Changes in the distribution of seasonal surface temperature are investigated in central Europe using observations between 1961 and 2004 and a set of IPCC SRES A2 and B2 climate change simulations. A piecewise detrending methodology is used to distinguish between intrinsic and trend-induced variability changes. Mean and interannual variability changes are standardized with the intrinsic variability of the respective dataset. Within this framework, the strongest temperature changes in mean since 1990 are found for the summer season, both in observations and climate models. Estimates for variability changes show a weak increase (decrease) in summer (winter), but these changes are not statistically significant at the 90% level. For the 21st century all climate scenario runs suggest large relative increases in mean for all seasons with maximum amplitude in summer. Although changes in relative variability vary substantially between the models, there is a tendency for increasing (decreasing) variability in future summers (winters).
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 In this paper, observed and modeled central European land temperature distributions are investigated for each season separately. A temporal analysis of changes in mean and variance is conducted for recent observations and for scenarios of the 21st century. Relative changes in these quantities are compared between models and observations including the associated uncertainties.
 There are many different methodologies to quantify distribution changes, depending on both the parameter of interest and the space and time scales considered. For distributions described by large data samples, such as daily data, non-parametric quantile-based methods are more robust than parametric approaches [Ferro et al., 2005]. For small data samples, such as seasonal mean temperature, moment-based methods are superior due to their higher statistical efficiency. For example, the estimation of the standard deviation from the inter-quartile range with a sample size 30 is only as efficient as its direct estimation with a sample size 12. Therefore we estimate mean () and interannual standard deviation (s) of seasonal temperatures assuming a Gaussian behavior. The moments are calculated for all possible contiguous (running window) 30-year periods available. The reference period is the World Meteorological Organization (WMO) 1961–1990 standard normal period if not indicated otherwise.
 For Gaussian distributions, changes are described by a combination of a shift in mean (location) and/or a change in standard deviation (scale). Applying this simple conceptual model to real climate data can be difficult. For example high quality and homogeneous data are needed to avoid spurious shifts [see, e.g., Begert et al., 2005]. Another critical issue is the limited number of observations with which the climate space is sampled. This can result in considerable non-stationarities between 30-year windows [WMO, 1967; Scherrer et al., 2005]. These effects must be accounted for when making statements about changes in intrinsic variability as will be demonstrated below.
 In order to properly compare observations against model results and the models among each other, standardized changes in mean ( − 0)/s0 and variability s/s0 are used henceforth. Here the subscript 0 indicates the estimates based on the reference period. Plots with standardized Mean versus Standard Deviation change (referred to as MSC plots hereafter) are used to illustrate the changes in both parameters simultaneously [cf. Sardeshmukh et al., 2000; Scherrer et al., 2005].
 Time series with trends are not strictly Gaussian and the calculation of standard deviation measures using such data leads to a trend-induced inflation of variability as noted by Räisänen  and Schär et al. . The effect of a linear trend upon estimates of variability can be quantified by the ratio between the standard deviation st of the series with a superimposed linear trend of magnitude α per time step and the standard deviation s of the pure white noise series. The analytical derivation (see auxiliary material) shows that:
In this study the sample size N = 30 and therefore γ = 77.5. For central European conditions, typical summer temperature trends are ∼1 to 2 K for the last 30 years, and typical standard deviations are ∼1 K. Thus, the inflation factors are in the order of 1.04 to 1.16. However, locally and for some specific periods the inflation can be much larger (see auxiliary material).
Figure 1 schematically illustrates the effect of variability inflation on time series, distributions and MSC plots. The period of interest is compared with the reference period, in general both having different trends. Figure 1a shows a case where the trend is constant over three consecutive 30-year periods. The distributions are broadened due to variability inflation. In the MSC plot no increase in variability can be detected since it measures changes with respect to the reference period. Figure 1b shows a case where the trends gradually increase from one 30-year period to the next. The distributions have different widths depending on their trends, which results in a variability change in the MSC plot. This effect needs to be corrected for when the focus is on changes in intrinsic variability. In this study piecewise detrending for both series (i.e. investigated 30-year period and reference period) is used to eliminate the influence of the trend on the variability estimates (see Figure 1c).
