1. bookVolume 26 (2022): Edizione 2 (April 2022)
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Dynamics of hydrological droughts propagation in mountainous catchments

Pubblicato online: 29 Apr 2022
Volume & Edizione: Volume 26 (2022) - Edizione 2 (April 2022)
Pagine: 111 - 124
Ricevuto: 20 Sep 2020
Accettato: 09 Feb 2022
Dettagli della rivista
License
Formato
Rivista
eISSN
2084-6118
Prima pubblicazione
01 Jan 1984
Frequenza di pubblicazione
4 volte all'anno
Lingue
Inglese
Abstract

In the study, hydrological drought was identified assuming that the occurrence of river low-flow is a symptom of drought, and is also a good estimator of its progress. The research was conducted in the upper Dunajec river catchment, for which a series of daily discharges from 20 gauging stations during the period 1989–2018 were available. The low-flow periods were identified on the basis of the Threshold Level Method, which corresponds to the seventieth percentile of the flow duration curve. On the basis of a developed algorithm, 41 drought events were identified. Analysis included spatial parameters referring to range, severity, concentration, continuation, and the development pace of hydrological drought. Finally, on the basis of cluster analysis, five dynamic types of hydrological drought were identified.

Keywords

Introduction

Drought is a hydrometeorological extreme which, in origin, is dependent on climate changeability. Nevertheless, the duration and intensity of droughts are significantly altered by retention and hydrological processes in river basins. This phenomenon is usually defined as an extremely dry period which causes a serious disturbances in the structure of the water balance in an area (Maunder 1992; Nagarajan 2009). Drought is usually initiated by a lack of precipitation (meteorological drought). However, rainfall shortage effectively begins the process of drought development only when it occurs in a typical period of groundwater alimentation from rainfall, or when, due to various factors, groundwater retention is very low (Dębski 1970). The limited supplies of rainwater for groundwater reservoirs are usually compounded by evapotranspiration. A prolonged period without precipitation results in a gradual loss of soil moisture from the vadose zone, which in turn leads to the soil drying out. Rainfall that occurs during a drought does not supply the groundwaters in the saturated zone, but generates surface runoff to river channels and outflow from catchments. These processes lead to the development of soil drought, and in the context of economic consequences, agricultural drought (Wilhelmi et al. 2002).

Any further increase in the water deficit results in hydrological drought (Hisdal, et al. 2001; Dingman 2002; Nagarajan 2009). Aquifers that are cut off from water supplies are continuously drained through streams and springs. This leads to a fall in the groundwater table (groundwater low-flow) and, accordingly, to the recession of surface waters, which are usually in a hydraulic connection with groundwaters (surface water low-flow). The recession rate of groundwater resources during this period, and thus the pace of low-flow development, depends almost exclusively on the degree to which the groundwater reservoirs are filled (Jokiel 1994; Somorowska 2004). During the growing season, this process can be accelerated significantly by evapotranspiration. Winter hydrological drought develops not due to the lack of water but because of its temporary retention in snow cover. It may be intensified by riverbed freezing during severe frosts, which prevents all forms of drainage. This type of drought is highly seasonal in nature (Pfister et al. 2006; van Loon et al. 2010).

Hydrological drought develops very slowly both temporally and spatially. There are a number of methodological concepts of hydrological drought identification in the literature, but to date no uniform methodology has been developed which would make it possible to unambiguously (automatically) indicate the point of drought onset and termination. There are also many problems with assessing its intensity and range. Studies of hydrological drought have been predominantly based on the analysis of low-flows, which are considered to be a good indicator of its development because they appear during the final phase of the response to alimentation shortages (Tomaszewski 2012; Tokarczyk 2013; Kozek & Tomaszewski 2018). Low-flow is considered to be a seasonal phenomenon and an integral component of the flow regime of any river. It is defined as a period characterized by low river flows or flows that occur in dry weather conditions (Smakhtin 2001). However, assessing a single low-flow event as a whole drought indicator is insufficient because the event might persist for a much shorter period than the drought and, moreover, it occurs in riverbeds (in a river cross-section), whereas hydrological drought develops within catchment areas. The reliable identification of hydrological drought requires access to daily discharge data derived from an appropriate number of hydrological stations located in different parts of a river system. These types of studies have already been carried out in the Warta and Biebrza river catchments, where hydrological drought identification was based on the analysis of low-flows from between ten and twenty water gauges (Kozek & Tomaszewski 2018, 2019). In the afore-mentioned studies, an attempt was introduced and successfully applied to establish a relatively universal and automated criteria for hydrological drought identification. As a result, the analysed droughts were valorised in relation to their duration, severity, and developmental direction. The analyses and conclusions made by the authors of these studies indicated that the methodology might also be applied in other geographical regions.

Assessing low-flow parameters has been the basis for many methodologically different studies on hydrological drought. Farat et al. (1995) identified hydrological droughts in Poland, defining the phenomenon by when low-flow was recorded in at least 10 water-gauging stations at the same time. In contrast, Tokarczyk (2013) proposed a hydrological drought index constructed on the basis of the probability distribution of low-flow duration and volume. As a result, a comparable scale of hydrological drought intensity for a single catchment was obtained. Indicators based on the estimation of water balance components such as the Palmer Severity Drought Index (PDSI) or the Standardized Precipitation Index have also been used in studies on hydrological drought (Tabrizi et al. 2010; Zhai et al. 2010; Liu et al. 2012; Tokarczyk & Szalińska 2014; van Loon 2015). Applying these indexes allowed the drought's spatial distribution to be evaluated based on standardized relative characteristics. However, identifying and tracking the drought's developmental pace, dynamics, and changes in intensity were seriously limited in these cases.

It is worth noting that most studies on hydrological drought stress either the spatial pattern or the hydrological features of a low-flow regime. There are few publications that approach both subjects equally. The aim of this study is to verify and develop the methodology used in the spatial assessment of hydrological drought proposed by Kozek & Tomaszewski (2018, 2019). The characteristics they used to assess drought in catchments placed in lowland and lake district areas have been applied in this study to assess the dynamics of hydrological drought development in mountain catchments, which are characterized by much greater spatial differentiation in their physico-geographical conditions, especially hydrometeorological conditions. In addition, some indicators were proposed and applied that enabled the concentration, continuation, and developmental pace of hydrological drought to be assessed, both in terms of time and space.

Study area and data

The research area covered the Dunajec river catchment, which is closed-off at the Nowy Sącz water-gauging station (Fig. 1). The study area was placed in the central part of the Polish Carpathians and covered an area of 4,341 km2 (Tab. 1). The Dunajec is one of the biggest rivers in the Carpathians. It begins after the confluence of the Biały and Czarny Dunajec streams near the city of Nowy Targ. Both of these streams are recipients of many mountain streams whose springs originate in the Tatra mountains at altitudes very often exceeding 1,600 m asl. The reach of the river that the authors studied flows through the Sub-Tatra region, the Pieniny mountains, and the Western Beskids.

