1 Introduction

Drought has been traditionally perceived as an event of slow onset, developing gradually over seasonal or longer time scales (Wilhite 2000). Following the U.S. Drought Monitor (Svoboda et al. 2002), drought events with unusually quick onset and intensification were termed “flash drought” (hereafter FD), emerging into the spotlight particularly after a widespread FD event in summer 2012 in the central US (Otkin et al. 2016). More recently, FDs were generally recognized as an extreme subseasonal climatic phenomenon with a rapid onset and intensification (Lesinger and Tian 2022) capable of causing substantial socioenvironmental impacts (Jin et al. 2019; Hoell et al. 2020).

Many studies have attempted to present specific definitions of FDs and their distinction from longer-term droughts. For example, Pendergrass et al. (2020) suggested three basic principles for FD definition: rapid onset, high intensification rate, and severity of the resulting condition. This means that FDs should not only develop quickly, but the conditions should also reach a state that would still be classified as a drought event if it developed slowly. This definition was also supported by other authors (Christian et al. 2019; Osman et al. 2022) with length of the intensification window varying from 14 days (Parker et al. 2021; Pendergrass et al. 2020) up to 30 days (Christian et al. 2019, 2021).

The base datasets and methods used for FD assessment also substantially differ (Otkin et al. 2018). Lesinger and Tian (2022) mentioned two categories of approaches to FD identification:

  1. (1)

    Evaporative demand FDs are defined mainly by indices, usually based on actual and potential evapotranspiration ratios, such as the evaporative stress index (Christian et al. 2021), derived from satellite data, or the evaporative demand drought index (Parker et al. 2021), derived from reanalysis data. Precipitation deficit indices based on temperature and precipitation data were also sometimes used (Mo and Lettenmaier 2016).

  2. (2)

    Soil moisture FDs are based on actual soil moisture values and anomalies that can be derived from various sources, such as satellite data (Ford and Labosier 2017), modeling approaches (Chen et al. 2019) or in situ measurements (Ford et al. 2015). Many studies have used the 0–40 cm soil layer (Ford and Labosier 2017; Otkin et al. 2021; Lesinger and Tian 2022).

In both of these categories, the resulting values of either indices or actual soil moisture were usually transformed into percentiles based on individual locations and seasons (Otkin et al. 2018).

Another important aspect of FD delimitation was either the minimum change in the percentile values that must be achieved during the aforementioned time window or defined percentile thresholds. In that case, the implemented variable had to be above an upper threshold at the start of the time window and under a lower threshold at the end of the time window for the event to be classified as a FD. Ford and Labosier (2017), Christian et al. (2021), Osman et al. (2021) and Lesinger and Tian (2022) used the 40th percentile as the upper threshold and the 20th percentile as the lower threshold.

In terms of studied regions, the vast majority of contemporary papers focused on the continental US where the FD definitions originated. Despite papers dealing with different regions such as China (e.g., Wang et al. 2016; Zhong et al. 2022), Australia (Parker et al. 2021) or even all of Europe (Shah et al. 2022), insufficient focus on FDs appears nearly everywhere outside North America, including the Central European region. For example, the only study dealing with FDs in the Czech Republic was conducted by Mozny et al. (2012), who used in situ soil moisture observations from seven stations and defined FD as a rapid soil moisture decline within a three-week period. No comparable studies on a regional level exist in other Central European countries.

Even though aforementioned FD studies did not focus on their connection to atmospheric circulation, a number of studies related to drought in general focused on this problem. For example, Park Williams et al. (2017) analyzed major drought events since 1895 and their major circulation drivers in the US, concentrating on unique anticyclonic conditions during the 2016 event. Okumura et al. (2017) studied effect of La-Niña events on circulation over the US and drought occurrence. Wei et al. (2021) found close connection between droughts in northeastern China and anomalies of the western Pacific subtropical high. Raziei et al. (2012) discovered that droughts in Iran were driven by certain circulation types derived from 500 hPa geopotential. On a pan-European scale, oscillation indices like NAO index were often used (e.g., Kingston et al. 2015). They were also used on a smaller (regional) scale (e.g., Irannezhad et al. 2017), for which different classifications of circulation types have often been used, such as Hess–Brezowsky “Grosswetterlagen” classification (Hess and Brezowsky 1952; Werner and Gerstengarbe 2010) or Lamb weather types (Lamb 1972) and their objective versions (Jenkinson and Collison 1977; Blenkinsop et al. 2009). For example, Fleig et al. (2011) identified anticyclonic circulation types and certain airflow directions as drought triggers in Denmark and British Isles. Haslinger et al. (2019) found anticyclonic types to be the most important driver of winter and spring droughts in the Alpine region. The importance of anticyclonic circulation types with higher temperatures and evapotranspiration together with small or none precipitation was confirmed also for central Europe (e.g., Beck et al. 2015; Lhotka et al. 2020), while the effect of airflow direction somewhat changed according to specific locations (Řehoř et al. 2021c; Zahradníček et al. 2015).

