Spatial Variability of Average Annual and Monthly Minimum River Flow in Poland

Abstract

The aim of this article is to analyse the spatial variability of SNQ, the average annual minimum river flow, as well as SNQm (m = 1, 2, …12), the average monthly minimum river flow in Poland. The data were obtained from the Institute of Meteorology and Water Management – National Research Institute (IMWM-NRI) in the form of the daily flow series from the period between 01 Nov 1990 and 31 Oct 2020 from 433 gauging cross-sections located within the territory of Poland. The results of the analyses are presented on maps of the physiographic regions of Poland (the Coastlands, the Lakelands, the Lowlands, the Highlands, the Carpathians and the Sudety Mountains). In order to compare SNqm – the unit average minimum monthly flow between the physiographic regions, the Kruskal-Wallis test with the Dunn (Bonferroni) adjustment was performed. In order to evaluate the spatial variability of the SNqm, the hypothesis was verified for each gauging station that the Spearman correlation coefficient between the SNqm and the zero point of the gauge was different from zero. The SNqm flow changed over the year. As expected, the highest values were observed in March and April, and the lowest in July and August. Regardless of the month, the rivers in the central part of Poland (the Lowlands) were less water abundant than those in other regions of the country while the greatest flows were observed in the mountain rivers. Statistically, no difference was observed between the SNqm in the Coastlands, the Carpathians and the Sudety Mts., and in nearly all of the months between the SNqm in the Lakelands and the Lowlands. In the whole territory of Poland, the river flow was dependent on the altitude of the catchment, while the strongest correlation was observed in the mountain regions.

Full text

Katarzyna Baran-Gurgul1
ORCID: 0000-0003-0247-6136
Katarzyna Kołodziejczyk2
ORCID: 0000-0003-1918-9344
Agnieszka Rutkowska3
ORCID: 0000-0002-5418-5659
SPATIAL VARIABILITY OF AVERAGE ANNUAL
AND MONTHLY MINIMUM RIVER FLOW IN POLAND
1 PK Cracow University of Technology, Faculty of Environmental and Energy Engineering,
Department of Geoengineering and Water Management, Poland
Katarzyna.Baran-Gurgul@pk.edu.pl
2 PK Cracow University of Technology, Faculty of Environmental and Energy Engineering,
Department of Geoengineering and Water Management, Poland
3 University of Agriculture in Kraków, Faculty of Environmental Engineering and Land Surveying,
Department of Applied Mathematics
Abstract
The aim of this article is to analyse the spatial variability of SNQ, the average annual minimum river ow, as well as SNQm
(m = 1, 2, …12), the average monthly minimum river ow in Poland.
The data were obtained from the Institute of Meteorology and Water Management – National Research Institute (IMWM-NRI)
in the form of the daily ow series from the period between 01 Nov 1990 and 31 Oct 2020 from 433 gauging cross-sections
located within the territory of Poland. The results of the analyses are presented on maps of the physiographic regions of Poland
(the Coastlands, the Lakelands, the Lowlands, the Highlands, the Carpathians and the Sudety Mountains).
In order to compare SNqm – the unit average minimum monthly ow between the physiographic regions, the Kruskal-Wallis
test with the Dunn (Bonferroni) adjustment was performed. In order to evaluate the spatial variability of the SNqm, the hypo-
thesis was veried for each gauging station that the Spearman correlation coecient between the SNqm and the zero point of
the gauge was dierent from zero.
The SNqm ow changed over the year. As expected, the highest values were observed in March and April, and the lowest
in July and August. Regardless of the month, the rivers in the central part of Poland (the Lowlands) were less water abundant
than those in other regions of the country while the greatest ows were observed in the mountain rivers.
Statistically, no dierence was observed between the SNqm in the Coastlands, the Carpathians and the Sudety Mts., and
in nearly all of the months between the SNQm in the Lakelands and the Lowlands.
In the whole territory of Poland, the river ow was dependent on the altitude of the catchment, while the strongest correlation
was observed in the mountain regions.
Keywords: SNQm, average annual river ow, spatial variability, regional variability
GEOINFORMATICA POLONICA
22: 2023
DOI 10.4467/21995923GP.23.001.18600

