Keywords

1 Introduction

Atmospheric circulation defined as three dimensional motion of the air, is counted amongst crucial climatic drivers (Barry and Carleton 2001). Air masses flowing from various directions differ in physical properties thus determining the type of weather occurring over particular area and accompanying meteorological phenomena. It has been proved that the occurrence of heavy precipitation is strongly related to both direction of air advection and type of baric centre (Niedźwiedź 1981, 2003a). These relations vary regionally (Łupikasza 2013). Assessment of trends in flood precipitation is usually impossible due to its rare occurrence. Therefore knowledge about the changes in circulation patterns favouring flood precipitation events can give a hint on possible future trends in the events. This chapter discusses change in circulation patterns favouring flood precipitation occurrence. The climatology of atmospheric circulation serving as a basis for further sections is presented in Sect. 2. The linkage between flood precipitation occurrence and atmospheric circulation and its influence on long-term variability of high precipitation events are discussed in Sect. 3. Section 4 concerns changes in circulation types and indices that are favourable for flood precipitation occurrence thus indicating possible future changes in flood conditions. The chapter uses 142-year (1874–2015) long series of circulation types and indices and 65-year long (1951–2015) series of precipitation data which are discussed in subsequent sections.

2 Climatology of Circulation Types and Indices

Processes associated with many environmental problems, including water quality and quantity, are influenced by atmospheric circulation (Yarnal 1993). The impact of atmospheric circulation on precipitation in Poland so far has been presented by Twardosz and Niedźwiedź (2001), Degirmendžić et al. (2004), Niedźwiedź et al. (2009). Atmospheric circulation, as it is shown in the next section, also triggers flood precipitation which was recognized to occur mainly in warm part of the year with maximum in summer (Kundzewicz et al. 2012). This section discusses the climatology of atmospheric circulation in the periods of flood precipitation occurrence, namely in warm-half year (May–October) and in summer (JJA). We used a catalogue of circulation types created for the Upper Vistula Basin (Niedźwiedź 1981, 2016) and three regional circulation indices (Niedźwiedź 1978, 2000): zonal westerly circulation index (Wi), meridional southerly circulation index (Si) and cyclonicity index (Ci). The catalogue covers the period from September 1873 to December 2015 and consists of 21 circulation types denoted by direction of air advection (e.g. N—northern, SE—south-eastern, etc.) and the type of pressure system (a—anticyclonic, c—cyclonic). Sixteen of the 21 types are advectional types whereas the further four are non-advectional types (Ca—central anticyclonic, centre over or very near the Tatra Mountains, Ka—anticylonic wedge, ridge, Cc—centre of cyclone above or very near the Southern Poland, Bc—cyclonic trough). Days with fuzzy or complicated sea level pressure (SLP) pattern or with col were marked by x. The classification of advectional types is methodologically similar to the well-known Lamb (1972) classification for the British Isles with the only difference that transitional types were not included into Niedźwiedź’s classification.

The method by Murray and Lewis (1966), originally used for the British Isles, was modified and adopted to calculate circulation indices for the Southern Poland. Regional circulation indices were calculated on the base of the circulation types frequencies (Niedźwiedź 2000). In order to do so points were assigned to each circulation type depending on the direction of air advection as follows:

  • zonal westerly circulation index (Wi): +2 for W, +1 for NW and SW, −2 for E and −1 for NE and SE,

  • meridional southern circulation index (Si): +2 for S, +1 for SW and SE, for N −2 and −1 for NW and NE,

  • cyclonicity index (Ci): +2 for Cc and Bc, +1 for other cyclonic types (Nc, NEc, … etc.), −2 for Ca and Ka, −1 for other anti-cyclonic types (Na, NEa, … etc.).

Monthly values of every index were calculated as a total of the assigned points. The total was then divided by doubled number of days in a month (season or year) thus being expressed as percentage. The indices can theoretically vary from +100 to −100 % meaning:

  • Wi index: westerly (Wi = +100 %) or easterly (Wi: −100 %) advection throughout an entire month,

  • Si index: southerly (Si = +100 %) or northerly (Si = −100 %) advection throughout an entire month,

  • Ci index: cyclonic (Ci = +100 %) or anticyclonic (Ci = −100 %) circulation types throughout an entire month.