Figure 1

The Dunajec river catchment to Nowy Sącz water-gauge station. Numbering of sub-catchments as in Tab. 1

Source: own elaboration

Selected characteristics of the investigated catchments (1989–2018)

No. River - water-gauge A [km2]* avgH* [m asl.] Q70% [m3/s] q70% [dm3/s/km2] ALq [dm3/s/km2] AAq [dm3/s/km2] AHq [dm3/s/km2]
1 Czarny Dunajec - Koniówka 134 1443.04 1.96 14.62 10.24 32.10 84.74
2 Dunajec – Nowy Targ 431.8 1370.38 3.95 9.15 6.52 20.26 53.37
3 Dunajec – Nowy Targ-Kowaniec 681.1 1367.85 7.16 10.51 7.72 21.75 53.09
4 Dunajec – Sromowce Wyżne 1278.3 1486.53 14.3 11.19 8.58 21.93 55.01
5 Dunajec – Krościenko 1580.3 1457.98 16.4 10.38 7.88 20.87 53.44
6 Dunajec – Gołkowice 2046.9 1407.70 19.5 9.53 7.43 19.39 49.76
7 Dunajec – Nowy Sącz 4341 1388.99 34 7.83 6.01 15.58 38.41
8 Kościeliski Stream – Kościelisko-Kiry 34.5 1540.25 0.82 23.77 15.88 51.50 134.31
9 Lepietnica – Ludźmierz 50.7 898.42 0.4 7.89 5.52 19.58 53.18
10 Wielki Rogoźnik – Ludźmierz 124.3 811.04 0.76 6.11 4.22 14.86 37.65
11 Biały Dunajec – Zakopane-Harenda 58.4 1385.29 1.12 19,18 13.51 42.04 110.78
12 Biały Dunajec – Szaflary 210.1 1313.51 2.8 13,33 9.88 26.09 61.27
13 Poroniec – Poronin 78.8 1360.62 0.73 9.26 6.63 13.02 53.96
14 Białka – Łysa Polana 63.1 1733.43 1.06 16.8 10.76 52.21 143.48
15 Białka – Trybsz 2 202.3 1569.16 3.06 15.13 10.31 37.85 101.45
16 Niedziczanka – Niedzica 136.4 769.00 0.74 5.43 3.40 15.27 42.07
17 Grajcarek – Szczawnica 73.6 868.10 0.54 7.34 5.36 16.92 43.16
18 Ochotnica – Tylmanowa 107.6 840.73 0.76 7.06 5.21 15.55 37.84
19 Poprad – Muszyna-Milik 1695.1 779.74 9.72 5.73 4.43 12.55 30.98
20 Poprad – Stary Sącz 2071 707.99 11.9 5.74 4.39 12.49 30.42

A – sub-catchment area, avgH – average altitude of sub-catchment, Q70% – flow corresponding to the seventieth percentile of the flow duration curve; specific flows: q70% – seventieth percentile of FDC, ALq – average value of the annual minimum flows, AAq – average value of the annual mean flows, AHq – average value of the annual maximum flows.

Source: own elaboration based on data from the Polish Institute of Meteorology and Water Management;

Hydrological Division of Poland (IMGW 1980, 1983)

The upper Dunajec river catchment is characterized by a significant variety of hydrogeological and hydrometeorological conditions due to its mountainous location (Ziemońska 1973; eds Dynowska & Maciejewski 1991). The upper part of the catchment belongs to a region with the highest density of springs in Poland. The average value for the Polish part of the Tatra mountains is estimated to be 4.8–5.5 springs/km2 (Ziemońska 1966; Małecka 1985). The fissure-karst outflows, with a yield of several dm3/s, form the most numerous group here. These are supplied directly from carbonate formations in the lower subtatric and high-tatric series, or through weathering or morainic covers. However, in terms of yield, the most important crenological objects within the study area are Vauclusian springs, which are supplied from extensive karst systems (Chochołowskie, Lodowe, Goryczkowe, Bystra, and Olczyskie Vauclusian springs). They are located at an altitude of 970–1,200 m asl. Their seasonal yield may exceed 1,000 dm3/s, and, occasionally, may even reach 10,000 dm3/s (Różkowski et al. 2015). For Vauclusian springs, such high yields are conditioned by high amounts of precipitation as well as by hydrogeological conditions (the presence of cracks and karst fissures in the carbonate formations allows water infiltration and migration through the karst canal system) (Barczyk 2008). Apart from the above-mentioned crenological objects, small springs with an average yield of 0.5 dm3/scan found on the crystalline basement in the studied catchment. Moreover, there are numerous springs supplied from shallow slope covers; however, their yield does not usually exceed a few litres per second (Małecka 1997).

The Dunajec river is characterized by pluvio-nival alimentation (Wrzesiński 2017). In winter, mostly in January and February, severe drought induced streamflow deficits occur in the main river and its Tatra tributaries, which are determined by snow cover and ice retention. Flood waves have snow-melt origins (mostly in May), or are caused by heavy summer rainfalls (June and July). Floods occur in spring, and low-flow periods at the end of autumn and the beginning of winter in the Beskids’ tributaries of the Dunajec river (Dynowska 1972; Ziemońska 1973). In the upper part of the studied catchment (the high parts of the Tatra mountains), the highest average annual specific flows in Poland are found; these may exceed 50 dm3/s/km2. In the lower part of the catchment, these values decrease to 10 dm3/s/km2. The characteristics of the flows in the mountainous areas differ significantly from those in the lowlands, where average annual specific flows range from less than 2 up to about 5 dm3/s/km2 (Jokiel 2004). The lowlands are also areas of long-lasting river low-flows with the greatest drought streamflow deficits. In turn, in the mountain catchments, low-flows are characterized by their shorter duration and smaller streamflow deficits, but relatively high frequency of occurrence (Zielińska 1963). During the multi-year period 1989–2018, the average value for the annual minimum flow (ALq) in the studied catchment amounted to about 8 dm3/s/km2 (this is more than the average annual flow for the lowlands). The values for ALq ranged from 3.4 dm3/s/km2 (Niedziczanka river) to less than 16 dm3/s/km2 (Kościeliski Stream) (Tab. 1). The highest ALq values were characteristic of streams in the upper part of the studied catchment, which are supplied from extensive karst systems. A similar distribution can be observed for annual maximum flows. Their highest average values were recorded in the upper Białka river (143.48 dm3/s/km2) and Kościeliski Stream catchments (134.31 dm3/s/km2). The large spatial variability in the flows for the studied area is determined by a significant variability in precipitation conditions, as well as a variety of other physico-geographical factors, mainly hydrogeological and orographic ones.

The base Flow Index varies across a range of 20–60%. In the Tatra and Pieniny mountains, base flow contribution reaches 50–60% because of the capacious groundwater reservoirs found in the carbonate rocks. In the lower part of the catchment, groundwater retention potential is much less, which results in a low Base Flow Index value, ranging between 20% and 30% (Dynowska 1972; Jokiel 1994).

The Polish Carpathians have been the subject of low-flow and hydrological drought studies many times. Analyses have been conducted at a regional scale, for groups of catchments, and single streams (e.g. Tlałka 1982; Strzebońska-Ratomska 1994; Kostuch 2004; Baran-Gurgul 2014). These works have involved methodical questions, low-flow regime analyses, determinant factor identification, and comparative studies. However, they have never analysed specific single drought events on the scale of a whole investigated area or as a group of catchments. As a result, questions involving the typical times for low-flow and drought occurrence, drought streamflow deficits and their variability, and many related characteristics, are widely recognized, whereas, the dynamics of the spatial development, range, intensity, and continuity of drought during a single event remain to be fully investigated.