PRZESTRZENNE ZRÓŻNICOWANIE ŚREDNIEGO MINIMALNEGO
ROCZNEGO PRZEPŁYWU NA OBSZARZE POLSKI
Abstrakt
Celem pracy jest ocena przestrzennego zróżnicowania średniego minimalnego rocznego przepływu SNQ, a także przepływu
SNQm (m = 1, 2, …12) w poszczególnych miesiącach w Polsce.
W pracy wykorzystano pozyskane z IMGW-PIB ciągi dobowych przepływów z okresu od 1.11.1990 do 31.10.2020 roku
w 433 przekrojach wodowskazowych zlokalizowanych na obszarze Polski. Wyniki analiz przedstawiono na mapach na tle re-
gionów zycznogeogracznych (pobrzeża, pojezierza, niziny, wyżyny, Karpaty i Sudety).
Do porównania średnich SNq
m
w każdym miesiącu, między regionami zycznogeogracznymi wykorzystano test Kruskala-
-Wallisa z poprawką Dunna (Bonferroniego), a do oceny siły zróżnicowania przestrzennego przepływów SNq
m
określono
współczynnik korelacji Spearmana między SNqm a wysokością położenia zera wodowskazu, a także zwerykowano hipotezę
o istotności tego współczynnika.
W ciągu roku przepływ SNqm zmienia się; spodziewanie największe wartości obserwuje się w marcu i kwietniu, a najniższe
w lipcu i sierpniu. Zdecydowanie najmniej zasobne w wodę są, niezależnie od miesiąca, rzeki środkowej i nizinnej części Polski,
a największe przepływy obserwuje się w rzekach górskich.
Nie obserwuje się statystycznej różnicy między SNqm na pobrzeżach, w Karpatach oraz Sudetach i w prawie wszystkich
miesiącach między pojezierzami i nizinami.
Na obszarze Polski przepływ zależy od wysokości położenia zlewni, przy czym najsilniejsza zależność występuje w ob-
szarach górskich.
Słowa kluczowe: SNQm, średni minimalny roczny przepływ, zróżnicowanie przestrzenne, zróżnicowanie regionalne
1. INTRODUCTION
One of the most crucial aspects involved in the pre-
servation of water resources is ensuring that water or-
ganisms have optimal conditions to live. This issue has
been found at the centre of many European directives
and national legal acts. In Polish hydrology and water
management, there is a notion of ‘characteristic ows’
which denotes the values of some ow characteristics at
a river cross-section. Among such ows, the following
may be distinguished: SNQ – the mean ow calculated
from the minimum annual ows in a multiannual period
and SNQm (m = 1,2, …, 12) – the mean monthly ow
calculated from the monthly minimum ows in a mul-
tiannual period [1].
According to the Polish Water Law Act [2], the SNQ
ow provides the basis for calculating the charges for
water services and consumption. This cost consists of
a xed rate and a variable rate dependent on the amount
of consumed surface water (art. 270, 271, 274). The rate
for water services depends, respectively, on the amount
of consumed water, water source (meaning whether
the water has been sourced from the surface or under-
ground), its intended use, and its average low ow from
the multiannual period SNQ, whereby a multiannual
period consists of at least 20 hydrological years [2] (ar-
ticle 270, point 6).
In Poland, the SNQ or SNQm ows are also used in
calculating the minimum required ow and the ecolo-
gical ow, as well as dening the streamow drought
(especially in older publications).
Streamow drought is most commonly dened as
a continuous period during which streamow at a given
cross-section is below Q
g
, an assumed threshold ow
[3, 4, 5, 6]. In their research, many Polish authors
[4, 7–15] assume SNQ as the Q
g
ow. Zielińska [16] de-
ned streamow drought as a continuous period during
which streamow at a given cross section is below the
SNQ and distinguished summer and winter droughts,
based on their origin. Summer streamow droughts re-
sult from the prolonged lack of atmospheric precipita-
tion, combined with high air temperatures and intense
evaporation. Winter streamow droughts, on the other
hand, start in rivers at sub-zero air temperatures or result
from the prolonged lack of precipitation during autumn
(surface runo stops because snowfall becomes retained
on the surface). The lowest ows occur in frozen rivers.
The SNQ ow, as well as the minimum annual ows
in the rivers of Poland, have been the subject of stud-
ies of several authors. Stachý at al. [17] proposed the
8KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