To fill the existing territorial gap in FD research, the first goal of our paper was to conduct a comprehensive spatiotemporal analysis of FDs within the Central European region (consisting of the Czech Republic, Slovakia and the northern part of Austria) in the 1961–2021 period. The second goal was to investigate which large-scale circulation types of the objective circulation classification lead to onset and duration of FD events and which contributed to their ending, including analysis of changes in precipitation, temperature and evapotranspiration as variables directly driving soil moisture during FD events.

2 Data

2.1 Study area

The study area (Fig. 1a) included the entire area of the Czech Republic (78,870 km2) and Slovakia (49,036 km2) and the northern part of Austria on the left bank side of the Danube River (12,715 km2), representing 140,621 km2. The mean areal annual precipitation total reached 694 mm, varying from 445 to 1593 mm (Fig. 1b), and the mean areal annual temperature was 8.1 °C, varying from − 3.1 to 11.0 °C (Fig. 1c) for the period 1961–2021.

Fig. 1
figure 1

The area analyzed in this study: a physical-geographical map; b mean annual precipitation totals for the 1961–2021 period; c mean annual temperatures for the 1961–2021 period

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2.2 The SoilClim model

The water balance model SoilClim, simulating soil moisture in 0.5 × 0.5 km grids, was first introduced by Hlavinka et al. (2011), and it has been continuously developed and improved since then as a core part of the Czech Drought Monitor System (Trnka et al. 2020) and the “Interdrought” project with a Central European scope (Interdrought 2022). SoilClim is principally based on the modeling approach suggested by Allen et al. (1998). SoilClim is applied to each grid and accounts not only for the soil water holding capacity within the grid but also for the type of vegetation cover, phenological development, root growth and snow cover accumulation, sublimation, and melting (Trnka et al. 2010). This study used its most recent setup “MS4”, described in full detail by Řehoř et al. (2021b). MS4 considers four soil layers (0.0–0.1, 0.1–0.4, 0.4–1.0 and 1.0–3.0 m) and calculates soil moisture based on the relationship between inflow (water infiltration) and outflow (evapotranspiration and deep percolation) water-balance components. The cascading approach for water movement from the upper to lower soil layer is used when the topsoil is more than 50% saturated. In the case of higher soil water content in the topsoil, the soil water is allowed to seep into the subsoil, which mimics macropores and preferential water transports (Hlavinka et al. 2011).

SoilClim estimates of the soil moisture content are affected by the maximum soil water holding capacity (MSWC) for each of the soil layers in each grid. This parameter is estimated through a combination of digital maps and detailed soil physical data from, which have been collected by the Czech and Slovak National Soil Survey (more details in Trnka et al. 2015a, b). The MSWC is calculated by assuming a 3.0 m soil profile, unless the soil database indicates a shallower soil depth. SoilClim dynamically simulates the vegetation cover, which changes canopy parameters (e.g. root depth or crop height) during the growing season based on the thermal time and vernalization requirements (in the case of winter crops and perennials). Therefore, crop parameter Kc (Allen et al. 1998) and the root growth dynamics vary for individual vegetation covers throughout the year (or the vegetation season). To simplify the seasonal variations in crop cover compositions on arable land grids (which dominate the landscape), a fixed proportion of crops on each arable grid is assumed. In these grids, the soil moisture content is computed using spring and winter (C3) crops (based on the current spring barley and winter wheat yields) and spring (C4) crops (maize); then, the three considered crops are weight-averaged.

The calculation uses station series of daily temperature, vapor pressure, global radiation, wind speed and precipitation totals provided by the Czech Hydrometeorological Institute (CHMI), Slovak Hydrometeorological Institute (SHMI) and GeoSphere Austria (former known as Central Institute for Meteorology and Geodynamics - ZAMG). Corresponding data were first quality controlled and homogenized (Štěpánek et al. 2013) and then spatially interpolated into grids using regression kriging based on terrain features (e.g., altitude, slope) as predictors for the entire 1961–2021 period and the study area.

The resulting volumetric soil moisture was converted into “relative soil saturation” (AWR), in which a value of 100 represents field capacity and 0 stands for wilting point. Because FDs are characterized by a rapid soil moisture decrease in the upper soil layer, we worked further only with AWR data for the 0–40 cm soil layer (similar to Otkin et al. 2021), created by merging the data for the 0–10 cm and 10–40 cm layers from the original SoilClim calculations. To contemplate drought as an AWR anomaly from each grid’s long-term normal conditions, AWR data were converted into percentile values, calculated for each grid and day of the year, using a 21-day window and the entire 1961–2021 period.