Frequencies of particular circulation types in summer (JJA) and warm-half year (May–Oct) over the Upper Vistula Basin are shown in Fig. 1. The seasonal patterns are similar with clear maximum of anticyclonic wedge lying over the area during 16 % (JJA) or 14 % (May–Oct) of days. The second most frequent type—Bc—occurring with the frequency of 13 % (JJA) or 11 % (May–Oct) of days per season, is known to bring precipitation to the whole Poland (Morawska-Horawska 1971; Niedźwiedź 2003a, b). Among the advectional types, these with the air advection from the west dominated in case of both anti-cyclonic and cyclonic situations which results from location of the area within the moderate climatic zone of the western winds. The types constituted 9–10 % of both summer and warm half-year days. Over the Upper Vistula Basin the air quite often flowed from the northwest (5–7 % depending on baric system and season) (Fig. 1). The frequencies of other circulation types varied from 1 % (Cc type) to 5 % (Na, NEa and Ea types). The Nc and NEc types, which flood precipitation in the Upper Vistula Basin is usually associated to, were not very common (2–3 %), however, the maximum of their occurrence fell at the turn of the spring and summer (April, May, June, July) which is a flood prone period. The frequencies of circulation types in the 1951–2015 period did not differ much from these described above for the 1873–2015 period. The differences in the frequencies of majority of types did not exceed 1 % despite of Wa, Ca and Ka types. In the 1951–2015 the types Wa and Ka occurred less frequently while the type Ca was noted more frequently than in the 1873–2015 period.

Fig. 1
figure 1

Frequency of circulation types in summer (JJA) and warm half-year (May–Oct) over the Tatra Mountains in the 1873–2015 period

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Annual course of the circulation indices presented in Fig. 2 again indicates the domination of air advection from the west particularly from June to March with maximum in December (Wi: +26 %). This was only May (Wi: −4) when eastern airflow was more frequent than western one. The frequency of anticyclonic types was clearly higher than cyclonic types from August (Ci: −12 %) to October (Ci: −16 %) and in January (Ci: −15 %) with highest intensity in September (Ci: −17 %). April was the only month with positive Ci index (+4 %) indicating, in this case slight prevalence of cyclonic types (Fig. 2). The intensity and direction of meridional advection also changed throughout the year. The Si index was positive from September to April, but noticeable prevalence of southerly advection was found in October (Si: +11 %), November (Si: +14 %) and December (Si: +8 %). Northerly advection prevailed from May to August and was the most intense in July (Si: −7 %). The atmospheric circulation was very variable in April and May when all circulation indices were closest to 0 ranging between +4 and −4 % (Fig. 2).

Fig. 2
figure 2

Annual course of circulation indices over the Tatra Mountains (1873–2015). Wi—zonal westerly circulation index, Si—meridional southerly circulation index, Ci—cyclonicity index

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3 Relation Between Flood Precipitation and Circulation Patterns

Synoptic conditions favouring flood precipitation occurrence in Poland were mentioned for the first time by Kaczorowska (1933) and Milata (1955). They found that majority of extremely high, flood precipitation were noted during air advection from the northern sector under an influence of low pressure system or at days with centre of low (Cc type) or the through (Bc type) located over Tatras (Morawska-Horawska 1971; Cebulak 1992; Cebulak and Niedźwiedź 2000; Niedźwiedź 1999, 2003a, b; Mudelsee et al. 2004; Ustrnul and Czekierda 2001, 2009; Kundzewicz et al. 2012; Niedźwiedź et al. 2015; Ruiz-Villanueva et al. 2016). These circulation types were usually related to low pressure systems moving from the Adriatic Sea along the Vb van Bebber (1891) path. After reaching Hungary or Ukraine, the systems were usually blocked by high pressure system with its centre located over the Eastern Europe. This finally led to orographically forced convection of moist air along the northern slopes of the Tatra Mountains and resulting long-lasting rains (Niedźwiedź 2003a, b). Such a situation (Nc) happened in 30 June 1973 and caused record-breaking daily rainfall (300 mm) noted at Hala Gąsienicowa station (Cebulak 1992; Cebulak and Niedźwiedź 2000) and between 16 and 18 July 1934 when 3-day rainfall total reached 422 mm at the same station and led to damaging flood (Niedźwiedź 2003a, b).