9SPATIAL VARIABILITY OF AVERAGE ANNUAL AND MONTHLY MINIMUM RIVER FLOW IN POLAND
direct method, the method based on multiple correlation
and the methods based on interpolation and extrapola-
tion of mean minimum ows while, Ozga-Zieliński and
Walczykiewicz [1] carried out the analysis of the meth-
ods for calculating the SNQ. The methods depend on the
length of the series in a multiannual period and phys-
iographic catchment characteristics. Wałęga et al. [18]
veried the applicability of the Punzet and Stachý for-
mulas in several mountain catchments. Wałęga and
Młyński [19] analysed the seasonality of the minimum
ows, while Banasik et al. [20] proved the decrease of
the SNQ value in the last 30-year period in two lowland
catchments.
The minimum required ow Qn was used in Poland
since the 1960s. There are several denitions of Q
n
in lit-
erature, for example by Kostrzewa [21], Witowski [22],
the Małopolska school [23], the Wrocław school [24],
Florkowski [23], or the National Foundation for Envi-
ronmental Protection and Water Management [25]. The
most commonly used denition is the one formulated
by Kostrzewa [21] according to which the minimum
required ow is the amount of water expressed in m3·s–1,
which should be maintained as minimum in a given
cross-section due to biological and social circumstances.
This ow is dened based on two criteria [21]:
• the hydrobiological criterion – Qn is calculated as
the product of the SNQ ow and the coecient
dependent on the hydrological type of the river
and its catchment area, and
• the shing criterion aiming at estimating the nec-
essary amount of water within a streambed needed
for the ichthyofauna to develop well. The ow Qn
is determined based on the SNQm analysis in par-
ticular phases of the sh life cycle, for the follow-
ing three phases during the year: spawning and
reproduction, preying and the development of ju-
venile sh, and nally hibernation.
The SNQ ow also serves as the basis for calculat-
ing the minimum required ow in case of applying the
methods by Florkowski or by the National Foundation
for Environmental Protection and Water Management,
whereas Stochliński utilizes the SNQm in the Małopol-
ska method.
In Poland, the minimum required ow is currently
a priority in terms of water use, which results from the
regulations of the directors of the Regional Water Man-
agement Board (RWMB) who decide on the conditions
on the use of water in particular water regions. It is the
responsibility of all users under the concession to abide
by them [2] (article 403, point 2, subpoint 11).
As aforementioned, there are several methods of cal-
culating Q
n
in Poland, however currently there is no one
standardised methodology. Polish Water Law does not
specify any denitions of the minimum required ow
either. The values of this type of ow are, on the other
hand, determined in two special cases [2] (article 403,
points 7 and 8):
a) for permits required by the Polish Water Law Act
granted for the needs of rearing or breeding of
sh or other aquatic organisms – the minimum
required ow should be at 50% of the SNQ,
b) and in case of using recycled water, the mini-
mum required ow may be decreased by 50% of
the SNQ.
The introduction of the term ‘ecological ow’ orig-
inates from the Water Framework Directive and Guid-
ance Document No 31 [26]. This type of ow is dened
in dierent ways. For example, Tharme [27] denes it
as a ow which should remain within the river system
or be supplied to it in order to maintain the good condi-
tion of water in the riverbeds, nearshore zones, marshes,
oodplains or the river mouth.
Depending on the scale of the analysed location,
available data, the time allocated for the assessment
as well as the technical and nancial capacity, it is
possible to apply dierent methods of establishing the
requirements of the ecological ow [28]. At the mo-
ment, in the world, over 200 methods of designing the
ecological ow have been proposed. These methods
may be divided into the following groups [27–31]: hy-
drological, hydraulic, habitat, holistic. Thanks to its
simplicity, the most commonly used category of de-
signing ecological ows in the world are hydrological
methods which are based mainly on the historical ow
series [28]. Hydrological methods are based on val-
ues such as: average ows (average annual or average
low ow) or the values achieved from the ow dura-
tion curve at dierent time scales (annual, seasonal, or
monthly) as well as the geomorphological characteris-
tics of the catchment (area, stream gradient, etc.). One
of the methods of this type is the simplied method by
Kostrzewa based on the SNQ.
In Poland, ecological ow is dened for a bioperiod
in a selected cross-section of the studied catchment as:

