Trends in winter circulation over the British Isles and central Europe in twenty-first century projections by 25 CMIP5 GCMs

Winter midlatitude atmospheric circulation has been extensively studied for its tight link to surface weather, and automated circulation classifications have often been used to this end. Here, eight such classifications are applied to daily sea level pressure patterns simulated by an ensemble of CMIP5 GCMs twenty-first century projections for the British Isles and central Europe in order to robustly estimate future changes in frequency, persistence, and strength of synoptic-scale circulation there. All methods are able to identify present-day biases of models reported before, such as an overestimated occurrence of zonal flow and underestimation of anticyclonic conditions and easterly advection, although the strength of these biases varies among the methods. In future, models show that the zonal flow will become more frequent while the strength of the mean flow is not projected to change. Over the British Isles, the models that better simulate the latitude of zonal flow over the historical period indicate a slight equatorward shift of westerlies in their projections, while the poleward expansion of circulation—expected in future at global scale—is apparent in those models that have large errors. Over central Europe, some classifications indicate an increase in persistence and especially in frequency of anticyclonic types, which is, however, shown to be rather an artifact of some methods than a real feature. On the other hand, the easterly flow is robustly projected to become markedly weaker in central Europe, which we hypothesize might be an important factor contributing to the projected decrease of cold extremes there.

The large-scale atmospheric circulation in the northern midlatitudes has been extensively studied owing to its link to local climate elements, which is especially tight in winter (e.g., Beck et al. 2007; Broderick and Fealy 2015; Cattiaux et al. 2012, 2013a; Plavcová et al. 2014; Cahynová and Huth 2016). In particular, future changes of circulation are of great interest as—at smaller spatial scales—they may considerably mitigate or enhance the expected thermodynamic changes to the climate system caused by increasing concentrations of radiatively active gasses (Belleflamme et al. 2015; Horton et al. 2015). For instance, increased persistence of circulation may amplify the incidence and severity of temperature extremes (Kyselý 2007, 2008; Blenkinsop et al. 2009; Buehler et al. 2011; Plavcová and Kyselý 2016) and changes in synoptic-scale weather systems may alter extremity and spatial distribution of precipitation (Blenkinsop et al. 2015; Röthlisberger et al. 2016).

Observational and observation-based datasets have been widely used to study various aspects of circulation over the North Atlantic Ocean and Europe including its links to meteorological elements and environmental phenomena there. Recently, simulations by regional climate models (RCMs) and global climate models (GCMs) have also become very popular in this kind of studies since they allow not only for the study of atmospheric variability and trends but also for an investigation of the response of atmosphere to individual forcings (Barnes and Screen 2015). Moreover, models are less constrained by limitations typical for observational datasets such as data inhomogeneities and limited time span (Shepherd 2014; Reichler 2016).

Nonetheless, the reliability and usability of model simulations has still been limited by the longstanding issue that they often fail to reproduce various aspects of the historical climate closely enough. The main weakness of most GCMs in simulating winter Euro-Atlantic circulation—including those participating in the Coupled Model Intercomparison Project phase 5 (CMIP5) (Taylor et al. 2012)—is an overestimation of the meridional pressure gradient (e.g., Brands et al. 2013; Wójcik 2015), that is, a tendency toward the positive phase of the North Atlantic Oscillation (e.g., Marshall et al. 2001), the main mode of winter Euro-Atlantic climate variability. Therefore, GCMs tend to overestimate westerlies carrying relatively warm and moist maritime air masses to Europe, while the occurrence of persistent blocking anticyclones over the northeast Atlantic Ocean or Europe that would divert the westerlies and be conductive to the advection of cold continental or Arctic air masses to Europe are suppressed (e.g., Blenkinsop et al. 2009; Demuzere et al. 2009; Pastor and Casado 2012; Cattiaux et al. 2013a; Zappa et al. 2014; Hoskins and Woolings 2015; Otero et al. 2017; Rohrer et al. 2017). Furthermore, projections of late twenty-first century winter circulation indicate that the westerly circulation could become even more frequent over most of Europe with a significant impact on temperature (Plavcová and Kyselý 2013; Otero et al. 2017).

