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Human society and natural systems are intrinsically adapted to the local climate mean and variability. Therefore, changes relative to the local expected variability are highly relevant for assessing impact and planning for adaptation as the climate changes. We analyse the emerging climate signal relative to the diagnosed internal variability (signal-to-noise ratio, S/N) of a set of recently published climate indices over Europe. We calculate the signal-to-noise ratio with respect to a recent baseline (1951–1983) which relates to recent societal experience. In this framework, we find that during the 2000–2016 period, many areas of Europe already experienced significant changes in climate extremes, even when compared to this recent period which is within living memory. In particular, the S/N of extreme temperatures is larger than 1 and 2 over 34% and 4% of Europe, respectively. We also find that about 15% of Europe is experiencing more intense winter precipitation events, while in summer, 7% of Europe is experiencing stronger drought-inducing conditions.

Extended periods without precipitation observed for example in Central Europe including Germany during the seasons from 2018 to 2020, can lead to water deficit and yield and quality losses for grape and wine production. However, irrigation infrastructure is largely non–existent. Regional climate models project changes of precipitation amounts and patterns, indicating an increase in frequency of occurrence of comparable situations in the future. In order to assess possible impacts of climate change on the water budget of grapevines, a water balance model was developed, which accounts for the large heterogeneity of vineyards with respect to their soil water storage capacity, evapotranspiration as a function of slope and aspect, and viticultural management practices. The model was fed with data from soil maps (soil type and plant available water capacity), a digital elevation model, the European Union (EU) vineyard–register, observed weather data and future weather data provided by regional climate models and a stochastic weather generator. This allowed conducting a risk assessment of the drought stress occurrence for the wine–producing regions Rheingau and Hessische Bergstraße in Germany on the scale of individual vineyard plots. The simulations showed that the risk for drought stress varies substantially between vineyard sites but might increase for steep–slope regions in the future. Possible adaptation measures depend highly on local conditions and to make targeted use of the resource water, an intense interplay of different wine-industry stakeholders, research, knowledge transfer, and local authorities will be required.

N. Ban et al., Here we present the first multi-model ensemble of regional climate simulations at kilometer-scale horizontal grid spacing over a decade long period. A total of 23 simulations run with a horizontal grid spacing of ∼3 km, driven by ERA-Interim reanalysis, and performed by 22 European research groups are analysed. Six different regional climate models (RCMs) are represented in the ensemble. The simulations are compared against available high-resolution precipitation observations and coarse resolution (∼ 12 km) RCMs with parameterized convection. The model simulations and observations are compared with respect to mean precipitation, precipitation intensity and frequency, and heavy precipitation on daily and hourly timescales in different seasons. The results show that kilometer-scale models produce a more realistic representation of precipitation than the coarse resolution RCMs. The most significant improvements are found for heavy precipitation and precipitation frequency on both daily and hourly time scales in the summer season. In general, kilometer-scale models tend to produce more intense precipitation and reduced wet-hour frequency compared to coarse resolution models. On average, the multi-model mean shows a reduction of bias from ∼ −40% at 12 km to ∼ −3% at 3 km for heavy hourly precipitation in summer. Furthermore, the uncertainty ranges i.e. the variability between the models for wet hour frequency is reduced by half with the use of kilometer-scale models. Although differences between the model simulations at the kilometer-scale and observations still exist, it is evident that these simulations are superior to the coarse-resolution RCM simulations in the representing precipitation in the present-day climate, and thus offer a promising way forward for investigations of climate and climate change at local to regional scales., Open access funding provided by University of Innsbruck and Medical University of Innsbruck., The ETH team, MZ, CNRM IPSL, ICTP, SMHI, Met-Office, DMI, CMCC, HZG, KNMI acknowledge funding from the HORIZON 2020 EUCP (European Climate Prediction System) project (https://www.eucp-project.eu, grant agreement No. 776613). AL-G acknowledges support by the Spanish government through grant BES-2016-078158 and MINECO/FEDER co-funded project MULTI-SDM (CGL2015-66583-R).

This paper is a contribution to the special issue on Advances in Convection-Permitting Climate Modeling, consisting of papers that focus on the evaluation, climate change assessment, and feedback processes in kilometer-scale simulations and observations., A recently launched project under the auspices of the World Climate Research Program’s (WCRP) Coordinated Regional Downscaling Experiments Flagship Pilot Studies program (CORDEX-FPS) is presented. This initiative aims to build first-of-its-kind ensemble climate experiments of convection permitting models to investigate present and future convective processes and related extremes over Europe and the Mediterranean. In this manuscript the rationale, scientific aims and approaches are presented along with some preliminary results from the testing phase of the project. Three test cases were selected in order to obtain a first look at the ensemble performance. The test cases covered a summertime extreme precipitation event over Austria, a fall Foehn event over the Swiss Alps and an intensively documented fall event along the Mediterranean coast. The test cases were run in both “weather-like” (WL, initialized just before the event in question) and “climate” (CM, initialized 1 month before the event) modes. Ensembles of 18–21 members, representing six different modeling systems with different physics and modelling chain options, was generated for the test cases (27 modeling teams have committed to perform the longer climate simulations). Results indicate that, when run in WL mode, the ensemble captures all three events quite well with ensemble correlation skill scores of 0.67, 0.82 and 0.91. They suggest that the more the event is driven by large-scale conditions, the closer the agreement between the ensemble members. Even in climate mode the large-scale driven events over the Swiss Alps and the Mediterranean coasts are still captured (ensemble correlation skill scores of 0.90 and 0.62, respectively), but the inter-model spread increases as expected. In the case over Mediterranean the effects of local-scale interactions between flow and orography and land–ocean contrasts are readily apparent. However, there is a much larger, though not surprising, increase in the spread for the Austrian event, which was weakly forced by the large-scale flow. Though the ensemble correlation skill score is still quite high (0.80). The preliminary results illustrate both the promise and the challenges that convection permitting modeling faces and make a strong argument for an ensemble-based approach to investigating high impact convective processes., IG and LS have been supported by the Croatian Science Foundation (HrZZ) project CARE (no. 2831). JF acknowledges support by the Spanish R + D programme through MINECO/FEDER co-funded project INSIGNIA (CGL2016-79210-R). AL-G is supported by the Spanish government though grant BES-2016-078158 and MINECO/FEDER co-funded project MULTI-SDM (CGL2015-66583-R). JM and KW-S gratefully acknowledge the support by the German Science Foundation (DFG) through project FOR 1695. DM, MP, and HT gratefully acknowledge the support received via the Austrian Science Fund (FWF) project NHCM-2 (no. P24758-N29) and the projects HighEnd:Extremes and EASICLIM, funded by the Austrian Climate Research Programme (ACRP) of the Klima- und Energiefonds (nos. KR13AC6K10981 and KR16AC0K13160, respectively). SS and TL acknowledge the support of NOTUR project no. NN9280K and the Research Council of Norway and its basic institute support of their strategic project on Climate Services. RMC and PMMS gratefully acknowledge the support of the SOLAR project (PTDC/GEOMET/7078/2014) financed by the Portuguese Foundation for Science and Technology. EJ Kendon gratefully acknowledges funding from the Joint Department of Energy and Climate Change (DECC) and Department for Environment Food and Rural Affairs (Defra) Met Office Hadley Centre Climate Programme (GA01101). S. Khodayar research is supported by the Bundesministerium für Bildung und Forschung (BMBF; German Federal Ministry of Education and Research). Support of Ministry of Education, Youth and Sports of the Czech Republic for funding the participation in Euro-CORDEX activities via the scheme INTER-TRANSFER under the Grant no. LTT17007. Funding from the Research Council of Norway through the SUPER (Grant no. 250573) and HYPRE (Grant no. 243942) projects.

