Anomalously heavy monthly and seasonal precipitation in the Polish Carpathian Mountains and their foreland during the years 1881–2010

The paper addresses the frequency, amount and geographic coverage of anomalously heavy precipitation in southern Poland in relation to atmospheric circulation at the monthly and seasonal scales between 1881 and 2010. The Carpathian Mountains and their foreland were selected for the study as an area known for its high precipitation totals and frequent precipitation-triggered natural disasters, such as floods and landslides. Records from 18 stations were used to identify anomalously heavy precipitation (AHP) defined for the purposes of the study, as the top quartile (Q75 %) plus 1.5 times the interquartile gap (H) of the precipitation total (P ≥ Q75 % + 1.5H). The study found that most cases of AHP were recorded at one single station each. This suggests that, in addition, to the influence of circulation, local factors also play a major role in the formation of particularly heavy precipitation. The greatest absolute anomalously high precipitation totals were recorded in two disparate parts of the study area: (i) its western part exposed to wet air masses from over the Atlantic Ocean brought in by the dominant western circulation in the temperate zone and (ii) elevated parts of its south-eastern part. Two months with AHP (AHP months) occurred over the entire area (18 stations) in May 1940 and 2010. The latter case had both the greatest absolute totals (over 500 mm) and relative totals defined as their ratio to the long-term average (500 %), and it triggered a catastrophic flood in the Upper Vistula basin.


Introduction
Periodic surpluses or deficits o f precipitation m ay be regarded as dangerous m eteorological and hydrological events. I f suf ficiently large, they can have a significant im pact on num erous areas o f hum an activity. O ver long spells, they lead to exces sive w ater surpluses or acute droughts. The tem perate E uro pean climate, m ainly influenced b y the strong variability o f atmospheric circulation, is characterised by the occurrence o f long spells o f various types o f weather, including heavy p re cip ita tio n , h e a t w av es an d co ld p erio d s (T w ard o sz and K ossow ska-Cezak 2015). Some studies also suggest a poten tial role o f increased concentrations o f carbon dioxide in an increased incidence o f extrem e p recipitation (Palm er and R aisanen 2 0 0 2 ; R aisanen 2 0 0 5 ). R aisanen (2 0 0 5 ) uses ensem ble averages to claim th at the variab ility increases slightly in m o st areas, so th at the contrast betw een the h ig h an d low precip itatio n extrem es grow s larger w ith increasing C O 2.
The objective o f the study w as to determine the quantity, frequency, duration and spatial extent o f anom alously heavy m onthly and seasonal precipitation and the type o f circulation favouring the form ation o f such precipitation in the P olish Carpathian M ountains and their foreland betw een 1881 and 2010. The project was inspired b y the exceptionally w et M ay o f 2010 that caused catastrophic floods and num erous land slides in m uch o f Central Europe (M aciejowski et al. 2011; W oźniak 2012, 2013). Christensen and C hristensen (2003) suggest that, in future, catastrophic floods o f this type are likely to increase in frequency in this part o f the continent. A reas prone to exceptionally high rainfall totals, w hether daily or m onthly, include, in particular, m ountains w here the effect is augm ented b y adiabatic cooling o f m o ist air m asses in forced ascent. F o r th is reason, th e h ig h est precipitation totals, regardless o f the tim e interval, are recorded in m ountainous areas o f low and m ediu m lat itudes, including P oland (for exam ple, the daily total o f 300 m m in H ala G ąsienicow a in the P olish Tatra M o u n tains on 30 June 1973).
Existing studies on precipitation in different areas o f south ern Poland found no clear-cut trends in the totals (Niedźwiedź et al. 2009;W oźniak 2013). The latest IPCC R eport (IPCC 2013), on the other hand, states that the frequency and inten sity o f heavy precipitation events have likely increased in Europe. In particular, it finds an increase in the frequency o f m onths w ith anom alously heavy precipitation (Schonwiese et al. 2

Sources and data
T he stu d y is b ased o n m o n th ly to tals o f p recip itatio n re c o rd e d a t 18 sta tio n s, in c lu d in g 14 in th e P o lis h C a r p a t h i a n M o u n t a i n s a n d 4 in t h e i r f o r e l a n d (Table 1, F ig. 1), d u rin g th e p erio d 1 8 8 1 -2 0 1 0 . The s ta tio n s w e r e s e le c te d to r e p r e s e n t lo w -a l t i t u d e C arp ath ian catch m en t basins.