In the contemporary world, in almost every river basin, the use of water management has more or less affected river flow and water balance. Assessing hydrological drought characteristics, which may improve strategies for the mitigation of the negative effects of water shortage periods, should consider all the conditions impacting low-flows in a river network. In the upper Dunajec river catchment, there are a variety of water management systems that determine the modification of water circulation in local catchments. One particular system within the investigated area is a complex of dammed reservoirs, Czorsztyn-Sromowce Wyżne, on the Dunajec river, which was initiated in 1997 for flood control and hydropower purposes. These reservoirs have had a significant impact on downstream flow in the area of high and mean flows: flood wave reduction and power generation (Żelaziński 2012; Kędra et al. 2016). The analysis of low-flows based on the year 2003 indicated a decrease in drought streamflow deficit in the Dunajec river below the dam (Chełmicki & Bieńkowski 2005). During multi-year periods, changes in drought streamflow deficits might take various directions. Since the construction of the Czorsztyński dam there has been a rise, and multiannual stabilisation, of annual minimum flows, which was proved by Tomaszewski (2021). As this study does not involve the assessment of anthropogenic impact on low-flow changes, or a comparative analyses of drought behaviour between catchments, the interpretation of the results will involve a wide range of factors affecting the spatial patterns and dynamics of hydrological drought development.

The basic hydrometrical material used for this research was derived from 20 water-gauging stations serviced by the Polish Institute of Meteorology and Water Management (Fig. 1, Tab. 1). Selected stations were relatively evenly distributed across the whole catchment area: seven of these on the main river, and the others on the tributaries. The group of selected sub-catchments reflected the widest possible scope of factors for determining low-flows and hydrological drought development in a mountain catchment.

The input data were the daily discharge series for the period 1989–2018, which was characterized by highly dynamic hydrometeorological conditions. The lowest sums of precipitation, which determined prolonged low-flow periods and severe hydrological droughts, occurred at the beginning of the investigated multi-year period (the end of the 1980s and the beginning of 1990s) as well as at the beginning of the twenty-first century, and again between 2012 and 2016. In the meantime, there were years of higher sums of precipitation that resulted in serious floods.

Study methods
Identification of low-flow periods

Any identification of hydrological drought needs to estimate river low-flow periods, which are considered a symptom of drought. In the presented study, low-flows were identified on the basis of the Threshold Level Method, using the Peak Over Threshold, assuming that a low-flow was a period in which daily discharges were below the established threshold value. The truncation level was assumed to be a flow rate corresponding to the seventieth percentile of the flow duration curve determined by the daily values for the whole multi-year period. The seven-day period was taken as the minimum low-flow duration, while some low-flow episodes separated by an interruption lasting no longer than three days were analysed as inherently homogeneous events by combining their duration and volume (Yevjevich 1967; Hisdal et al. 2004; Tomaszewski 2012). Based on the above criteria, low-flows occurring in the streams of the Dunajec river catchment were identified and their basic parameters, such as duration and drought streamflow deficit volume, were estimated (Fig. 2a).

Figure 2

(a) Basic parameters of low-flows using the example of episodes from 1994–1995 on the Dunajec river (Nowy Targ-Kowaniec water-gauging station); and (b) a graphical illustration of the estimation of Relative Drought Streamflow Deficit (RSD). Tn – low-flow duration, Vn – drought streamflow deficit volume of the low-flow event [m3], Vmax – maximum possible streamflow deficit volume during the low-flow event, i.e. when the discharge value equals 0 [m3], Q70% – flow corresponding to the seventieth percentile of the flow duration curve

Source: own elaboration and Tomaszewski 2012 (changed)

Identification of hydrological drought

One of the main aims of this study was to apply methods which would optimize the process of identifying hydrological drought. The proposed algorithm included both spatial and temporal selection criteria. At first, it was assumed that the occurrence of river low-flow was a result of the appearance of hydrological drought in the catchment. In order to avoid stochastic discharge fluctuations which were not determined by hydrological drought in origin, the minimum duration of hydrological drought was defined (minDt) (Kozek & Tomaszewski 2019). This idea was developed assuming that this time period would be equal to the average multiannual value of the duration of the observed low-flow episodes for all the investigated water gauges. In the studied Dunajec river catchment, this parameter amounted to 37 days. This means, for the studied catchment, one of the following conditions had to be met in order to identify a hydrological drought:

- a river low-flow lasting continuously for a minimum of 37 days (equal to minDt) must occur in at least one water-gauge station, or

- a low-flow lasting less than minDt in one water gauge must be continued at successive water gauges for up to 37 days or more in total (minDt), and there cannot be any day without low-flow in this period (i.e., there could not be a day when there was no low-flow registering in any of the water gauges in the catchment) (Fig. 3).

Figure 3

An example of hydrological drought identification in the Dunajec river catchment in 2008. Numbering of sub-catchments as in Tab. 1

Source: own elaboration

During a low-flow episode, which indicates a well-developed hydrological drought, alimentation impulses determined by thaws or heavy rains might appear. As a result, discharge increases beyond the threshold level and might be interpreted as a streamflow drought termination. However, if the impulse is separated, it finishes in surface or subsurface channel alimentation only, and then the discharge quickly goes back to the low-flow level because there is no significant supply of catchment water resources. In order to eliminate the effects of short-term hydrometeorological fluctuations, it was assumed that if a break in the streamflow drought (when there was no low-flows in any of the water gauges in the catchment) was no longer than one-quarter of the defined minimum duration for hydrological drought (here: 9 days), hydrological drought was continued and analysed as an inherently homogeneous event. A longer break, up to half the defined minimum duration of hydrological drought (here: 18 days), was also acceptable, however, following the break there must have been a low-flow episode whose duration was equal to, or longer than, the defined minimum duration of hydrological drought (minDt).

The characteristics of hydrological drought

The indices for the dynamics and patterns were estimated for all identified hydrological droughts. The first of these was the Hydrological Drought Duration (Dt), calculated as the difference between the date of the first low-flow occurrence and the last low-flow occurrence (termination) in the catchment (Fig. 3). For the spatial assessment of hydrological drought the Drought Range Index (DRI) was used. This indicated what part of the catchment was covered by drought at its maximum stage of development, and was estimated as the percentage contribution of sub-catchment areas covered by drought for the whole catchment area (Kozek & Tomaszewski 2018): DRI=i=1NADii=1NAi100% DRI = {{\sum\nolimits_{i = 1}^N {A{D_i}} } \over {\sum\nolimits_{i = 1}^N {{A_i}} }} \cdot 100\% where: DRI – Drought Range Index [%], ∑ADi – the sum of sub-catchment areas covered by the hydrological drought [km2], ∑Ai – sum of all sub-catchment areas [km2], N – number of sub-catchments.

The problem of the intensity of the hydrological drought was assessed using the Drought Severity Index (DSI). This was estimated by using the Relative Drought Streamflow Deficit (RSD), which is considered a good estimator of drought severity (Kozek & Tomaszewski 2018, 2019). The RSD was created by transforming the streamflow deficits, and was calculated as the percentage contribution of the drought streamflow deficit volume, and the maximum possible streamflow deficit volume during the investigated period (Fig. 2b, Tomaszewski 2012): RSD=VnVmax100% RSD = {{{V_n}} \over {{V_{\max }}}} \cdot 100\% where: RSD – Relative Drought Streamflow Deficit [%], Vn – drought streamflow deficit volume of the low-flow event [m3], Vmax – maximum possible streamflow deficit volume during the low-flow event, i.e. when discharge value equals 0 [m3].

DSI is calculated as a weighted average of the relative deficits for all water gauges, where the weight is the catchment area (Kozek & Tomaszewski 2018): DSI=i=1N(RSDiAi)i=1NAi DSI = {{\sum\nolimits_{i = 1}^N {\left( {RS{D_i} \cdot {A_i}} \right)} } \over {\sum\nolimits_{i = 1}^N {{A_i}}}} where: DSI – Drought Severity Index [%], RSDi – Relative Drought Streamflow Deficit in the catchment i [%], Ai – area of the sub-catchment [km2], N – number of sub-catchments where low-flows have occurred.