Systematic biases in climate models hamper their direct use in impact studies and, as a consequence, many statistical bias adjustment methods have been developed to calibrate model outputs against observations. The application of these methods in a climate change context is problematic since there is no clear understanding on how these methods may affect key magnitudes, for example, the climate change signal or trend, under different sources of uncertainty. Two relevant sources of uncertainty, often overlooked, are the sensitivity to the observational reference used to calibrate the method and the effect of the resolution mismatch between model and observations (downscaling effect). In the present work, we assess the impact of these factors on the climate change signal of temperature and precipitation considering marginal, temporal and extreme aspects. We use eight standard and state‐of‐the‐art bias adjustment methods (spanning a variety of methods regarding their nature—empirical or parametric—, fitted parameters and trend‐preservation) for a case study in the Iberian Peninsula. The quantile trend‐preserving methods (namely quantile delta mapping (QDM), scaled distribution mapping (SDM) and the method from the third phase of ISIMIP‐ISIMIP3) preserve better the raw signals for the different indices and variables considered (not all preserved by construction). However, they rely largely on the reference dataset used for calibration, thus presenting a larger sensitivity to the observations, especially for precipitation intensity, spells and extreme indices. Thus, high‐quality observational datasets are essential for comprehensive analyses in larger (continental) domains. Similar conclusions hold for experiments carried out at high (approximately 20 km) and low (approximately 120 km) spatial resolutions., Participation of S. Herrera and J.M. Gutiérrez was partially supported by the project AfriCultuReS (European Union's Horizon 2020 program, grant agreement no, 774652). S. Lange acknowledges funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 641816 (CRESCENDO).

Compound flooding arises from storms causing concurrent extreme meteorological tides (that is the superposition of storm surge and waves) and precipitation. This flooding can severely affect densely populated low-lying coastal areas. Here, combining output from climate and ocean models, we analyse the concurrence probability of the meteorological conditions driving compound flooding. We show that, under a high emissions scenario, the concurrence probability would increase globally by more than 25% by 2100 compared to present. In latitudes above 40o north, compound flooding could become more than 2.5 times as frequent, in contrast to parts of the subtropics where it would weaken. Changes in extreme precipitation and meteorological tides account for most (77% and 20%, respectively) of the projected change in concurrence probability. The evolution of the dependence between precipitation and meteorological tide dominates the uncertainty in the projections. Our results indicate that not accounting for these effects in adaptation planning could leave coastal communities insufficiently protected against flooding., Concurrent coastal extremes - storm surges and flooding from precipitation - are 2.5 times as frequent in latitudes higher than 40∘N under a high emission scenario by 2100 compared to today, according to an analysis of climate and ocean model output.

VALUE is a network that developed a framework to evaluate statistical downscaling methods including model output statistics such as simple bias correction and quantile mapping; perfect prognosis methods such as regression models and analog methods; and weather generators. The first experiment addresses the downscaling performance in present climate with perfect predictors. This paper presents a synthesis of the VALUE special issue, with a focus on the results of this first experiment. This paper presents a synthesis of the results. Model output statistics performs mostly well, but requires predictors at a resolution close to the target one. Perfect prog performance depends crucially on model structure and predictor choice. Weather generators perform in principle well for all aspects that can be expressed by the available model structure. Inter-annual variability is underrepresented by both perfect prog and weather generator approaches. Spatial variability is poorly represented by almost all participating methods (inherited by model output statistics from the driving model, not represented by the perfect prog and weather generator methods). Further studies are required to systematically assess (a) the role of predictor choice for perfect prog; (b) the performance of spatial weather generators, to study the performance based on GCM predictors; (c) downscaling skill in simulated future climates; and (d) the credibility of simulated predictors in a future climate., VALUE was funded from 2012 to 2015 as EU COST Action ES1102.

We demonstrate both analytically and with a modelling example that cross-validation of free-running bias-corrected climate change simulations against observations is misleading. The underlying reasoning is as follows: a cross-validation can have in principle two outcomes. A negative (in the sense of not rejecting a null hypothesis), if the residual bias in the validation period after bias correction vanishes; and a positive, if the residual bias in the validation period after bias correction is large. It can be shown analytically that the residual bias depends solely on the difference between the simulated and observed change between calibration and validation periods. This change, however, depends mainly on the realizations of internal variability in the observations and climate model. As a consequence, the outcome of a cross-validation is also dominated by internal variability, and does not allow for any conclusion about the sensibility of a bias correction. In particular, a sensible bias correction may be rejected (false positive) and a non-sensible bias correction may be accepted (false negative). We therefore propose to avoid cross-validation when evaluating bias correction of free-running bias-corrected climate change simulations against observations. Instead, one should evaluate non-calibrated temporal, spatial and process-based aspects.