We examined the relation between high precipitation, defined here as daily totals ≥50 and ≥100 mm, and atmospheric circulation in order to select patterns favouring the occurrence of flood rains. We used daily precipitation series covering the 1951–2015 period from Zakopane (844 m above sea level) and Kasprowy Wierch (1991 m above sea level) stations and the catalogue of circulation types and circulation indices (Niedźwiedź 2016) described in Sect. 2. Moreover we used North Atlantic Oscillation Index (NAO) which is proved to be an important teleconnection pattern triggering precipitation over the vast areas of northern hemisphere including Europe (Hurrel and van Loon 1997; Hurrel 2001). Precipitation data were made available by Institute of Meteorology and Water Management, National Research Institute (IMGW, PIB). Some data for the 2000–2015 period comes from synoptic data-base OGIMET (Valor and López 2016) and were used after detailed quality control. Average (1951–2015) annual number of days with precipitation ≥50 mm was very low reaching 1 day at Zakopane station (81 days in the whole period) and 3 days at Kasprowy Wierch station (192 days in 65 years). In the Tatra Mountains majority of days with high precipitation (≥50 mm) occurred from May to October (Zakopane: 95 % of days, Kasprowy Wierch: 89 % of days) with maximum in summer (Zakopane: 75 % of days, Kasprowy Wierch: 69 % of days). Therefore we performed the analysis for warm half-year (May–October) and summer (JJA).

Frequency and conditional probability of high precipitation occurrence (≥50 mm) in particular circulation types showed in Fig. 3, allowed selecting flood-generating patterns. Conditional probability is a method used to assess relationships between variables while taking into account the frequency of these variables. The statistic provides information about the degree to which each of the synoptic situations considered favours flood precipitation occurrence, and thus has a prognostic value. The probability of the occurrence of Event E1 (precipitation ≥50 mm) on condition of the occurrence of Event E2 (a specific circulation type) is expressed as (Wilks 2006):

Fig. 3
figure 3

Frequency (upper panel) and conditional probability (lower panel) of daily precipitation ≥50 mm in circulation types in warm half-year (May–Oct) and in summer (JJA) in the Tatra Mountains (1951–2015)

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$$\Pr \left\{ {\frac{{{\text{E}}_{1} }}{{{\text{E}}_{2} }}} \right\} = \frac{{\Pr \{ {\text{E}}_{1} \cap {\text{E}}_{2} \} }}{{\Pr \{ {\text{E}}_{2} \} }}*100\,[\% ]$$
(1)

The conditional probability of high precipitation in the circulation types is low, with the highest values not exceeding 8 % in Zakopane and 18 % at Kasprowy Wierch station, which is due to the relatively low frequency of precipitation ≥50 mm and to high frequency of circulation types, which occur every day. Despite this, the results obtained provide valuable information, which can be used in modelling precipitation at various spatial and temporal scales.

At both stations majority of high precipitation occurred at days with air advection from the north (Nc) and north-east (NEc) under an influence of low pressure system. The frequency of high precipitation in these types varied between 25 and 27 % at Kasprowy Wierch and 20–32 % in Zakopane depending on season and circulation type. Noticeable fraction of high precipitation was noted during cyclonic trough (Bc circulation type) located over the Upper Vistula Basin—20–22 % in Zakopane and 18–17 % at Kasprowy Wierch. Frequency of high precipitation in other cyclonic types did not exceed 8 % (May–Oct) and 10 % (JJA) in Zakopane and 6 % (May–Oct) and 8 % (JJA) at Kasprowy Wierch.

Conditional probability of high rainfall at days with Nc and NEc types was much higher than in other types, particularly at Kasprowy Wierch station. Unlike in case of frequency, the probability of high precipitation occurrence in type Cc was higher than in type Bc (Fig. 3). We assume that particular circulation type favours flood events occurrence if conditional probability of high rainfalls in that type exceeds by at least 50 % the probability of precipitation occurrence regardless of the circulation conditions. At both stations and seasons four circulation types met this condition, thus being recognized as favouring for flood precipitation occurrence—Nc, NEc, Cc and Bc (Fig. 3). At Kasprowy Wierch station Ec circulation type also favoured high precipitation events. Majority of flood precipitation (≥100 mm) that has occurred at Kasprowy Wierch station (10 of 15 events) and Zakopane (all events) were induced by Nc and NEc types (Tables 1 and 2).