2.3 Circulation types

An objective classification of circulation types, centered on the examined area (49.27° N, 16.78° E), was implemented. The classification was based on the principles of Jenkinson and Collison (1977) (first applied for Central Europe by Plavcová and Kyselý 2011), using daily mean sea level pressure (SLP) at 16 points distributed around the center of the region (Fig. 2) to calculate flow strength, flow direction and vorticity. This method enabled us to comprehend the variable nature of European SLP fields and their pressure systems, combining both the airflow direction and (anti-)cyclonic character of the circulation type. ERA5 reanalysis (Hersbach et al. 2020) was used to derive the SLP values at given points. Nine anticyclonic (A, AN, ANE, AE, ASE, ASW, AW, ANW), nine cyclonic (C, CN, CNE, CE, CSE, CS, CSW, CW, CNW) and eight directional (N, NE, E, SE, S, SW, W, NW) circulation types were defined; unclassified days were attributed to type U (for more details of the classification, see Řehoř et al. 2021a, c). The mean SLP schemes during the individual circulation types are shown in Fig. S1.

Fig. 2
figure 2

Positions of the 16 points used for sea level pressure inputs into the calculation of circulation types (the geographic center of the study area is indicated by a cross)

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3 Methods

To define and delimit FD occurrence in each individual grid, all the main aspects of FDs reported in Sect. 1 were incorporated into four following criteria:

  1. (i)

    Maximum length of window for FD onset.

  2. (ii)

    Upper threshold: a percentile value above which AWR has to be at the beginning of the onset window.

  3. (iii)

    Lower threshold: a percentile value below which AWR must decline before the end of the onset window.

  4. (iv)

    Minimum persistence: the number of days in which the AWR has to stay below the lower threshold.

In agreement with many papers (e.g., Ford and Labosier 2017; Christian et al. 2021; Osman et al. 2021; Lesinger and Tian 2022), threshold values were selected as the 40th percentile for the upper threshold and the 20th percentile for the lower threshold. The onset window length was set to 21 days, and the minimum persistence was set to 14 days. The minimum persistence was selected with respect to the actual potential of the delimited FD to affect the environment, considering the main possible application of our study toward potential environmental and agricultural damages, such as increased wildfire occurrence or crop damage.

To divide the entire study area into smaller regions based on the actual similarity of the FD occurrences in individual grids, hierarchical agglomerative clustering was applied, similar to the work of Mckinnon et al. (2016) or Lesinger and Tian (2022) for continental US. Because the input data were in a binary form (FD occurrence/no FD occurrence), Jaccard similarity (Ivchenko and Honov 1998) between every pair of grids was calculated, and the resulting matrix was used as input for the clustering process. Ward’s method (Everitt et al. 2001) was used for the hierarchical agglomerative clustering process. It merges clusters that cause the smallest increase in the error sum of squares. The resulting clusters were validated by the silhouette method (Rousseeuw 1987), calculating the similarity of grids within a cluster compared to grids from other clusters.

To analyze the spatiotemporal variability of FDs within individual clusters, a series of mean percentages of grid points affected by FDs were calculated. Linear trends for these series were calculated using the nonparametric Theil–Sen regression (Sen 1968; Theil 1992), which is more robust to possible outliers than standard linear regression. The statistical significance of trends was evaluated using the nonparametric Mann–Kendall test (Mann 1945; Kendall 1975) for p < 0.05.

Because conducting an analysis of FD circulation drivers requires delimitation of specific time intervals with high FD concentrations within individual clusters, FD episodes were delimited. At first, periods with FDs affecting > 50% of grids within individual clusters for a minimum of seven consecutive days were selected. These periods were investigated individually based on the development of the precipitation deficit described by the daily precipitation quotient Qd:

$$\text{Q}_\text{d}=\text{P}_\text{d}/\text{P}_0-1$$

where Pd is the precipitation total for a given day and P0 is the mean precipitation for the corresponding day of the year in the 1961–2021 period (with a 21-day smoothing window). Consequently, Qd = − 1 in the case of no precipitation, Qd = 0 in the case of mean precipitation, Qd = 1 in the case of 2x of mean precipitation, etc. Therefore, ƩQd expresses a cumulative precipitation deficit/surplus.

For all delimited FD periods, ƩQd was calculated for their three phases in each cluster according to the following criteria:

  1. (i)

    Phase 1 – onset: This phase begins when a precipitation deficit starts to develop (at most 21 days before 50% of grids are affected by FD) and ends on the day before > 50% of grids within a cluster are affected by FD. Therefore, it represents the initial phase of an FD episode and includes the factors that led to the FD origin.

  2. (ii)

    Phase 2 – event duration: This phase starts on the first day when > 50% of grids within a cluster are affected by FD and ends on the day with the maximum negative value of ƩQd. It represents the main part of the FD episode, during which the drought condition persists or deepens.

  3. (iii)

    Phase 3 – end: This phase starts on the day after the maximum negative value of ƩQd and ends on the last day > 50% of grids within a cluster are affected by FD. It represents the period that resulted in the end of the drought conditions and therefore the end of the whole FD episode.

Figure 3 presents a simplified scheme illustrating the determination of FD Phases 1–3 based on the development of ƩQd (Fig. 3a) and percentage of grids affected by FD (Fig. 3b) with four boundary points delimiting beginning and end of individual phases.