3. Data and Models
 Two types of 2 m temperature datasets with seasonal resolution are considered. The first is the observed land-surface temperature dataset CRUTEM2v [Jones and Moberg, 2003]. The second is a set of seven IPCC SRES A2 and seven B2 greenhouse gas scenario runs used in the third IPCC assessment report 2001 (available from http://ipcc-ddc.cru.uea.ac.uk). Ten of these scenarios cover the period 1961–2099, two are available for the 1980–2099 and two for the 2000–2099 period (Table 1). The region of interest is central Europe, defined here as the model individual's land grid points in the area covering 3°W to 27°E and 44°N to 55°N.
Figure 2 shows the standardized running 30-year estimates of mean and standard deviation for the observed central European mean temperature from 1961–1990 onwards (i.e. the 30-year windows 1962–1991, 1963–1992, …, 1975–2004). Black (grey) lines show standard deviation estimates based upon raw (detrended) data. For DJF a more or less regular increase is found in the mean, corresponding to ∼0.4 standard deviations of the 1961–1990 period (s0 hereafter). A step-like decrease in variability of almost 20% occurs when the extraordinarily cold winter 1962/63 drops out of the running 30-year period [Scherrer et al., 2005].
 A bootstrap resampling technique is used to determine the 5–95% confidence range of the mean and standard deviation change (see shading). 5000 samples in combination with a kernel density estimator are used. The confidence range for the combined 30-year estimate is an ellipse-like area spanning ∼±0.2–0.4 s0 for both the mean and standard deviation. These values are used hereafter to determine the statistical significance of the results.
 The 1975–2004 estimate for DJF just leaves the 1961–1990 confidence range. Larger positive mean changes are found for MAM (∼0.5 s0) and even larger ones for JJA (>0.75 s0), indicating that the relative changes have been stronger in summer than in winter. Increasing variability is particularly found for the JJA season. An additional jump-like increase is observed if the extremely warm summer 2003 is included (last data point). The autumn season (SON) shows slightly negative changes in mean and no changes in variability [cf. Klein Tank et al., 2005].
 The differences between the analysis using raw or piecewise detrended data are small for DJF and SON (Figures 2a and 2d). For MAM the moderate variability increase is reversed into a small decrease (Figure 2b). Most pronounced is the reduction of the variability increase for JJA from 20–50% to 10–15% (Figure 2c). This indicates that more than half of the observed variability increase is inflated due to the linear trend differences in the data.
5. Modeled Changes From 1961 to 2003
 The same analysis is now applied to climate simulations of the current climate using IPCC SRES scenario A2 and B2 runs for the years 1961 to 2003 (Table 1). In these runs the external forcing is prescribed in terms of time-dependent greenhouse gas and aerosol concentrations. This forcing is not identical to the observed 1961–2003 forcing, as for example discussed by Hansen and Sato  and references therein. For both scenarios, the total radiative forcing from greenhouse gases plus direct and indirect aerosol effects with respect to the pre-industrial (1750) level amounts to 1.33 Wm2 in the year 2000. By 2010, the A2 and B2 forcing amount to 1.74 and 1.83 Wm−2 respectively [IPCC, 2001, Table II.3.11, p. 823]. The smaller A2 radiative forcing is due to a transiently higher aerosol load. In comparison, best estimates of the observed forcing in 2000 amount to ∼1.8 Wm−2 [IPCC, 2001, p. 393; Hansen et al., 2005].