Numerous studies have analyzed possible causes of aforementioned circulation biases over the Euro-Atlantic domain (or midlatitudes in general), suggesting several issues. Some of these issues are related to the model representation of other components of the planetary circulation, including their natural variability and response to external forcings, such as changes of intensity and size of the Hadley circulation (Previdi and Liepert 2007; Allen et al. 2014; Tao et al. 2016) and its interaction with Rossby waves (Kidston et al. 2013) and changes in the polar vortex induced by fluctuations in stratospheric ozone concentrations (Smith and Polvani 2014; Calvo et al. 2015). Other studies pointed to errors in sea surface temperatures (Wang et al. 2014), including differences in modes of internal sea-surface temperature variability between models and observations such as the Pacific Decadal Oscillation (Allen et al. 2014) and Atlantic Multidecadal Oscillation (Han et al. 2016; Peings et al. 2016), couplings between surface, free troposphere, and stratosphere (e.g., Manzini et al. 2014; Furtado et al. 2015; Reichler 2016), imperfect representation of the stratosphere due to too shallow atmosphere in some models (Charlton-Perez et al. 2013; Lee and Black 2015), aerosol forcing (Allen et al. 2012), and unresolved subgrid processes (e.g., Cattiaux et al. 2013b).

Additionally, research has recently flourished on the ongoing Arctic Amplification (AA) of global near-surface warming, effects of which may be important not only for Arctic climate but —via changes in atmospheric dynamics caused by decreased meridional gradients—also for climate of lower latitudes [see, e.g., the latest review by Francis et al. (2017) and references there]. These high-to-mid latitude teleconnections are, nonetheless, generally missing or very weak in most CMIP5 models (Woolings et al. 2014; Barnes and Polvani 2015; Boland et al. 2017), the models projecting—on top of the exaggerated westerlies—a gradual shift of the westerlies poleward, as part of the expansion of planetary circulation due to global warming (e.g., Bender et al. 2012; Reichler 2016; Tao et al. 2016). To date, there is no agreement on the role of the Arctic in the ongoing and future climate changes (Barnes and Screen 2015). Clearly, considerable effort will be necessary to produce models output of which would closely resemble the real atmosphere, especially considering the limitations of existing observational datasets and our incomplete knowledge of the climate system.

Many of the studies on atmospheric dynamics focus on large, continental or hemispheric scales. However, recent and projected changes in circulation, for example in the position and variability of jets (Barnes and Polvani 2013; Grise and Polvani 2014; Simpson et al. 2014), frequency of blocking (Dunn-Sigouin and Son 2013; Masato et al. 2014), and midlatitude flow waviness (Cattiaux et al. 2016; Peings et al. 2017) appear highly spatially variable. Studies oriented on synoptic-scale circulation can complement the image by showing how circulation is projected to change in highly populated regions and on daily basis, which can help interpret the reasons of projected changes in temperature and precipitation and also the processes leading to biases in downscaled RCMs (Addor et al. 2016).

The most popular approach to analyzing synoptic-scale circulation and its link to surface climate is that of automated circulation classifications. Simply put, a circulation classification consists in (a) finding a few patterns (circulation types) that together represent the entire variety of daily (monthly) mean circulation—for example, sea level pressure (SLP)—patterns reasonably well, and subsequently (b) classifying each pattern to the most similar type. Thus, the whole circulation data set is reduced to a calendar of days, where each day holds a code number or a simple abbreviation referring to a particular circulation type instead of a complex pattern. Many statistical methods can be used to find the representative types and quantify the pattern-to-type similarity, each leading to a classification of its own. The result is further shaped by other decisions such as the choice of the variable(s), spatial and temporal domains of data sets, and the number of types. A reader is referred to Huth et al. (2008) for an in depth review of this research method.

Circulation classifications have already been used to analyze GCM output, both in terms of validation of GCM historical runs and analysis of GCM projections. Over the Euro-Atlantic domain, output of various CMIP3 (Meehl et al. 2007) GCMs were evaluated by Demuzere et al. (2009), Rust et al. (2010), Lorenzo et al. (2011), Pastor and Casado (2012), and Perez et al. (2014) over several different regions. Perez et al. (2014) analyzed output of a large ensemble of CMIP5 GCMs over the northeast Atlantic region focusing mainly on validation of models. Recently, two studies have combined multiple classifications to obtain more robust results, one using classifications by the Jenkinson–Collison method for smaller “sliding” spatial domains (Otero et al. 2017), the other repeating validation of GCMs by eight distinct classification algorithms and for four geographical domains including the two domains analyzed here (Stryhal et al. in review).

