Mapping climate change in European temperature distributions

Climate change poses challenges for decision makers across society, not just in preparing for the climate of the future but even when planning for the climate of the present day. When making climate sensitive decisions, policy makers and adaptation planners would benefit from information on local scales and for user-specific quantiles (e.g. the hottest/coldest 5% of days) and thresholds (e.g. days above 28 ° C), not just mean changes. Here, we translate observations of weather into observations of climate change, providing maps of the changing shape of climatic temperature distributions across Europe since 1950. The provision of such information from observations is valuable to support decisions designed to be robust in today’s climate, while also providing data against which climate forecasting methods can be judged and interpreted. The general statement that the hottest summer days are warming faster than the coolest is made decision relevant by exposing how the regions of greatest warming are quantile and threshold dependent. In a band from Northern France to Denmark, where the response is greatest, the hottest days in the temperature distribution have seen changes of at least 2 ° C, over four times the global mean change over the same period. In winter the coldest nights are warming fastest, particularly in Scandinavia.


Introduction
Global warming consists of complex changes in local climate which have implications for sectors as diverse as water management (Milly et al 2008, DEFRA 2012 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. et al 1999), building design (DEFRA 2012, CIBSE 2005, agriculture (Challinor and Wheeler 2008, Lobell and Burke 2008, IPCC 2007b, Porter and Semenov 2005 and insurance (Mills 2005). Providing guidance at these local scales is a key element of efforts to supply 'climate services' (WMO 2011). This is intrinsically challenging because organizations are vulnerable to different aspects of climate: different thresholds, variables and spatial patterns in the distribution of weather variables which constitutes climate (IPCC 2007a, Stainforth et al 2007. Assessments of where and which societal vulnerabilities are changing fastest require information on how all these aspects are co-varying. Here we use a gridded dataset of observations (Haylock et al 2008) to provide such information by mapping the changing shape of local climate (Chapman et al 2013) across Europe. The implications are highlighted for some societally relevant thresholds including freezing point and temperatures related to labour productivity (Hsiang 2010, Zivin andNeidell 2010) and building overheating (DEFRA 2012, CIBSE 2006. The approach provides information at scales relevant for both local decisions and national planning, while also being of significance for the evaluation of climate models (van Oldenborgh et al 2009) and the study of processes which influence local climate change. Our aim is to process observations of weather variables into observations of climate change. Some choices are inevitable in this process and the implications of these are tested, but the incorporation of methodological assumptions is minimized to the greatest extent possible so that the results can be interpreted as representing the robustly identifiable changes in climate experienced over the last 60 years as closely as possible.
Section 2 provides a description of the dataset used, along with the interpretational approach adopted and the rationale for such an approach. Section 3 illustrates the application of the method at three locations. Given the large natural variability in climatic datasets, a key element of the analysis is the process for identifying robust messages. Examples are presented of illustrative situations in which robust messages can and cannot be extracted. In section 4 maps of observed changes in European climate are generated for summer and winter, for a selection of quantiles representing the changing shape of the temperature distributions, and for two application-relevant thresholds. The implications of these results are reviewed in the conclusions.