Biases in climate model simulations introduce biases in subsequent impact simulations. Therefore, bias correction methods are operationally used to post-process regional climate projections. However, many problems have been identified, and some researchers question the very basis of the approach. Here we demonstrate that a typical cross-validation is unable to identify improper use of bias correction. Several examples show the limited ability of bias correction to correct and to downscale variability, and demonstrate that bias correction can cause implausible climate change signals. Bias correction cannot overcome major model errors, and naive application might result in ill-informed adaptation decisions. We conclude with a list of recommendations and suggestions for future research to reduce, post-process, and cope with climate model biases. Bias correction methods aim to remove introduced bias for climate model simulations; however, improper use can result in spurious climate signals. This Perspective considers the issues of bias correction and makes recommendations for research to overcome model biases.

Temporal variability is an important feature of climate, comprising systematic variations such as the annual cycle, as well as residual temporal variations such as short-term variations, spells and variability from interannual to long-term trends. The EU-COST Action VALUE developed a comprehensive framework to evaluate downscaling methods. Here we present the evaluation of the perfect predictor experiment for temporal variability. Overall, the behaviour of the different approaches turned out to be as expected from their structure and implementation. The chosen regional climate model adds value to reanalysis data for most considered aspects, for all seasons and for both temperature and precipitation. Bias correction methods do not directly modify temporal variability apart from the annual cycle. However, wet day corrections substantially improve transition probabilities and spell length distributions, whereas interannual variability is in some cases deteriorated by quantile mapping. The performance of perfect prognosis (PP) statistical downscaling methods varies strongly from aspect to aspect and method to method, and depends strongly on the predictor choice. Unconditional weather generators tend to perform well for the aspects they have been calibrated for, but underrepresent long spells and interannual variability. Long-term temperature trends of the driving model are essentially unchanged by bias correction methods. If precipitation trends are not well simulated by the driving model, bias correction further deteriorates these trends. The performance of PP methods to simulate trends depends strongly on the chosen predictors., EU COST Association, Grant/Award Number: ES1102; Ministry of Education, Youth, and Sports of the Czech Republic, Grant/AwardNumber:LD12029

More intense precipitation will increase the flood potential from concurring storm surges and precipitation in the future., In low-lying coastal areas, the co-occurrence of high sea level and precipitation resulting in large runoff may cause compound flooding (CF). When the two hazards interact, the resulting impact can be worse than when they occur individually. Both storm surges and heavy precipitation, as well as their interplay, are likely to change in response to global warming. Despite the CF relevance, a comprehensive hazard assessment beyond individual locations is missing, and no studies have examined CF in the future. Analyzing co-occurring high sea level and heavy precipitation in Europe, we show that the Mediterranean coasts are experiencing the highest CF probability in the present. However, future climate projections show emerging high CF probability along parts of the northern European coast. In several European regions, CF should be considered as a potential hazard aggravating the risk caused by mean sea level rise in the future.

The propagation of drought from meteorological drought to soil moisture drought can be accelerated by high temperatures during dry periods. The occurrence of extremely long-duration dry periods in combination with extremely high temperatures may drive larger soil moisture deficits than either extreme occurring alone, and lead to severe impacts. In this study, we propose a framework to both characterise long-duration meteorological droughts that co-occur with extremely high temperatures and quantify their probability. We term these events as long-duration, dry and hot (DH) events and characterise them by their duration (D) and magnitude (M). D is defined as the consecutive number of days with precipitation below 1 mm, while M is the maximum daily maximum temperature during an event. A copula-based approach is then employed to estimate the probability of DH events. The framework is applied to Europe during the summer months of June, July and August. We also assess the change in probability that has occurred over the historical period 1950–2013 and find an increased probability of DH events throughout Europe where rising temperatures are found to be the main driver of this change. Dry periods are becoming hotter, leading to an increase in the occurrence of long-duration dry periods with extremely high temperatures. Some parts of Europe also show an increased probability of long-duration events although the relative change is not as strong as that seen with temperature. The results point to a predominant thermodynamic response of DH events to global warming and reaffirm previous research that soil moisture drought events are setting in faster and becoming more severe due to a change in the contributing meteorological hazards. It is hoped that the framework applied here will provide a starting point for further analysis of DH events in other locations and for the assessment of climate models.

Special Issue: VALUE: Validating and Integrating Downscaling Methods for Climate Change Research., Credible information about the properties and changes of extreme events on the regional and local scales is of prime importance in the context of future climate change. Within the EU-COST Action VALUE a comprehensive validation framework for downscaling methods has been developed. Here we present validation results for extremes of temperature and precipitation from the perfect predictor experiment that uses reanalysis-based predictors to isolate downscaling skill. The raw reanalysis output reveals that there is mostly a large bias with respect to the extreme index values at the considered stations across Europe, clearly pointing to the necessity of downscaling. The performance of the downscaling methods is closely linked to their specific structure and setup. All methods using parametric distributions require non-standard distributions to correctly represent marginal aspects of extremes. Also, the performance is much improved by explicitly including a seasonal component, particularly in case of precipitation. With respect to the marginal aspects of extremes the best performance is found for model output statistics (MOS), weather generators (WGs) as well as perfect prognosis (PP) methods using analogues. Spell-length-related extremes of temperature are best assessed by MOS and WGs, spell-length-related extremes of precipitation by MOS and PP methods using analogues. The skill of PP methods with transfer functions varies strongly across the methods and depends on the extreme index, region and season considered., This work has been carried out as part of the EU‐COST Action VALUE (ES1102). The authors are particularly grateful for the instructive and very helpful comments of two anonymous reviewers. P.M.M.S. thanks the Portuguese Foundation for Science and Technology (FCT) for funding under Project SOLAR‐PTDC/GEOMET/7078/2014.