The goal of this paper is to analyze synoptic-scale circulation as it appears over the British Isles and central Europe from the point of view of automated circulation classifications of CMIP5 GCM twenty-first century projections. Multiple classifications are produced for each region to achieve robust results; the methods are described together with data sets in Sect. 2. In Sect. 3, we show GCM biases and projected trends of frequency, persistence, and air flow strength of circulation types and discuss the results with regard to other studies on observed and projected variability and trends of winter Northern Hemisphere climate. Two hypotheses are tested in detail: (1) whether westerlies shift poleward and (2) whether anticyclonic circulation becomes more persistent. Last, a few concluding remarks are given in Sect. 4.

Eight methods [Table 1; see Appendix for their brief description or Philipp et al. (2010) for detailed information] are consecutively used to define circulation types in daily SLP patterns produced by five atmospheric reanalyses (Table 2) over 40 climatological winters (DJF) from December 1960 to February 2000. Each method defines 9–10 types and each reanalyzed pattern is classified with one of these. Therefore, since eight distinct classifications are produced, each reanalyzed pattern is classified with eight types. This approach was used by Stryhal and Huth (2017) who showed that—in order to reliably intercompare circulation in two datasets—one classification is highly insufficient as it often leads to misinterpretation of results. Furthermore, they also showed that two patterns from two reanalyses referring to the same day may be classified with two different types, hence it is reasonable to use more reanalyses to account for observation uncertainty.

Note that the numbers of types we chose may not be optimal for each of the classifications, and somewhat different results might have been obtained if we had based our analyses on a different number. Nine types are, nevertheless, one of the preferred numbers suggested within the COST Action 733 “Harmonisation and Applications of Weather Type Classifications for European regions” (Philipp et al. 2010) for cases in which more classifications are used and compared. We respected this suggestion with the exception of the hybrid methods, for which ten types are the bare minimum.

In the next step, simulations for winter months from the historical runs (1960–2000) and projections under RCP8.5 scenario (2009–2099) by an ensemble of 25 CMIP5 GCMs (Table 3) are classified with the types defined on reanalyses in the way consistent with the particular classification method [for more details refer to Stryhal and Huth (in review)]. Thus, the same criteria are applied to classify both reanalyses and models. Note that it is not feasible to run classifications independently on reanalysis and GCM output because the two resultant catalogs could not be compared.

All classifications were computed by the cost733class-1.2 software (Philipp et al. 2016), which is freely available from http://cost733.geo.uni-augsburg.de/cost733wiki. Prior to classification, all data sets were interpolated by bicubic splines to a grid of 1 degree longitude by 1 degree latitude.

The study is carried out separately for two regions: the British Isles and central Europe. Two classifications, one for each domain, are displayed in Fig. 1 as an example, which also shows the spatial extent of the two regions and illustrates how individual types are plotted in graphs. Since there are 75 types for each domain, which is simply too many to display, we visualize the types in the rest of the paper by utilizing two circulation indices calculated from their mean patterns: the direction of flow over the center of the domain and the vorticity. The two indices are computed by applying to the mean patterns of types the same formulae that the Jenkinson–Collison method uses to classify daily patterns (for the formulae and more information on the method, see, e.g., Jones et al. 2013).

Example classifications. a The classification by Grosswettertypes for the British Isles: mean patterns of circulation types (left) and representation of the mean patterns as a function of air flow direction and vorticity (right). b Same as a, except for the classification by SANDRA for central Europe

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We focus on three properties of the simulated circulation separately for the historical (validation) period and for three consecutive 30-year time slices of the projections, namely on the frequency of occurrence of types, their persistence (mean length of episodes, an episode being a sequence of days classified with the same type), and the strength of air flow, the latter also utilizing the Jenkinson–Collison formulae applied to mean patterns of types. For each property, we first show the bias of the GCM ensemble by comparing the multi-model median with the reanalysis median and expressing the bias as percentage of the reanalysis median, which is also shown for reference. Subsequently, the change in a circulation property for each time slice is shown in the same units but taking the historical simulations as reference.

Previous research clearly stated that the selection of the method, be it a circulation index or circulation classification method, is a highly important factor of any study. Combining the results obtained for eight classifications, it is easier to identify biases and signals of change in the types. Note that more information on this issue and on results of validation of 32 CMIP5 GCMs for four Euro-Atlantic domains can be found in a standalone paper by Stryhal and Huth (in review). Here, the result of validation of the subset of 25 GCMs (for which projections were available) is shown in Figs. 2b and 3b. Note that the pictures contain results for all circulation types regardless the classification.

