In this paper, we investigate space time patterns of meteorological drought events in the Greater Alpine Region (GAR) of Europe. A long-term gridded dataset of monthly precipitation sums spanning the last 210 years is used to assess abnormally dry states using a shortfall below a monthly precipitation percentile threshold. These anomalies are calculated for 1, 3, 6, and 12 monthly moving averages. Contiguous areas of grid points below the threshold are indicating drought areas which are analyzed with respect to their drought severity. The severity is quantified by taking the average deviation from the threshold and the size of the drought area into account. The results indicate that the most severe dry anomalies in the GAR occurred in the 1860s, the 1850s, and the 1940s. However, no significant trends of dry anomaly severity are found over the last 210 years. A spatial clustering analysis of the detected drought areas shows distinct spatial patterns, with the Main Alpine Crest as a frequent divide between dryer areas in the north and wetter areas in the south, or vice versa. The patterns are highly significant and similar for all averaging time scales. The clusters are more clearly defined in winter than in summer. Droughts in the north are most frequent in the second half of the nineteenth century, while in the south and east, they are most frequent in the late twentieth century. 1 Introduction the most recent occurrences. They were caused by prolonged periods with below average precipitation which led, in com- From a first snapshot, the Greater Alpine Region (GAR; Auer bination with high temperatures, to severe drought related et al. 2007) is a water-rich area, exhibiting annual precipitation impacts (van Lanen et al. 2016; García-Herrera et al. 2010) totals from 400 to even beyond 3000 mm/year (Isotta et al. not only in the GAR but also in large areas across Europe. 2014). However, water scarcity is a serious issue in some parts However, not only in the warm season has an accumulated of the area in some years which may cause substantial threats precipitation deficit has large impacts on society. In the Alps, to drinking water supply, irrigation water supply, energy pro- winter sports are a major economic branch, depending heavily duction (through cooling water and hydropower generation), on sufficient snowfall in winter. A succession of three ex- and river navigation. tremely dry winters in a row (1987/1988 to 1989/1990) sub- Within the last decades, several droughts struck large parts stantially affected winter tourism (Abegg et al. 2007). of Europe and the GAR (Spinoni et al. 2015; Hoerling et al. Additionally, there is a close link between winter precipitation 2012; Parry et al. 2012; Bradford 2000; van der Schrier et al. (e.g., via melt of the snow pack) and flow characteristics of 2006), e.g., the summer droughts of 2003 and 2015 as two of rivers with a snow covered catchment during summer since insufficient snow pack might trigger low flows in the warm season downstream (Jenicek et al. 2016;Nester et al. 2012; * Klaus Haslinger Parajka and Blöschl 2008). Especially, a deficit of accumulat- email@example.com ed precipitation during winter may lead to low flow events of such rivers (Parajka et al. 2016). Besides, any formal way to calculate any kind of indicator Climate Research Department, Central Institute for Meteorology and Geodynamics (ZAMG), Hohe Warte 38, 1190 Vienna, Austria the term drought itself must be clarified. For example, Wilhite and Glantz (1985) discuss the issue of drought severity exten- Institute for Hydraulic and Water Resources Engineering, and Centre for Water Resource Systems, Vienna University of Technology, sively and identify four types of drought: meteorological, ag- Karlsplatz 13, 1040 Vienna, Austria ricultural, hydrological, and socioeconomic drought. Within Department of Geography and Regional Research, University of this paper, we focus on meteorological droughts (precipitation Vienna, Althanstraße 14, 1190 Vienna, Austria K. Haslinger et al. deficit) as they trigger all other drought types (van Loon 2015; Index (RDI, Tsakiris and Vangelis 2005)for theBeijing- Stagge et al. 2015; Haslinger et al. 2014). Several studies have Tianjin-Hebei metropolitan areas and the work of Patel et al. investigated long-term precipitation characteristics and (2007) who investigated spatial drought patterns based on the change in the GAR, e.g., the studies of Brunetti et al. (2006, SPI in the region of Gujarat (India). 2009) and Auer et al. (2005), who found increasing trends in From the existing literature, no complete picture can be drawn precipitation north of the Alps and slightly decreasing trends on the spatial patterns of meteorological drought in the GAR. south of the Alps from 1800 to 2003. These trends are con- The most comprehensive work on drought in the GAR conduct- nected to a dipole like feature of precipitation from north to ed by van der Schrier et al. (2007) did not analyze the spatial south which strengthened somewhat over the past 200 years. aspects of observed droughts. Consequently, an investigation of Additionally, they reported a slight shift in precipitation sea- drought patterns in the GAR is still missing. Yet the GAR pro- sonality with positive trends in winter and spring, vides the possibility to investigate the spatial dimension of counteracted by negative trends from July to November. drought in a worldwide unique long-term (200+ years) assess- Brunettietal. (2006) also analyzed spatial patterns of ment, enabling to investigate spatial patterns of droughts and precipitation in the GAR, based on principal component changes of those over the last two centuries. Particularly, consid- analysis (PCA) of the precipitation time series. They ering global climate change, it is of utterly importance to enhance found four homogeneous sub-regions in the GAR in terms our understanding of past droughts to better assess possible future of their inter-annual precipitation variability. The PCA of developments. Stepping into these detected research gaps, we Brunetti et al. (2006) uses all the data of the probability aim to analyze the long-term (200+ years) characteristics of distribution of precipitation; thus, those patterns for the drought patterns in the GAR. The more specific aims of the paper dry tail of the distribution might look different. Van der are (i) to detect areas under drought using accumulated precipi- Schrier et al. (2007) investigated soil moisture variability tation on different time scales and to quantify the drought severity in the GAR, based on the self-calibrating Palmer Drought of the area, (ii) to assess similarities of these drought areas in Severity Index (scPDSI; Wells et al. 2004). They used the order to obtain main drought patterns, and (iii) to investigate previously defined sub-regions of Brunetti et al. (2006) possible long-term changes of drought patterns over the past regionalizationtoassess dryand wetepisodes.Vander 200+ years. Schrier et al. (2007) left it open whether the predefined sub-regions are suitable for a dry episodes analysis. Several studies investigated spatial and temporal patterns 2Data of drought occurrence globally or in other regions of the world. General assessments of drought characteristics and The spatial domain of this investigation is the European trends from global datasets are given for example in Greater Alpine Region (GAR; Auer et al. 2007)which Sheffield and Wood (2008), Trenberth et al. (2014), or Dai stretches from 4°–19° E to 43°–49° N (Fig. 1). The GAR is (2011), highlighting regional differences in drought trends known for high-quality, long-term climate information back to and large uncertainties considering the input data but on 1760, the so-called HISTALP database (Böhm et al. 2009). In average increasing trends due to increased this paper, gridded data of monthly precipitation sums cover- evapotranspiration. Spatial patterns of droughts on a global ing the whole GAR are used. This dataset was created by scale are investigated for example by Sheffield and Wood Efthymiadis et al. (2006) by gridding the available (2007) or Spinoni et al. (2014). Particular interest on spatial HISTALP stations with precipitation measurements, which patterns on a regional scale was given by Soulé (1990)who are at maximum density nearly 200 stations. For the purpose analyzed various kinds of the Palmer Drought Severity Index of this paper, the dataset was updated until 2010 using similar through a PCA for the USA. The results showed more regions techniques as for the original dataset described in the follow- with smaller extent for faster responding indices (e.g., ing section. The dataset therefore covers the period 1801– Palmer’s Z-Index) and less individual regions with larger ex- 2010. It has a spatial resolution of 10′, which is roughly tent for slower reacting indices (e.g., Palmer Hydrological 15 km. Index), which implies that the spatial characteristics are de- The gridding is performed by the Banomaly approach^ pendent on the time scale of the droughts. Similar results were (e.g., Jones and Hulme 1996), which splits the precipitation found for the Iberian Peninsula by Vincente-Serrano (2006) field in two components. One is the long-term mean compo- who conducted an analogous analysis based on the nent, the climatology fields. Efthymiadis et al. (2006)used a Standardized Precipitation Index (SPI; McKee et al. 1993), high-resolution monthly precipitation climatology of the ETH comparing different accumulation time scales from 1 to Zürich (Schwarb 2000) from 1971 to 1990 which utilizes a 36 months. Other examples are the work of Cai et al. (2015) very dense station network in order to capture the complex who performed a regionalization of drought characteristics spatial features of precipitation in the GAR. The second com- based on a modified version of the Reconnaissance Drought ponent is the anomaly field. It is derived by interpolating Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... Fig. 1 Map of Central and Southern Europe. The broken line indicates the boundaries of the Greater Alpine Region; the solid line represents a generalized outline of the 1000 m a.s.l. isoline of the Alps which should help in locating the mountainous areas of the domain in the following figures station anomalies relative to the averaging period of the cli- Mishra and Singh 2010;Heim 2002; Wilhite and Glantz matology (1971–1990) using the angular distance weighting 1985). During the last decades, especially three indices are approach. The combination of the high-resolution climatology in use for research and operational applications: the Palmer and the smoother anomaly fields yields the final absolute pre- Drought Severity Index—PDSI (Palmer 1965), the cipitation fields. However, it should be noted that only stations Standardized Precipitation Index—SPI (McKee et al. 1993), up to 2000 m a.s.l. are used; thus, uncertainties of the gridding and the Standardized Precipitation Evapotranspiration in the high elevated areas of the GAR should be kept in mind. Index—SPEI (Vincente-Serrano et al. 2010). The SPI can be In this paper, we use the gridded precipitation data to assess calculated from precipitation data alone; for the calculation of abnormally dry states in space which could subsequently lead the PDSI and SPEI, potential evapotranspiration (PET) would to soil moisture, streamflow, or groundwater