This work analyses three uncertainty sources affecting the observation-based gridded data sets: station density, interpolation methodology and spatial resolution. For this purpose, we consider precipitation in two countries, Poland and Spain, three resolutions (0.11, 0.22 and 0.44°), three interpolation methods, both areal- and point-representative implementations, and three different densities of the underlying station network (high/medium/low density). As a result, for each resolution and interpolation approach, nine different grids have been obtained for each country and inter-compared using a variance decomposition methodology. Results indicate larger differences among the data sets for Spain than for Poland, mainly due to the larger spatial variability and complex orography of the former region. The variance decomposition points out to station density as the most influential factor, independent of the season, the areal- or point-representative implementation and the country considered, and slightly increasing with the spatial resolution. In contrast, the decomposition is stable when extreme precipitation indices are considered, in particular for the 50-year return value. Finally, the uncertainty due to station sub-sampling inside a particular grid box decreases with the number of stations used in the averaging/interpolation. In the case of spatially homogeneous grid boxes, the interpolation approach obtains similar results for all the parameters, excepting the wet day frequency, independently of the number of stations. When there is a more significant internal variability in the grid box, the interpolation is more sensitive to the number of stations, pointing out to a minimum stations’ density for the target resolution (six to seven stations)., VALUE has been funded as EU COST Action ES1102. Participation of S.H. and J.M.G. was partially supported by the project MULTI‐SDM (CGL2015‐66583‐R, MINECO/FEDER). P.M.M.S. and R.M.C. wish to acknowledge the projects SOLAR (PTDC/GEOMET/7078/2014) and FCT UID/GEO/50019/ 2013 ‐ Instituto Dom Luiz, both financed by the Fundação para a Ciência e Tecnologia.

Special Issue: VALUE: Validating and Integrating Downscaling Methods for Climate Change Research: et al., VALUE is an open European collaboration to intercompare downscaling approaches for climate change research, focusing on different validation aspects (marginal, temporal, extremes, spatial, process-based, etc.). Here we describe the participating methods and first results from the first experiment, using “perfect” reanalysis (and reanalysis-driven regional climate model (RCM)) predictors to assess the intrinsic performance of the methods for downscaling precipitation and temperatures over a set of 86 stations representative of the main climatic regions in Europe. This study constitutes the largest and most comprehensive to date intercomparison of statistical downscaling methods, covering the three common downscaling approaches (perfect prognosis, model output statistics—including bias correction—and weather generators) with a total of over 50 downscaling methods representative of the most common techniques. Overall, most of the downscaling methods greatly improve (reanalysis or RCM) raw model biases and no approach or technique seems to be superior in general, because there is a large method-to-method variability. The main factors most influencing the results are the seasonal calibration of the methods (e.g., using a moving window) and their stochastic nature. The particular predictors used also play an important role in cases where the comparison was possible, both for the validation results and for the strength of the predictor–predictand link, indicating the local variability explained. However, the present study cannot give a conclusive assessment of the skill of the methods to simulate regional future climates, and further experiments will be soon performed in the framework of the EURO-CORDEX initiative (where VALUE activities have merged and follow on). Finally, research transparency and reproducibility has been a major concern and substantive steps have been taken. In particular, the necessary data to run the experiments are provided at http://www.value-cost.eu/data and data and validation results are available from the VALUE validation portal for further investigation: http://www.value-cost.eu/validationportal., This work has been performed in the framework of the VALUE COST Action ES1102, under FP7 programme J.M.G. and S.H. acknowledge partial funding from MULTI-SDM project (MINECO/FEDER, CGL2015-66583-R). B.H. and D.R. acknowledge COMPLEX project (FP7-ENV-2012, No: 308601). M.T. was supported by HOPE project (MINECO, CGL2014-52571-R). Participation of M.D., P.S. and R.H. was funded by the Ministry of Education, Youth, and Sports of the Czech Republic contracts LD12029, LD14043 and LD12059, respectively.

The spatial dependence of meteorological variables is crucial for many impacts, for example, droughts, floods, river flows, energy demand, and crop yield. There is thus a need to understand how well it is represented in downscaling (DS) products. Within the COST Action VALUE, we have conducted a comprehensive analysis of spatial variability in the output of over 40 different DS methods in a perfect predictor setup. The DS output is evaluated against daily precipitation and temperature observations for the period 1979–2008 at 86 sites across Europe and 53 sites across Germany. We have analysed the dependency of correlations of daily temperature and precipitation series at station pairs on the distance between the stations. For the European data set, we have also investigated the complexity of the downscaled data by calculating the number of independent spatial degrees of freedom. For daily precipitation at the German network, we have additionally evaluated the dependency of the joint exceedance of the wet day threshold and of the local 90th percentile on the distance between the stations. Finally, we have investigated regional patterns of European monthly precipitation obtained from rotated principal component analysis. We analysed Perfect Prog (PP) methods, which are based on statistical relationships derived from observations, as well as Model Output Statistics (MOS) approaches, which attempt to correct simulated variables. In summary, we found that most PP DS methods, with the exception of multisite analog methods and a method that explicitly models spatial dependence yield unrealistic spatial characteristics. Regional climate model-based MOS methods showed good performance with respect to correlation lengths and the joint occurrence of wet days, but a substantial overestimation of the joint occurrence of heavy precipitation events. These findings apply to the spatial scales that are resolved by our observation network, and similar studies with higher resolutions, which are relevant for small hydrological catchment, are desirable., EU, Grant/Award Number: EU COST Action ES1102.

MV acknowledges funding from French National Research Agency (ANR): ANR-project StaRMIP (grant agreement ANR-12-JS06-0005-01). SMcG acknowledges contributions from U.S. Department of Defense ESTCP Grant: RC-201666 and U.S. Department of Energy RGCM Grant: DE-SC0016438.

Climate models are our major source of knowledge about climate change. The impacts of climate change are often quantified by impact models. Whereas impact models typically require high resolution unbiased input data, global and regional climate models are in general biased, their resolution is often lower than desired. Thus, many users of climate model data apply some form of bias correction and downscaling. A fundamental assumption of bias correction is that the considered climate model produces skillful input for a bias correction, including a plausible representation of climate change. Current bias correction methods cannot plausibly correct climate change trends, and have limited ability to downscale. Cross validation of marginal aspects is not sufficient to evaluate bias correction and needs to be complemented by further analyses. Future research should address the development of stochastic models for downscaling and approaches to explicitly incorporate process understanding.