Table 1 Synoptic conditions (P—precipitation, CT—circulation type, AmT—air mass type, F—atmospheric front) at days with high precipitation (P ≥ 100 mm) at Kasprowy Wierch station in the period 1951–2015
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Table 2 Synoptic conditions (P—precipitation, CT—circulation type, AmT—air mass type, F—atmospheric front) at days with high precipitation (P ≥ 100 mm) at Zakopane station in the 1951–2015 period
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Łupikasza and Niedźwiedź (2015) recognized that relations between high precipitation occurrence and air advection from the north (Nc type) and the north-eastern (NEc type) directions under an influence of low is stable in long-term course in both summer and warm-half year particularly at Kasprowy Wierch station. In Zakopane located in the centre of the city at the bottom of Tatras the relations discussed are more complicated and less stable in time but of a similar nature. Typical synoptic situations generating heavy precipitation within the Upper Vistula Basin (mainly in Tatras) are presented in Fig. 4. On 18 July 1970 stationary cyclonic system laying over Ukraine caused intense flow of polar maritime old and moist air mass from the north (Nc situation). The air mass was orographically lifted along the northern slopes of the Carpathian Mountains which produced prolonged three days intense rainfall. On that day rainfall amount reached 275 mm at Leskowiec station (870 m) in Skawa catchment and 234 mm at Stańcowa station in Orawa catchment (Niedźwiedź 2003a, b) (Fig. 4). Similar situation but with NE air flow happened on 16 July 1934 when the highest rainfall amounting to 285 mm was noted in Witów (Black Dunajec catchment). Slightly lower total of 255 mm was measured at Hala Gąsienicowa station (1520 m) located on the northern slopes of the Tatra Mountains. The highest-ever total for the whole Upper Vistula Basin was reached during one day duration rainfall on 30 June 1973 with Nc circulation type and cold front passing the area when 300 mm * 24 h−1 and 232 mm * 24 h−1 were, respectively, measured at Hala Gąsienicowa station and at the top of Kasprowy Wierch (1991 m). This rainfall was interrupted by the anticyclonic ridge coming from the France and Germany. As it has already been mentioned cyclones causing such extreme rainfall in the Upper Vistula Basin come usually form the Adriatic Sea along the Vb trajectory designated in Europe by van Bebber (1891). This is clearly seen in Fig. 5 presenting the composite maps of sea level pressure and baric topography of the levels of 850 and 500 hPa created as an average pattern from 15 days with precipitation ≥100 mm at Kasprowy Wierch station using the NCEP/NCAR reanalysis data (Kalnay et al. 1996). The cyclone is also vivid at the 850 hPa level while it takes the form of cyclonic trough at the 500 hPa level (Fig. 5).

Fig. 4
figure 4

Synoptic maps for selected days with precipitation ≥100 mm in the Upper Vistula Basin (based on published maps of Polish Meteorological Service: PIM, PIHM and IMGW PIB)

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Fig. 5
figure 5

Composite maps of averaged SLP (hPa) and geopotential heights (gpm) of 850 hPa (TB 850) and 500 hPa (TB 500) from 15 days with precipitation ≥100 mm at Kasprowy Wierch stations (see Table 1 for details), Red arrows—direction of air flow. Maps were created with the software and database of the NOAA/ESRL Physical Science Division, Boulder, CO, USA http://www.esrl.noaa.gov/psd/data/composites/day/ (color figure online)

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Despite air advection and pressure system type, synoptic situation is also characterized by air mass and meteorological fronts. In the Upper Vistula Basin about 80 % of precipitation ≥50 mm (Table 3) and almost all precipitation ≥100 mm (Tables 1 and 2) formed within the moist polar maritime air (mP) or polar maritime old air (moP). About 40 % of high precipitation resulted from orographically forced convection since they occurred at days without meteorological fronts. That is occluded front out of all meteorological fronts which favours the most high precipitation occurrence. It however should be mentioned that the flood precipitation events (≥100 mm) in the Upper Vistula Basin has occurred at various meteorological fronts (Tables 1 and 2). It can also be mentioned that in Europe frontal precipitation clearly dominates in winter (Łupikasza 2013).