drought. To ac- be required. We intentionally do not use the PDSI or the SPEI, count for the different time scales on which these effects may because (i) the incorporation of a temperature-based PET (oth- arise, the precipitation values are summed up by a moving er variables are not available for the GAR for this time period) window approach over a 3-month (3M), a 6-month (6M), introduces additional uncertainty (e.g., Sheffield et al. 2012) and a 12-month (12M) time scale, similar to the procedure and (ii) we are interested in understanding the spatial patterns to calculate the Standardized Precipitation Index (SPI) on dif- of precipitation deficit; investigating the climatic water bal- ferent accumulation time scales (see McKee et al. 1993). ance would introduce more aspects and processes, e.g., land- atmosphere interaction which might obscure the original intensions. 3Methods Instead of using the SPI, we use precipitation quantiles on four different accumulation time scales (1, 3, 6, and Depending on the available data, different approaches have 12 months) to quantify meteorological drought conditions in been used so far to depict drought (Zargar et al. 2011; the GAR. Quantiles introduce a lower boundary (zero), which K. Haslinger et al. makes a severity assessment, as described below, much more scaling the mean deviation from the threshold level by straightforward. As highlighted by Naresh Kumar et al. the number of affected grid points. The severity of a DA (2009), the SPI underestimated the severity of dry and wet is givenbyEq. (1). extremes due to distribution fitting issues which underpins the advantage of using quantiles. S ¼ ∑ðÞ −1ðÞ q−t =t ð1Þ i¼1 i∈DA The procedure to identify dry areas is displayed in Fig. 2.Figure 2a shows an example of a precipitation where S is the severity which is a dimensionless measure; n is the field, the December of 1829. The spatial patterns of this number of all grid points i, detected within a DA; and q is the quantile value and t the threshold (fixed at 0.2). This implies that field are characterized by low precipitation in the north- west of the domain, well below 50 mm/month. In con- the severity is higher, if either the DA or deviation from the trast, in some coastal areas of Croatia, precipitation sums threshold is large. Highest severities are given, if the DA as well exceed 300 mm/month. In the same manner as for calcu- as the threshold deviation is large. lating the SPI, a Gamma-distribution (Wilks 2011)is In Fig. 3, examples of four individual DAs are displayed. fitted to the time series at every grid point. The parame- Figure 3a shows a meteorological drought on a 1M time scale ters of the distribution are individually estimated for all in February 1814, affecting mostly the southern part of the the Januaries, Februaries, and so on and repeated for all GAR. The affected area is rather large, while the mean three accumulation time scales. This procedure ensures quantile value is rather low (0.077), resulting in a larger value of the overall severity of 982. In contrast, the DA from comparability of anomalies across seasons, independent of the climatological mean of the precipitation sum. February to April 1930 (M time scale; Fig. 3b) is considerably smaller, impacting mostly the western part of Austria. In com- From the estimated Gamma distribution, the precipita- tion values (e.g., for the example of 1829 in Fig. 2a) are bination with a mean quantile value of 0.125, the severity is assigned to percentile values (Fig. 2b). Obviously, regions only 39. However, this DA is not considered in the further in the northwest faced rather low values, well below the analysis since it is below our chosen area threshold (20% of 10% percentile, indicating a relatively unusual month. As the GAR). Another example with large spatial extent, but low a next step, a threshold of the percentile values is deter- mean quantile deviation from the threshold is displayed in Fig. mined to separate dry areas from non-dry areas. We chose 3c. This DA on a 6M time scale (May–October 1822) covers the 20% percentile, which is a widely used threshold for large areas in the east, but the mean quantile value is 0.141, drought identification (e.g., Svoboda et al. 2002). The yielding a severity of 299, which is considerably lower than the severity of February 1814 (Fig. 3a). A last example, for the threshold is indicated as a gray outline in Fig. 2b. As a next step, all spatially neighboring grid points below the 12M time scale, shows the DA from July 1954 to June 1955 in Fig. 3d. The spatial extent is not large, but the mean quantile threshold are aggregated to regions, which we term drought areas (DAs). In Fig. 2c, two identified DAs, A value is low, which gives a severity of 258, comparable to the and B, of December 1829 are displayed. All key attributes severity in Fig. 3c, but affecting not nearly half of the area. of a detected DA are summarized by a lookup table cov- Some guidance on the probability distribution of the severity ering the region ID, the grid point IDs, longitudes, lati- is shown by Table 1 which displays the severity values asso- tudes, quantile values, and the month and year of occur- ciated with certain quantiles. In general, the severity is some- rence. For further analysis throughout the paper, we use what decreasing with higher accumulation time scale. The only DAs with a minimum size of 20% relative to the median ranges between 648 and 571, whereas the 95% whole GAR. quantile lies between 1879 and 1621. There is indeed a theo- retical upper bound of the severity which relates to the size of For our study, the affected area of a drought by itself is an important drought measure. Therefore, we decided to