation events exhibit increased variability in many stations, although the total precipitation trend is negative.
Results from GEV and GPD for TMAX (middle row) show a regional upward sign, but of smaller magnitude compared to TMIN. Specifically, the median 5-year return value for the POT of TMAX (TMAXMAX) is 35 °C (39 °C) and exhibits a median change of 0.4%. This corresponds to an almost 6-year return value under past climate.
Finally, the bottom row shows very high spatial coherence, higher than TMAX and PREC. The median amplitude of the 5-year return level for the POT of TMIN is 23 °C (25 °C for GEV) with the 80% of the values in the (19, 26) range; the change in the return level is generally positive with a median of 1.4%, but it can locally reach 4% (10% for GEV). Positive magnitude of change appears at most stations with the largest positive changes located in the east part of the country (the picture is coherent with the variability of TN95p). In particular, one can easily see a W–E gradient of change, with the dry east zone demonstrating larger sensitivity to the extremes changes than the mean ones. Similarly, the change in the 5-year return values for TMINMAX (GEV) varied between − 0.7 °C (−2.3%) and 2.5 °C (9.6%) (median = 0.9 °C or 3.4%). Both GEV and GPD show a shift of TMIN extremes towards warmer values in the majority of the stations. In other words, the domain mean 5-year return value for TMINMAX and POT of TMIN under present climate (1979–2001) is equal to the 7-year return value under past climate (1956–1978).
Now, we attempt to quantify the changes in the extreme events in terms of changes in the fitted parameters of the GEV (Figure 7) and GPD (Figure 8) models. In other words, we are interested in the changes in the parameters of the EVT model that can accompany changes in the frequency and intensity of extreme events. Therefore, we tested the joint sensitivity of the 5-year return level and peaks over the 95th percentile to changes introduced by the variation of each of these three (two for GPD) parameters.
Increase (decrease) in extreme precipitation (5-year return level and 95th percentile) is, at most stations, tied to quasi-linear increases (decreases) of the location parameter and especially the scale parameter. In contrast, the non-stationarity of the climate has influenced the positive shape parameter in both directions.
For GEV, the increase in the 5-year return level of the extreme temperatures is, in most stations, tied to increases in the location parameter. For the GPD, the scale parameter becomes the principal factor that affects the extremes both linearly and proportionally.
The results are similar to the maximum temperature for the factor's prioritation and importance but demonstrate increased sensitivity.
To summarize, for GEV, the location parameter is found to be more important in the temperature time series and the scale and location parameters in the precipitation time series. For GPD, the changes in the scale parameter have direct implications on the estimated 5-year return values.
The application of two independent methods for the analysis of the observed changes in temperature and precipitation extremes over Greece was evaluated; the first one is based on the trend analysis of the calculated indices of extremes, the second one consists in fitting an EVD to the sample of observed extremes (peaks, peaks over threshold) to accurately assess potential changes in the shape of the distribution of temperature and precipitation observations. The main results are as follows:
1.Temperature indices. Between 1955 and 2002, almost 74% of the stations showed a significant increase in the annual occurrence of warm nights (along the global trend) followed by the annual duration of tropical nights and the annual maximum of the minimum temperature. Those three indices as well as the DTR exhibit a significant regional trend. Generally, extreme minimum temperature indices have been increasing at a faster rate than that of extreme maximum temperatures. This asymmetry in the changes in cold versus warm extremes was confirmed by the changes in the fitted parameters of the distribution of temperature observations. The most notable shift was seen in the probability distribution of the warm nights towards warmer conditions between 1955–1978 and 1979–2002. For the other indices, the distributions are also different (with a lower level of statistical significance though), except for the cold nights and the annual minimum of TMIN and TMAX. The observed warming occurs predominantly in the summer and is physically linked to the weakening of the Etesian winds because of the less frequent expansion of the low over the southeastern Mediterranean (Feidas et al., 2004).
2.Precipitation indices. The total annual precipitation as well as the frequency and intensity of extreme precipitation have been significantly decreased over the region; however, the extreme precipitation percentage has a widespread pattern without clear trend. This result is of opposite sign with the global positive trend in total precipitation (Alexander et al., 2006) or the increases in extreme precipitation in the mid-latitudes (Groisman et al., 2005). No difference in the statistical distribution was seen for the extreme precipitation percent and the maximum 1-day precipitation amount. The reduction in the total precipitation and the fewer rain days are linked to the positive phase of the NAO that resulted in an increase in the frequency and persistence of anticyclones over the Mediterranean (Alpert et al., 2002; Feidas et al., 2007).
3.Tail Modelling of Temperature. The changes in the peak temperature extremes are most sensitive to the changes in the location of the distribution of annual extremes. The highest range of change was found for the scale parameter, pointing out that the most influenced factor is the interannual variability of the extremes. The results for the importance of the parameters are in agreement with the previous global (Kharin and Zwiers, 2005) and regional studies (Goubanova and Li, 2007). The domain mean 5-year return value for the maximum TMIN and the peaks over the 95th percentile of TMIN under present climate (1979–2001) have increased coherently over the domain and correspond to the 7-year return value under past climate (1956–1978). Results for TMAX also show a regional upward sign of smaller magnitude.
4.Tail Modelling of Precipitation. Changes in the precipitation extremes are associated with changes in both the scale and location of the fitted distribution. Similar to temperature, the highest range of change was found for the scale parameter. The results for the 5-year return level of precipitation in the last quarter of the twientieth century show similar values compared to the previous quarter. However, the pattern is dramatically different for the eastern part of the domain (marine) where a decrease in the 5-year return level is found.
Deterministic climate model simulations (Christensen et al., 2007; De'que et al., 2007) project warming for the eastern Mediterranean, that is largest in the summer, and decrease in the total precipitation and the number of rainy days. In terms of extremes, an increased number of heatwaves is very likely (Diffenbaugh et al., 2007; Tolika et al., 2009), whereas extreme precipitation does not show any coherent sign among models. Further, interannual temperature variability is likely to increase in summer (Vidale et al., 2007). Although generally climate models have been more successful in simulating temperature extremes than precipitation extremes (eg., Kiktev et al., 2003) due to the better representation of the physical processes involved, it appears that projected extremes are mainly a further amplification of the historical extremes analyzed in this work. Such conditions are associated with increased drought and fire risk in the summer with severe consequences for the economy of the region.
Dr I. Kioutsioukis would like to acknowledge funding from the EU-GEMS research project. The authors also wish to thank the anonymous reviewers for their critical comments on the earlier version of this manuscript and Dr Mariliza Koukouli for the review of the English text.