Q
e,b
= p
b
· SNQ
b
· A, where: p
b
is a tabularised value
of the coecient for control catchments, determined
based on pilot studies for a given ichthyological type of
river and particular bioperiods, SNQb is a unit average
low runo in the bioperiod determined by relating the
SNQb of a given stream in a studied catchment to A, the
catchment area A to cross-section [32].
To date, there have been a large number of pub-
lications on the subject of low ows and streamow
drought – some of them also on the scale of the whole
country. For example, Stachý et al. [7, 8] assessed the
magnitude of runo in Poland and presented it, in form
of maps, the average annual (SNQ) and the lowest an-
nual (NNq) unit runos from the area of Poland from
the 20-year period between 1951 and 1970.
Usually studies are carried out on a single river [12,
14, 15] or possibly several selected regions of Poland
[33–35]. However, most of the older works were based
on short multiannual periods and did not include a large
number of stream gauges. This publication, unlike the
aforementioned works, is based on complete and long
daily series of ows from the last 30-year hydrological
period, with data measured in over 400 cross-sections
located throughout Poland.
Stachý et al. [7, 8] calculated the number of occur-
rences of ows lower than the SNQ in particular months
for 180 gauging cross-sections. The month or the group
of months with the highest number of ows lower than
the SNQ was recognised as the typical period of oc-
currence of streamow drought. Streamow drought
was divided into early-winter (November-December),
winter (January-February), summer (June through Au-
gust) and autumn (September-October). It was also
observed that the lowest values of the SNq
m
(below
0.1 dm
3
∙s
–1
∙km
–2
) occurred in the region between the
middle Oder and the middle Warta, the runos below
0.5 dm
3
∙s
–1
∙km
–2
, dominate in the Lowlands, while in
the uplands and the mountains – they do not exceed
0.5 dm
3
∙s
–1
∙km
–2
. Runos below 1 dm
3
∙s
–1
∙km
–2
occur
primarily in the Sudety Mts. and the Carpathians, as
well as in the Pomeranian Lakeland. Also, Zielińska
[16] considered the region of the Polish Lowland as one
of the greatest and long-lasting hydrological droughts.
The SNQ ow is, therefore, one of the most import-
ant hydrological characteristics necessary to complete
hydrological documentation which form the basis of
planning and design in terms of water engineering, pre-
venting the eects of drought and managing the inland
surface water resources, including granting administra-
tive decisions [1].
The aim of this work is to analyse the spatial vari-
ability of the SNq and SNq
m
(m = 1, 2, …12) – the
unit average annual minimum ow SNQ, as well as
the and the unit average monthly minimum river ow
in Poland.
2. DATA AND METHODS
The series of average daily ows were used from
the period between 1st November 1990 and 31st Octo-
ber 2020 (30 hydrological years) at 433 gauging cross-
-sections located throughout Poland. The data were
obtained from the IMWM-NRI. The location of the
cross-sections is presented in Fig. 1, on the map of Po-
land divided into physiographic regions based on Solon
et al. [36]: the Coastlands, the Lakelands, the Lowlands,
the Uplands, the Carpathians and the Sudety Mts. In
order to compare the average ows in dierent gauging
cross-sections, their values were standardised by divid-
ing by the catchment areas.
The catchments analysed in this study were located
throughout Poland. The area of the country is inclined
from south east towards north west. The Lowlands are
located in the north and central Poland, whereas the
mountains and the Highlands in the south.
Lowland terrain dominates in Poland – approxi-
mately 75% of its area is located below 200 m a.s.l.
The most of the gauges (311 out of 433) were located
in the lowlands, out of which three lay below the sea
level (Tczew on the Vistula, Trzebiatów on the Reda
and Bągart on the Elbląg). 111 gauges were highland
cross-sections (located at the altitudes between 200
and 500 m a.s.l.), whereas the remaining 11 lay in the
mountains. The gauge located at the highest altitude
was Jakuszyce on the Kamienna (H = 849.5 m a.s.l.).
The catchment areas decreased as the altitudes of the
location of the zero points of gauges increased, as the
Spearman rank correlation coecient was -0.369 and
was statistically signicant (Fig. 2).
Approximately a quarter (119 out of 433) of catch-
ments had areas below 300 km
2
, which means they
may be considered small. The areas of the 140 out of
314 catchments were below 1,000 km
2
. Several very large
catchments were analysed in this study – the areas of
42 catchments were above 10,000 km
2
, while there were
12 catchments with the area exceeding 50,000 km2.
10 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

Fig. 1. Location of gauging cross-sections in Poland with information on the gauging station elevation H [m a.s.l] based on
physiographic regions according to the regionalization of Solon et al [36]
Ryc. 1. Położenie wodowskazów w Polsce wraz z informacją o wysokości H położenia zera tych wodowskazów, H [m n.p.m.]
na tle regionów zycznogeogracznych, zgodnie z regionalizacją Solona i in. [36]
Fig. 2. Scatterplot that shows the relationship between catchment area A and gauging station elevation H; rS is a Spearman cor-
relation coecient, asterisk * means a signicant correlation (at the signicance level α = 0.05)
Ryc. 2. Wykres rozrzutu przedstawiający zależność powierzchni zlewni A zamkniętej przekrojem wodowskazowym od wyso-
kości H położenia zera tych wodowskazów; rS jest współczynnikiem korelacji Spearmana, a symbol * oznacza korelację istotną
statystycznie (na poziomie istotności α = 0.05)
11SPATIAL VARIABILITY OF AVERAGE ANNUAL AND MONTHLY MINIMUM RIVER FLOW IN POLAND