This index evaluates the progress of hydrological drought for the entire studied catchment. Its value ranges from 0% to 100%, where severity level changes proportionally to percentage: 100% theoretically denotes a complete lack of water in the river channels.

The temporal evenness of streamflow deficit distribution during the hydrological drought was estimated using the Drought Concentration Index (DCI). This introduced characteristic is based on the Lorenz concentration coefficient (Gastwirth 1972; Jokiel & Kostrubiec 1981). The dependent variable is the sum of drought streamflow deficits from all water gauges and the operand is the time step. A graph of the drought concentration curve is created by cumulating the percentages of both variables after ordering the dependent variable (Fig. 4). The area between the curve and diagonal of the graph indicates the degree of drought concentration, which increases in proportion to this area. The Drought Concentration Index is calculated according to the formula: DCI=FcFs DCI = {{{F_c}} \over {{F_s}}} where: DCI – Drought Concentration Index, Fe – concentration area, Fs – half square area.

Figure 4

The curve of hydrological drought concentration (example of drought from 23.08 – 31.10.2018)

Source: own elaboration

High values for the concentration index indicate a high concentration of drought, which indicates a significant accumulation of water shortages in one or a few short periods during a drought. This proves the considerable depletion of water resources at a particular moment in the drought's duration. A decrease in the DCI index is determined by a gradual, more even distribution of streamflow deficits at all time steps, which in turn may be related to the stability of the formation of streamflow deficits during the studied period.

The dynamics of hydrological drought propagation were assessed on the basis of the Drought Development Pace Coefficient (DDPC): DDPC=i=1N((Qmin)t100%Dt)N D{D_P}C = {{\sum\nolimits_{i = 1}^N {\left( {{{\left( {{Q_{\min }}} \right)t \cdot 100\% } \over {{D_t}}}} \right)} } \over N} where: DDPC – Coefficient of Drought Development Pace [%], (Qmin)t – the number of days from the beginning of the drought to the minimum low-flow occurrence in the catchment [days], Dt – drought duration [days], N – number of sub-catchments.

This index ranges from 0% to 100%. A result equal to 50% indicates that the maximum drought intensity occurred exactly in the middle of its duration. Lower values denote the appearance of the highest water shortages in the first half of the drought's duration, which means that its propagation was relatively fast but the process of water resource renewal in the catchment lasted much longer. Results in the range of 50–100% should be interpreted in the opposite way. The changeability of this characteristic during a drought episode was assessed on the basis of Pearson's variation coefficient (Cv(DDPC)). A low value for this coefficient indicates a similar length of time for the highest drought intensity across all sub-catchments, which might be interpreted as a spatially homogenous hydrological drought with a clear core. High coefficient values indicate a high variability in the pace of drought's development in different parts of the catchment.

Hydrological drought is very often characterized by a complex progression, which results in a few, or many, river low-flow episodes. In one part of the catchment there may be a short and severe episode but in another part, a prolonged but mild one, etc. From this point of view, the assessment of the temporal and spatial continuation of drought which indicates its course and degree of development in the catchment is of high importance. For further analysis, the Drought Continuation Index (DCnI) was constructed: DCnI=i=1N(LFt)iDtN100% DCnI = {{\sum\nolimits_{i = 1}^N {\left( {L{F_t}} \right)i} } \over {{D_t} \cdot N}} \cdot 100\% where: DCnI – Drought Continuation Index [%], (LFt)i – low-flow duration at water gauge station i [days], Dt – drought duration [days], N – number of water gauge stations.

This characteristic ranges from 0% to 100%. A result equal to 100% indicates the total development of hydrological drought across the whole catchment, which means that in every investigated water gauge, low-flows persisted throughout the whole of the drought episode. A decrease in the DCnI value shows a lower degree of drought development in temporal or spatial terms. This could be caused by the spatial differentiation of hydrometeorological conditions or a variability in temporal low-flows determined by short-duration alimentation impulses such as thaws or rainfall.

Results and discussion
Distribution and variability of hydrological droughts

In accordance with the established criteria, 41 hydrological droughts were identified in the studied catchment (Fig. 5, Tab. 2). Droughts in which the main phase of the water shortages occurred in the winter season were dominant. However, droughts in summer and autumn also occurred. In a few cases, streamflow deficits were so stable and severe that the droughts had a multi-seasonal character.

Figure 5

Multiannual course of hydrological drought characteristics in the upper Dunajec river catchment. DSI – Drought Severity Index, DRI – Drought Range Index, DDPC – Drought Development Pace Coefficient, DCI – Drought Concentration Index, DCnI – Drought Continuation Index. Numbering of droughts as in Tab. 2

Source: own elaboration

Characteristics of hydrological droughts in the upper Dunajec river catchment (1989–2018)

No. Period Dt [days] DSI [%] DRI [%] DCI DDPC [%] cv(DDPC) DCnI [%]
1 01.11.1988–21.03.1989 141 32.88 96.79 0.48 13.44 1.02 58.19
2 14.10.1989–04.04.1990 173 22.68 91.17 0.64 41.41 0.32 37.33
3 05.06.1990–02.09.1990 90 17.32 94.55 0.67 72.94 0.30 32.87
4 15.12.1990–17.05.1991 154 26.63 96.79 0.59 30.66 0.57 44.50
5 08.06.1991–01.08.1991 55 15.18 13.16 0.76 52.12 0.39 11.77
6 27.11.1991–25.03.1992 120 24.63 93.93 0.49 45.09 0.46 45.92
7 06.06.1992–17.10.1992 134 25.88 96.79 0.59 63.94 0.13 44.27
8 11.12.1992–26.03.1994 471 23.29 90.84 0.34 65.11 0.41 45.14
9 27.06.1994–20.04.1995 298 23.40 96.79 0.54 50.28 0.52 45.18
10 23.07.1995–22.04.1996 275 27.87 100.00 0.43 63.49 0.37 62.80
11 10.11.1996–29.04.1997 171 15.70 100.00 0.47 41.96 0.35 59.18
12 17.09.1997–15.11.1997 60 27.60 100.00 0.59 73.57 0.12 12.25
13 30.07.1998–28.09.1998 61 9.95 97.75 0.37 63.39 0.32 52.79
14 19.11.1998–01.04.1999 134 27.00 95.79 0.37 41.09 0.51 55.71
15 31.07.1999–29.03.2000 243 24.32 98.18 0.59 57.40 0.40 37.80
16 19.08.2000–17.03.2001 212 24.04 100.00 0.41 69.86 0.22 61.82
17 06.10.2001–19.03.2002 165 24.48 100.00 0.55 48.09 0.42 52.39
18 19.04.2002–26.05.2002 38 8.81 24.05 0.43 52.63 0.57 11.32
19 07.12.2002–18.04.2003 133 34.06 100.00 0.40 58.05 0.15 63.61
20 31.05.2003–17.03.2004 292 26.80 100.00 0.39 63.36 0.28 65.62
21 22.08.2004–04.04.2005 227 17.63 100.00 0.52 67.67 0.32 47.16
22 02.09.2005–02.04.2006 213 26.21 100.00 0.31 61.83 0.33 79.48
23 11.07.2006–04.09.2007 421 22.26 100.00 0.71 40.94 0.67 34.81
24 14.12.2007–10.04.2008 119 20.97 86.62 0.55 38.18 0.60 26.43
25 12.05.2008–20.09.2008 132 15.33 92.18 0.73 49.38 0.55 24.73
26 19.10.2008–28.03.2009 161 15.28 98.18 0.55 39.07 0.62 36.86
27 08.09.2009–22.10.2009 45 15.11 86.61 0.45 56.35 0.21 35.78
28 03.01.2010–22.03.2010 79 13.99 98.83 0.43 63.56 0.35 47.66
29 15.10.2010–06.04.2011 174 17.46 92.68 0.52 66.26 0.43 26.81
30 29.08.2011–05.04.2012 220 31.05 100.00 0.37 64.66 0.29 72.39
31 29.06.2012–13.04.2013 289 25.64 100.00 0.47 43.67 0.40 55.40
32 23.07.2013–07.04.2014 259 17.61 100.00 0.63 35.81 0.68 33.28
33 03.11.2014–27.03.2015 145 19.50 88.65 0.59 48.55 0.45 29.48
34 23.06.2015–16.11.2015 147 25.14 98.30 0.50 48.23 0.27 51.53
35 15.12.2015–03.05.2016 141 20.90 98.30 0.57 24.23 0.35 35.32
36 07.06.2016–16.07.2016 40 9.66 31.41 0.67 76.07 0.21 19.88
37 29.12.2016–23.03.2017 85 11.95 78.82 0.59 50.37 0.22 38.35
38 21.06.2017–02.09.2017 74 14.19 88.01 0.76 71.52 0.27 23.99
39 30.12.2017–31.03.2018 92 23.26 68.72 0.66 66.30 0.06 29.67
40 29.04.2018–13.07.2018 76 15.27 8.21 0.51 58.88 0.58 5.99
41 23.08.2018–31.10.2018 70 14.01 83.93 0.58 77.45 0.20 33.71