Fig. 3
figure 3

Schematic illustration of a development of the summed daily precipitation quotient ƩQd and b percentage of grids affected by FD during Phases 1–3, including four boundary points (1)–(4) delimiting beginning and end of individual phases

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The main analyses in this paper were performed for the winter half-year (October–March, WHY) and the summer half-year (April–September, SHY), although some analyses were also provided for the entire year (ANN), standard seasons (December–February DJF; March–May MAM; June–August JJA; and September–November SON) and for seasons shifted by one month (January–March JFM; April–June AMJ; July–September JAS; October–December OND), which correspond well to the AWR annual cycle in Central Europe (e.g., Trnka et al. 2015a; Řehoř et al. 2021b).

In order to terminologically differentiate FDs from other droughts considered within the paper, we used “long-term soil drought” (further as LTSD) as a general term to include all commonly used definitions of soil drought for comparation purposes in the discussion.

4 Results

4.1 Spatiotemporal variability of flash droughts

Based on the results of the hierarchical agglomerative clustering, four clusters were selected for further spatiotemporal analyses (Fig. 4a; Fig. S2 shows clustering levels of 2–7 for comparison). Cluster I includes most of Bohemia and the highland regions of northern Austria. The driest leeward lowland regions of Bohemia are included in cluster II, together with most of Moravia and lowland parts of southwestern Slovakia and northern Austria. The northeastern Moravian mountainous region belongs to cluster III, together with northwestern Slovakia and parts of central and eastern Slovakia. The greater part of Slovakia belongs to cluster IV. The four selected clusters are easily interpretable by the combination of the west–east position and lower–higher altitude gradients as well as the windward–leeward effects of the main mountain ranges. Furthermore, validation of cluster analysis by the silhouette method (Fig. 4b) showed a moderate decrease in intracluster similarity going from two to four clusters but a massive drop in similarity in the case of five clusters. This confirmed our choice of four clusters instead of other options as an optimal compromise between the level of detail in the division of the study area into individual regions and their specific features.

Fig. 4
figure 4

Division of the study area into four clusters by Ward’s method (a) and intracluster similarity for 2–20 cluster levels according to the silhouette method (b)

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The temporal variability of FDs was expressed by the mean percentages of grid points affected by FD and by the number of days within FD episodes in the four clusters for the SHY and WHY during the 1961–2021 period (Fig. 5). Interannual variability in each cluster as well as differences between individual clusters were higher in the WHY than in the SHY. The largest affected area in the WHY was detected in 1991 in clusters I–II and in 2011 in clusters III–IV, while in the case of the SHY, the largest affected area occurred in 2003 in all clusters except for cluster II, with the maximum in 1973. All linear trends in the mean affected area were decreasing in the WHY, ranging from a slope of − 0.09%/10 years in cluster II to − 0.81%/10 years in cluster IV, but none of the trends were statistically significant. In contrast, all clusters in the SHY exhibited similar increasing trends between 0.54 and 0.65%/10 years; only the trend in cluster III was statistically significant. The highest number of days within FD episodes in the WHY was in 1972 (cluster I), in 1991 (cluster II), in 2011 (cluster III) and in 1983 (cluster IV), while in SHY, it was in 1973 in clusters I–III and in 1994 in cluster IV. The exact occurrence of individual FD episodes and their phases is shown in Fig. S3.

Fig. 5
figure 5

Fluctuations in the mean area of flash droughts and their linear trends (a, b) and in the number of days within flash drought episodes (c, d) in the four clusters for the winter half-year (a, c) and the summer half-year (b, d) in the 1961–2021 period (statistical significance of trends: *p < 0.05)

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For seasonal linear trends (Table 1), the majority of them were not statistically significant. In the mean affected area, only MAM and AMJ stood out with statistically significant increasing trends in clusters I–II for MAM and in clusters I–III for AMJ (particularly high with slopes of 0.81–0.88%/10 years). In the number of FD episode days, significant increasing trends were found for cluster I in MAM and JFM as well as for clusters I–II in AMJ. In contrast to the affected area trends, cluster I in OND and cluster IV in the WHY experienced statistically significant decreasing trends.

Table 1 Linear trends in the annual and seasonal mean areas of flash droughts (a) and in the number of days within flash drought episodes (b) for the four clusters in the 1961–2021 period
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Box plots of the mean area of FDs in the WHY (Fig. 6a) and SHY (Fig. 6b) show the lowest median in cluster II and the highest in cluster IV. Clusters I and IV demonstrate the highest variability expressed by interquartile range as well as maximum affected area in WHY. In SHY, the maximum affected area was found in cluster III. The distribution of the WHY (Fig. 6c) and SHY (Fig. 6d) values was expressed by density plots, revealing a higher density of values of approximately 5% in cluster II, particularly in the WHY, and a lower density in cluster IV, particularly in the SHY.

