The Analysis of Long-Term Trends in the Meteorological and Hydrological Drought Occurrences Using Non-Parametric Methods—Case Study of the Catchment of the Upper Note´c River (Central Poland)

: The study aims to identify long-term trends in the changes of drought occurrences using the Mann-Kendall (MK) test and the Theil-Sen estimator. Trend research was carried out on the example of the catchment area of the Upper Note´c River, which covers an agricultural area of Poland with some of the lowest water reserves. The meteorological droughts were identiﬁed based on the Standardized Precipitation Index (SPI), while the hydrological droughts were determined on the basis of the Standardized Runoff Index (SRI) in various time scales (1, 3, 6, 9 and 12 months) in the period of 1981–2016. The relationship between SPI and SRI was determined on the basis of the Pearson correlation analysis. The results showed that statistically signiﬁcant trends (at the signiﬁcance level of 0.05) were identiﬁed at 3 out of 8 meteorological stations (downward trend at Kłodawa station and upward trend for drought at Sompolno and Kołuda Wielka stations). Statistically signiﬁcant hydrological droughts showed an increase in occurrences at the Łysek station, while a downward trend was noted at the No´c Kalina station. No trend was found at the Pako´s´c station. The analysis of the correlation between meteorological and hydrological droughts showed a strong relationship in dry years. The maximum correlation coefﬁcient was identiﬁed in longer accumulation periods i.e., 6 and 9 months. The example of the catchment of the Upper Note´c River points to the necessity of using several indicators in order to assess the actual condition of the water reserves.


Introduction
Drought is a natural disaster characterized by long-term water scarcity [1][2][3]. Drought is one of the most serious natural threats that causes damage to various aspects of the environment, society, and economy [4,5]. No universal definition of drought has been established due to the wide variability in water supply and demand worldwide [6,7]. There are four categories of drought in the literature: meteorological, agricultural, hydrological, and socioeconomic [8][9][10][11][12][13]. Drought damage is a serious issue in numerous countries around the world. Due to its nature, drought is difficult to monitor, and its effects are often poorly documented. Among the various sectors of the economy, agriculture is one of the most vulnerable to drought, where its effects are also most noticeable [14][15][16]. Numerous reports and scientific articles indicate that forecasts of future climate conditions suggest an increase in the frequency and intensity of droughts in some regions of the world [17][18][19][20][21]. The increase in the frequency of drought occurrence in recent years has not been limited to arid and semi-arid regions [22][23][24][25][26], but has been gradually becoming more common in The obtained results will help the departments of state administration, responsible for water resources management, make informed decisions and establish a long-term local development strategy, regulating the sustainable management of water resources.

Study Area and Dataset
The research was carried out in Poland, a region located in a temperate climate zone with a predominance of polar-sea air masses. The amount of precipitation in Poland varies temporally and spatially. The average annual precipitation in Poland recorded in the period of 1981-2010 was 603 mm. The lowest annual precipitation total of 500 mm was observed in the central part of the country, and the highest-970 mm, in the south of Poland [49]. The area covered by the analysis includes the Upper Noteć catchment, closed by the water gauge in Pakość ( Figure 1). The catchment area up to the Pakość station is 2301.98 km 2 . This catchment is located in the historical region of Kujawy, which is extremely important for agriculture. Arable land within the catchment area accounts for 76.07% of the catchment area, while forest areas account for 11.4%. It is also the region with the lowest annual precipitation in Poland and the area with the highest water shortages in agriculture [50].  [51,52]. Map elaborated in the coordinate system: WGS 84/UTM zone 34N; (b) own elaboration made with [52][53][54], location of the stations based on [55,56] and Table 1, location of the lignite open pits based on [56,57]. Meteorological station Izbica Kujawska is out of catchment area according to coordinates from Table 1. Location of the hydrological station Pakość is determined by cartographic issues. Map elaborated in the coordinate system: WGS 84/UTM zone 34N. In terms of annual precipitation, the Upper Noteć area is one of the regions with the lowest precipitation in Poland. Total annual precipitation in the period of 1980-2016 ranged from 500.1 mm (Kołuda Wielka) to 542.5 mm (Strzelno) ( Table 1)  In terms of hydrology, the catchment area of the Upper Noteć is categorised as one of the areas with the most limited water resources [58]. According to Tomaszewski and Kubiak-Wójcicka [59], the average long-term unit runoff of the Noteć measured at the Pakość water gauge in the period of 1951-2015 amounted to 2.41 dm 3 ·s −1 ·km −2 . This is the lowest unit runoff value recorded in Poland, with an average of 5.5 dm 3 ·s −1 ·km −2 [34]. Both precipitation and discharge in the catchment area of the Upper Noteć River are among the lowest in Poland. During the analysed period of 1980-2016, the unit runoff of the Noteć River at the Pakość station was 2.21 dm 3 ·s −1 ·km −2 . The highest values of the maximum discharge were recorded in July 1980 at all hydrological stations. The maximum discharge at the Pakość station was 69.3 m 3 ·s −1 (unit runoff 30.1 dm 3 ·s −1 ·km −2 ), and the lowest discharge was recorded in October 2003 (0.23 dm 3 ·s −1 ·km −2 ) ( Table 2). At the Noć Kalina station, the lowest discharge was recorded in September 1989 and August 1992. However, the lowest discharge at the Łysek station was recorded from August to December 2015 and in January 2016, at which time virtually no discharge occurred in the watercourse bed.

Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI)
Two indicators were used to determine droughts: the Standardized Precipitation Index (SPI), which defines meteorological droughts, and the Standardized Runoff Index (SRI), which defines hydrological droughts. Data from 8 meteorological stations: 5 located within the catchment area of the Noteć River (Pakość, Strzelno, Sompolno, Izbica Kujawska, Kołuda Wielka) and 3 in its close vicinity (Kłodawa, Gniezno and Janowiec Wielkopolski) were used to determine meteorological droughts.
The Standardized Precipitation Index (SPI) is one of the most frequently used indicators of a meteorological drought, and was developed on the basis of the normalization of precipitation probabilities [60]. This indicator defines a precipitation deficit and allows the monitoring of droughts in different time frames. The SPI is recommended by the World Meteorological Organisation (WMO) for determining the phenomenon of drought [61]. For more information on the formulation of SPI, its advantages and limitations, see papers [62][63][64].
The SPI was calculated on the basis of monthly precipitation totals for 5 meteorological stations in the upper catchment area of the Noteć River (Izbica Kujawska, Strzelno, Kołuda Wielka, Sompolno and Pakość) and 3 stations in its close vicinity (Kłodawa, Gniezno and Janowiec Wielkopolski). The daily precipitation data were aggregated into monthly time scales, and fitted to a two-parameter gamma distribution function. The SPI was calculated for each month at different timescales. Therefore, 5 different time series were analysed, i.e., 1-, 3-, 6-, 9-and 12-months. SPI values define the deviation from the median expressed in units of standard deviation, which was calculated according to the formula: In order to calculate the SPI, the compliance of the distribution of the transformed variable f (P) with the normality distribution was tested using the x 2 -Pearson normality test [65].
The Standardized Runoff Index (SRI) is calculated according to the same procedure as the SPI, however it is based on the discharge data [66][67][68][69]. A 2-parameter logarithmic function was used as a normalizing function when calculating the SRI [70]. The detailed calculation method is presented in the study [9,47]. The probabilities were transformed into standard normal distribution. The application of SPI allows for the differentiation of the intensity of a drought using a set of SPI thresholds: −1, −1.5, −2 and 1.0, 1.5, 2 for moderate, severe and extreme droughts and precipitations, respectively [28].
The proposed approach is based on the assessment of water resources under different hydroclimatic conditions and the determination of different intensity classes. The adoption of standardized indicators allowed for the classification of drought intensity, which is presented in Table 3. Extreme events were identified for the indicator values above 1.0, when rainy periods occur, and for the indicator values below −1.0, when there are droughts.