From weather to climate
Observations of weather variables are taken on at least a daily basis at thousands of weather stations around the world. Many of these datasets stretch back to the mid-20th century with some going back hundreds of years (Parker et al 1992). Several recent initiatives have taken these data and constructed high-resolution gridded datasets of daily weather information across large regions (Haylock et al 2008, Yatagai et al 2012. Some of these processed datasets, and even some of the underlying station data, are openly available for use by researchers and policy makers. For many purposes, however, they are of limited direct value because they don't provide information about the aspects of changing climate which impact policy/business decisions and climate impacts research. By acknowledging that climate is inherently a distribution, and changing climate a changing distribution (Stainforth et al 2007, IPCC 2012, Hansen et al 2012, these data can be analysed in a model independent manner to provide a more valuable picture of how local climate is changing; one which more closely reflects perceptions of climate change. A description of climate change on a regional basis requires an exploration of correlated variations across multiple dimensions: space (geographical variations), likelihood (rare versus common events in the climatic distribution), variable (the aspect of climate under consideration), and time (the period over which a change is considered). Using the state-of-the-art E-OBS dataset (Haylock et al 2008), which runs from 1950 to 2011, we present climate change variations in space and quantile for four variables: maximum and minimum daily temperatures in summer and winter.
The E-OBS dataset is constructed using data from 2316 stations but the station density varies considerably across Europe (see Haylock et al 2008) with the highest density of stations in the UK, the Netherlands and Switzerland, and relatively low densities in the Balkans, Scandinavia, Iberia and Northern Africa. The E-OBS data at 0.5 • × 0.5 • resolution is used in this analysis; higher resolution gridded data is available but the use of such data for this purpose is not considered justified given the density of the underlying observational network.
At 0.5 • × 0.5 • the data has a resolution of roughly 40-50 km. The term 'local climatic distributions' is used to refer to results on this scale. 'Regional' behaviour refers to the results across clusters of several such grid boxes. The grid box resolution is somewhat higher than the typical resolution of global circulation models (GCMs, ∼100 km) but a little lower than is typical in regional climate models (∼25 km). To the extent that the E-OBS dataset reflects the underlying observations it is appropriate to examine grid box results individually. This is not the case for GCMs where the numerical solution is not expected to necessarily be representative of the solutions of the continuous equations at the smallest scale of the model. The method described herein could be applied to, and interpreted for, individual grid boxes and even individual station data, thus providing higher resolution information than is available from models. However, gridded observational datasets are also subject to limitations, due to in-homogeneities in the data and inaccuracies arising from the interpolation procedures (Hofstra et al 2009(Hofstra et al , 2010. These limitations are more significant in regions with fewer stations. As a consequence the results below are more reliable in some regions than others; in North Africa they are not considered at all reliable because there are so few stations. Spatial correlation patterns are however outputs of the approach. Here we focus on regionally consistent behaviour because this is unlikely to be the result of inaccuracies in the dataset. The application of the approach to individual grid boxes or individual station data would require careful analysis of the reliability of the data at that location. Our aim is to maintain as close a link as possible to the underlying observed quantities while representing them in terms of climate, a set of distributions. It is commonly accepted that climate change could lead to changes in the mean, changes in the mean and variance, or to more complicated variations in the shape of climatic distributions (IPCC 2012), but there have been very few studies on what observations tell us about such changes at the local scale (see Vinnikov et al 2002 for one such). This information would be valuable not only for decision makers but also as a guide for research into how local geographic factors affect the consequences of synoptic scale changes. Previous studies which have considered regional distributions or extremes, have made assumptions including: (i) the presence of a continuous linear trend over time (Reich 2012, Simolo et al 2010, Min et al 2013, Alexander et al 2006, (ii) spatial dependences (Simolo et al 2010, Reich 2012, Alexander et al 2006, and (iii) that the changing shape can be captured by changes in only low order moments (e.g. mean and variance) . Such assumptions are debatable given the complexity of the drivers of local climate. The possibility of multi-decadal climatic oscillations (Schlesinger andRamankutty 1994, Chambers et al 2012) suggests that the first is an oversimplification while the last is questionable in such a complex nonlinear system. Regarding the second, the presence of spatial dependences is of course clear, but applying assumptions regarding their character at any given quantile, and their consistency across any given region, risks providing misleading information unless it can be founded on well understood physical mechanisms. We therefore propose a method which remains as close as possible to simply representing the data. Any spatial, variable or likelihood relationships which arise can thus be interpreted with greater confidence, simplifying their use in societal planning. If, in the future, their physical basis can be understood then this can provide a foundation for better local information regarding plausible future climate change.