the grid. If all the grid points would show no precipitation at all at a given time step, equivalent to a quantile value of zero, define also the severity of a detected drought area by Fig. 2 Example of a precipitation field of December 1829 (a), the corresponding quantiles; the gray contour line represents the 20th percentile (b), and the detected contiguous drought areas for the selected date A and B (c) Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... Fig. 3 Four examples of identified DAs on a 1-month (a), 3-month (b), 6-month (c), and 12-months (d) time scale. Every DA is described through three attributes exemplarily: the time period of occurrence (time), the quantile mean of the DA, and the severity the severity would be 2895, which is the number of all land the sum-of-squares criterion for a previously defined number surface grid points in the GAR. of clusters (Bishop 1995). The crucial part of the clustering The main methodological framework of this investigation algorithm is the determination of an optimal number of clus- is the clustering of spatial patterns of DAs in order to gain ters. In this paper, we use the silhouette width approach information on the spatial behavior of meteorological drought. (Rousseeuw 1987) which describes the similarity of an object We identify similarity patterns of DAs by a k-means clustering to the assigned cluster as well as the dissimilarity to all other approach. We use the monthly DA-fields, where all grid points clusters. It ranges between − 1 and + 1, with higher values with percentile values outside the 0–0.2 range are set to zero, indicating better clustering solutions. The significance and in order to avoid biases arising from prominent wet features in stability of a given clustering solution are assessed through space, and all grid points below the threshold boundary are set the clustering stability (Hennig 2007) approach. to one. Within the k-means approach, Euclidian distances (Wilks 2011) between data points are calculated, which are matrices with binary information on drought (one) and no 4 Results drought (zero). The distances are iteratively minimized trough 4.1 Drought areas and their severity Table 1 DA severity associated with different quantiles stratified by accumulation time scale Figure 4 shows the top 100 DAs in terms of their severity, Quantile Severity stratified by the accumulation time scale. The DAs cluster around the middle of the 19th, as well as the twentieth century 1 month 3 months 6 months 12 months and in the 1890s if only the 1M time scale is considered. On a 1M time scale, 13 DAs of the topmost ones are detected in the 50% 648 604 583 571 1860s, 9 in the 1850s, and 8 in both the 1920s and 1940s. 80% 1160 1112 1040 960 Decades with rather low numbers of extreme DAs are the 90% 1557 1437 1335 1285 1820s (0 DAs) and the 1810s (1 DA), for example. Time 95% 1879 1699 1629 1621 periods of prolonged dry conditions are revealed considering K. Haslinger et al. Fig. 4 Time of occurrence and magnitude of the top 100 drought areas (DAs) for the GAR described by their time scale (y-axis and indicated by different color shadings) and by their severity (size of the symbols) higher aggregation levels. On a 3M and 6M time scale, the in the given time series. Since the accumulation procedure 1940s show the highest DA occurrence (12 and 16 DAs respec- might introduce autocorrelation in the time series, these were tively), followed by the 1920s on a 3M time scale with 9 DAs prewhitened before significance assessment. As can be seen in and the 1860s on a 6M time scale with 13 DAs. On a 12M time Fig. 5, both the frequency and the severity show in general no scale, the 1830s (20 DAs), 1850s (18 DAs), and the 1860s (17 significant trend, no matter what time scale is considered with DAs) are identified as periods of maximum drought occurrence. p values ranging between 0.11 and 0.48. It should be noted that, as an additional effect of using Table 2 lists the top five DAs in terms of their severity per moving averages of the monthly precipitation sums in the time time scale. The overall driest month on record was September domain, DAs tend to cluster around similar years for different 1865, followed by April of the same year. This DA affected time scales. This is apparent mostly for the 12M line in Fig. 4. 99.5% of the whole GAR and shows an average precipitation For example, the outstanding DA of October 1949 is anomaly of − 90 mm which equals 9% with respect to the long- surrounded by other, but smaller DAs along time. term (1801–2010) mean. The overall deficit volume in this par- The presented occurrence diagrams in Fig. 4 show a dis- ticularmonthis61km of water. The driest 3M period was April tinct decadal to multi-decadal scale variability of DA frequen- to June, again in 1865. The area under dry conditions covers cy. However, there is no apparent trend in the occurrence of 98.4% and the overall precipitation anomaly is −144 mm, droughts. We analyzed time series of annual averages of DA resulting in a deficit volume of 97 km . The second and third severity and frequency using the non-parametric Mann- driest 3M periods occurred in winter 1857/1858, with similar Kendall trend test for estimating the significance of the trend precipitation anomalies of −139 and − 152 mm respectively. Fig. 5 Time series of annual averages of DA severity (blue) and annual frequency of DAs (red) stratified by accumulation time scale and the estimated trend line; respective values of Kendall’s τ and the significance of the trend given by the p value are given in the upper right corner Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... Table 2 Characteristics of the top five drought areas (DAs) per