Table 3 Correlation coefficients between number of days with selected circulation characteristics (circulation types and circulation indices) and number of days with precipitation ≥30 mm
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It is not the rule that circulation types favouring high precipitation occurrence also govern its long-term variability. Therefore, to check temporal dependence between flood rainfalls and atmospheric circulation we calculated correlations coefficients (Pearson, Spearman, Kendall) between selected circulation characteristics (number of days with selected circulation types: Nc, NEc, N+NEc, Bc and Cc+Bc, indices: Wi, Si, Ci and NAO) and precipitation. Parametric Pearson correlation coefficient measures the degree of linear relation between two variables whereas nonparametric Spearman and Kendall correlation coefficients measure nonlinear relations. Statistical significance of correlation between variables proved by three different coefficients enhance the robustness of the relation between extreme precipitation occurrence and atmospheric circulation. We used the number of days with precipitation ≥30 mm which is more frequent than precipitation ≥50 mm thus deliver more robust results. The correlation coefficients included in Table 3 indicated significant impact of Nc and NEc types on the long-term variability in high precipitation frequency while the role of Bc and Cc types was insignificant. This means that increase in the frequency of Nc and NEc types may result in more frequent flood conditions. In summer (JJA) high precipitation was also negatively correlated with W index revealing that intensification of eastern air flow may also increase the frequency of flood conditions. Increase in the frequency of cyclonic conditions impacted the frequency of high precipitation only at Kasprowy Wierch station in summer half-year (Table 3).

4 Variability and Trends in Circulation Types and Indices Impacting the Frequency of Flood Precipitation

Statistically significant relations between high precipitation and atmospheric circulation allowed us to make assumption that trends in the frequency of selected circulation types (Nc and NEc) and indices (Wi in JJA and Ci in May–Oct) will cause similar trends in flood precipitation frequency. Statistical significance of trends in circulation and precipitation characteristics was tested with Mann-Kendall method taking α = 0.05 as a statistical significance level while trend slope was calculated with least squares method.

Long-term courses of circulation types and indices significantly influencing high precipitation occurrence are shown in Fig. 6 for warm half-year (May–Oct) and in Fig. 7 for summer (JJA). In warm half-year trends in all circulation characteristics were positive however significant ones were only found in the frequency of Nc type and Ci index indicating possible increase in high precipitation frequency. Since the beginning of the research period to the end of the thirties most of the circulation characteristics were lower than their long-term averages, which particularly concerns Nc type and Ci index. In subsequent decades the long-term course of circulation characteristics varied depending on type and index. In the 50-year period between 1930 and 1980 there was an intensification of the air advection from the north (Nc). High frequency of NEc type was found in seventies and eighties which coincided with high frequency of floods in those decades in Poland and at the turn of the first and second decades of the 21st century. Low frequencies of these circulation types during 1982–1995 was in phase with relatively dry conditions in the Southern Poland without the floods within the Upper Vistula Basin. In the next more wet years the great floods happened in July 1997 and May 2010. Cyclonic activity since the beginning of the thirties was higher than in previous decades (Fig. 6). In the sixties and seventies there was a sequence of years with the Ci index values consequently higher than long-term average.

Fig. 6
figure 6

Long-term course of the number of days with selected circulation types (Nc, NEc, N+NEc) and Ci index (left axis: dashed dark grey line—annual values, solid thick grey line—11-y Gauss filter, straight black line—linear trend) favouring the occurrence of high precipitation in Tatra Mountains and their departures from average 1874–2015 (right axis: light grey bars) in the warm half-year (May–Oct)

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Fig. 7
figure 7

Long-term course of the number of days with selected circulation types (Nc, NEc, N+NEc) and Wi index (left axis: dashed dark grey line—annual values, solid thick grey line—11-y Gauss filter, straight black line—linear trend) favouring the occurrence of high precipitation in Tatra Mountains and their departures from average 1874–2015 (right axis: light grey bars) in summer (JJA)

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The similarity between changes in selected circulation characteristics and precipitation frequency (≥30 mm at Kasprowy Wierch station) in warm half-year is evidenced in Fig. 8. This figure shows short-term trends in parameters discussed calculated for 30-year moving periods. In majority of 30-year periods there was an agreement between direction of trends in high precipitation frequency and circulation characteristics particularly for NEc type which was recognized as the most impactful indicator for high precipitation trends. Trends in the frequency of NEc type can partly explain trends in high precipitation frequency. Regardless of insignificant trends the relations between these variables were clear.