Relative frequency (I; left column), persistence (II; middle column), and air flow strength (III; right column) of circulation types for the British Isles: a median of five reanalyses (Dec1960–Feb2000; “HIST”), b bias of the 25-member GCM ensemble (the ratio of GCM-ensemble median for 1960–2000 to reanalysis median × 100% − 100), c–e change for three consecutive time slices 2009–2039, 2039–2069, and 2069–2099, in turn, relative to the historical period. The change in calculated in the same way as the bias, except taking the GCM-ensemble median as reference. Bars are used in b–e to highlight the results for all classes excluding those around zero. Note that all panels—including those showing only model data—use vorticity and airflow indices as computed from reanalysis data to ease comparison. Note that the color legend varies depending on the dataset and variable

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Same as Fig. 2, except for central Europe

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British Isles

Over the British Isles, the dominant types are directional types with advection from southwest to west (Fig. 2a), which are simulated reasonably well, considering all the three parameters, that is, frequency (Fig. 2Ib), persistence (Fig. 2IIb), and flow strength (Fig. 2IIIb), having only modestly overestimated frequency. There is, however, a vast underestimation of both frequency and persistence of types with advection from the eastern directional quadrant. Not only these types with anticyclones over the North Atlantic Ocean or northern Europe but also all high-vorticity types in which the anticyclone lies close to the Isles occur typically more than 25% less often in models than in reanalyses and last shorter time. The inability of CMIP5 models to properly simulate the occurrence and persistence of anticyclones over the North Atlantic Ocean is well known (see, e.g., Dunn-Sigouin and Son 2013) and can be considered one of the main hindrances to reliability of the model output.

In the near future (Fig. 2Ic), there is a marked decrease in the frequency of advection from south and southeast, which can be linked to a downward trend in easterly circulation over central Europe (Fig. 3Ic). Nevertheless, the main trend over the whole century is a gradual decrease in the occurrence of nearly all types of circulation, the increase being limited almost exclusively to westerly types (only later in the century, also south- and northwesterly types occur more often than today). Interestingly, the westerly—or any other— types do not become more persistent. Apparently, the dynamics of synoptic-scale circulation—in terms of the frequency of transitions between episodes of different types—is projected to increase in the future. Whether this change will affect weather and climate variability cannot be deduced solely from our results. In theory, more frequent transitions may increase the inter-diurnal variability of weather, however, inter-annual variability of climate might decrease since the extremity of extremes might weaken, the extremes being often linked to long persisting spells of one circulation type. Coupled with the fact that the types with advection of relatively cold air masses are projected to become both less frequent and less persistent, and recent studies have suggested a decrease of winter temperature variability under warming of mid- and high-latitudes (Cattiaux et al. 2013a; Sillmann et al. 2013; Hoskins and Woolings 2015; Ayarzagüena and Screen 2016; O’Sullivan et al. 2016; Borodina et al. 2017; Rhines et al. 2017), a decrease of temperature variability is more likely in future.

One of trends in planetary circulation related to global warming with important consequences for weather is the poleward shift of midlatitude westerlies. Modelling experiments widely support this hypothesis [see Reichler (2016) and references there], although for the Euro-Atlantic domain in winter the projected shift is only weak (Barnes and Polvani 2013; Grise and Polvani 2014; Simpson et al. 2014). All the classifications by cluster analysis (k-means, k-medoids, and SANDRA) can be used to assess this northward shift since they produce three zonal types for the British Isles that differ in the latitude of zonal flow maxima; the SANDRA classification is shown here in detail to illustrate the biases and trends in projections. Figure 4a–c displays, in turn, mean patterns of the types, relation between errors and near-future changes in frequency for individual models, and changes for the ensemble. Approximately half of the models highly (by 50% and more) overestimates the occurrence of the “southerly” zonal type. The 12 models with the large overestimation systematically differ in their projected change for the central and southerly zonal types from the rest of the models (Fig. 4IIIb): while the models overestimating the southerly zonal type indicate only minor changes in zonal circulation as a whole (except the increased occurrence of the northerly zonal type in the end of the century), the other models project an increase of westerlies that is stronger for the southerly than the northerly zonal type. Constraining projections on the basis of results of validation is problematic (Notz 2015; Borodina et al. 2017); however, should we consider the latter group of models more reliable owing to their better simulations, not only that a gradual poleward shift of westerlies cannot be expected over western Europe but rather an equatorward shift of the westerlies, as well as a stronger increase of frequency of zonal flow than indicated by the whole ensemble, would be plausible.