Based on the series of daily ows, the series of
monthly minimal ows was obtained, rst for each
month separately, m = 1, 2, ..., 12. Then the unit aver-
age monthly minimum ow SNqm, m = 1, 2, …, 12 was
computed by division of the average value of these min-
ima by the catchment area. These ows were superim-
posed on the map of Poland divided into physiographic
regions [36] and global regional average SNqm
mean, min-
imum SNqm
min and maximum SNqm
max values observed in
physiographic regions were also determined. The aver-
age annual minimum ow SNQ was also calculated, and
then the unit average annual minimum ow SNq was
computed as the division of SNQ by the catchment area.
For each month, the SNqm were compared between
physiographic regions [36] using the Kruskal-Wallis
test with Dunn (Bonferroni) adjustment at the signif-
icance level of α = 5%.
The Kruskal–Wallis rank sum test is a non-paramet-
ric method for testing whether samples originate from
the same distribution. The null hypothesis for this test
is that there is no dierence in the median values of the
considered groups and the alternative hypothesis is that
at least one population median of one group is dierent
from the population median of at least one other group.
If the results of a Kruskal-Wallis test are statistically
signicant, then it is appropriate to conduct post hoc
test (Dunn’s test) to determine exactly which groups
are dierent [37].
The Bonferroni adjustment is a method that allows
many comparison statements to be made while still as-
suring the overall condence coecient is maintained
[38]. If multiple hypotheses are tested, the probability
of observing a rare event increases, and therefore, the
likelihood of incorrectly rejecting a null hypothesis (and
making a type I error) increases. The Bonferroni correc-
tion compensates for that increase by testing each indi-
vidual hypothesis at a signicance level of α/m, where
α is the desired overall alpha level and m is the number
of hypotheses.
For the evaluation of the spatial variability of the
SNq
m
ows, the Spearman correlation coecient was
calculated between the SNqm and the zero point of the
gauge. The hypothesis that the coecient is dierent
from zero was also veried.
All statistical calculations were performed using the
GNU R software package [39]. For all the tests consid-
ered in the paper, the signicance level α = 0.05 was
assumed.
3. RESULTS
In each of the 433 studied gauging cross-sections,
the unit average monthly ows SNqm, m = 1, 2, …, 12
were calculated. For each month, a spatial distribution
of SNqm was depicted on the map of Poland with phys-
iographic regions (Fig. 3 and 4). In each month, the
range of SNq
m
was divided into ve categories and a his-
togram of SNqm was also plotted. In order to compare
the maps, the ranges of SNqm values divided into ve
categories are marked blue, green, yellow, orange and
red (from the lowest to the highest SNqm values).
During year, the SNq
m
changed expectedly.
The highest average area values of SNq
m
occurred
during the time of spring thaw – in March and April
(the medians of SNq
m
in these months were above
5.5 dm
3
s
–1
km
–2
, while the average values – approxi-
mately 6.3 dm3s–1km–2). In turn, the lowest values were
observed in summer and autumn – between July and
September (the medians of SNqm in these months were
above 2.7–2.8 dm3s–1km–2, while the average values –
3.2–3.6 dm3s–1km–2) (Fig. 5).
Regardless of the month, the most of the observed
SNq
m
ows belonged to the two rst categories (blue
and green spots on maps and blue and green bars in
histograms). In January, February and March, these
owsmade up between 75 and 82% of all ows, in
September, October, November and December between
85 and 88%, whereas in the remaining months – be-
tween 92 and 98%.
In all months, the lowest average SNqm ows were
observed in the Lowlands (boxplots in Figures 3 and 4),
higher values were observed in the Lakelands and the
Uplands, and the highest ones – in the Coastlands, the
Carpathians and the Sudety Mts.
In all of the maps, the highest SNqm ows occurred
rarely (red spots). Their fraction was not above 0.9%
of all ows, while their values substantially exceed-
ed the SNq
m
values in the remaining part of Poland.
Such values were also observed in higher parts of the
mountains.
High values of the SNq
m
(red, orange and yellow
spots in the maps – Fig. 3 and 4) were usually observed
in the south and south-western part of the country, as
well as in the north of Poland. The lowest values of
the SNqm occurred mostly in the central part of Poland.
Because the land elevation throughout the country in-
creases from north-west towards the south, it may seem
12 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

Fig. 3. Spatial distributions of the average monthly SNqm flow in Poland, from January to June, along with histograms
and box-whisker plots for individual physiographic regions; the colours of the gauging stations (points on the map)
correspond to the colours of histogram bars, and the colours of regions correspond to the colours of boxplots
Ryc. 3. Przestrzenne rozkłady średnich miesięcznych przepływów SNqm na obszarze Polski, od stycznia do czerwca,
wraz z histogramami i wykresami typu pudełko-wąsy dla poszczególnych regionów fizyczno-geograficznych; kolory
stacji wodowskazowych odpowiadają kolorom na histogramach, a kolory regionów – kolorom na wykresach typu
pudełko-wąsy
Fig. 3. Spatial distributions of the average monthly SNq
m
ow in Poland, from January to June, along with histograms and
box-whisker plots for individual physiographic regions; the colours of the gauging stations (points on the map) correspond to
the colours of histogram bars, and the colours of regions correspond to the colours of boxplots
Ryc. 3. Przestrzenne rozkłady średnich miesięcznych przepływów SNqm na obszarze Polski od stycznia do czerwca wraz z hi-
stogramami i wykresami typu pudełko-wąsy dla poszczególnych regionów zycznogeogracznych; kolory stacji wodowska-
zowych odpowiadają kolorom na histogramach, a kolory regionów – kolorom na wykresach typu pudełko-wąsy
13SPATIAL VARIABILITY OF AVERAGE ANNUAL AND MONTHLY MINIMUM RIVER FLOW IN POLAND