The m o n th ly p recip itatio n d atabase w as b u ilt u sin g nu m ero u s p u b lic atio n s o f th e P o lish w ea th er service, e s p e c ia lly its a n n u a l h y d ro g ra p h ic a l, m e te o ro lo g ic a l and p recip itatio n reports. T he old est precipitation data, 1 8 8 1 -1 8 9 0 , w e re fo u n d in th e stu d y o f H e llm a n n ( 1906). T he p erio d 1 8 9 5 -1 9 1 2 w as com pleted w ith data from the A ustro-H ungarian Jah rb u ch H ydrographischen Z entralbureaus k. k. M inisterium furoffentliche A rbeiten.  A range o f criteria used b y clim atologists to determ ine precipitation anomalies, especially the older ones, has been review ed in num erous clim atological studies and reports. O ne o f the m ore popular m ethods used to identify anom alous months, seasons and years is the standard deviation, which, in m ost cases, is applied as a doubled or even tripled value (e.g., Schonwiese et al. 2003). In recent years, a percentile-based m e th o d h a s fo u n d its w a y in to stu d ie s o n d a ily (e.g ., Ł u pikasza 2010) an d m onthly p recipitation (e.g., M iętus et al. 2005). However, despite the m ethod's growing popular ity and even certain deliberate efforts to increase this effect, the fact that the frequency o f anom alous values (determined from em pirical distribution) in this m ethod is itself a fixed value has ruled it out from a study that is trying to identify such frequencies. A nother drawback, from the point o f view o f this study, is that the m ethod does n ot utilise the concept o f an anom aly as a deviation o f a given value from at least a 30year average, as defined by the W M O 's International M eteo rological Dictionary (International M eteorological 1992).
In their selection o f a cut-off criterion, the authors adopted a slightly different approach. Since anomalies, b y definition, are rare, the anom alously high totals w ere identified to fit betw een the top quartile (Q75 %) plus 1.5x the interquartile gap H (H = Q75 %-Q25 %) and the highest value o f the record.
In statistics, values exceeding the interquartile gap are know n as " extrem e" and those exceeding triple the value o f the gap are know n as "outliers" (Statistica 2010). Such outlier values m ay be regarded as either errors o f m easurem ent or errors in recording, or, alternatively, as a result o f exceptional condi tions that caused such values to actually occur (Stedinger et al. 1993). In the case o f precipitation, w hich is characterised by high natural variability o f timing, values exceeding the upper quartile plus 1.5x the interquartile gap w ill be regarded as non-standard values that deviate considerably from the typical statistical distribution, in other words: anom alous values.
The "interquartile" criterion is defined b y the formula: 1.5*(q(0.75) -q (0 .2 5 )) + q(0.75) w here q(p) m eans p-quantile. The factor 1.5 is chosen on the basis o f experience in precipitation data analysis as a figure giving extreme precipitation similar to that defined b y intui tion. The criterion w ould obviously be profoundly dependent on the shape o f the right-hand tail o f the probability distribu tio n w h ich d escribes th e data. Since p o ssib le theoretical m odels are different and, moreover, m ay be m odified b y as suming different values o f the shape parameter, the interquar tile criterion w ould be equivalent to quantiles in the range from 0.9 to 0.997 (Fig. 2). The first value w as obtained with a Pareto distribution w ith a shape param eter c = 2 and the last w ith a norm al distribution. The interquartile criterion itself does n o t assum e any particular model, as it is based on em pirical quartiles. The probability depends on the shape parameter of the given distribution (excluding normal, which has no such parameter). The highest p = 0.9965 is obtained for normal distribution, and the lowest asymptotic p = 0.951 produces the Pareto as well as the Weibull distributions The interquartile criterion was selected for its superior pre cision in obtaining o f the final result w hen com pared to a sim pler choice o f quantiles Q95 or Q99. Since Q95 and espe cially Q99 are based on an inherently lim ited observation samples, the relative errors o f their values are large. In con trast, quantiles Q25 and Q75 are free from this deficiency. In a sample o f N = 300, the expected errors o f quantiles (calculated according to the binom ial distribution) are as follows: Q75-10 %, Q95-25 % and Q99-57 %.