As climate change research becomes increasingly applied, the need for actionable information is growing rapidly. A key aspect of this requirement is the representation of uncertainties. The conventional approach to representing uncertainty in physical aspects of climate change is probabilistic, based on ensembles of climate model simulations. In the face of deep uncertainties, the known limitations of this approach are becoming increasingly apparent. An alternative is thus emerging which may be called a ‘storyline’ approach. We define a storyline as a physically self-consistent unfolding of past events, or of plausible future events or pathways. No a priori probability of the storyline is assessed; emphasis is placed instead on understanding the driving factors involved, and the plausibility of those factors. We introduce a typology of four reasons for using storylines to represent uncertainty in physical aspects of climate change: (i) improving risk awareness by framing risk in an event-oriented rather than a probabilistic manner, which corresponds more directly to how people perceive and respond to risk; (ii) strengthening decision-making by allowing one to work backward from a particular vulnerability or decision point, combining climate change information with other relevant factors to address compound risk and develop appropriate stress tests; (iii) providing a physical basis for partitioning uncertainty, thereby allowing the use of more credible regional models in a conditioned manner and (iv) exploring the boundaries of plausibility, thereby guarding against false precision and surprise. Storylines also offer a powerful way of linking physical with human aspects of climate change.

We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously.

Compound events are extreme impacts that depend on multiple variables that need not be extreme themselves. In this study, we analyze soil moisture drought as a compound event of precipitation and potential evapotranspiration (PET) on multiple time scales related to both meteorological drought and heat waves in wet, transitional, and dry climates in Europe during summer. Drought indices that incorporate PET to account for the effect of temperature on drought conditions are sensitive to global warming. However, as evapotranspiration (ET) is moisture limited in dry climates, the use of such drought indices has often been criticized. We therefore assess the relevance of the contributions of both precipitation and PET to the estimation of soil moisture drought. Applying a statistical model based on pair copula constructions to data from FluxNet sites in Europe, we find at all sites that precipitation exerts the main control over soil moisture drought. At wet sites PET is additionally required to explain the onset, severity, and persistence of drought events over different time scales. At dry sites, where ET is moisture limited in summer, PET does not improve the estimation of soil moisture. In dry climates, increases in drought severity measured by indices incorporating PET may therefore not indicate further drying of soil but the increased availability of energy that can contribute to other environmental hazards such as heat waves and wildfires. We therefore highlight that drought indices including PET should be interpreted within the context of the climate and season in which they are applied in order to maximize their value.

Statistical downscaling methods (SDMs) are techniques used to downscale and/or bias correct climate model results to regional or local scales. The European network VALUE developed a framework to evaluate and intercompare SDMs. One of VALUE’s experiments is the perfect predictor experiment that uses reanalysis predictors to isolate downscaling skill. Most evaluation papers for SDMs employ simple statistical diagnostics and do not follow a process-based rationale. Thus, in this paper, a process-based evaluation has been conducted for the more than 40 participating model output statistics (MOS, mostly bias correction) and perfect prognosis (PP) methods, for temperature and precipitation at 86 weather stations across Europe. The SDMs are analysed following the so-called “regime- oriented” technique, focussing on relevant features of the atmospheric circulation at large to local scales. These features comprise the North Atlantic Oscillation, blocking and selected Lamb weather types and at local scales the bora wind and the western Iberian coastal-low level jet. The representation of the local weather response to the selected features depends strongly on the method class. As expected, MOS is unable to generate process sensitivity when it is not simulated by the predictors (ERA- Interim). Moreover, MOS often suffers from an inflation effect when a predictor is used for more than one station. The PP performance is very diverse and depends strongly on the implementation. Although conditioned on predictors that typically describe the large- scale circulation, PP often fails in capturing the process sensitivity correctly. Stochastic generalized linear models supported by well- chosen predictors show improved skill to represent the sensitivities.

To assess potential impacts of climate change for a specific location, one typically employs climate model simulations at the grid box corresponding to the same geographical location. For most of Europe, this choice is well justified. But, based on regional climate simulations, we show that simulated climate might be systematically displaced compared to observations. In particular in the rain shadow of mountain ranges, a local grid box is therefore often not representative of observed climate: the simulated windward weather does not flow far enough across the mountains; local grid boxes experience the wrong air masses and atmospheric circulation. In some cases, also the local climate change signal is deteriorated. Classical bias correction methods fail to correct these location errors. Often, however, a distant simulated time series is representative of the considered observed precipitation, such that a non-local bias correction is possible. These findings also clarify limitations of bias correcting global model errors, and of bias correction against station data.

We investigate how well a suite of regional climate models (RCMs) from the ENSEMBLES project represents the residual spatial dependence of daily precipitation. The study area we consider is a 200 km×200 km region in south central Norway, with RCMs driven by ERA-40 boundary conditions at a horizontal resolution of approximately 25 km×25 km. We model the residual spatial dependence with pair-copula constructions, which allows us to assess both the overall and tail dependence in precipitation, including uncertainty estimates. The selected RCMs reproduce the overall dependence rather well, though the discrepancies compared to observations are substantial. All models overestimate the overall dependence in the west-east direction. They also overestimate the upper tail dependence in the north-south direction during winter, and in the west-east direction during summer, whereas they tend to underestimate this dependence in the north-south direction in summer. Moreover, many of the climate models do not simulate the small-scale dependence patterns caused by the pronounced orography well. However, the misrepresented residual spatial dependence does not seem to affect estimates of high quantiles of extreme precipitation aggregated over a few grid boxes. The underestimation of the area-aggregated extreme precipitation is due mainly to the well-known underestimation of the univariate margins for individual grid boxes, suggesting that the correction of RCM biases in precipitation might be feasible

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License.-- et al., VALUE is an open European network to validate and compare downscaling methods for climate change research. VALUE aims to foster collaboration and knowledge exchange between climatologists, impact modellers, statisticians, and stakeholders to establish an interdisciplinary downscaling community. A key deliverable of VALUE is the development of a systematic validation framework to enable the assessment and comparison of both dynamical and statistical downscaling methods. In this paper, we present the key ingredients of this framework. VALUE's main approach to validation is user- focused: starting from a specific user problem, a validation tree guides the selection of relevant validation indices and performance measures. Several experiments have been designed to isolate specific points in the downscaling procedure where problems may occur: what is the isolated downscaling skill? How do statistical and dynamical methods compare? How do methods perform at different spatial scales? Do methods fail in representing regional climate change? How is the overall representation of regional climate, including errors inherited from global climate models? The framework will be the basis for a comprehensive community-open downscaling intercomparison study, but is intended also to provide general guidance for other validation studies., VALUE is funded via the EU FP7 programme as EU COST Action ES1102.

