Dynamics of hydrological droughts propagation in mountainous catchments

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

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 (minD_t) (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 minD_t) must occur in at least one water-gauge station, or

Figure 3

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 (minD_t).

The indices for the dynamics and patterns were estimated for all identified hydrological droughts. The first of these was the Hydrological Drought Duration (D_t), 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): (1) DRI=∑i=1NADi∑i=1NAi⋅100% DRI = {{\sum\nolimits_{i = 1}^N {A{D_i}} } \over {\sum\nolimits_{i = 1}^N {{A_i}} }} \cdot 100\% where: DRI – Drought Range Index [%], ∑AD_i – the sum of sub-catchment areas covered by the hydrological drought [km²], ∑A_i – 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): (2) RSD=VnVmax⋅100% 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): (3) DSI=∑i=1N(RSDi⋅Ai)∑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 [%], RSD_i – Relative Drought Streamflow Deficit in the catchment i [%], A_i – 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: (4) DCI=FcFs DCI = {{{F_c}} \over {{F_s}}} where: DCI – Drought Concentration Index, F_e – concentration area, F_s – half square area.

Figure 4

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 (DD_PC): (5) DDPC=∑i=1N((Qmin)t⋅100%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: DD_PC – Coefficient of Drought Development Pace [%], (Q_min)_t – the number of days from the beginning of the drought to the minimum low-flow occurrence in the catchment [days], D_t – 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(DD_PC)). 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: (6) DCnI=∑i=1N(LFt)iDt⋅N⋅100% DCnI = {{\sum\nolimits_{i = 1}^N {\left( {L{F_t}} \right)i} } \over {{D_t} \cdot N}} \cdot 100\% where: DCnI – Drought Continuation Index [%], (LF_t)_i – low-flow duration at water gauge station i [days], D_t – 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.

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

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 DD_PC 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 DD_PC 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 (DD_PC=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

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.

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.

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 (D_t), concentration (DCI), and development pace (DD_PC). 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): (7) xs=xi−xsδ xs = {{{x_i} - {x_s}} \over \delta } where: x_s – standardised variable, x_i – original variable, x_s – arithmetic average of the sample, δ – standard deviation of the sample.

The three series of standardised variables (D_t, DCI, DD_PC) 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

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: (8) Rm=dh+ddh⋅b {R_m} = {d_h} + {d_{dh}} \cdot b where: R_m – “Mojena rule” distance, d_h – average of the clusters’ linkage distance, d_dh – 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, R_m 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 R_m) (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

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, DD_PC - 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 DD_PC values (Fig. 8b). An episode in 1989, which reached its highest intensity at the beginning of its duration (DD_PC=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.