Fig. 6
figure 6

Boxplots (median, lower and upper quartile, minimum and maximum) (a, b) and density plots (c, d) of the mean area of flash droughts for the four clusters in the winter half-year (a, c) and summer half-year (b, d) in the 1961–2021 period

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Table 2 shows that most FD episodes occurred in cluster IV (40), while only 19 episodes occurred in cluster II. The mean length of Phase 1 was the largest in cluster IV (20.0 days) and smallest in cluster III (18.9 days), while Phase 2 was the longest in cluster II (22.4 days) and shortest in cluster I (20.0 days). Phase 2 was by far the shortest and varied between 2.9 and 3.5 days.

Table 2 Basic parameters of FD episodes for the four individual clusters in the 1961–2021 period
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4.2 Meteorological patterns during flash droughts

To describe the typical course of meteorological patterns during FD episodes, anomalies of the three following variables were calculated (Fig. 7): daily precipitation totals, actual evapotranspiration (ETa) modelled by SoilClim (different from potential evapotranspiration) and maximum air temperature (TMAX). Concerning the WHY, Phase 1 was characterized by an almost 70% decrease in precipitation in all clusters, while ETa stayed at normal values. TMAX was above the mean, particularly in cluster II (by 2 °C) but also in other clusters (the lowest anomaly of 0.4 °C in cluster I). The decrease in precipitation was even deeper in Phase 2 (up to − 81% anomaly in cluster I), and there was also some decrease in ETa; TMAX decreased under the mean in clusters II and IV and was slightly above in clusters I and III. Phase 3, marking the end of the FD episode, was characterized by above-mean precipitation, with a positive anomaly of 46–66% in clusters I–III and as high as 126% in cluster IV. ETa returned to normal values, while TMAX was in a range of 1–2 °C above the mean in all clusters.

For the SHY, precipitation totals and ETa behaved almost identically to those of the WHY; however, TMAX stayed close to the mean in Phase 1 but reached very high anomalies of 2.3–2.6 °C in Phase 2. In Phase 3, the precipitation increase was most pronounced in clusters II and III (approximately 100%), while it was lower but still present in clusters I and III (26% and 51%, respectively). ETa stayed approximately 35% under the mean and TMAX above the mean; however, it exhibited a strong west–east gradient with anomalies ranging from almost 3 °C in cluster I to less than 1 °C in cluster IV.

Fig. 7
figure 7

Mean anomalies in daily precipitation total (Prec., %), actual evapotranspiration (ETa, %) and maximum air temperature (TMAX, °C) during Phases 1–3 of FD episodes for the four clusters in the winter half-year (WHY) and summer half-year (SHY) during the 1961–2021 period

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The analysis of anomalies in precipitation, ETa and TMAX (cf. Figure 7) aimed mainly to describe differences between the WHY and SHY in terms of meteorological conditions triggering FDs. Precipitation behaved very consistently during the year with a massive decrease in Phase 1 and an even larger decrease in Phase 2. This decrease was more pronounced compared to similarly defined phases for LTSD episodes, showing that FD occurrences were always associated with immediate precipitation shortages.

TMAX behaved in a more complicated manner. In the WHY, TMAX decreased between Phases 1 and 2, especially in cluster II, from above-mean to below-mean values. This could be connected to the character of stable anticyclonic patterns, particularly in DJF, causing stable stratification of the atmosphere or direct temperature inversion. This could be a case of the lower TMAX in cluster II, mainly consisting of lowlands, while clusters I and III with more highlands experienced higher TMAX. For the SHY, TMAX anomalies were near the mean values in Phase 1; however, they rose high above the mean in Phase 2. This again corresponds to the meteorological character of anticyclonic patterns (including heat-wave situations) in the SHY, with lower temperatures at the beginning and gradually rising under radiation warming (sometimes complemented by warm airflow). This distinct TMAX behavior also highlights that FD episodes were often driven by one meteorological event compared to seasonal droughts resulting from the accumulation of water deficits over a longer time.

ETa anomalies started at near-mean values and decreased below the mean in Phase 2, even in the case of the SHY with very high TMAX values. However, it just points out the quick development of soil moisture deficit in the concerned 0–40 cm soil layer, causing a shortage of available water that could evaporate, rapidly lowering ETa. This also demonstrates the advantage of complex soil moisture modeling compared to still broadly used meteorological drought indices (e.g., SPI, SPEI or PDSI), which often indicate an unrealistic level of water deficit accumulation, while in reality, the lack of available water in the topsoil layer greatly limits ETa.

4.3 Flash droughts and circulation types

To characterize the mean circulation patterns in the analyzed area for the entire 1961–2021 period, the frequencies of individual types and their groups were calculated. In the WHY, anticyclonic types had the highest frequency at 47.4%, followed by directional types (37.9%) and cyclonic types (14.2%); 0.5% of days remained unclassified. In the SHY, the frequency decreased for anticyclonic types to 44.9% and for directional types to 33.2%, while it increased for cyclonic types to 18.9% and unclassified types to 3.0%. The frequencies of individual circulation types (Fig. 8) were similar for the majority of types in both half-years. The types ASW, AW, SW and W were much more frequent in the WHY, while for the types AN, ANE, N, NE and U in the SHY, the opposite was true.

