## 1. Introduction

Most observations of (near-) surface meteorological variables like temperature, precipitation and wind velocity, particularly long time series, are obtained at surface weather stations, that is at fixed locations in space. From these measurements, selective information is obtained on intrinsically two- or three-dimensional fields that vary on diverse spatial scales. Statistical methods have thus been widely applied for characterising this spatial variability (e.g. Huff and Shipp, 1969; Bacchi and Kottegoda, 1995; Gunst, 1995; Grimes and Pardo-Iguzquiza, 2010). In particular, knowledge of the spatial autocorrelation of the variables is important for many applications. For example, it is essential for many modelling techniques that are applied for the interpolation of the meteorological fields in space and time (Baigorria *et al.*, 2007; Grimes and Pardo-Iguzquiza, 2010; Baigorria and Jones, 2010). Moreover, it is required for data assimilation and can be helpful in subseasonal climate forecasting (Koster *et al.*, 2008). For paleoclimate studies dealing with the reconstruction of a climate parameter from a proxy archive, the spatial correlation of the reconstructed variable can be used to assess the spatial representativeness of the archive. Spatial correlation of wind damages should be accounted for in the construction of insurance policies (De Silva *et al.*, 2008). Finally, spatial correlations have to be taken into account when exploring regional trends in surface climate (Gunst, 1995; Douglas *et al.*, 2000).

Precipitation has been the focus of many studies dealing with spatial correlation patterns in surface fields, since, on the one hand, it is an important input parameter for several applications, e.g. in hydrology and, on the other hand, exhibits a very large variability in space, demanding the application of advanced statistical methods (Grimes and Pardo-Iguzquiza, 2010). Typically, correlation-length scales are larger for steady precipitation related to the passage of synoptic-scale low-pressure systems than for showers and convective events (Huff and Shipp, 1969). In mid-latitudes, this leads to larger correlation lengths in winter than in summer (Baigorria *et al.*, 2007). Furthermore, the spatial coherency increases with increasing accumulation period of the precipitation (Bacchi and Kottegoda, 1995). In addition to station measurements, remote sensing data have also been used as a basis for investigating the spatial autocorrelation of precipitation, particularly in the tropics (e.g. Ricciardulli and Sardeshmukh, 2002). For temperature, the variability in space usually is smaller and correlation-length scales are much larger than for precipitation (Shen *et al.*, 2001; Koster *et al.*, 2008). Correlation scales of near-surface wind velocity are relatively large over the ocean and for weak winds, but become smaller when wind speed increases (Brown and Swail, 1988). However, absolute values of the correlation lengths differ substantially between different measurement systems (Wylie *et al.*, 1985), also because wind measurements are rather complicated. Over land, the correlation scales are smaller than over the ocean and depend on the complexity of the terrain (Reid and Turner, 2001).

An intrinsic feature of classical correlation analysis is that two time series are compared to each other as a whole, making the correlation coefficient sensitive to the coherency of the bulk of the data, but not that much to the extremes, since these are relatively rare (of course, this sensitivity also depends on the specific type of correlation statistics). Nevertheless, for several of the applications mentioned above, e.g. related to paleoclimatology, insurance issues or climate change, it is important to know about the spatial coherency of extreme meteorological events. It is not *a priori* clear if these extremes have the same spatial correlation properties as the bulk of the data. Several studies addressed this issue by calculating correlation coefficients of frequencies of extreme events on a yearly or seasonal basis (e.g. Douglas *et al.*, 2000; Gellens, 2000). In this way, the spatial coherency of the influence of a climate state on extreme weather is explored. However, it is also an interesting question in which way single events and related weather patterns are spatially coherent in a statistical sense. This question of representativeness (cf. Reid and Turner, 2001) of extreme weather events cannot be addressed using seasonal or yearly data, but must be analysed in an event-based manner. This is the focus of the present study, which investigates the representativeness of extreme precipitation, temperature and wind events at different observation sites in central Europe. Therefore, a simple measure is defined for the coherency and statistical representativeness of such events. Furthermore, possible reasons for the different coherency characteristics of the variables are explored by analysing the synoptic-scale atmospheric patterns accompanying the extreme events.

The main data base for the present investigation is a set of meteorological surface observations from Germany and Switzerland, which is presented in Section 2.1. On the basis of these data, a simple statistical method for analysing the spatial coherency of extreme events is proposed, as described in Section 2.2. Results of this method are presented in Section 3.1. Since one major motivation for this study has been to investigate the spatial representativeness of proxy data, the main reference point of the analysis is the station Trier-Petrisberg, close to the Eifel region in western Germany where several maar lakes are located that may be used as archives of extreme weather proxies in future research (Pfahl *et al.*, 2009; Sirocko, 2009). In Section 3.2, the atmospheric conditions during extreme weather events at Trier-Petrisberg are explored with the help of meteorological reanalysis data. Finally, Section 4 summarizes the results and gives a short outlook on future activities.