Mann-Kendall Test
The Mann-Kendall test [71,72] is a non-parametric statistical method used to determine whether a time series has a monotonic upward or a downward trend. It is a rank-based procedure that is particularly suitable for data with abnormal distribution that contain outliers and non-linear trends [73].
The Mann-Kendall S statistic is described with the Formula (2): where: x j and x k -values of the variable in individual years j and k, where j > k, n-the series count (number of years).
Positive "S" values represent an upward trend, while negative values indicate a downward one. The calculation of "sgn (x j − x k )" is done via Equation (3).
The S statistic shows a tendency to quickly move towards normality, and for n > 10 this statistic has an approximately normal distribution with the mean of 0 and the variance described by the Formula (4): The normalized Z test statistic is determined by the Formula (5): In the Mann-Kendall test, the null hypothesis is that there is no significant trend in the data series. The trend is significant if the null hypothesis cannot be accepted. The acceptance region at the significance level of α = 0.05 is defined by the range of −1.96 ≤ Z ≤ 1.96 (no significant trend), while the rejection region was determined by Z < −1.96 (significant downward trend) and Z > 1.96 (significant upward trend), where Z is the normalized test statistic [47].

Sen's Slope
The Mann-Kendall test is an effective method of identifying trends in a time series, but does not indicate the magnitude of the trends. The test might be supplemented with a non-parametric Sen's method. In order to estimate the actual slope of the existing trend, the non-parametric Sen's method was used [80]. The main advantage of the Sen's slope estimator is its resistance to the presence of extreme values [81].
The slope β expressed by the Theil-Sen estimator (β) is described by the Formula (6): A positive value of β indicates an upward (increasing) trend, and a negative value indicates a downward (decreasing) trend in the time series.
The Mann-Kendall test and Theil-Sen estimator were performed by means of a RStudio [82] with packages: "readxl" [83] and "trend" [84]. Information about what equations are used in the "trend" package for Mann-Kendall test and Theil-Sen estimator is available at [85]. QGIS ver. 3.10.9 and QGIS ver. 3.10.9 with GRASS ver. 7.8.3. were used in the study. Additionally, GIMP ver. 2.10.18 and Inkscape ver. 1.0.1 were used as graphic tools. In preparation of the Figure 3 the Inverse Distance Weighting (IDW) interpolation was used.

Pearson's Correlation Analysis
The Pearson correlation coefficient (r) was used to detect the relationship between meteorological droughts and hydrological droughts. With the use of this coefficient, it was possible to determine the linear relationship between the SPI and SRI variables in different accumulation periods. The value of the correlation coefficient is in a closed range [−1, 1]. The greater its absolute value, the stronger the linear relationship between the variables. 0-means there is no linear relation, 1-means a positive relation, and −1-means a negative relation between the variables.

The Characteristics of Droughts in the Period of 1981-2016
SPI values were calculated separately for all eight weather stations for the time scales of 1, 3, 6, 9 and 12 months. Depending on the selected accumulation period, the range of SPI values was different for individual meteorological stations, as follows: SPI−1 from −3.54 to 3.59, SPI−3 from −3.01 to 2.94, SPI−6 from −3.32 to 2.65, SPI−9 from −3.47 to 2.93 and SPI−12 from −3.38 to 2.77 ( Table 4). The longer the indicator's accumulation period, the lower the drought intensity. The most intense meteorological droughts were recorded in the following periods: 1982-1985, 1989-1996, 2002-2006, 2008-2009 In the longer accumulation periods i.e., 6, 9 and 12 months, the number of months was similar and amounted to 60 to 75 months for SPI−6, 59 to 74 months for SPI−9 and 59 to 79 months for SPI−12.
Greater differentiation was recorded in the cases of hydrological drought occurrences (SRI) at the station in Łysek, Noć Kalina and Pakość ( Table 5). The SRI values in Łysek were characterized by the largest range i.e., from −5.22 to 2.00. The most intense droughts were recorded from April to December of 2016, which was related to relatively minor discharges of the Noteć River during this period. At the Noć Kalina station, the SRI values recorded were from −3.16 to 2.49. The most intense hydrological droughts were recorded from May to September of 1990, depending on the period of accumulation. The SRI values in Pakość were characterized by a lower amplitude and ranged from −2.33 to 3.05. The number of months with SRI values below −1.0 ranged from 75 to 81 months, and in Noć Kalina-from 77 to 101 months. The hydrological droughts (SRI ≥ −1.0) at the station in Łysek were characterized by a short duration, from 6.5% to 8.3% of the analysed period, and high intensity. The number of wet months (SRI ≥ 1.0) ranged from 6.0% to 9.3% of all the months of the analysed multiannual period. The largest number of months with SRI values ≤ −1.0 was recorded at the Noć Kalina station i.e., from 17.9% to 23.4% of the analysed multi-year period, while the wet months constituted between 13.4% and 17.6% of this period. The hydrological station in Pakość closes the catchment area of the Upper Noteć River. The lower intensity of hydrological droughts at the Pakość station and their much shorter duration compared to the Noć Kalina and Łysek stations may have resulted from anthropogenic activities carried out in the area. These activities were mainly related to the lignite open pits, which ran south of the Łysek and Noć Kalina stations (Lubstów), as well as the operation of a new open pit mine located north of the Łysek station (Tomisławice).
The spatial distribution of the number of months with meteorological drought occurrences in the catchment area of the Upper Noteć is shown in Figure 3. The number of months with droughts in the accumulation period of 1 month does not present large spatial differentiation. Larger differences are noticeable in the period of 3-and 12-month accumulation. In the case of SPI−3, the months with droughts in the southern part of the catchment lasted the longest, while in the SPI−12 period they were the longest in the western part of the catchment. Figure 4 shows the average values of SPI from 8 stations as well as the development of hydrological drought occurrences (SRI) recorded at the station in Pakość. The number of months with averaged meteorological droughts is between 13.4 and 15% of all the analysed months. As presented in Figure 4, the development of hydrological droughts is related to meteorological droughts.