Fig. 8
figure 8

Mean relative frequencies (%) of circulation types in the winter half-year (WHY) and summer half-year (SHY) over the study area in the 1961–2021 period

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Deviations in the relative frequencies of groups of circulation types are presented in Fig. 9. In WHY, the deviations were generally smaller than those in the SHY, with only smaller positive deviations in the frequencies of anticyclonic types in Phase 1 (particularly in clusters II and IV) and negative deviations in cyclonic and directional types. The deviations increased in Phase 2, ranging from 14.3% (cluster III) to 20.8% (cluster II) for anticyclonic types, from − 4.5% (cluster II) to − 8.1% (cluster IV) for cyclonic types and from − 8.9% (cluster III) to − 16.4% (cluster II) for directional types. Larger differences between clusters appeared in Phase 3. In cluster I, cyclonic types were slightly more frequent and directional were slightly less frequent compared to average, but in clusters II and III, both anticyclonic and cyclonic types were less frequent, while for directional types, it was the opposite. In cluster IV, anticyclonic types occurred much less frequently (–16.0%), while both cyclonic and directional types were more frequent. During the SHY, the circulation changes were different and much more pronounced. During the onset of FD episodes in Phase 1, anticyclonic types were much more frequent, with deviations ranging from 21.8% (cluster IV) to 26.5% (cluster III), while both cyclonic (from − 12.3 to − 16.2%) and directional (from − 7.5 to − 8.7%) were less frequent. The deviations were smaller in Phase 2, ranging from 8.7 to 14.8% for anticyclonic types and from − 9.6 to − 12.4% for cyclonic types, while the frequencies of directional types exhibited no deviations. During Phase 3, the frequency of anticyclonic types massively decreased, particularly in cluster I (–34.9%), while the deviation was slightly lower in cluster II (–17.6%). The frequency of cyclonic types increased, particularly in clusters I–III (from 17.7 to 21.1%), while the frequency of directional types slightly increased in all clusters, except cluster II.

Fig. 9
figure 9

Deviation in relative frequencies of groups of circulation types during Phases 1–3 of flash drought episodes in the four clusters in the winter half-year (WHY) and summer half-year (SHY) during the 1961–2021 period

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For the individual circulation types driving the occurrence of FDs, Table 3 shows pairs of types with the highest positive/negative deviations in their frequency during Phases 1–3 of FD episodes for each cluster and half-year. In the WHY, both Phases 1 and 2 were characterized by the highest positive deviations of type A, except for cluster I with a higher deviation of type S in Phase 2. Type A was frequently complemented by types SE or ASE. On the other hand, substantial negative deviations appeared for the westerly directional types (SW, W and NW). The situation was reversed in Phase 3, with the largest negative deviations for type A and the largest positive deviations for the types with westerly airflow, except cluster I with type CS. In the case of the SHY, type A still exhibited large positive deviations in Phase 1 but was complemented by types AE or ANE. In Phase 2, type AE exhibited the largest positive deviations in all clusters, complemented by types E, ASE and A. Large negative anomalies appeared for type C in both Phases 1 and 2 and for type W in Phase 2. Phase 3 was characterized by massive positive deviations for the SW type in cluster I and for the CSE type in clusters II and III. On the other hand, type A exhibited massive negative deviations in clusters I, III and IV. Type U was remarkable in Phase 3 with large positive deviation of 6.1% in cluster IV, while experiencing only minor deviations in other clusters and phases.

Table 3 Circulation types with the highest relative positive (P) and negative (N) deviations from their 1961–2021 mean frequencies in Phases 1–3 of FD episodes for the four clusters I–IV during the winter (WHY) and summer (SHY) half-years
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In terms of circulation drivers of FD, it is not surprising that the connection is much stronger in the SHY than in the WHY because of multiple disrupting factors that can occur in WHY, including snow cover or soil freezing, due to which circulation patterns sometimes were not able to directly and immediately influence soil moisture development, which brings an additional uncertainty into the WHY results compared to the SHY results. Nevertheless, the development of FD episodes was clearly connected to a higher frequency of anticyclonic types even in the WHY, particularly in Phase 2. Among individual circulation types, types AE and ASE mostly accompanied the A type in Phase 2 in clusters II–IV, while in cluster I, southern advection seemed to play a larger role. Phase 3 shows the most distinct differences between individual clusters. While cluster I experiences a higher frequency of cyclonic types, directional types are more frequent in clusters II–IV. In the case of the SHY, Phase 1 was the most crucial regarding circulation drivers, with a massive surplus of anticyclonic types and an almost total absence of cyclonic types, representing only approximately 3% of the Phase 1 types; the frequency of directional types also decreased. In Phase 2, all anomalies were smaller, and the frequency of directional types returned to mean values. This is explained by the frequency of individual types, with directional types E and SE having positive anomalies. In Phase 3, unlike in the WHY, there was a massive decrease in the frequencies of anticyclonic types in all clusters.