Fig. 4. Spatial distributions of the average monthly SNqm flow in Poland, from July to December, along with
histograms and box-whisker charts for individual physiographic regions; the colors of the gauging stations (points on
the map) correspond to the colors of histogram bars, and colors of regions correspond to colors of boxplots
Ryc. 4. Przestrzenne rozkłady średnich miesięcznych przepływów SNqm na obszarze Polski od lipca do grudnia wraz z
histogramami i wykresami typu pudełko-wąsy dla poszczególnych regionów fizyczno-geograficznych; kolory stacji
wodowskazowych odpowiadają kolorom na histogramach, a kolory regionów – kolorom na wykresach typu pudełko-
wąsy
Fig. 4. Spatial distributions of the average monthly SNqm ow in Poland, from July to December, along with histograms and
box-whisker charts for individual physiographic regions; the colors of the gauging stations (points on the map) correspond to
the colors of histogram bars, and colors of regions correspond to colors of boxplots
Ryc. 4. Przestrzenne rozkłady średnich miesięcznych przepływów SNqm na obszarze Polski od lipca do grudnia wraz z histogra-
mami i wykresami typu pudełko-wąsy dla poszczególnych regionów zycznogeogracznych; kolory stacji wodowskazowych
odpowiadają kolorom na histogramach, a kolory regionów – kolorom na wykresach typu pudełko-wąsy
14 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

that the correlation between the SNqm and the elevation
should not be high. Indeed, the Spearman correlations
between SNqm and the altitude of the zero point of the
gauges were not high, however in all months, they were
positive and statistically signicant (Table 1).
The maximum of the average regional values of
SNqm, were observed in the Carpathians and the Sude-
ty Mts. in April; in the remaining regions – in March,
while the minimum occurred in all of the regions in
August (Fig. 6a). The highest regional values of the
SNqm exceeded 10 dm3∙s–1∙km–2 in the Carpathians and
the Sudety Mts., which in terms of the gures were
nearly 8 dm3s–1km–2 in the Coastlands, approximately
5 dm3∙s∙km–2 in the Lakelands and the Uplands, and be-
low 5 dm3s–1km–2 in the Lowlands.
The maximum of the lowest regional values of the
SNqm was observed in March, while in the Uplands in
April. The minimum values were observed in July (the
Lowlands and the Lakelands), August (the Uplands)
and September (the Carpathians, the Sudety Mts. and
the Coastlands) (Fig. 6b). It can also be observed that
the values of the highest minimum (regional) SNq
m
in the Carpathians were signicantly higher during the
whole year than anywhere else in Poland.
The highest regional values of the SNqm, observed
in the Carpathians and the Sudety Mts., were markedly
higher compared to other regions, whereas during the
months of thaw, they exceeded 25 dm3s–1km–2 (Fig. 6c).
In order to better visualize the variability of the SNq
m
during year, the number of gauging stations with the
lowest (Fig. 7a) and the highest (Fig. 7b) values of the
SNqm was computed for each month separately.
As expected, the largest number of gauges (in all
regions) showed the minimum values of the SNq
m
at
the end of summer (in all regions, most frequently in
August), while the maximum values of the SNqm were
found at the beginning of spring (in all regions, most
frequently in March).
Regardless of the month, the lowest average SNqm
ows were observed in the Lowlands (boxplots in Fig-
ures 3 and 4), while higher ones were in the Lakelands
and the Uplands, and the highest – in the Coastlands,
the Carpathians and the Sudety Mts.
In order to verify whether the SNqm diered signi-
cantly in particular regions, the Kruskal-Wallis test was
applied. In all of the months, the p-value of the test
was below 2.20E-16 (Table 2) which implies that in all
months the SNqm diered between the six regions.
In order to recognize the pairs of regions where the
medians of the SNq
m
diered, the post-hoc Dunn test
(with Bonferroni adjustment) was applied. Results were
given in Table 2.
Fig. 5. Distribution of the average monthly SNqm ow in Poland
Ryc. 5. Rozkład średniego miesięcznego przepływu SNqm na obszarze Polski
Table. 1. The Spearman correlation coecient between SNqm and H; asterisk * shows a signicant correlation (at the signi-
cance level α = 0.05)
Tabela 1. Współczynnik korelacji Spearmana między SNqm a wysokością położenia zera wodowskazu; * oznacza korelację
istotną statystycznie (na poziomie istotności α = 0.05)
month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
r0.065* 0.081* 0.219* 0.256* 0.246* 0.276* 0.250* 0.213* 0.202* 0.197* 0.187* 0.106*
15SPATIAL VARIABILITY OF AVERAGE ANNUAL AND MONTHLY MINIMUM RIVER FLOW IN POLAND