In summary, the proposed m ethod o f identifying anom a lously heavy precipitation has been clearly defined and is sim ple to use. The num ber o f m onths w ith anom alously heavy precipitation m atches intuitive expectations, i.e. a range from no such cases (0) to a m axim um o f nine, w hich is discussed later on.
This study focused chiefly on m onths w ith anom alously heavy precipitation and seasons, but some consideration was also given to years w ith anom alously heavy precipitation.
In order to identify a dependence o f anom alously high m onthly precipitation on atm ospheric circulation, the authors used the calendar o f circulation types in southern Poland de vised b y T. N iedźw iedź ( 1981,2014).
M ountains (Wisła) in the w esternm ost part o f the area exposed to w et w esterly w inds (Table 1). In particular, the highest precipitation totals o f the period, at ca. 1700 m m , w ere record ed in the highest Carpathian range o f the Tatras, but stations from this range w ere not included in the study, as their earliest com plete series o f records w as only in the m id-tw entieth cen tury. Precipitation generally increased not ju st w ith an increase in altitude along the N -S axis, b ut also w ith longitude from east to w est (i.e. w ith a decreasing continental com ponent o f the climate). L andform also played a role, as precipitation totals w ere significantly low er in m id-m ountain basins, e.g. N ow y Sącz (Table 1).
There is one general annual precipitation pattern across the area: the values peak in July and bottom out in February or January. This is illustrated by three stations: Kraków, Rabka and Zakopane, representing the N -S altitude profile (Fig. 3).  The study also investigated seasons w ith (AHP seasons) and found 173 such occurrences (Table 3). This gives an av erage o f nearly 10 (9.6) A H P seasons per station or 2.4 AHP seasons per calendar season, i.e. one seasonal A H P per ap proxim ately 50 years. The actual distribution varied broadly fro m 2 a t J a r o s ław to 50 in B ie ls k o -B ia ła , M a k ó w Podhalański an d D ukla. The m ost represented season was autum n at 68 (i.e. 39 %), and the least represented w as winter a tju st2 1 (i.e. 12 %) (Table 3). In other words, during the study period, the average num ber o f A H P seasons varied from ca. 1 in w inter to ca. 4 in autumn. A ll stations recorded a seasonal A H P in autumn, one station h ad no springtime A H P season, and five stations noted no such seasons in sum m er and winter. W hen the overall num ber o f A H P seasons and the num ber o f years with an A H P season are com pared, it transpires that the same spring or autum n with A H P w as recorded at three to four stations (Table 3), w hile summ ers and w inters w ith A H P were smaller in area at ju st two stations on average.
The study also identified 27 years w ith A H P (Table 3). Five stations recorded three such years, w hile W isła and Zakopane recorded none. A ll such years were recorded b y ju st one sta tion in a given calendar year producing an average o f 1-year A H P per station (27 AHP years in 27 years, Fig. 4).

Anomalously high totals
A nom alously high precipitation totals varied v ery w idely across the study area. In all three intervals studied, i.e. months, 130 years) ( Table 2). This translates into nearly 40 m onths (39.6) w ith AHP, on average, at each station, w hich m eans that, in a given calendar m onth, there w ere, on average, 3.3 m onths w ith A H P w ith A H P in a given calendar m onth p er ca. 40 years. The n um ber o f A H P m onths p er sta tio n varied w idely from 29 in R zeszów to 48 in N o w y Sącz (Fig. 4).
The annual count o f A H P m onths varies widely. O f the 712 A H P m onths identified (Table 2), the highest num bers were found in M ay and July at 86 each (i.e. 24 %) follow ed by February at 80 (i.e. 11% ); the low est w as recorded in N ovem ber at 32 (i.e. 4 %). To put the seem ingly high overall num ber o f A H P m onths o f 712 in the right proportions as an anomaly, one should view it from the point o f view o f an individual station, w hich, on average, has to w ait 3 -5 years to record another A H P m onth. Certain stations recorded five calendar m onths w ithout any anom alously high precipitation total. On the other hand, the highest incidence o f A H P m onths at a single station w as 9 (July in Jasło).