accumulation time scale Time scale Time period Affected area Mean percentile value Absolute anomaly Relative anomaly Deficit volume Severity (−)(%) (−) (mm) (%) (km ) 1 month September 1865 2782 99.5 0.007 − 90 9 61 April 1865 2765 100.0 0.009 − 73 14 50 March 1929 2663 100.0 0.016 − 61 14 42 March 1953 2602 97.7 0.016 − 63 12 42 April 1893 2556 96.0 0.016 − 71 16 46 3 months April–June 1865 2520 98.4 0.023 − 144 50 97 December 1857–February 1858 2477 97.2 0.024 − 139 36 93 November 1857–January 1858 2342 98.0 0.035 − 152 41 102 March–May 1852 2315 100.0 0.040 − 119 53 82 February–April1834 2278 99.6 0.042 − 121 45 83 6 months April–September 1865 2546 99.4 0.023 − 232 60 158 February–July 2003 2505 99.4 0.026 − 214 59 146 March–August 2003 2504 97.8 0.023 − 219 60 148 July–December 1921 2449 99.0 0.029 − 264 55 180 December 1851–May 1852 2403 100.0 0.034 − 206 56 142 12 months November 1948–October 1949 2389 98.7 0.022 − 376 65 240 January–December 1921 2229 90.1 0.029 − 389 64 241 February 1852–January 1835 2174 92.1 0.037 − 347 68 220 February 1865–January 1866 2156 91.4 0.037 − 325 70 204 November 1920–October 1921 2107 90.4 0.039 − 347 68 216 Also, on a 6M time scale, the year of 1865 reaches the top patterns are similar. In winter (DJF), DAs are most frequent position with the period from April to September. Within these in the 1850s and 1860s on a 1M time scale (6 DAs) and in 6 months, only 60% of average precipitation was observed, the 1850s on a 3M time scale (6 DAs). In summer (JJA), the resulting in a deficit volume of 158 km .Onranks twoandthree, 1850s and 1940s show highest frequency of DAs on a 1M time a more recent event is recorded, namely the time from February scale (6 DAs), whereas the 1860s, 1920s, and 1940s show the to August 2003, with a deficit volume of nearly 150 km . highest number of DAs on a 3M time scale (5 DAs). Considering a 12M time scale, the driest period occurred from November 1948 to October 1949, followed by the time from 4.2 Spatial patterns January to December in 1921. Both show similar deficit vol- umes of 240 and 241 km , respectively. In this section, the spatial patterns of DAs are analyzed using a Considering drought occurrence stratified by seasons, some- k-means clustering approach. The aim is to allocate every de- what different patterns are observed as can be seen in Fig. 6.We tected DA (c.f. Fig. 3) to a cluster of DAs with similar spatial defined the cold season (warm season) as the half year span- properties. The result of the k-means clustering is a flag for the ning October to March—ONDJFM (April to September— DAs indicating their spatial affiliation, e.g., all DAs covering AMJJAS). In addition, we considered the core season within the northwest of the GAR are assigned to the same cluster. these half years: winter (DJF) and summer (JJA). DAs in the As described in Section 3, the optimal number of clusters cold season are clearly more likely in the second half of the has to be defined beforehand, which is carried out with the nineteenth century, although the biggest event on a 1M time silhouette width approach (Rousseeuw 1987). scale occurred in March 1929 and on a 6M time scale in March Figure 7 shows the silhouette width of different clustering 1949. The decades with the highest number of DAs in the cold solutions stratified by different time scales. First of all, silhouette season are the 1850s on a 1M time scale (6 DAs), the 1880s on widths of the clustering on different time scales are rather similar. a 3M time scale (7 DAs), and the 1850s, 1880s, 1890s, and If averaged over all time scales, the peak is at four clusters with 1970s on a 6M time scale. The warm season experiences most silhouette widths of 0.30 for the 1M, 3M, and 6M time scales DAs in the 1940s on a 1M time scale (7 DAs), in the 1920s on a and 0.25 for the 12M time scale (c.f. Table 3), indicating optimal 3M time scale (9 DAs) and in the 1860s on a 6M time scale (8 clustering with four clusters. These values can be interpreted, DAs). Considering the core season winter and summer, the following Kaufmann and Rousseeuw (2005), as Bweak K. Haslinger et al. Fig. 6 Time of occurrence and magnitude of the top 50 drought areas boundaries, for example, 6M DAs in the cold season are only those (DAs) at different time scales (indicated by different color shadings) detected in March, since the 6M time scale refers to the accumulation stratified by season. The two top most panels show the DAs in the half- from October to March; for this reason, there are only three time scales years (cold season ONDJFM and warm season AMJJAS); the two bottom displayed in the half-year plots and two time scales in the seasonal plots. most panels show the DAs in seasons (winter DJF and summer JJA). The The size of the circles indicates the severity of the event attribution of a DA to a distinct season follows strictly their defined structures which may be artificial,^ which is consistent with the interpreted as Bhighly stable^ (Hennig 2007); here, we have only present analysis, since the objects for the clustering are binary two clusters below this threshold, indicating that the clustering fields which may overlap to some degree, but may be assigned solution is highly stable and significant, although silhouette to different clusters. For further analysis, we choose four clusters. widths are low, given the fact that cluster objects tend to overlap To further assess the quality of the clustering solution, we calcu- to some degree. lated the Cluster Stability (Hennig 2007). In this approach, the The obtained clusters are termed after the region within the data is resampled by a bootstrapping approach and the similari- GAR they are mostly affecting: northwest, southwest, east, ties (using the Jaccard coefficient) of the original to the and a cluster termed all dry which contains DAs covering very resampled clusters are calculated. The mean of these similarities large parts of the GAR. Figure 8 shows the clusters displayed indicates the stability of a given cluster. The results for the clus- as a fraction value which indicates how often grid points from tering using four clusters are summarized in Table 3.The cluster a DA are assigned to a given cluster (e.g., northwest) in rela- stability ranges between 0.97 and 0.68, with higher values found tion to the overall size of the cluster (e.g., how often DAs are at lower accumulation time scales. Values above 0.85 can be assigned to cluster northwest in total). Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... circumstances. To underpin these results, we performed an addi- tional analysis assessing the probability of change from dry to non-dry conditions in space. Therefore, all grid points identified as DAs per time step were flagged as 1 and all the others were flagged as zero. We then calculated the probability for the change in space from dry conditions (grid point value = 1) to near nor- mal or wet conditions (grid point value = 0) between pairs of grid points in the north-south direction as well as in the west-east directions. The number of times a pair of grid points shows a 1/0 (dry/non-dry or vice versa) combination is counted and re- lated to the whole number of time steps. The result is a percent- age probability for a change from dry to wet in one direction Fig. 7 Silhouette widths for different cluster solutions and different time scales of the DAs between pairs of grid points. The mean of these calculations for both directions (north-south, west-east) is displayed in Fig. 9. The most striking feature of this figure is the similarity of The maps support the results from the k-means clustering, spatial patterns independent of the accumulation time scale. All clearly showing a band along the main alpine crest with the of these cluster composites show rather similar shapes and near- highest change probabilities, which are somewhat larger at higher ly identical locations of the centerofmass. Forexample,the time scales. The change probabilities in space reach up to 6% northwest cluster always shows highest fractions near the bor- along the main Alpine Ridge and some areas at the southern rim der triangle of France, Germany, and Switzerland, whereas the of the Alps where the mountainous terrain gives way to the Po- center of cluster southwest is located in the Po Plain. The cluster Plain. The role of the Alps as a boundary of a north-south divide is rather clear, also seen in the k-means clustering results, but east tends to dominate the whole eastern half of the domain with a center in western Hungary. Moreover, the lower cluster more restricted to the western part of the area. However, there is stability at 12M time scale (cf. Table 3) is also reflected in the no similar boundary in a west-east direction. Although the clus- lower fraction gradient from north to south compared to the tering revealed an east cluster, the boundary is fuzzier and not as lower time scales 1M and 3M. The remaining cluster is the all marked as for the north/south clusters. This fuzziness is also dry cluster, which indicates DAs where large parts of the do- confirmed by the spatial change probability assessment, showing main are below the 20th percentile threshold. The similarity of no clear areas with enhanced probability in a west/east direction. cluster composites across time scales indicates that DAs are In order to assess seasonal differences of spatial drought caused by persistent atmospheric circulation patterns leading patterns, the clustering approach was carried out for winter (DJF) and summer (JJA) DAs separately, where we used a to precipitation deficit in one of the three sub parts or the whole domain. Our choice of four clusters is based on the mean sil- sub-sample of the 3M DAs detected in February (covering December through February) and in August (covering June houette widths across all time scales. However, Fig. 7 also indicates that for a 12M time scale, compared to the other time through August). Following the silhouette width approach, the optimal number of clusters is 4 for winter and 2 for summer; scales, more clusters (six) would lead to slightly enhanced clus- ter results. Additional investigations of the patterns with six cluster stability is again high with a mean value across clusters clusters on a 12M time scale (not shown) revealed consistent in winter of 0.72 and in summer of 0.84. results, as two additional clusters emerge from a splitting of In Fig. 10, the cluster composites for winter and summer cluster northwest into a western and a eastern part and a split- are displayed. Winter shows some similarities with the all year ting of cluster east into a northern and a southern part. cluster solutions: the first cluster dominates the north of the From the above analysis, it becomes clear that the Alps are a domain, again with a clear boundary along the Alpine crest; major divide between dry and wet conditions under certain clusters two and three are more in the south and along the western and eastern fringe of the Alps. There is again an all Table 3 Silhouette width and cluster stability of the k-means approach dry cluster indicating widespread drought across the GAR. In summer, the characteristics of the patterns are different. In Time scale 1 month 3 months 6 months 12 months general, the two clusters show a northwest-southeast contrast too, but the region boundaries are rather fuzzy and the Alpine Silhouette width [−] 0.30 0.30 