In 61 out of 180 analysed cases (15 paired regions
× 12 months) it was conrmed that the SNqm ows did
not dier between regions. No dierence was shown
in all months between the median of the SNq
m
in the
Coastlands, the Carpathians or the Sudety Mts. In most
of the year (apart from January and February), there
was no dierence either between the SNq
m
in the Lakelands
and Lowlands. Interestingly, for most of the year the signi-
cant dierence between median SNq
m
can be observed
in the Uplands and the Mountains (Uplands – Carpathi-
ans from November to July, and Uplands – Sudety Mts.
from November to May).
Fig. 6. SNqm values: a) average, b) the lowest, c) the highest observed in particular physiographic regions
Ryc. 6. Wartości SNq
m
: a) średnia b) najmniejsza, c) maksymalna zaobserwowana w poszczególnych regionach zyczno-
geogracznych
Fig. 7. The relative number of catchments with (a) the lowest and (b) the highest values of the SNqm in physiographic regions
Ryc. 7. Względna liczba zlewni, w których zaobserwowano: (a) najmniejszą wartość SNqm, (b) największą wartość SNqm w re-
gionach zycznogeogracznych
16 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

4. SUMMARY AND DISCUSSION
The dierences between geophysical regions in the
SNQm are mainly triggered by the spatial variability of
precipitation that is usually higher in Lakelands and
Coastlands than in Lowlands. This relation can be ob-
served mainly in winter months (Figures 3 and 4).
The central part of Poland is dominated by the Warta
River in the west and the Wieprz River in the east, togeth-
er with their tributaries. However both river basins are
under stress of permanent water scarcity due to very low
precipitation and intensive water use for industrial and
agriculture purposes (Warta), and intensive agriculture
production and steppization (Wieprz). These factors are
the main causes of very low SNQm values in all months
in the belt that comprises of the western part of the Lake-
lands and Lowlands and the eastern part of the Lowlands.
High SNQ
m
, values were observed in the Carpathians
which follows from the auence of aquifers. Bartnik
[40] notes that the main characteristic of the Carpathi-
an area is that the major role is played by precipitation
and evaporation processes in the formation of runo (as
compared with other parts of Poland). In the southern
part (the Carpathians and the Sudety Mountains) the
SNQm was relatively high at the end of winter and be-
ginning of spring. This might be explained by mountain
snowpack melting that contributes to the increase of
river discharges in the region.
Various methods of analyzing very low river ows
are used around the world. In the USA, the most widely
used river ow is 7Q10, which is dened as the lowest
7-day average with 10-year return period, using daily
discharge data [41]. In Europe, most commonly used
ows with the probability of exeedance equalling 70%,
Table 2. The results of the Kruskal-Wallis test (the last two lines) and the p-values of the multiple comparison post-hoc Dunn test
with the Bonferroni adjustment; the p-values less than 0.05 proved of signicant dierences between the SNqm median among
the physiographic regions in particular months
Tabela 2. Wyniki testu Kruskala-Wallisa i testu wielokrotnych porównań post-hoc Dunn z poprawką Bonferroniego (wartości p);
wartości p mniejsze niż 0.05 świadczą o istnieniu istotnych różnic między medianą SNq
m
pomiędzy regionami zyczno-
geogracznymi w konkretnych miesiącach
No Regions Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1Coastlands – Lakelands 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2Coastlands – Lowlands 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
3Lakelands – Lowlands 0.011 0.008 0.143 0.123 0.848 1.000 1.000 1.000 1.000 1.000 1.000 0.127
4Coastlands – Uplands 0.000 0.000 0.000 0.001 0.010 0.234 0.094 0.040 0.009 0.012 0.000 0.000
5Lakelands – Uplands 1.000 1.000 1.000 1.000 0.094 0.000 0.000 0.000 0.001 0.001 0.020 1.000
6Lowlands – Uplands 0.018 0.025 0.006 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002
7Coastlands – Carpathians 0.056 0.371 0.852 0.048 0.515 0.654 1.000 1.000 1.000 1.000 1.000 0.258
8Lakelands – Carpathians 0.026 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
9Lowlands – Carpathians 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
10 Uplands – Carpathians 0.012 0.000 0.000 0.000 0.000 0.001 0.012 0.071 0.166 0.271 0.001 0.010
11 Coastlands – Sudety Mts. 1.000 1.000 0.756 0.228 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
12 Lakelands – Sudety Mts. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
13 Lowlands – Sudety Mts. 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
14 Uplands – Sudety Mts. 0.000 0.000 0.000 0.000 0.002 0.094 0.161 0.386 0.042 0.066 0.011 0.000
15 Carpathians – Sudety Mts. 0.197 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Kruskal-Wallis statistic 139.4 151.5 168.8 156.8 139.4 143.0 142.5 132.7 132.3 118.1 140.0 133.9
p-value < 2.20E–16
17SPATIAL VARIABILITY OF AVERAGE ANNUAL AND MONTHLY MINIMUM RIVER FLOW IN POLAND