Three zonal types (columns I–III) defined by SANDRA for the British Isles that differ in the latitude of the polar front. a Mean patterns of types (in reanalyses). b Changes in the frequency of the types, 2009–2039 minus 1961–2000, in individual models plotted against the bias of the types: “group A” (red dots) includes 12 models with a marked overestimation (> 50%) of the type in III (zonal type with southerly position of the polar front), “group B” (blue dots) includes other models. c Changes in frequency for each type/period for the whole ensemble (grey columns), models in group A (red box plots) and models in group B (blue box plots). The box plots show 10th, 25th, 50th, 75th, and 90th percentiles

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Central Europe

Over central Europe, both GCM biases and projected changes show a pattern similar to those over the British Isles, although their magnitude tends to be larger. Namely, the occurrence of westerly (easterly) directional circulation is considerably over (under) estimated (Fig. 3Ib); moreover, models exaggerate the flow strength in nearly all types excluding some high vorticity types (Fig. 3IIIb). In projections, models show largest changes of frequency of occurrence for the types that have the largest errors (increase for westerlies and decrease for easterlies), these changes being consistent across all classifications and continuing the whole century (Fig. 3Ic–e). Additionally, the easterly flow is projected to become weaker (Fig. 3IIIc–e). Otherwise, trends in flow strength are found only for high vorticity types, which have only weak flow; that is, the models do not indicate that westerly flow will become stronger over the region. Regarding persistence, both biases and changes are generally small and inconclusive and depend on the classification under investigation.

Dependent on the classification are also trends in anticyclonic types. In total, 13 types are defined, which are on average underestimated in frequency by 26% and have a weak positive trend of their frequency for all three time slices. The trends are nevertheless opposite in classifications by cluster analysis (+ 10, + 10, and + 17%, in turn, for the three time slices), and in the remaining classifications (− 1, − 4, and − 6%). Clearly, the trend of anticyclonicity depends on how anticyclonic types are defined: if one requires only days with negative vorticity to be classified as anticyclonic, which hybrid methods do (see Fig. 5b), then anticyclonic types can be expected to become slightly less frequent over the century. On the other hand, many days with only weak negative or even positive vorticity can be classified with an anticyclonic type by clustering classifications as in this case the only criterion that governs the classification is the mean Euclidean distance over all respective pairs of gridded SLP values in the type and the daily pattern (note especially type #1 in Fig. 5a). Naturally, such trends then cannot be interpreted as purely trends in anticyclonicity. For instance, from all days classified with type #4 in the SANDRA classification of HadGEM2-CC (DJF 2009–2099) projections (see Fig. 5a and also Fig. 1b for the mean pattern in reanalyses), only about 35% of days are classified with the anticyclonic type in the Jenkinson–Collison classification, while nearly 60% of days are classified with one of the quasi-zonal types (SW, W, and NW flow) there. It is the marked increase of these quasi-zonal types over the whole century that causes this anticyclonic type to occur more often (by about 16% in the farthest time slice).

Projection of daily central-European SLP patterns in HadGEM2-CC twenty-first century RCP8.5 output onto a vorticity/flow direction plane for a days classified with SANDRA types #1 (red crosses) and #4 (black diamonds) and b days classified with Jenkinson–Collison type #10 (“pure anticyclonic” type)

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Regarding the persistence of circulation, one of important questions is whether central European anticyclonic and easterly circulation could become more persistent, which could lead to more severe cold spells, as these conditions generally lead to largest negative anomalies of temperature there (Plavcová and Kyselý 2016). For instance, Masato et al. (2014) showed that projections of some CMIP5 models indicate eastward shift of blocking anticyclones over Europe which might fuel easterly advection. Nevertheless, our results do not support this hypothesis, despite a moderate increase of persistence in some anticyclonic types in near future. Coupled with the negative trend in frequency of these types, synoptic conditions favoring cold anomalies seem to become rarer in future. The decreased strength of advection in easterly types, mentioned above, does not necessarily result in warmer temperatures since in observations it is rather radiative losses than cold advection that causes gradual cooling during such episodes (Plavcová and Kyselý 2016). However, dynamically downscaled models have been shown to decrease temperature in persistent episodes with easterly flow too quickly, which leads to their cold bias relative to observations (Blenkinsop et al. 2009; Plavcová and Kyselý 2016). Therefore, Plavcová and Kyselý (2016) hypothesized that the models simply exaggerate the cooling effect of cold advection. One reason for this exaggeration might be the overestimated strength of easterly flow shown in Fig. 3IIIb. Slowing down the flow in easterly types, as documented here, could remove—or at least reduce—this bias from projections and thus make the easterlies apparently warmer than what one could expect based solely on known radiation-temperature feedbacks. Naturally, future changes in areas of formation of cold continental polar or Arctic air masses such as diminishing snow (Cassou and Cattiaux 2016) and sea ice (Ayarzagüena and Screen 2016) covers are of utmost importance for changes in future European winter climate. However, a reduced effect of the cold advection on winter extremes due to weaker easterlies may be an important factor of its own and seems worth further investigation.