The application of climate change impact assessment (CCIA) studies in general and especially the linkages between different actor groups typically involved is often not trivial and subject to many limitations and uncertainties. Disciplinary issues like competing downscaling approaches, imperfect climate and impact model data and uncertainty propagation as well as the selection of appropriate data sets are only one part of the story. Interdisciplinary and transdisciplinary challenges add to these, as climate data and impact model data provision and their usage require at least a minimum of common work and shared understanding among actors. Here, we provide the VALUE perspective on current disciplinary challenges and limitations at the downscaling interface and elaborate transdisciplinary issues that hamper a proper working downscaling interface. The perspective is partly based on a survey on user needs of downscaled data that was distributed among 62 participants across Europe involving 22 sectors. Partly, it is based on the exchanges and experiences gained during the lifetime of VALUE that brought together different actor groups of different disciplines: climate modellers, impact modellers, statisticians and stakeholders. We outline a sketch that summarizes the linkages between the main identified actor groups: climate model data providers, impact modellers and societal users. We summarize review and structure current actors groups, needs and issues. We argue that this structuring enables involved actors to tackle these issues in a more organized and hence effective way. A key solution to several difficulties at the downscaling interface is to our understanding the development of guidelines based on benchmark tests like the VALUE framework. In addition, fostering communication between actor groups – and financing this communication – is essential to obtain the best possible CCIA as a prerequisite for robust adaptation.

Quantile mapping is routinely applied to correct biases of regional climate model simulations compared to observational data. If the observations are of similar resolution as the regional climate model, quantile mapping is a feasible approach. However, if the observations are of much higher resolution, quantile mapping also attempts to bridge this scale mismatch. Here, it is shown for daily precipitation that such quantile mapping–based downscaling is not feasible but introduces similar problems as inflation of perfect prognosis (“prog”) downscaling: the spatial and temporal structure of the corrected time series is misrepresented, the drizzle effect for area means is overcorrected, area-mean extremes are overestimated, and trends are affected. To overcome these problems, stochastic bias correction is required.

The beginning of the 21st century was marked by a number of severe summer floods in Central Europe associated with extreme precipitation (e.g., Elbe 2002, Oder 2010 and Danube 2013). Extratropical storms, known as Vb-cyclones, cause summer extreme precipitation events over Central Europe and can thus lead to such floodings. Vb-cyclones develop over the Mediterranean Sea, which itself strongly warmed during recent decades. Here we investigate the influence of increased Mediterranean Sea surface temperature (SST) on extreme precipitation events in Central Europe. To this end, we carry out atmosphere model simulations forced by average Mediterranean SSTs during 1970–1999 and 2000–2012. Extreme precipitation events occurring on average every 20 summers in the warmer-SST-simulation (2000–2012) amplify along the Vb-cyclone track compared to those in the colder-SST-simulation (1970–1999), on average by 17% in Central Europe. The largest increase is located southeast of maximum precipitation for both simulated heavy events and historical Vb-events. The responsible physical mechanism is increased evaporation from and enhanced atmospheric moisture content over the Mediterranean Sea. The excess in precipitable water is transported from the Mediterranean Sea to Central Europe causing stronger precipitation extremes over that region. Our findings suggest that Mediterranean Sea surface warming amplifies Central European precipitation extremes.

We present an analysis of daily extreme precipitation events for the extended winter season (October–March) at 20 Mediterranean coastal sites covering the period 1950–2006. The heavy tailed behaviour of precipitation extremes and estimated return levels, including associated uncertainties, are derived applying a procedure based on the Generalized Pareto Distribution, in combination with recently developed methods. Precipitation extremes have an important contribution to make seasonal totals (approximately 60% for all series). Three stations (one in the western Mediterranean and the others in the eastern basin) have a 5-year return level above 100 mm, while the lowest value (estimated for two Italian series) is equal to 58 mm. As for the 50-year return level, an Italian station (Genoa) has the highest value of 264 mm, while the other values range from 82 to 200 mm. Furthermore, six series (from stations located in France, Italy, Greece, and Cyprus) show a significant negative tendency in the probability of observing an extreme event. The relationship between extreme precipitation events and the large scale atmospheric circulation at the upper, mid and low troposphere is investigated by using NCEP/NCAR reanalysis data. A 2-step classification procedure identifies three significant anomaly patterns both for the western-central and eastern part of the Mediterranean basin. In the western Mediterranean, the anomalous southwesterly surface to mid-tropospheric flow is connected with enhanced moisture transport from the Atlantic. During ≥5-year return level events, the subtropical jet stream axis is aligned with the African coastline and interacts with the eddy-driven jet stream. This is connected with enhanced large scale ascending motions, instability and leads to the development of severe precipitation events. For the eastern Mediterranean extreme precipitation events, the identified anomaly patterns suggest warm air advection connected with anomalous ascent motions and an increase of the low- to mid-tropospheric moisture. Furthermore, the jet stream position (during ≥5-year return level events) supports the eastern basin being in a divergence area, where ascent motions are favoured. Our results contribute to an improved understanding of daily precipitation extremes in the cold season and associated large scale atmospheric features.

We develop a vector generalised linear model to describe the influence of the atmospheric circulation on extreme daily precipitation across the UK. The atmospheric circulation is represented by three covariates, namely synoptic scale airflow strength, direction and vorticity; the extremes are represented by the monthly maxima of daily precipitation, modelled by the generalised extreme value distribution (GEV). The model parameters for data from 689 rain gauges across the UK are estimated using a maximum likelihood estimator. Within the framework of vector generalised linear models, various plausible models exist to describe the influence of the individual covariates, possible nonlinearities in the covariates and seasonality. We selected the final model based on the Akaike information criterion (AIC), and evaluated the predictive power of individual covariates by means of quantile verification scores and leave-one-out cross validation. The final model conditions the location and scale parameter of the GEV on all three covariates; the shape parameter is modelled as a constant. The relationships between strength and vorticity on the one hand, and the GEV location and scale parameters on the other hand are modelled as natural cubic splines with two degrees of freedom. The influence of direction is parameterised as a sine with amplitude and phase. The final model has a common parameterisation for the whole year. Seasonality is partly captured by the covariates themselves, but mostly by an additional annual cycle that is parameterised as a phase-shifted sine and accounts for physical influences that we have not attempted to explicitly model, such as humidity.