Figure 3 shows the relative changes in mean and standard deviation for the periods 1961–1990 to 1975–2004 (DJF) and to 1974–2003 (MAM, JJA, SON) respectively. The analysis is performed using the piecewise detrending procedure. For JJA all models agree in showing a relatively large increase in mean which is somewhat smaller than observed. Four out of five model runs also indicate an increase in variability comparable to the observed one. For the other seasons there is less agreement among the models. The data are mostly within the large confidence ranges spanned by the observations. It is worth noting that several model runs show almost no changes in mean during the winter season (whereas the observations show a considerable trend), and all models suggest changes in mean during the autumn season (of the order 0.35 to 0.45 s0), whereas no trend is found in the observations. The inter-model spread is larger than the spread between the two scenarios A2 and B2 of the same model. Changes in variability are less consistent and within the observed confidence ranges.
6. 21st Century Scenario Distribution Changes
 Piecewise detrended climate simulations are used to quantify the temporal evolution of the expected changes in mean and variability in a future climate. In Figure 4 results from five models are depicted for 2005–2099 relative to the 1961–1990 reference period. In Figure 5 results from all seven models are depicted for 2030–2099 relative to the 2000–2029 reference period. Overall the dominant changes are an increase in the mean values of the temperature distributions. By the end of the period (2070–2099), the largest relative changes in mean are found in summer (A2: 3.5–11 s0, B2: 2.5–8 s0) followed by autumn (A2: 4–6.5 s0, B2: 2.5–5 s0), spring (A2: 2–4.5 s0, B2: 1.75–3.5 s0) and winter (A2: ∼2–5 s0, B2: 1–4 s0). The inter-model spread in changes in mean is largest in summer.
 Predicted changes in variability are less dominant and less consistent, both in terms of scenarios and models. Roughly three quarter of the values lie within the bootstrap range of the reference period uncertainties. In particular when considering all available model simulations (Figure 5), there is a tendency for increasing variability for both A2 and B2 runs in summer. This is consistent with recent studies using regional climate models [Schär et al., 2004; Vidale et al., 2005] and global climate models [Meehl and Tebaldi, 2004; Brabson et al., 2005]. For winter, decreasing variability is found for roughly two third of all A2 (B2) periods relative to 1961–1990. By the end of the period (2070–2099) changes are 0.35–1.3 (0.6–0.95) s0 for A2 (B2). Predominantly decreasing variability is also found for spring season periods where s2070–2099 = 0.3–1.2 (0.4–0.95) s0 for A2 (B2). The results for autumn are inconclusive although there is a tendency for decreasing variability with respect to the 2000–2029 period (s2070–2099 = 0.5 to 1.25 s0). Again, the inter-model spread is larger than the spread between the A2 and B2 scenario results.
7. Concluding Remarks
 Temporal changes in central European land temperature were examined in terms of relative changes in seasonal mean and interannual variability. Both observations and IPCC scenario runs have been scaled by their own intrinsic interannual variability to facilitate the comparison between the different datasets. Theoretical considerations show that the analysis of changes in variability requires a careful methodology, as temperature trends may imply an artificial inflation of variability. The effect is potentially large when distribution changes over a short time period are analyzed. We have corrected for this by piecewise detrending the time series.
 Overall the analysis shows that the dominant changes in temperature distributions are an increase in the mean values in both observations and scenario runs, consistent with earlier studies [IPCC, 2001; Räisänen, 2002]. In relative terms by far the largest change in mean is observed and predicted for summer. However, also the largest inter-model differences are occurring in the summer scenarios (by the end of the 21st century, the suggested warming varies between 3.5 and 11 s0). These differences also imply different absolute temperature distributions.
 With respect to changes in variability of observed seasonal mean temperature during the last decade, we estimate a decrease by ∼10% in winter, and an increase by ∼10 to 15% in summer. However, these changes are not statistically significant at the 90% level. For the 21st century, there is a large spread between the different climate change models analyzed. Overall, there is a tendency for increasing variability in summer and decreasing variability in winter and spring.
 Finally note that this study uses a limited number of low-resolution global climate models to estimate future climate distributions on a continental scale. The estimates could be improved by using regional climate models or ensemble systems.
 This study was supported by the Swiss NSF through the National Centre for Competence in Research Climate (NCCR-Climate). We acknowledge the constructive comments from two reviewers.