Dt – Drought Duration, DSI – Drought Severity Index, DRI – Drought Range Index, DCI – Drought Concentration Index, DDPC – Drought Development Pace Coefficient, cv(DDPC) – Pearson's variation coefficient of DDPC, DCnI – Drought Continuation Index.

Source: own elaboration

The average duration of the hydrological droughts was 162 days. The longest episodes lasted longer than a year and occurred during the periods 1992–1994 and 2006–2007. These were the result of a series of dry years that affected the entire country (Stachý 2011). Short droughts (lasting from 1 to 3 months) usually occurred in the warm season and were caused by intense evapotranspiration with limited rainwater supply.

The range of the hydrological droughts in the Dunajec river catchment ranged from 8.21% to 100% (Fig. 5). The average value for this characteristic amounted to 87%, which means that droughts mostly covered the entire catchment, and their development was determined by hydrometeorological factors that were active at a regional or wider scale. Droughts covering the maximum range dominated during 2001–2008, while episodes covering smaller areas were observed mainly at the end of the studied period. It is worth emphasizing that short-duration hydrological droughts with small ranges occurred mainly in warm seasons due to rainfall impulses and delayed thaws, which often interrupted the continuous progression of water shortages.

The hydrological droughts in the studied catchment were characterized by various degrees of severity. The DSI values ranged from 8.81% to 34.06% with an average of 21% (Fig. 5). The three most severe droughts occurred at the beginning, middle and at the end of the studied multiyear period. They covered the entire, or almost the entire, Dunajec river catchment. Although these droughts were not the longest (5–7 months), their development and continuation index varied in pace. It follows that severe hydrological droughts in mountain catchments can be determined by various factors with a variable course. However, slightly severe (DSI=21–30%) and moderate (11–20%) droughts dominated over the studied period. Minor episodes were characterized by short durations and usually occurred in small areas of the catchment.

The average development rate for hydrological droughts in the Dunajec river catchment was similar to the average rate for their disappearance. The average value of DDPC was 54%, which proves that the depletion and restoration of water resources had a similar dynamic in the mountain catchment under drought conditions. In the case of some prolonged events, rapid drought development but a slow recession was observed. The increase in total drought duration resulted in a shortening of the drought development time in relation to the length of its recession phase. This is related to the fact that the river flow recession curve is characterized by a constant maximum time for reaching the base flow, therefore, during a long hydrological drought, the discharge recession's end is reached in the first half of its duration.

The average variation coefficient for DDPC was 0.39 and ranged from 0.06 to 1.02. It can be stated that in the case of many droughts, the timing of the highest drought intensity across all sub-catchments was similar, thus, they can be interpreted as being spatially homogenous hydrological droughts with a clear core. Droughts which reached their maximum of intensity in the first half of their duration were characterized by a much greater variability in their pace of development. It was also observed that the course of drought continuation was clearly influenced by the drought development pace. Water shortages in quickly developing droughts can often be interrupted by alimentation impulses, therefore, the highest drought intensity occurs at different times in different sub-catchments.

Hydrological droughts in the Dunajec river catchment were characterized by an average degree of concentration (avgDCI=0.53). The highest concentration (0.76) was observed during relatively short summer droughts (lasting about 2 months). An almost equally high value for this characteristic (0.71) relates to the one of the longest events – the drought of 2006–2007. This is connected to the fact that a deficit of water resources was concentrated at the beginning of the drought (DDPC=34.81%) and resulted in low streamflow deficits during the latter part of drought. However, most of the identified droughts were characterized by a lower degree of concentration, which reflected a significant degree of stability in streamflow deficit formation in the mountains catchment, which was mainly due to the influence of the capacious groundwater reservoirs.

The drought continuation index (DCnI) ranged from 6% to over 79% for the studied catchment. Two identified droughts (2005–2006, 2011–2012) were characterized by a level of continuation above 70% (Fig. 5). These events were very similar because they were extensive, severe, and lasted more than six months. However, in most cases, the continuation process did not have such a high level (about 40%). Periodic changes in local hydrometeorological conditions may lead the drought to shift from one sub-catchment to another, which results in a low degree of drought continuation, even though its total duration is relatively long. An interesting correlation was also observed: events with a high degree of continuation were characterized by high severity but low concentration. This indicates a high degree of drought inertia, which, in turn, results in high autocorrelation across low-flows, and consequently, slow changes in streamflow deficit over successive days of the drought period.

The identified hydrological droughts were characterized by differences in spatial distribution. In almost one-third of cases, the investigated drought events covered the entire catchment area. Droughts with smaller ranges differed in terms of other features as well, as can be seen in the exemplary figure (Fig. 6). The 1999 drought had a big range (>95%) and was observed in every part of the study area, excluding several smaller sub-catchments. The 2002 drought had a smaller range; it covered slightly more than 24% of the catchment area and occurred in the central area (i.e. it was apparent in the sub-catchments of the middle section of the main river and its tributaries). The droughts’ intensities were also different. The first (1999) lasted almost five months, and its severity was high (27%); therefore, it can be considered a severe hydrological drought. The second (2002) lasted a little over a month (38 days) and its severity index did not reach 9%, which is an example of a mild hydrological drought.