0.30 0.25 crest is not as clear a separating feature as in the all year Cluster stability [−] analyses or in winter. This might be due to the different mech- Northwest 0.95 0.96 0.86 0.89 anisms of precipitation formation in summer which is usually Southwest 0.95 0.94 0.81 0.68 a mixture of stratiform precipitation through cold and warm East 0.97 0.93 0.85 0.86 front passages and convective precipitation which is either All dry 0.97 0.94 0.78 0.94 triggered by frontal systems or generated locally. Therefore, K. Haslinger et al. Fig. 8 Spatial patterns of DA clusters on different time scales. The cluster (e.g., how often DAs are assigned to cluster northwest in total); fraction value indicates how often grid points from a DA are assigned higher fraction values indicate higher accordance of DAs assigned to the to a given cluster (e.g., Northwest) in relation to the overall size of the given cluster the precipitation patterns in summer on monthly or even increase of DAs at the beginning of the time series can be multi-monthly averages tend to be more heterogeneous than explained by decreasing precipitation sums following the very those in other seasons with lower convective activity, resulting wet years within the first decades of the nineteenth century, in fuzzier cluster boundaries. with a rather low number of DAs. This pattern is also seen on longer accumulation time scales, but in addition, other char- acteristics emerge. Particularly, at the 6M and 12M time 4.3 Spatial patterns in time scales, two periods clearly stand out in terms of DA frequency, the time windows from 1850 to 1880 and from 1920 to 1950, The occurrence of the identified drought patterns in Section showing isolated peaks of 140–160 DA/30 years. 4.2 varies over time. Temporal variations are apparent from The fraction of clusters for these 30 year periods is not the overall frequency of DA and also in the partitioning be- homogeneous over time. As it was the case for the entire tween clusters as can be seen in Fig. 11. On a 1M time scale, region’s frequency, the differences in the frequency of the DA frequency is peaking in the period from 1860 to 1890 with single clusters are more pronounced at longer time scales. an overall amount of about 130 DA/30 years. The strong Fig. 9 Mean of the change probability between a pair of grid points within a DA and outside a DA in north-south and west-east directions on different accumulation time scales Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... Fig. 10 Spatial patterns of clusters on a 3M time scale for winter (DJF) size of a cluster; higher fraction values indicate higher accordance of DAs and summer (JJA). The fraction value indicates the number of cluster assigned to the given cluster assignments of a grid point to a distinct cluster in relation to the overall On the 12M time scale, there is no occurrence of DAs in the southeast cluster, whereas the late twentieth century peak is northwest region at the beginning of the nineteenth century. dominated by the southeast cluster, and the all dry cluster is Afterwards, a steep increase is visible until the period from not at all present. 1860 to 1890 showing, around 80 DAs/30 years. The north- Less variation over time of DA frequency is visible in sum- west cluster is the one with highest temporal dynamics along mer. After a steep increase during the beginning of the nine- with the east cluster. Both of them trigger the peaks in cluster teenth century, the frequencies range between 9 and 12 DA/ frequencies in the middle of the nineteenth and twentieth 30 years. However, the small overall variation is counteracted centuries. by periodical changes of the cluster fractions. From 1851 to In terms of seasonal variability, the results are not as coher- 1890 as well as from 1911 to 1960, the southeast cluster is ent as for the all year analyses. In Fig. 12, the relative cluster dominating, whereas in the other periods, the northwest clus- frequencies on a seasonal basis for winter and summer are ter occurs more frequently. shown. In winter, two pronounced peak periods are visible, one from 1851 to 1870 (16 DAs/30 years) and another from 1971 to 2000 (15 DAs/30 years). However, the two main 5 Discussion peaks are different with respect to their cluster fraction. The peak in the nineteenth century is composed of the occurrence The analyses of this paper suggest that the time periods of the of all four clusters with the least contribution from the 1850s through the 1870s and the 1940s were the driest in the Fig. 11 Absolute frequency of clusters for 30-year periods at different accumulation time scales. Bars are centered at the given 30-year period, e.g., the first bar at 1815 represents the 1801–1830 period K. Haslinger et al. Fig. 12 Absolute seasonal frequency of clusters on a 3M time scale enveloping winter (DJF) and summer (JJA). Bars are centered at the given 30-year period, e.g., the first bar at 1815 represents the 1801–1830 period GAR during approx. the last 200 years. This result is in line available climate variables of the HISTALP data base at once with the findings of van der Schrier et al. (2007) who assessed (temperature, precipitation, sunshine duration, cloudiness, and the moisture variability based on the scPDSI. Particularly, the air pressure). As a consequence, this regionalization might not year 1865 clearly stands out in terms of severity of DAs. The be useful for deriving homogenous drought regions. With our associated DAs developed on different time scales (1M, 3M, clustering approach, we were able to show that meteorological and 6M; c.f. Table 2) and led to severe drought impacts as droughts tend to develop in three sub-regions and one region some historical