5 Discussion

5.1 Selection of flash droughts parameters

In addition to the variety of approaches to selecting the FDs (e.g. Parker et al. 2021 or Christian et al. 2021), we considered the 21-day onset window, 40th/20th percentiles as thresholds and 14-day minimum persistence to be optimal, because it led to relative frequency of FD ranging mostly between 5% and 10% for the 1961–2021 period. Similar frequencies proved to be optimal in the case of usual drought delimitations (the 10th percentile has been used, for example, as an indication of severe drought in the U.S. Drought Monitor – Svoboda et al. 2002, as well as in central Europe by Trnka et al. 2015a; or Řehoř et al. 2020, 2021c), providing sufficient sample size for circulation analysis while maintaining criteria ensuring the severity of selected events. Because the correct setting of the above parameters for FD delimitation may significantly influence the results, we tested the effects of changing the parameters with respect to our results. Therefore, calculations were performed for the length of minimum persistence shortening to 10 and 7 days as well as with the lower threshold decreasing to the 10th percentile and the upper threshold increasing to the 50th percentile. All these versions were also calculated with the onset window prolonged to 28 days. For all 10 resulting delimitations, the frequencies of days with FDs were calculated for all grids in the entire 1961–2021 period and are expressed in Fig. S4. Regardless of the selected parameters, a higher frequency of FDs was found at middle altitudes, and a lower frequency was found in the lowlands and the highest mountains. Prolongation of the onset window to 28 days had almost no effect on the results; however, widening the lower/upper threshold range significantly decreased the FD frequency to a point that FDs were almost not occurring in lowland areas, making that delimitation unfitting. Shortening the minimum persistence to 10 or 7 days increased the FD frequency mainly in areas with already high FD frequencies in our original delimitation.

5.2 Spatiotemporal variability of flash droughts

Because of different FDs definitions and regions analyzed, the direct comparison of our results with other papers is relatively difficult. For example, Lesinger and Tian (2022) calculated FDs for the continental US similarly to us (based of soil moisture percentile drop) and got slightly higher mean FD frequency compared to our results (mostly in 5–15% range). Their FDs frequencies were not so clearly driven by altitude as in our case, however, they were lower in drier western part of the US. This coincides with the lowest FDs frequencies in dry leeward lowland areas in our results. Similar FD frequency distribution in the US was confirmed by Chen et al. (2019), Pendergrass et al. (2020) or Otkin et al. (2021), while Chen et al. (2019) found much lower FD frequency than other studies (only around 1%), due to stronger selected criteria. In Australia, Parker et al. (2021) used four different FD definitions which resulted in frequencies varying from 0 to 16%, while only one of the used definitions lead to significantly lower FD frequency in drier regions. Christian et al. (2021), analyzing the entire global land except deserts and polar regions and using very different approach from us (without soil moisture data), reported the FD frequency to be bound to climate zones: the highest one in the tropics, lower in temperate climate and the lowest in boreal climate. However, Central Europe was not analyzed in detail in their study.

Our study area was included in an FD study conducted by Shah et al. (2022) for the entire European continent, mainly comparing 1950–1984 to 1985–2019. They found a large increase in FDs, particularly in the northwestern part of our study area, while the Panonian region (including the southeastern part of our study area) did not experience an increase in FD frequency. Our results do not support such a strong division in the region. The differences could be caused particularly by using completely different soil moisture data and slightly different time periods.

Concerning the spatiotemporal variability of FDs, a comparison with LTSD seems to be most important because it has already been investigated many times and is known in detail in European scale (Kingston et al. 2015; Spinoni et al. 2015; Ionita et al. 2017). For example, as proven by Hänsel et al. (2019), this region is becoming significantly drier in the SHY, which partially corresponds to our results for FDs, but trends in FDs were much more moderate and rarely statistically significant. The best comparison is probably offered by studies based on the same soil moisture data coming from the SoilClim model, particularly by Trnka et al. (2015b, 2020); Řehoř et al. (2021b) for the Czech Republic and Řehoř et al. (2021c) for both the Czech and Slovak republics. All these studies found, compared to our FD results, steeper and usually statistically significant trends in LTSD occurrence in the SHY. Looking on individual years, this difference seems to be largely caused by the 2015–2020 period, which experienced a long LTSD episode, unprecedented even in the context of several past centuries (Büntgen et al. 2021) and caused by gradually accumulated precipitation deficits, accompanied by above-mean temperatures. However, this period had comparable or even lower FD frequency than other drier periods, such as in the early 1990s, 2003 or early 2010s. This is connected with the fact that during long LTSD episodes, such as 2015–2020, soil moisture is already so low that FD cannot occur although favourable meteorological conditions for FD development. On the other hand, FD occurrence in the 1970s seems to be more frequent in relative comparison with time series of LTSDs. Concerning the WHY, the discovered slightly negative trends in FDs were much more in line with LTSD analyses, including the fact that FD frequency decreased more apparently in the eastern part of the investigated region (cluster IV).