Figure 6

Spatial range of selected hydrological droughts in the upper Dunajec river catchment. DRI – Drought Range Index, DSI – Drought Severity Index, Dt – Drought Duration

A significant differentiation in the characteristics of the multiannual course of hydrological droughts in the Dunajec river catchment can be observed (Fig. 5). The studied multi-year period begins with droughts with restricted ranges. The most severe and extensive events occurred at the beginning of the twenty-first century, while droughts of a moderate severity and much smaller range dominated at the end of the 30-year studied period. Droughts from 2015–2018 were also relatively short, and occurred in both winter and summer. Additionally, the question as to whether any systematic time series component appeared in the studied multi-year course of spatial drought characteristics was also addressed. Hence, the identified linear trend equations were verified using the Student's t-test and Mann-Kendal test at the level of α=0.05 (Tab. 3). In general, no statistically significant linear trends were observed, and trends were characterized by relatively low determination coefficients (0.02–0.14). Only in the case of drought severity was a significant, slightly negative trend noticed. It is interesting that the trend in the mitigation of hydrological drought conditions during the investigated period was not accompanied by trends in other drought parameters, especially in range and duration, in such a vast catchment. Solving this problem needs both further more detailed studies and comparative studies.

Parameters for linear trend equations in the series of selected spatial hydrological drought characteristics for the upper Dunajec river catchment (1989–2018) (significance of trends at level α=0.05)

Dt DRI DSI DDPC DCnI DCI
a −1.59 −0.39 −0.20 0.25 −0.35 0.001
R2 0.04 0.04 0.14 0.04 0.06 0.02
p (t-Student test) 0.225 0.216 0.018 0.207 0.123 0.375
p (Mann-Kendall test) 0.185 0.296 0.010 0.301 0.111 0.345

a – slope coefficient of the trend line, R2 – determination coefficient, p - probability value; other symbols as in Tab. 2

Source: own elaboration

It is noteworthy that at the beginning, in the middle, and at the end of the analysed multi-year period, there were droughts of greater and lower range, severity, and duration (Fig. 5). Their rate of progression was slow, and the degree of concentration and continuation were low. Drought events of greater intensity appeared every few years, mainly determined by fluctuations in precipitation, which is an effect of the grouping of wet and dry years (Stachy 2011). Based on the presented results, it can be concluded that there is no strong systematic time component in the multiannual course of the hydrological droughts’ spatial features, which is usually determined by serious anthropogenic impacts or climate fluctuations. Obviously, in local sub-catchments, such influences might be observed, however, at the scale of the whole catchment area, droughts seem to develop unaffected in the investigated period and in terms of studied characteristics.

Classification of hydrological droughts

The substantial variability in the features of the identified hydrological droughts made it necessary to apply a statistical grouping procedure. The applied classification, based on cluster analysis, identified groups of similar drought events, which led to definitions for the types of hydrological droughts that occur in mountain catchments. In the first stage, it was necessary to select the variables (drought characteristics), which contributed a new quantity of information. A correlation matrix was created for this purpose, and any characteristics strongly correlated with each other were rejected. Finally, three drought characteristics were selected for further analysis: duration (Dt), concentration (DCI), and development pace (DDPC). It should be noted that the selected variables were expressed in various units and characterized by different statistical distributions. As a result, a data standardisation was conducted according to a commonly used procedure (Kreyszig 1979): xs=xixsδ xs = {{{x_i} - {x_s}} \over \delta } where: xs – standardised variable, xi – original variable, xs – arithmetic average of the sample, δ – standard deviation of the sample.

The three series of standardised variables (Dt, DCI, DDPC) formed the basis for hierarchical clustering. This consisted of gradually combining objects that were most similar to each other, into single clusters. As a result of the final combination of all groups, a cluster was formed which included 41 elements (all identified hydrological droughts). The clustering procedure was performed using Ward's method (Parysek 1982), and the results were presented as a dendrogram (Fig. 7a).

Figure 7

(a) Dendrogram of the similarity between hydrological droughts; and (b) the course of the GWZ index for the identification of the optimal number of classes. M – location of the stopping criterion according to Mojena's rule

Source: own elaboration

Determining the optimal number of clusters was the next important step in this procedure. For this purpose, the GWZ distance criterion (Grabiński et al. 1989) and the “Mojena rule” (Mojena 1977) were applied. The GWZ criterion consists of computing the distance quotient between individual clusters, beginning with the first two clusters. The results are presented in the graph in Fig. 7b, and the optimal number of groups is indicated by the first local maximum. This method provides appropriate results concerning division into a number of classes, and it has been recommended for use in cluster analysis by, among others, Milligan & Cooper (1985). In the present study, this criterion showed that the best division of droughts was into five taxonomic classes.

The second criterion, Mojena's rule is based on the formula: Rm=dh+ddhb {R_m} = {d_h} + {d_{dh}} \cdot b where: Rm – “Mojena rule” distance, dh – average of the clusters’ linkage distance, ddh – standard deviation of the clusters’ linkage distance, b – equation constant.

The value “b” was set as 1.25. This is the most common parameter value, as determined on the basis of studies by Milligan & Cooper (1985), and assuming the use of this parameter in the equation, Rm would be equal 6.2. This result indicated that the droughts in the Dunajec river catchment should be divided into five classes (the grouping was completed at the point where the distance of the closest summation was greater than Rm) (Fig. 7a). Both the applied methods resulted in the same optimal number of clusters, thanks to which, five types of hydrological drought were determined in the studied catchment.

The definitions of the identified types of droughts were made on the basis of the average values of the analysed parameters and their standard deviations. The average, low and high, and very low and very high values were determined for each characteristic, depending on the size of the deviation from the arithmetic average of all the analysed cases (Fig. 8a).

Figure 8

(a) Average values and standard deviations of selected drought parameters characterizing individual types of hydrological drought; and (b) their distribution according to the identified types of drought in the upper Dunajec river catchment

Source: own elaboration

The analysis of hydrological drought types was conducted on the basis of the average values for selected characteristics for all the droughts that formed the group. The differences between these average values and the average value for all events identified for the Dunajec river catchment, were statistically significant at the level of α=0.05 (as verified by the Student's t-test). Only in two cases (DCI - type A, DDPC - type B), was the difference insignificant, although this did not fundamentally affect the interpretation of the obtained results. It is worth noting that none of the identified types was defined as extreme, but there were episodes characterized by extreme values for some parameters in almost all of the identified types.

Type A includes the majority of hydrological droughts (12) that were characterized by average duration (Fig. 8a). During a drought of this type, there are about the same number of days with large and with small streamflow deficits, and its propagation is relatively rapid. A small amount of variability in drought duration and degree of concentration is observed in this group, while a slightly greater variability was noted for DDPC values (Fig. 8b). An episode in 1989, which reached its highest intensity at the beginning of its duration (DDPC=13.44%), had a great impact on the definition of type A droughts, which are characterized by a fast pace of development. Moreover, these droughts were extensive (they often covered the entire catchment), severe, and not very concentrated. They developed mostly in autumn (the first frosts and snowfall in the mountains, resulting in temporary water retention in snow cover and ice) and terminated with the spring thaw.

Type B is represented by nine long hydrological droughts lasting about eight months. Their duration was highly variable (Fig. 8b), and covered several episodes of average duration. The long-lasting drought of 2006–2007 (421 days), had a significant impact on the definition of this type. These droughts were characterized by an average degree of concentration, while the pace of both their development and recession was similar. All events of this type were very extensive and severe, but they were often interrupted by sudden water supplies, which resulted in large variability in their concentration and pace of development (Fig. 8b).

Type C includes six droughts which were also long (lasting about 9 months) (Fig. 8a). When analysing drought duration variability, one notices one outlier value on the graph (Fig. 8b). This is the longest identified drought in the Dunajec river catchment. Moreover, droughts of this type were poorly concentrated due to their long duration and high degree of continuation. These droughts were very extensive and very severe. They began in the warm season, and precipitation deficits, enhanced by evapotranspiration in the summer season, led to a depletion in resources in the catchment to such a degree that droughts of this type prolonged the winter season when water shortages occurred due to snow cover retention and the freezing of river channels.