Winter midlatitude atmospheric circulation has been extensively studied as its variations and changes have a marked effect on climate—and especially its extremes—over highly populated areas. Climate models—namely, output of historical runs and projections of CMIP5 models—have been an indispensable tool in this kind of research. Here we analyze projections of several circulation classifications for two European regions (British Isles and central Europe) and discuss them with respect to biases of these models.

Over both regions, the advection from the western quadrant becomes gradually more and more frequent in projections for the twenty-first century at the expense of nearly all other circulation types. These results can be deduced from all eight classifications that were used in the study; the magnitude of the changes does, however, depend on the classification. Both southerly and northerly advection becomes less frequent in projections, which does not support the hypothesis that circulation over Europe might become more meridional; on the contrary, it is in agreement with recent findings of Cattiaux et al. (2016) and Peings et al. (2017) who showed that future midlatitude westerlies will become less wavy in the region.

Furthermore, previous studies indicated a poleward expansion of large-scale circulation under global warming, although the northward shift of midlatitude westerlies in winter is generally weak over the Euro-Atlantic domain. Here we show that a poleward shift of zonal flow over the British Isles can be seen in a group of models that considerably (> 50% relative to reanalyses) overestimate the frequency of the circulation type with a southerly position of the zonal flow, while models simulating the latitude of zonal flow more realistically manifest rather an opposite trend. Therefore, putting more weight to models that simulate the zonal flow reasonably well would suggest even a slight equatorward shift of westerlies during the twenty-first century.

Trends in persistence of circulation and in the strength of flow are only weak, although over the British Isles a decrease of mean length of episodes is apparent. We hypothesize that this decrease will lead to larger inter-diurnal variability of weather, but it also favors decreased extremity of temperature since extremes are typically linked to persistent episodes of one circulation type, thus decreasing inter-annual winter variability. Over central Europe, easterly advection is projected to weaken. Since the models when dynamically downscaled likely overestimate of effect of cold advection on cold extremes relative to the effect of radiation losses, which leads to more severe cold spells in model output than in observations (Plavcová and Kyselý 2016), we hypothesize that the decrease in flow strength might markedly accentuate the expected decrease in frequency and severity of cold extremes due to other causes, such as changes in snow and sea ice cover. If true, the decrease in cold extremes over Europe in model projections may be exaggerated.

Last but not least, many of the strongest trends occur in circulation types that also have the largest biases. Therefore, users of the model output should not forget that there is a considerable uncertainty inherent to any results that are based on these data, especially if variables considerably affected by atmospheric dynamics, such as precipitation, as well as various environmental phenomena, are involved.

The work was funded by the Grant Agency of Charles University, Project 188214. We acknowledge all modeling groups for providing their GCM data and the Earth System Grid-Center for Enabling Technologies (ESG-CET) for enabling access to it. We thank NOAA/OAR/ESRL PSD, Boulder, Colorado, for the NCEP–NCAR reanalysis and Twentieth Century Reanalysis, version 2; ECMWF for ERA-40 and ERA-20C; and JMA for JRA-55. All developers of the COST733 software are greatly acknowledged, and so is the Institute of Geography, University of Augsburg, Germany, for maintaining the software and providing access to it.

Affiliations

1. Department of Physical Geography and Geoecology, Faculty of Science, Charles University, Albertov 6, 128 43, Prague 2, Czechia

   Jan Stryhal & Radan Huth

2. Institute of Atmospheric Physics, Czech Academy of Sciences, Boční II, 141 31, Prague 4, Czechia

   Jan Stryhal & Radan Huth

Corresponding author

Correspondence to Jan Stryhal.

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