5.3 Flash droughts and circulation types

This study of FDs is original in terms of their connection with circulation types, because none of cited papers dealt with this topic. Our study demonstrated important role of anticyclonic types particularly for FD initiation (Phase 1) in SHY (types A and AE) and for their persistence (Phase 2) in WHY (types A and ASE), while directional types E and SE played important role too. Types A and AE have been identified as important also for initiation and persistence of LTSD in Central Europe (Řehoř et al. 2021c), together with types AN and ANE, while role of ASE, SE and E was negligible. Lhotka et al. (2020) evaluated for the Czech Republic in 1948–2018 the tendency of individual circulation types to drought origin. The types SE, AE, ASE and A experienced the strongest tendency to short-term droughts (characterized by Palmer Z-index) in SHY and the types ASE and A in WHY, which coincides with results of our study, because short-term droughts may partly overlap with FDs. As for the tendency to long-term droughts (described by SPEI-4), Lhotka et al. (2020) found partially different circulation drivers. Haslinger et al. (2019) found in the Alps significant relationship of LTSD to circulation only in winter and spring and almost none in summer. This contradicts to our results with slightly stronger relationship to circulation types in SHY compared to WHY, however, the study areas barely overlap and the Alps have very different drought drivers.

Comparing generally the connection of FD phases to anomalies in circulation patterns, it was stronger and more direct compared to episodes of usually defined droughts, to which the same circulation classification was applied by Řehoř et al. (2021c), which resulted in smaller anomalies in the frequency of circulation types and their groups, even though the investigated regions were smaller and more spatially coherent.

Although the airflow direction is included in every circulation type of the objective classification, eight basic directions were used to summarize their general effects on FD episodes. The airflow direction also represents the SLP gradient over the study area. Fig. S5 shows anomalies in the frequencies of individual airflow directions during FD episodes. Compared to LTSD episodes, northern and northeastern directions were less frequent in Phases 1 and 2, favoring the southeastern direction, while eastern directions remained frequent in both cases. In the WHY, Phase 1 experienced a higher frequency of southeastern directions in all clusters. In Phase 2, it was valid for clusters II and III, while in cluster I, the anomaly was shifted toward the southern direction; cluster IV exhibited no anomaly. Phase 3 ending FD episodes were connected to westerly airflows in all clusters except for cluster I. No distinct directions drove Phase 1 in the SHY; however, the eastern and southeastern directions had the highest positive anomalies in Phase 2. In Phase 3, extreme positive anomalies in the southwestern direction frequency occurred in cluster I, while higher frequencies characterized northwestern and southeastern airflows in clusters II and III and western and southeastern directions in cluster IV.

6 Conclusion

The main results of the spatiotemporal analysis of FDs and their circulation drivers in Central Europe during the 1961–2021 period can be summarized as follows:

  1. i.

    The frequencies of FDs mostly decreased in the winter half-year and increased in the summer half-year, but most of the linear trends were not statistically significant. The April–June season was an exception with a significant frequency increase, which was nonsignificant only in the eastern part of the study area (cluster IV).

  2. ii.

    While FD episodes in the winter half-year were mostly driven by precipitation deficits, large positive TMAX anomalies in the summer half-year usually substantially contributed to FD episode development. A decrease in topsoil layer moisture quickly lowered ETa, reducing the actual cumulated water deficit.

  3. iii.

    Anomalies in the frequencies of circulation types during FD episodes were much larger in the SHY, although the connection to circulation patterns was clear in the winter half-year as well. The course of FD episodes was driven by a higher frequency of anticyclonic types. In the summer half-year, the onset of FD episodes was characterized by an extreme increase in the frequency of anticyclonic types, an absence of cyclonic types and a decrease in directional types, while during the course of FD episodes, these anomalies were smaller.

  4. iv.

    Type A showed the highest positive anomalies during the onset and course of FD episodes in both half-years, accompanied particularly by the types ASE and SE in the winter half-year and by types AE and E in the summer half-year, describing a slight shift in airflow directions causing FD.

  5. v.

    Compared to long-term soil drought, the relatively smaller increase in FD frequency was largely caused by the exceptional 2015–2020 drought episode, driven by longer accumulation of water deficit, which was not accompanied by anomalous FD occurrences because soil moisture often maintained such low levels that FD occurrence was technically impossible. Additionally, unlike in the case of long-term soil drought, northern and northeastern airflows did not particularly drive FD occurrence in favor of the southeastern direction.

FDs belong among the most impactful natural hazards particularly for agriculture in Central Europe, when they may highly negatively influence important crops during different phases of their growing cycle. The increasing frequency of FDs in the summer half-year, particularly in April–June, mainly driven by precipitation deficits, increasing maximum temperatures together with changes in the occurrence of anticyclonic types, should be seriously considered in the risk management as well as in future climate scenarios or projections. Moreover, comprehensive understanding of FDs could be beneficial in improving their forecasting.