90%, 95% [42]. In Russia the widely used indices are
1-day and 30-day summer and winter low ows [43].
Our results are based on continuous time series data
recorded at 433 stations. However, other databases that
were generated using novel methods based on arti-
cial intelligence, namely neural network algorithms,
can be also used in the future [44–46], for example, in
the USA National Water Model (NWM) retrospective
simulations are used [47]. Such databases have a very
ne spatial resolution and a global spatial coverage. As
regards the SNQ ows in the territory of Poland, such
databases can be used at places without river ow mea-
surements, e.g. in assessing the risk of drought.
For the purpose of this study, a much larger number
of gauges, as compared to previous works, was used and
the SNq and SNqm ows were determined in rivers from
six physiographic regions in Poland: the Coastlands, the
Lakelands, the Lowlands, the Uplands, the Carpathians
and the Sudety Mts.
During the year, the SNqm changed. In March, thaw
is observed in the whole country, however it is dierent
in various regions which inuenced the variability of
SNqm. The SNqm in March reached its maximum value
in the Coastlands, the Lakelands, the Lowlands, and
the Uplands, however it was not yet the highest in the
mountains. In April the thaw water runo could be still
observed in Poland, whereas the highest SNq
m
values
were noticed in the Carpathians and the Sudety Mts.
In May, after the thaw wave had passed, the SNqm, de-
creased in the whole country. The lowest values of the
SNq
m
occurred in the Lakelands and the Lowlands how-
ever, a large runo was still observed in the mountains
where thaw water was running down. In the following
months, especially in central Poland, the SNqm values
decreased which was the result of the lowering of pre-
cipitation, increasing air temperatures, evaporation and
transpiration. In the whole country, the smallest values
SNqm were observed in August, when the average re-
gional SNq
m
reached their annual minimum. In Septem-
ber, average runos increased their values to a small
degree, which was the result of the autumn precipitation
and low evaporation (especially in mountains). In winter
in the Carpathian and the Sudety Mts., long streamow
droughts often occurred, while in the remaining areas –
mainly in the Lowlands and the Lakelands – low levels
of rivers persisted. In October, streamow droughts did
not occur in such a large part of the country, which was
mainly due to the lower loss for evaporation. In the next
months (November, December, January), the runos in-
creased. However, in the Sudety Mts. and Carpathians,
the increase in SNqm was not very high because a part of
precipitation was accumulated as snowfall. In February,
thaw began in the whole of the country which intensi-
ed the runo. In mountains, owing to the persisting
low temperatures, runo increased later.
Similar conclusions were drawn by Bartnik [11]
who observed that the highest SNqm in Poland occurred
in the early spring – mainly in March, while the lowest –
mainly towards the end of summer (in August), and in
the Sudety Mts. at the turn of August and September.
Stachý et al. [7], in turn, emphasised that in Poland
summer and autumn streamow droughts were predom-
inant, whereas early-winter and winter ones occurred
mostly in the Upper Vistula catchment.
The rivers of the central part of Poland (the Low-
lands) were signicantly the least abundant in water,
while the greatest ows were observed in the mountain
rivers as well as the rivers of the Coastlands.
5. CONCLUSIONS
The spatial and temporal distribution of extremes are
very important in analyses of low ow, including SNQ.
This paper is a continuation of the research on the
temporal and spatial variability of characteristic ows
(monthly, annual) in Polish rivers, in regional approach.
In the previous article [48], it was shown, among oth-
ers, that average unit ows are statistically signicantly
positively correlated with the height of the water gauge
(with the highest values in the mountains and in the
Coantlands). Usually the smallest SNQ
m
occurred in
the central Poland – in Wielkopolska and in the Ma-
zowsze Lowland as well, and the largest values were
in the Mountains and in the Coastlands. Interestingly,
there was no signicant dierence in the SNqm between
the Coastlands, the Carpathians and the Sudety Mts.
In most months (all apart from January and February)
the dierence was not signicant between the Lake-
lands and the Lowlands. Because of the relatively high
ows in the Coastlands, the average low ow in each
of the months was not very strongly correlated with the
altitude (however signicantly and positively). This
means that in the whole of Poland the ow depended
on the location of the catchment, while the strongest
correlation occurred in the mountain areas. It appears
that the distribution of SNq
m
depends not only on the
18 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA

climatic conditions, but it results from overlapping hy-
drogeological and climatic conditions with anthropo-
genic activity.
The maps presented in this work can also be used as
a background to more detailed interregional analysis.
Research results can also be applied in various designs
and tasks relating to determining to the volume and use
of water resources.
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20 KATARZYNA BARAN-GURGUL, KATARZYNA KOŁODZIEJCZYK, AGNIESZKA RUTKOWSKA