Relatively short droughts were classified as type D (Fig. 8a). This group consists of six episodes that occurred in different seasons of the year. These droughts were characterized by a low degree of concentration and had their highest intensity occur at the midpoint of their duration. The values of the parameters that define this type of drought showed slight variability (Fig. 8b). There were only a few individual episodes of average duration and concentration. Droughts of type D were usually mild and covered a small part of the catchment.

The last type of drought (E) includes eight short events, which occurred in the warm season. In contrast to the droughts in previous group (type D), they developed relatively slowly and reach their maximum intensity in the second half of their duration. Due to the fact that in mountain catchments, in the summer season, droughts are often interrupted by sudden rainfall impulses, their development pace can change (Fig. 8b). These droughts and the previously described short droughts of type D, also varied in their degree of concentration. Type E droughts were further characterized by narrow ranges, similar to the events in the previous group, and an even smaller degrees of continuation. Droughts of this type were slightly more severe.

The hydrological drought classification provides some new information with respect to the dynamics of drought propagation in a mountain catchment. Due to this, it may be possible to recognize the regularities in drought development in mountains. The identified types of hydrological drought may allow for the creation of some schemes that are related to their development, taking into account the seasons in which the studied episodes occurred. This, in turn, can be used to improve strategies for the mitigation of the effects of drought and define the stages of action in environmental programs at the regional level.

Conclusions

The research which has been carried out proved that the spatial pattern and the dynamics of hydrological drought development in a mountain catchment is characterized by different conditions the determine the drought's range, severity, concentration, and temporal behaviours. The applied methodology allowed the synthetic indices for big and complex river catchments to be estimated. Droughts which fully covered the whole catchment area were identified in about 30% of the investigated episodes. The other events were characterized by differing spatial patterns and development dynamics, determined by the changeable local conditions in the mountain catchment. Hydrological drought duration also revealed a clear relationship between drought severity and range, which could be explained by the high inertia in the drought progression process. A high concentration in hydrological drought had a negative influence on its severity and degree of development as measured by the index of continuation. In general, no statistically significant linear trends were observed, except for the multiannual course of the drought severity index. A lack of serious systematic time components in the studied time series, which is usually determined by anthropogenic impact or climate fluctuations, indicates that, on the scale of the whole catchment area, droughts seemed to have developed unaffected by anthropogenic and climate fluctuation factors during the investigated period, and in terms of their studied characteristics.

The cluster analysis identified five types of dynamic development for hydrological drought. Their descriptions, in terms of duration, concentration, and development dynamics, which defined the behaviour and potential effects of drought events in a mountain catchment, are important from a cognitive as well as an practical point of view.

Similar studies using the same methodology were conducted for lowland the catchment on the Warta river (Kozek & Tomaszewski 2018) and for the Biebrza river catchment, which is located in a lake district area (Kozek & Tomaszewski 2019). Both these, and the presented study's results indicated ways in which specific geographical characteristics and river flow regimes influenced the dynamics of hydrological drought development as well as some regularities in their patterns. It is worth noting that, in a similar way to the presented catchment, statistically significant trends for complex drought characteristics were very rare in the other studies. The presented methodology is relatively new. One of its main features is the analysis of hydrological drought estimators based on transmissions of low-flow information between dependent sub-catchments in a hydrologically ordered hierarchy. This allows the internal dynamics of drought development to be followed, whereas most of the former studies estimated drought characteristics for single catchments and interpolated (extrapolated) them without causal or directional relationships. The development of presented methodology might improve strategies for the mitigation of hydrological drought effects across different spatial scales.

Figure 1

The Dunajec river catchment to Nowy Sącz water-gauge station. Numbering of sub-catchments as in Tab. 1Source: own elaboration
The Dunajec river catchment to Nowy Sącz water-gauge station. Numbering of sub-catchments as in Tab. 1Source: own elaboration

Figure 2

(a) Basic parameters of low-flows using the example of episodes from 1994–1995 on the Dunajec river (Nowy Targ-Kowaniec water-gauging station); and (b) a graphical illustration of the estimation of Relative Drought Streamflow Deficit (RSD). Tn – low-flow duration, Vn – drought streamflow deficit volume of the low-flow event [m3], Vmax – maximum possible streamflow deficit volume during the low-flow event, i.e. when the discharge value equals 0 [m3], Q70% – flow corresponding to the seventieth percentile of the flow duration curveSource: own elaboration and Tomaszewski 2012 (changed)
(a) Basic parameters of low-flows using the example of episodes from 1994–1995 on the Dunajec river (Nowy Targ-Kowaniec water-gauging station); and (b) a graphical illustration of the estimation of Relative Drought Streamflow Deficit (RSD). Tn – low-flow duration, Vn – drought streamflow deficit volume of the low-flow event [m3], Vmax – maximum possible streamflow deficit volume during the low-flow event, i.e. when the discharge value equals 0 [m3], Q70% – flow corresponding to the seventieth percentile of the flow duration curveSource: own elaboration and Tomaszewski 2012 (changed)

Figure 3

An example of hydrological drought identification in the Dunajec river catchment in 2008. Numbering of sub-catchments as in Tab. 1Source: own elaboration
An example of hydrological drought identification in the Dunajec river catchment in 2008. Numbering of sub-catchments as in Tab. 1Source: own elaboration

Figure 4

The curve of hydrological drought concentration (example of drought from 23.08 – 31.10.2018)Source: own elaboration
The curve of hydrological drought concentration (example of drought from 23.08 – 31.10.2018)Source: own elaboration

Figure 5

Multiannual course of hydrological drought characteristics in the upper Dunajec river catchment. DSI – Drought Severity Index, DRI – Drought Range Index, DDPC – Drought Development Pace Coefficient, DCI – Drought Concentration Index, DCnI – Drought Continuation Index. Numbering of droughts as in Tab. 2Source: own elaboration
Multiannual course of hydrological drought characteristics in the upper Dunajec river catchment. DSI – Drought Severity Index, DRI – Drought Range Index, DDPC – Drought Development Pace Coefficient, DCI – Drought Concentration Index, DCnI – Drought Continuation Index. Numbering of droughts as in Tab. 2Source: own elaboration

Figure 6

Spatial range of selected hydrological droughts in the upper Dunajec river catchment. DRI – Drought Range Index, DSI – Drought Severity Index, Dt – Drought Duration
Spatial range of selected hydrological droughts in the upper Dunajec river catchment. DRI – Drought Range Index, DSI – Drought Severity Index, Dt – Drought Duration

Figure 7

(a) Dendrogram of the similarity between hydrological droughts; and (b) the course of the GWZ index for the identification of the optimal number of classes. M – location of the stopping criterion according to Mojena's ruleSource: own elaboration
(a) Dendrogram of the similarity between hydrological droughts; and (b) the course of the GWZ index for the identification of the optimal number of classes. M – location of the stopping criterion according to Mojena's ruleSource: own elaboration

Figure 8

(a) Average values and standard deviations of selected drought parameters characterizing individual types of hydrological drought; and (b) their distribution according to the identified types of drought in the upper Dunajec river catchmentSource: own elaboration
(a) Average values and standard deviations of selected drought parameters characterizing individual types of hydrological drought; and (b) their distribution according to the identified types of drought in the upper Dunajec river catchmentSource: own elaboration

Characteristics of hydrological droughts in the upper Dunajec river catchment (1989–2018)