The 712 A H P m onths occurred in 212 m onths (13.6 % o f months), w hich m eans that there w ere years w hen an AHP m onth w as recorded at m ore than one station in a single cal endar month. M ay w as the no. 1 m onth o f this type w ith AHP m onths recorded in 15 years o f the p eriod at 18 stations (Table 2). This m eans that, on average, six stations recorded A H P in the same May. A t the other end o f the spectrum, the sm allest num ber o f stations recording anom alously heavy m onthly precipitation w as 2 in N ovem ber (32 A H P m onths in 15 years, Table 2).   (Table 4).
In relative terms, i.e. the A H P percentage o f the average m onthly precipitation, the size o f the anom aly ranges from an A H Pmax o f 245 % in January 1976 in W adowice to 484 % in M ay 2010 in W isła (Table 4). The greatest relative anomaly, however, w as not an A H Pmax, but an A H P in M ay 2010 at Żywiec at 500 % o f the average, w hen the total w as 463 m m (Pav. = 93 mm). This m eans that the greatest anom aly can exceed the low est anom aly by m ore than a factor o f 2.
A com parison o f extreme seasonal A H P values reveals that the highest w intertim e A H P is low er than the low est summ er tim e A H P (Table 5). Table 6 summ arises the 10 m onths with the highest totals in absolute (mm) and relative (% o f average) terms. O ver the 130-year period, 10 m onths is equivalent to a frequency o f ca. 5 %. July (6) (Table 7). T he greatest surplus values over the long-term averages w ere re corded in all seasons. The m axim um reached three tim es the average (spring o f 2010 in Wadowice).
The greatest surplus o f years w ith A H P over the long-term average (177 %) w as recorded in 2010 in K rakow and the low est (144 %) in the same year at Dukla.

Spatial extent of monthly and seasonal AHP
O ut o f the 212 A H P months, 43 % (91) occurred at a single station and 18 % (39) at two stations, w hich w ere not always neighbouring stations and w ere sometim es located very far apart (Table 8)      There is an interesting summ ertime pattern o f A H P m onths w ith at least six stations (Fig. 5). The largest num ber o f June A H P m onths occurred in the south-eastern part (including three in Sanok and at Wetlina), w hile only tw o occurred in the w estern part. In August, on the other hand, the w estern part had several A H P m onths, w hile the eastern had none.
The highest num ber o f July AHP m onths occurred in the w estern and central-northern part, while, in the south-eastern and eastern parts, there were only one or two.
The study looked at the frequency o f circulation types throughout the 130-year study period (Table 11) and in the 212 (Table 2) A H P m onths (Table 12) and at selected m onths w ith A H P recorded at all stations, at stations in the w estern part and at stations in the eastern part o f the area (Table 13). This procedure produced a som ew hat sim plified picture o f the types o f circulation conducive to the formation o f heavy pre cipitation. To obtain a full picture, the num bers o f days w ith various ranges o f precipitation totals at each station w ould have to be taken into account to differentiate betw een cyclonic and convective precipitation types.  A certain predom inance tow ards anticyclonic circulation (55 %) is a typical feature o f the atmospheric circulation vari ability over southern Poland (Table 11). Cyclonic circulation prevailed only in A pril (53 %). A s w as expected, cyclonic circu latio n w as fo und to fav o u r th e occurrence o f A H P months. It is im portant to point out here that it w as not a case o f an absolute prevalence o f cyclonic circulation types, but th eir above-average frequency during A H P m onths. The greatest frequency o f cyclonic types during A H P m onths was found in April at 60 %, w hich is 8 % more than the average. The greatest difference than the two frequencies was found in February at 16 % (with 43 %, on average, and 59 % in an AHP months) and in N ovem ber at 15 % (43 and 58 %).