International audience; We examine a statistical model for the description of the seasonal variation of extreme daily precipitation at 689 stations across the UK. The probability distribution for monthly maximum precipitation intensity is modelled with a generalised extreme-value distribution (GEV). Instead of modelling the distribution of precipitation maxima separately for every month, we propose an overall model with seasonally-varying location and scale parameters and a constant shape parameter. This model is tested against an augmented version with the shape parameter allowed to vary as well. Furthermore, we compare model adequacy for block length of one and two month and found no major improvements for the longer block-length. Based on this model, the 10 and 100-year return levels are calculated conditioned on the month of the year. The interpolation of return levels to a complete coverage of the UK allows for an identification of spatial patterns and their temporal evolution. These patterns suggest that different mechanisms for extreme precipitation are dominant in different regions of the UK.

The annual cycle of extreme 1-day precipitation events across the UK is investigated by developing a statistical model and fitting it to data from 689 rain gauges. A generalized extreme-value distribution (GEV) is fit to the time series of monthly maxima, across all months of the year simultaneously, by approximating the annual cycles of the location and scale parameters by harmonic functions, while keeping the shape parameter constant throughout the year. We average the shape parameter of neighbouring rain gauges to decrease parameter uncertainties, and also interpolate values of all model parameters to give complete coverage of the UK. The model reveals distinct spatial patterns for the estimated parameters. The annual mean of the location and scale parameter is highly correlated with orography. The annual cycle of the location parameter is strong in the northwest UK (peaking in late autumn or winter) and in East Anglia (where it peaks in late summer), and low in the Midlands. The annual cycle of the scale parameter exhibits a similar pattern with strongest amplitudes in East Anglia. The spatial patterns of the annual cycle phase suggest that they are linked to the dominance of frontal precipitation for generating extreme precipitation in the west and convective precipitation in the southeast of the UK. The shape parameter shows a gradient from positive values in the east to negative values in some areas of the west. We also estimate 10-year and 100-year return levels at each rain gauge, and interpolated across the UK.

Precipitation is highly variable in space and time; hence, rain gauge time series generally exhibit additional random small-scale variability compared to area averages. Therefore, differences between daily precipitation statistics simulated by climate models and gauge observations are generally not only caused by model biases, but also by the corresponding scale gap. Classical bias correction methods, in general, cannot bridge this gap; they do not account for small-scale random variability and may produce artifacts. Here, stochastic model output statistics is proposed as a bias correction framework to explicitly account for random small-scale variability. Daily precipitation simulated by a regional climate model (RCM) is employed to predict the probability distribution of local precipitation. The pairwise correspondence between predictor and predictand required for calibration is ensured by driving the RCM with perfect boundary conditions. Wet day probabilities are described by a logistic regression, and precipitation intensities are described by a mixture model consisting of a gamma distribution for moderate precipitation and a generalized Pareto distribution for extremes. The dependence of the model parameters on simulated precipitation is modeled by a vector generalized linear model. The proposed model effectively corrects systematic biases and correctly represents local-scale random variability for most gauges. Additionally, a simplified model is considered that disregards the separate tail model. This computationally efficient model proves to be a feasible alternative for precipitation up to moderately extreme intensities. The approach sets a new framework for bias correction that combines the advantages of weather generators and RCMs.

In his comment, G. Bürger criticizes the conclusion that inflation of trends by quantile mapping is an adverse effect. He assumes that the argument would be “based on the belief that long-term trends and along with them future climate signals are to be large scale.” His line of argument reverts to the so-called inflated regression. Here it is shown, by referring to previous critiques of inflation and standard literature in statistical modeling as well as weather forecasting, that inflation is built upon a wrong understanding of explained versus unexplained variability and prediction versus simulation. It is argued that a sound regression-based downscaling can in principle introduce systematic local variability in long-term trends, but inflation systematically deteriorates the representation of trends. Furthermore, it is demonstrated that inflation by construction deteriorates weather forecasts and is not able to correctly simulate small-scale spatiotemporal structure.

A multi-model ensemble of regional climate projections for Europe is employed to investigate how the time of emergence (TOE) for seasonal sums and maxima of daily precipitation depends on spatial scale. The TOE is redefined for emergence from internal variability only; the spread of the TOE due to imperfect climate model formulation is used as a measure of uncertainty in the TOE itself. Thereby, the TOE becomes a fundamentally limiting timescale and translates into a minimum spatial scale on which robust conclusions can be drawn about precipitation trends. Thus, minimum temporal and spatial scales for adaptation planning are also given. In northern Europe, positive winter trends in mean and heavy precipitation, and in southwestern and southeastern Europe, summer trends in mean precipitation already emerge within the next few decades. However, across wide areas, especially for heavy summer precipitation, the local trend emerges only late in the 21st century or later. For precipitation averaged to larger scales, the trend, in general, emerges earlier.

[1] The representation of the annual cycle of heavy daily precipitation events across the United Kingdom within 14 regional climate models (RCMs) and the European observation data set (E-OBS) over the 1961–2000 period is investigated. We model extreme precipitation as an inhomogeneous Poisson process with a non-stationary threshold and use a sinusoidal model for the location and scale parameter of the corresponding generalized extreme value distribution and a constant shape parameter. First we fit the statistical model to the UK Met Office 5 km gridded precipitation data set (UKMO). Second the statistical model is fitted to 14 reanalysis driven 25 km resolution RCMs from the ENSEMBLES project and to E-OBS. The resulting characteristics from the RCMs and from E-OBS are compared with those from UKMO. We study the peak time of the annual cycle of the monthly return levels, the relative amplitude of their annual cycle and the relative bias of their absolute values. We show that the performance of the RCMs depends strongly on the region. The RCMs show deficits in modeling the characteristics of the annual cycle, especially in modeling its relative amplitude and mainly in Eastern England. However the peak time of the annual cycle is adequately simulated by most RCMs. E-OBS exhibits considerable biases in the absolute values of all monthly return levels, but the relative amplitude and the phase of the annual cycle of heavy precipitation are well represented. Our results imply that studies which rely on the explicit annual cycle of simulated heavy precipitation should be carefully considered.