Fig. 8
figure 8

Short-term trends in selected circulation types (Nc, NEc, N+NEc) favouring the occurrence of high precipitation in Tatra Mountains (grey bars) and in the number of days with precipitation ≥30 mm (black bars) calculated for 30-year moving periods between 1874 and 2015 (circulation types frequency) and between 1951 and 2015 (number of days with precipitation) in warm half-year

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Long-term variability in circulation types frequencies in summer resembled those in warm half-year but these growing trends in neither of types were significant. On the contrary, zonal westerly circulation index which impacts the frequency of high precipitation in summer was significantly dropping throughout the entire research period at both stations (Fig. 7). Such a downward tendency indicated intensification of air advection from the eastern sector and possible increase in flood precipitation (negative correlation with high precipitation). The eastern air flow was particularly intense (the lowest index values) in the sixties, seventies and in the first half of the eighties when the occurrence of flood events was enhanced while in the dry period of c.a. 1982–1996 Wi index was relatively high.

5 Conclusions

We investigated changes in atmospheric condition favouring the occurrence of flood precipitation in order to assess current and possible future changes in flood condition in the Upper Vistula Basin. We used the catalogue of circulation types created for the Upper Vistula Basin covering 143 years long period and related regional circulation indices as well as NAO index.

In summer and warm half-year the Upper Vistula Basin was usually under an influence of anticyclonic wedge (Ka circulation type) and cyclonic trough (Bc circulation type). The most frequent of all advectional types were those with air flow from the western direction which is a dominant wind within the moderate climate zone.

The occurrence of flood precipitation over the Upper Vistula Basin is strongly linked to the frequency of air advection from the north and north-east under an influence of low pressure system (Nc and NEc circulation types). The circulation types Nc and NEc which were recognized as favouring the most flood precipitation are not frequent within the Upper Vistula region; nevertheless the maximum of their occurrence falls in the flood prone period which is the turn of spring and summer. The linkage between high precipitation occurrence and Cc, Bc and Ec types (last type only at Kasprowy Wierch station) is also noticeable though weaker than in case of previously mentioned types. Unlike Cc, Bc and Ec types, the frequencies of Nc and NEc types also significantly trigger the long-term variability in flood precipitation frequency. Most flood precipitation events were associated with polar maritime or polar maritime old air masses and were a result of orographically forced convection or were related to occluded front. The correlation between long-term courses of circulation indices and high precipitation was much lower compared to circulation types Nc and NEc. Significant connection was only found between long-term variability in high precipitation frequency and Wi index in summer (JJA) at both stations and Ci index at Kasprowy Wierch station in warm half-year (May–Oct).

Trends in majority of circulation characteristics favouring the occurrence of high precipitation and impacting its long-term variability were not statistically significant with an exception of the frequency of Nc type and Ci index in May–Oct and Wi index in summer. Significant increase in both variables (Nc frequency and Ci index) in warm half-year and intensification of air advection from the north-east (decreasing trend in Wi) in summer may lead to increase in the frequency of flood conditions in these seasons.

The results show that the occurrence and long-term variability of flood precipitation in the Tatra Mountains is most strongly linked to the frequency of air advection from the north-eastern sector under an influence of low pressure system which did not undergo significant changes. Regardless insignificant trends the variability in the frequency of NEc circulation type meaningfully determines the occurrence and variability in high precipitation occurrence thus was recognized as indicator of flood conditions. Such atmospheric conditions (NEc circulation type), usually induced by stationary low pressure systems located over Ukraine and originated from the Adriatic Sea, in combination with orography have caused the most damaging floods in the Upper Vistula Basin. Despite the atmospheric circulation the orography plays crucial role in generating flood precipitation not only in the Tatra Mountains but also in the other high mountains of the Europe (Sénési et al. 1996; Rotunno and Ferretti 2001; Pradier et al. 2004; Seibert et al. 2007).