The identification of robust changes in climate
The local climate for a variable at some time in the past can conceptually be represented by a distribution, D1. In the present day the same variable has distribution D2. Our interest is in how, or whether, D1 and D2 differ. Consider daily maximum (hereafter 'daytime') summer (June/July/August) temperatures in the gridbox around Bordeaux. A distribution of this variable is constructed using 9 years of data centred on 1954 and compared with another using 9 years of data centred on 1997 (see figure 1(a) and appendix A). From this can be extracted the change in the probability of remaining below a certain threshold, C ( figure 1(a)). The thresholds of relevance vary according to the natural or human system of interest. Two aspects of economic interest are labour productivity, which has been shown to decrease when daytime temperatures exceed about 28 • C (Hsiang 2010, Zivin andNeidell 2010) and overheating in buildings, which has been related to temperatures exceeding 28 and 26 • C (DEFRA 2012, CIBSE 2006. For these, as for many thresholds it is most intuitive to consider the change in the exceedance probability (− C) which has increased by 0.17 at 28 • C for summer days in Bordeaux over this period.
For such information to be useful its robustness must be assessed. Repeating the analysis using ten different period pairs with equal length separations in time (i.e. 1954-1997, 1955-1998, . . . , 1963-2006, see appendix A), produces ten pairs of distributions and ten assessments of the change in exceedance probability over a 43 year period (figures 1(b)-(d)). This represents an estimate of the range of behaviour due to short timescale variability (see Chapman et al 2013) while also capturing the diversity of longer timescale variability in the data. They are not, however, independent samples. We therefore take a conservative approach to the evaluation of these ten values by considering only the smallest and largest change (see appendix B). A large value for the smallest change suggests a robust, large signal over the last 60 years at the given threshold e.g. 0.17 at 28 • C around Bordeaux ( figure 1(b)). A small value for the largest change implies a robust signal of little change, e.g. −0.04 at 28 • C in the Algarve, Portugal (figure 1(c)). A large range (maximum minus minimum values for − C) implies no clear signal e.g. −0.04 minimum with 0.24 maximum at 28 • C in Piedmont, Italy ( figure 1(d)).
This approach quantifies changes between two periods in time; it cannot attribute (Stott 2003) these changes to, for instance, the enhanced greenhouse effect or multi-decadal internal climatic oscillations (Schlesinger andRamankutty 1994, Chambers et al 2012). This is not a detriment when optimizing plans for the climate of the present day. Information on where and how vulnerabilities are changing is useful irrespective of the physical drivers, particularly when planning requirements, or conventional approaches, are based on illustrative past years (Hitchin et al 1983) or probability distributions constructed over historic periods (Milly et al 2008). In the context of either human-induced climate change or multi-decadal oscillations, the method can be interpreted as quantifying how global, or large scale, variations in the system, manifest themselves on the smaller scales of human society (at least in locales where land-use change is not considered a significant factor).
The ability to separate long timescale variations (which the analysis captures) from shorter ones (which are incorporated within the individual cdfs) is limited by the timeseries of observations available (see appendix A). However, the approach makes no assumptions of spatial relationships so when coherent spatial patterns of change emerge it provides confidence that such patterns represent a signal which is robust in that region.

Maps of climate change
Mapping the smallest changes in the threshold exceedance probability produces some clear patterns for both a zero degree threshold in daily minimum (hereafter 'nighttime') temperatures in winter and a 28 • C threshold in daytime temperatures in summer-see figure 2. In many parts of Ireland, northern England, southern Scotland and southern Sweden, the fraction of winter nights which fall below zero degrees has decreased by at least 0.05-0.1. North west Italy and the western Pyrenees show even greater changes in this threshold. Most of southern Sweden and coastal Norway have in addition seen a substantial decrease (∼0.05-0.15) in the fraction of winter daytime temperatures which fall below zero (figure S3 available at stacks.iop.org/ERL/8/034031/ mmedia). These changes presumably relate to observed changes in snow reliability in Scandinavian skiing resorts (Moen and Fredman 2007). In summer, the 28 • C threshold in daytime temperatures is changing fastest in western France, eastern Spain and central Italy; changes in the fraction of days above this threshold are often greater than 0.15 in these regions. Smaller but nevertheless substantial changes (>0.06, sometimes >0.1) with implications for labour productivity and building design/management are seen across northern France, Germany and Eastern Europe; even across southern England changes greater than 0.04 are found.
Although changes in frequency are important for impact-specific thresholds, for research objectives such as understanding the processes which link climate at different spatial scales, and for climate model evaluation, it is more useful to have information on the changing local distributions.  figure 1(a)). Again a large (small) value for the smallest (largest) change over ten samples is interpreted as providing an indication of robust large (small) changes.
The smallest (largest) change in five quantiles across the distributions of summer daytime and winter nighttime temperatures are presented in figures 3 and 5 (figures 4 and 6). Daytime summer temperatures tend to increase most in the upper quantiles in many regions (figure 3). At the 0.95 quantile a band across northern Europe from northern France to Denmark and southern Sweden show substantial changes of at least 2 • C ( figure 3(a)). At the 0.75 and 0.5 quantiles the greatest changes are further south in central France and Germany ( figure 3(b)). Eastern Spain and central Italy show very substantial changes, in some places at least 2.5 • C, across the whole distribution, but for most regions the low, 0.25 and 0.05 quantiles, show smaller changes. Much of southern and western Iberia along with Norway and Sweden reveal either robustly small changes or no clear signal at all quantiles (figures 4 and 3). By contrast it is the lowest quantiles which show large change in nighttime winter temperatures (figures 5 and 6) for large parts of Europe. This is evident in only the most extreme, 0.05 quantile, for central western Europe but for Norway and Sweden it is seen in all quantiles below the median, where the smallest changes can be over 3 • C. Changes in Spain are close to zero and sometimes negative even in the lowest quantiles but in central and southern Portugal they are positive across all quantiles. The relatively small size of the region with a positive signal and the substantial difference with that seen in the surrounding region suggests that this result should be treated cautiously without further understanding of the underlying datasets or the processes responsible.
Changes in summer nighttime temperatures are smaller than in daytime temperatures; smallest values less than 1.5 • C across most of Europe (figures S5 and S6 available at stacks. iop.org/ERL/8/034031/mmedia). Few large scale regional patterns are evident although northern Portugal is a hot spot for mid-to-upper quantiles. The strong signal in nighttime temperatures in winter in central western Europe is not apparent in daytime winter temperatures but large changes are found in this variable in the lowest quantiles in central Italy and the northern Balkans (figure S7 available at stacks.iop. org/ERL/8/034031/mmedia). The signal in daytime winter temperatures in Scandinavia is clear but less strong than in the nighttime values.