No. Period Dt [days] DSI [%] DRI [%] DCI DDPC [%] cv(DDPC) DCnI [%]
1 01.11.1988–21.03.1989 141 32.88 96.79 0.48 13.44 1.02 58.19
2 14.10.1989–04.04.1990 173 22.68 91.17 0.64 41.41 0.32 37.33
3 05.06.1990–02.09.1990 90 17.32 94.55 0.67 72.94 0.30 32.87
4 15.12.1990–17.05.1991 154 26.63 96.79 0.59 30.66 0.57 44.50
5 08.06.1991–01.08.1991 55 15.18 13.16 0.76 52.12 0.39 11.77
6 27.11.1991–25.03.1992 120 24.63 93.93 0.49 45.09 0.46 45.92
7 06.06.1992–17.10.1992 134 25.88 96.79 0.59 63.94 0.13 44.27
8 11.12.1992–26.03.1994 471 23.29 90.84 0.34 65.11 0.41 45.14
9 27.06.1994–20.04.1995 298 23.40 96.79 0.54 50.28 0.52 45.18
10 23.07.1995–22.04.1996 275 27.87 100.00 0.43 63.49 0.37 62.80
11 10.11.1996–29.04.1997 171 15.70 100.00 0.47 41.96 0.35 59.18
12 17.09.1997–15.11.1997 60 27.60 100.00 0.59 73.57 0.12 12.25
13 30.07.1998–28.09.1998 61 9.95 97.75 0.37 63.39 0.32 52.79
14 19.11.1998–01.04.1999 134 27.00 95.79 0.37 41.09 0.51 55.71
15 31.07.1999–29.03.2000 243 24.32 98.18 0.59 57.40 0.40 37.80
16 19.08.2000–17.03.2001 212 24.04 100.00 0.41 69.86 0.22 61.82
17 06.10.2001–19.03.2002 165 24.48 100.00 0.55 48.09 0.42 52.39
18 19.04.2002–26.05.2002 38 8.81 24.05 0.43 52.63 0.57 11.32
19 07.12.2002–18.04.2003 133 34.06 100.00 0.40 58.05 0.15 63.61
20 31.05.2003–17.03.2004 292 26.80 100.00 0.39 63.36 0.28 65.62
21 22.08.2004–04.04.2005 227 17.63 100.00 0.52 67.67 0.32 47.16
22 02.09.2005–02.04.2006 213 26.21 100.00 0.31 61.83 0.33 79.48
23 11.07.2006–04.09.2007 421 22.26 100.00 0.71 40.94 0.67 34.81
24 14.12.2007–10.04.2008 119 20.97 86.62 0.55 38.18 0.60 26.43
25 12.05.2008–20.09.2008 132 15.33 92.18 0.73 49.38 0.55 24.73
26 19.10.2008–28.03.2009 161 15.28 98.18 0.55 39.07 0.62 36.86
27 08.09.2009–22.10.2009 45 15.11 86.61 0.45 56.35 0.21 35.78
28 03.01.2010–22.03.2010 79 13.99 98.83 0.43 63.56 0.35 47.66
29 15.10.2010–06.04.2011 174 17.46 92.68 0.52 66.26 0.43 26.81
30 29.08.2011–05.04.2012 220 31.05 100.00 0.37 64.66 0.29 72.39
31 29.06.2012–13.04.2013 289 25.64 100.00 0.47 43.67 0.40 55.40
32 23.07.2013–07.04.2014 259 17.61 100.00 0.63 35.81 0.68 33.28
33 03.11.2014–27.03.2015 145 19.50 88.65 0.59 48.55 0.45 29.48
34 23.06.2015–16.11.2015 147 25.14 98.30 0.50 48.23 0.27 51.53
35 15.12.2015–03.05.2016 141 20.90 98.30 0.57 24.23 0.35 35.32
36 07.06.2016–16.07.2016 40 9.66 31.41 0.67 76.07 0.21 19.88
37 29.12.2016–23.03.2017 85 11.95 78.82 0.59 50.37 0.22 38.35
38 21.06.2017–02.09.2017 74 14.19 88.01 0.76 71.52 0.27 23.99
39 30.12.2017–31.03.2018 92 23.26 68.72 0.66 66.30 0.06 29.67
40 29.04.2018–13.07.2018 76 15.27 8.21 0.51 58.88 0.58 5.99
41 23.08.2018–31.10.2018 70 14.01 83.93 0.58 77.45 0.20 33.71

Selected characteristics of the investigated catchments (1989–2018)

No. River - water-gauge A [km2]* avgH* [m asl.] Q70% [m3/s] q70% [dm3/s/km2] ALq [dm3/s/km2] AAq [dm3/s/km2] AHq [dm3/s/km2]
1 Czarny Dunajec - Koniówka 134 1443.04 1.96 14.62 10.24 32.10 84.74
2 Dunajec – Nowy Targ 431.8 1370.38 3.95 9.15 6.52 20.26 53.37
3 Dunajec – Nowy Targ-Kowaniec 681.1 1367.85 7.16 10.51 7.72 21.75 53.09
4 Dunajec – Sromowce Wyżne 1278.3 1486.53 14.3 11.19 8.58 21.93 55.01
5 Dunajec – Krościenko 1580.3 1457.98 16.4 10.38 7.88 20.87 53.44
6 Dunajec – Gołkowice 2046.9 1407.70 19.5 9.53 7.43 19.39 49.76
7 Dunajec – Nowy Sącz 4341 1388.99 34 7.83 6.01 15.58 38.41
8 Kościeliski Stream – Kościelisko-Kiry 34.5 1540.25 0.82 23.77 15.88 51.50 134.31
9 Lepietnica – Ludźmierz 50.7 898.42 0.4 7.89 5.52 19.58 53.18
10 Wielki Rogoźnik – Ludźmierz 124.3 811.04 0.76 6.11 4.22 14.86 37.65
11 Biały Dunajec – Zakopane-Harenda 58.4 1385.29 1.12 19,18 13.51 42.04 110.78
12 Biały Dunajec – Szaflary 210.1 1313.51 2.8 13,33 9.88 26.09 61.27
13 Poroniec – Poronin 78.8 1360.62 0.73 9.26 6.63 13.02 53.96
14 Białka – Łysa Polana 63.1 1733.43 1.06 16.8 10.76 52.21 143.48
15 Białka – Trybsz 2 202.3 1569.16 3.06 15.13 10.31 37.85 101.45
16 Niedziczanka – Niedzica 136.4 769.00 0.74 5.43 3.40 15.27 42.07
17 Grajcarek – Szczawnica 73.6 868.10 0.54 7.34 5.36 16.92 43.16
18 Ochotnica – Tylmanowa 107.6 840.73 0.76 7.06 5.21 15.55 37.84
19 Poprad – Muszyna-Milik 1695.1 779.74 9.72 5.73 4.43 12.55 30.98
20 Poprad – Stary Sącz 2071 707.99 11.9 5.74 4.39 12.49 30.42

Parameters for linear trend equations in the series of selected spatial hydrological drought characteristics for the upper Dunajec river catchment (1989–2018) (significance of trends at level α=0.05)

Dt DRI DSI DDPC DCnI DCI
a −1.59 −0.39 −0.20 0.25 −0.35 0.001
R2 0.04 0.04 0.14 0.04 0.06 0.02
p (t-Student test) 0.225 0.216 0.018 0.207 0.123 0.375
p (Mann-Kendall test) 0.185 0.296 0.010 0.301 0.111 0.345

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