evidence shows (c.f. Soja et al. 2013). covering most of the domain. The results are partly consistent Interestingly, the year of 1865 is not known for severe drought with the PCA of Auer et al. (2007), since our clusters north- impacts on agriculture. Although 1865 shows the most severe west and southwest are to some extent comparable to regions DA on a 6M time scale from April to September, it was the northwest and southwest of Auer et al. (2007). However, clus- enveloping months April and September that were the most ter east is in our case not separated into a northern and a severest overall (c.f. Table 2). However, the aftermaths of southern part as is the case in Auer et al. (2007), which is a these strong anomalies emerged later in winter. A historical fundamental difference. Interestingly, accumulating the pre- Viennese report on January 1866 stated: BIn Leopoldstadt (a cipitation on different time scales does not usually affect these part of Vienna) water scarcity is becoming noticeable. Many patterns in contrast to investigations for, e.g., the Iberian wells fell dry.^ And BIncreasing water scarcity. The streambed Peninsula (Vincente-Serrano 2006). of the Danube Channel is covered with thousands of dead These findings along with the change probability assess- fish.^ (BlLkNÖ 1866; originally in German language, ment in space from dry to non-dry states suggest that the Main translation by the authors). But not only on a local scale was Alpine Crest is a distinct boundary between different manifes- the severe dry anomaly noticeable. In a study by Pekarova et tations of the climate in the GAR. We found that the change al. (2006), who investigated long-term streamflow trends probability from north to south for a dry to normal/wet condi- across Europe, the authors found the 1860s and 1940s as out- tion is even enhanced if longer accumulation time scales are considered. This indicates that precipitation anomalies are per- standing dry periods for Western and Central European major river systems. Unfortunately, no north/south distinction sistent over several months, which may be related to re- among catchments has been carried out in their study. occurring weather conditions, enhancing the spatial differ- Investigations of more recent drought events in Europe show ences in anomalies. This dipole-like feature of precipitation increasing dry and continental conditions during the last in the GAR was initially detected by Böhm et al. (2003)and 20 years in the Carpathian Region (Spinoni et al. 2013)and analyzed in more detail by Brunetti et al. (2006). They found also increasing drought conditions in the Balkans and Italy, that the north-south (N-S) dipole feature is more prominent whereas in Central Europe, no general trend is noticeable than the west-east (W-E) feature, which is in line with the (Spinoni et al. 2015). The results of these papers underpin findings of our study. However, they also found an increasing our results which show increased DA frequency in the south- trend in N-S dipole, which they attribute to negative precipi- east of the GAR, particularly in winter and no (1M and 3M) or tation trends in the southern part and mostly positive trends in even decreasing (6M and 12M) DA frequency in the north- northern parts of the GAR. This reflects our finding of dom- west cluster during the second half of the twentieth century. inating south and east clusters on higher accumulation time However, it is important to assess also the spatial charac- scales in the second half of the twentieth century. teristics of meteorological droughts in the GAR, since climate With respect to seasonal aspects, the spatial patterns in variability and precipitation regimes are rather diverse. winter (DJF) based on a 3M time scale are to some extent Regional aspects have been considered, for example, in van similar to the all year analyses indicating, again, a pronounced der Schrier et al. (2007) who analyzed moisture variability in border along the Alpine Crest between dry and normal/wet four different regions in the GAR. But the regionalization was conditions based on an optimal cluster solution of four clus- based on the PCA of Auer et al. (2007) which treated all ters. For summer, however, this picture is not as clear. The Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from... Foundation as part of the Vienna Doctoral Programme on Water quantitative assessment of an optimal clustering suggested Resource Systems (DK Plus W1219-N22) is acknowledged. two clusters to be the best following the silhouette width ap- proach, resulting in a northwest and a southeast cluster. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http:// Furthermore, the cluster borders are much fuzzier and the creativecommons.org/licenses/by/4.0/), which permits unrestricted use, Alpine Crest is not as strong a boundary as in the all year distribution, and reproduction in any medium, provided you give appro- and winter clusters. The reason for this may lie in the domi- priate credit to the original author(s) and the source, provide a link to the nance of convective precipitation which is either embedded in Creative Commons license, and indicate if changes were made. frontal systems or generated locally, producing heterogeneous spatial patterns of precipitation. References 6 Conclusions Abegg BS, Jetté-Nantel S, Crick F, de Montfalcon A (2007) Climate change impacts and adaptation in winter tourism. In: Agrawala S Considering the long-term perspective of more than 200 years (ed) Climate change in the European Alps: adapting winter tourism of drought patterns in the GAR, we conclude that the time and natural hazards management. 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