Concluding remarks
Previous work has demonstrated that timeseries of local temperatures are sufficiently long to identify a warming   trend (van Oldenborgh et al 2009); this work uses them to provide a picture of changing local climate distributions of value to both policy makers and researchers. Given the relatively short timeseries and the large natural variations it is important to focus on aspects which are robust in the record. Thus changes are highlighted only when they are consistently large, or small, when analysed over different periods, and only when a consistent message is seen across a region. In identifying locations/quantiles/variables with substantial changes, a conservative approach has been taken by presenting the smallest change found over the multiple periods analysed.
The analysis presented herein has used gridded observations. The approach could be applied to reanalysis datasets or directly to the underlying station data, both of which come with different underlying limitations. One might expect the large scale patterns to be similar to those presented herein but the sensitivity of the results to different ways of processing the observational data would be informative in the identification of robust local changes.
These results illustrate that at specific quantiles, local changes can be substantially more than four times greater than the global mean annual mean change. They are not well represented by the local mean change because the local distributions change shape in a manner which does not allow for a simple relationship between the mean and other quantiles. These are important points for policy negotiations based on the two degrees guardrail (Richardson et al 2009). The results demonstrate the complex pattern of changes seen in recent European climate. They represent a key input to climate services and provide a yard stick against which scientists and users can evaluate model-derived data. For regional climate research they represent observations of climate change against which theories of global/local relationships can be assessed; a key step towards the provision of decision-relevant climate predictions on sub-continental scales.
only for the season under consideration (June/July/August for summer, December/January/February for winter), the cumulative distribution function (cdf), C, is constructed using τ years of data centred on year t 1 . A second cdf is constructed for some later period centred on t 2 and changes evaluated in terms of both the changing quantile function for specific temperatures, C T (figures 1(a) and 2), and changing quantiles ( T q ) for specific values of cumulative probability, q (figures 1(a) and 3-6).
In a stationary climate, C would be independent of t; variations between time periods would be a consequence only of the finite sample size specified by τ . Both C T and T q must be interpreted in the context of such natural variability. The impact of high frequency variations (inter-and intra-year) is explored by varying τ (see the supplementary materials available at stacks.iop.org/ERL/8/034031/mmedia). (See Chapman et al 2013 for an illustration using synthetic data built from mathematically defined distributions.) The impact of low frequency variations (decadal timescales) is evaluated by repeating the analysis n times while maintaining the same value of t (= t 2 −t 1 ) i.e. multiple evaluations of the change over time windows of equal length but with different start and end dates.
Given the limited length timeseries available a balance must be struck between n, τ and t. Each should be as large as possible in order to (respectively): (i) evaluate the impact of low frequency natural variability, (ii) maximize the resolution of the cdfs and thus minimize the uncertainty resulting from high frequency variability, and (iii) maximize the signal/noise of any long term changes. We use n = 10, τ = 9 and t = 43. With τ = 9, the cdfs consist of >800 values. The results are robust to higher and lower values of τ -see supplementary figures S9-S16 (available at stacks.iop.org/ERL/8/034031/ mmedia).
C T is extracted directly from the cdfs. T q is calculated using the method of Chapman et al (2013).

Appendix B. Smallest/largest changes
The exceedance probability for temperature T is (1 − C T ) and thus a change in exceedance probability is simply − C T . In figure 2 (figures 3 and 5) each grid box is calculated independently and shows the value of − C T ( T q ) for the cdf pair where | C T | (| T q |) is a minimum i.e. the 'signed equivalent' of the minimum absolute value of the change in exceedance probability across all ten sample pairs. This is termed the 'smallest change'. Figures 4 and 6 contain maps of the signed equivalent of the maximum absolute change-termed 'the largest change'.