Bias correcting climate models implicitly assumes stationarity of the correction function. This assumption is assessed for regional climate models in a pseudo reality for seasonal mean temperature and precipitation sums. An ensemble of regional climate models for Europe is used, all driven with the same transient boundary conditions. Although this model-dependent approach does not assess all possible bias non-stationarities, conclusions can be drawn for the real world. Generally, biases are relatively stable, and bias correction on average improves climate scenarios. For winter temperature, bias changes occur in the Alps and ice covered oceans caused by a biased forcing sensitivity of surface albedo; for summer temperature, bias changes occur due to a biased sensitivity of cloud cover and soil moisture. Precipitation correction is generally successful, but affected by internal variability in arid climates. As model sensitivities vary considerably in some regions, multi model ensembles are needed even after bias correction. Key Points: - Bias correction in general improves future climate simulations - Cloud cover, soil moisture and albedo changes may cause temperature bias changes - Precipitation biases in arid regions are affected by internal variability

We investigate future changes in the annual cycle of heavy daily precipitation events across the British Isles in the periods 2021–2060 and 2061–2100, relative to present day climate. Twelve combinations of regional and global climate models forced with the A1B scenario are used. The annual cycle is modelled as an inhomogeneous Poisson process with sinusoidal models for location and scale parameters of the generalized extreme value distribution. Although the peak times of the annual cycle vary considerably between projections for the 2061–2100 period, a robust shift towards later peak times is found for the south-east, while in the north-west there is evidence for a shift towards earlier peak times. In the remaining parts of the British Isles no changes in the peak times are projected. For 2021–2060 this signal is weak. The annual cycle’s relative amplitude shows no robust signal, where differences in projected changes are dominated by global climate model differences. The relative contribution of anthropogenic forcing and internal climate variability to changes in the relative amplitude cannot be identified with the available ensemble. The results might be relevant for the development of adequate risk-reduction strategies, for insurance companies and for the management and planning of water resources

We study the influence of synoptic scale atmospheric circulation on extreme daily precipitation across the United Kingdom, using observed time series from 689 rain gauges. To this end we employ a statistical model, that uses airflow strength, direction and vorticity as predictors for the generalised extreme value distribution of monthly precipitation maxima. The inferred relationships are connected with the dominant westerly flow, the orography, and the moisture supply from surrounding seas. We aggregated the results for individual rain gauges to regional scales to investigate the temporal variability of extreme precipitation. Airflow explains a significant fraction of the variability on subannual to decadal time scales. A large fraction of the especially heavy winter precipitation during the 1980s and 1990s in north Scotland can be attributed to a prevailing positive phase of the North Atlantic Oscillation. Our statistical model can be used for statistical downscaling and to validate regional climate model output.

Precipitation downscaling improves the coarse resolution and poor representation of precipitation in global climate models and helps end users to assess the likely hydrological impacts of climate change. This paper integrates perspectives from meteorologists, climatologists, statisticians, and hydrologists to identify generic end user (in particular, impact modeler) needs and to discuss downscaling capabilities and gaps. End users need a reliable representation of precipitation intensities and temporal and spatial variability, as well as physical consistency, independent of region and season. In addition to presenting dynamical downscaling, we review perfect prognosis statistical downscaling, model output statistics, and weather generators, focusing on recent developments to improve the representation of space-time variability. Furthermore, evaluation techniques to assess downscaling skill are presented. Downscaling adds considerable value to projections from global climate models. Remaining gaps are uncertainties arising from sparse data; representation of extreme summer precipitation, subdaily precipitation, and full precipitation fields on fine scales; capturing changes in small-scale processes and their feedback on large scales; and errors inherited from the driving global climate model. © 2010 by the American Geophysical Union.

We investigated the influence of atmospheric noise on the generation of interannual El Niño variability. Therefore, we perturbed a conceptual ENSO delay model with surrogate windstress data generated from tropical windspeed measurements. The effect of the additional stochastic forcing was studied for various parameter sets including periodic and chaotic regimes. The evaluation was based on a spectrum and amplitude-period relation comparison between model and measured sea surface temperature data. The additional forcing turned out to increase the variability of the model output in general. The noise-free model was unable to reproduce the observed spectral bandwidth for any choice of parameters. On the contrary, the stochastically forced model is capable of producing a realistic spectrum. The weakly nonlinear regimes of the model exhibit a proportional relation between amplitude and period matching the relation derived from measurement data. The chaotic regime, however, shows an inversely proportional relation. A stability analysis of the different regimes revealed that the spectra of the weakly nonlinear regimes are robust against slight parameter changes representing disregarded physical mechanisms, whereas the chaotic regime exhibits a very unstable realistic spectrum. We conclude that the model including stochastic forcing in a parameter range of moderate nonlinearity best matches the real conditions. This suggests that atmospheric noise plays an important role in the coupled tropical pacific ocean-atmosphere system.

Received 13 April 2005; revised 4 July 2005; accepted 8 July 2005; published 10 August 2005. (1) We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Nino/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886-1908 and 1964-1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/ Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling. Citation: Maraun, D., and J. Kurths (2005), Epochs of phase coherence between El Nino/Southern Oscillation and Indian monsoon, Geophys. Res. Lett., 32, L15709

In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs.

In our analysis [Rahmstorf et al., 2004], we arrived at two main conclusions: the data of Shaviv and Veizer [2003] do not show a significant correlation of cosmic ray flux (CRF) and climate, and the authors' estimate of climate sensitivity to CO2 based on a simple regression analysis is questionable. After careful consideration of Shaviv and Veizer's comment, we want to uphold and reaffirm these conclusions. Concerning the question of correlation, we pointed out that a correlation arose only after several adjustments to the data, including shifting one of the four CRF peaks and stretching the time scale. To calculate statistical significance, we first need to compute the number of independent data points in the CRF and temperature curves being correlated, accounting for their autocorrelation. A standard estimate [Quenouille, 1952] of the number of effective data points is NEFF ≅ N1+2∑k=1Nr1(k)r2(k) where N is the total number of data points and r1, r2 are the autocorrelations of the two series. For the curves of Shaviv and Veizer [2003], the result is NEFF = 4.8. This is consistent with the fact that these are smooth curves with four humps, and with the fact that for CRF the position of the four peaks is determined by four spiral arm crossings or four meteorite clusters, respectively; that is, by four independent data points. The number of points that enter the calculation of statistical significance of a linear correlation is (NEFF− 2), since any curves based on only two points show perfect correlation; at least three independent points are needed for a meaningful result.