Generally, the type o f circulation, i.e. cyclonic vs. anticyclonic, has a stronger im pact on the form ation o f an A H P than the direction o f air advection. In all A H P m onths, there oc curred one o f the m ost frequent circulation types, i.e. western cyclonic circulation (Wc) or cyclonic trough (Bc). Betw een O ctober and M arch, w estern cyclonic type prevails ranging from 12 % in M arch (com pared to the average o f 10.6 %) to 19 % in N ovem ber (12.1 %). O ther cyclonic types o f the w estern sector, SW c and N W c (com bined 9 -1 7 %), and the Wa type (10-16 %) also played a considerable role. In winter, especially in January, the m id-latitude frontal disturbances have a tendency to converge over Poland producing higher precipitation totals in w estern advection than w ith other sec tors (Twardosz 2009). For the rest o f the year, the cyclonic trough Bc is m ore frequent, at 11-15 %, on average, followed in frequency b y high-pressure w edge Ka, at 10-14 %. C yclon ic trough was found to be m ost conducive to A H P m onths in the eastern part o f the area; e.g. in July 1980, its frequency was 23 % or twice as high as the average o f this m onth (Table 13). In sum m er A H P m onths, northern sector circulation was also m ore frequent, especially in the w estern part o f the area. For example, in July 1960, the frequency o f ju st one o f the types in th is sector, N c, w as four tim es h ig h e r th a n th e average (Table 13). These circulation types were conducive to heavy and lasting precipitation, prim arily in cold or stationary front zones (Twardosz 2009). Sim ilar patterns o f circulation influ ence causing heavy precipitation were identified in other areas o f the country (Kossowska-Cezak 1997). The same circula tion types accom panied nearly all days w ith precipitation in K rakow during A H P o f M ay o f 2010 (W oźniak 2012). High m onthly precipitation totals in southern Poland can also coin cide w ith anticyclonic circulation types, especially the anticyclonic w edge K a (Twardosz 2009). In summer, local dow n pours can form in uniform air m asses as a result o f strong therm al convection.
In M ay 2010, anom alously high precipitation totals in the entire Polish Carpathian M ountains were accom panied pri m arily b y cyclonic trough (Bc) and northern circulation, both tw ice as frequent as the average (Table 13). The A H P o f M ay 1940 also covered the entire area, b u t the totals were lower. Eastern circulation, m ainly cyclonic, dom inated for m ore than one third o f that m onth (Table 13).

Conclusion
The study identified anom alously heavy precipitation (AHP) at 18 stations in the Polish C arpathian M ountains and their foreland over a 130-year period spanning 1881-2010. A rath er stringent statistical criterion w as used as a cut-off at the upper quartile value plus 1.5x o f the interquartile gap.
It w as d em o n strate d th a t w h ile A H P o cc u rre d in all months, in seasons and in entire years, they w ere also infre quent. There were betw een one m onthly A H P (months with anom alously heavy precipitation, A H P m onths) per 5 years in June to one A H P m onth per 10 years in O ctober and betw een one A H P season (season w ith AH P) per 7 years in autum n to one A H P season in 10 years in winter.
M ost A H P w as spatially lim ited to one or tw o stations, typically neighbouring ones, thus clearly suggesting that local conditions, as w ell as circulation-related factors, influenced their occurrence.
A H P recorded in M ay had the largest area coverage w ith an average o f five stations, w hile those recorded in N ovem ber were the sm allest at two stations on average.
Two Cyclonic circulation, as expected, prevailed in m onths with AHP. Betw een O ctober and M arch, w estern sector circulation types prevailed, especially the w estern cyclonic type (Wc), while, for the rest o f the year, it w as the cyclonic trough (Bc) follow ed b y an anticyclonic w edge (Ka). These opposite circulation types point to the alternative origins o f AHP: either on active atmospheric fronts or on convective types.
In term s o f the hydrological and geom orphological effects o f AHP, the least dangerous are the A H Ps recorded in w inter w hich m ay have sim ilar surplus values to those occurring in other seasons but feature the low est totals o f all, are the least frequent and cover the smallest areas at a tim e (one to two stations). This effect is explained b y the annual precipitation cycle, w hich reaches its low est point in winter. Sum m er AHP events also covered small areas (no m ore than four stations), due to the local nature o f rainfall o f convectional origin, but are m ore frequent than in w inter and feature the highest rain fall totals (up to 600-800 mm ). A H P in spring and autumn covers the largest areas (11 -1 2 stations).
Generally, A H P w as dem onstrated to be a rare and spatially lim ited phenom enon. Indeed, during the 130 years o f the study period, there were no A H P seasons that w ould cover all o f the stations in a single season. They were overw helm ingly up to one third o f the stations (6/18).
The results o f the study have a potential practical applica tion due to the inform ation on the frequency, scale and spatial coverage o f A H P in various seasons in southern Poland, a region characterised b y average precipitation higher than any where else in the country (except the Sudety M ountains) and w hich m ay lead to dangerous hydrological or geom orphological events, such as floods and landslides.