Trends in Meteorological and Hydrological Drought Occurrences
The results of the trend analysis for a series of SPI values (time scales of 1, 3, 6, 9 and 12 months) for individual meteorological stations are presented in Table 6. A statistically insignificant trend was noted at most meteorological stations. Out of eight meteorological stations, a statistically significant upward trend was recorded at only two stations, and a downward trend at one station (the drought intensified). The downward trend in the SPI value for the meteorological station in Kłodawa means that the meteorological drought increases in the period of accumulation of 3-12 months. The Z value obtained for the Kłodawa station was relatively high and ranged from −1.817 to −4.317, and the Theil-Sen slope was between −0.0007 and −0.0018. The test results for the Kłodawa station (Tables 6 and 7) show that the expected Z value is negative for the indices, and the Theil-Sen slope is also always negative.   The upward trend in the SPI value at the stations in Sompolno and Kołuda Wielka indicates that the phenomenon of meteorological drought is decreasing. The highest Z values, between 3.25 and 5.08, were obtained during the 3-, 6-, 9-and 12-month accumulation periods, while the Theil-Sen slope values were between 0.009 and 0.0019.
In the case of hydrological droughts, a statistically significant downward trend was recorded at the Łysek station in all analysed periods of accumulation. This means a noticeable increase in drought occurrences in the analysed multi-year period of 1981-2016. Z values were negative and ranged from −5.34 to −6.27, while Theil-Sen values were between −0.0013 to −0.0019. An upward trend was recorded at the Noć Kalina station. Z values ranged from 2.21 to 4.07, while the Theil-Sen slope ranged from 0.0008 to 0.0017. In the case of Pakość station, the trend was statistically insignificant. The Z value calculated in the 12-month accumulation period in Pakość approaches the region of a trend acceptance, which might indicate that the trend in Pakość in the longer accumulation period is determined by the occurrence of hydrological droughts at the Łysek station. Spatial distributions of trends (significant and insignificant) for a series of SPI and SRI values for the 1, 3-, 6-, 9-and 12-month time scales are shown in Figure 3.

Correlations between SPI and SRI Values
In order to establish the relationship between meteorological droughts occurring in the catchment area of the Upper Noteć and hydrological droughts, an analysis of the correlation between the SPI and SRI indices was carried out using the Pearson correlation analysis. The results showed that the strongest correlation between SPI and SRI in the analysed period of 1981-2016 was obtained at the 12-month time scale (r = 0.51) ( Figure 5). In the case of individual years, the highest correlation indicators between hydrological and meteorological droughts varied depending on the length of the accumulation period. The strength of the relationship between SPI and SRI in the catchment area of the Upper Noteć River was higher for long accumulation periods (6 and 9 months), and lower for the short ones (1 and 3 months). The highest correlation values for the 1-month accumulation period were recorded in 1998 (r = 0.76), while for the 3-month accumulation period the highest values were recorded in 1982 (r = 0.83) and 1996 (r = 0.81). For the 6-month accumulation period, the maximum correlation index was recorded in 1987 (r = 0.94) and in 1982 (r = 0.91). High values were obtained in 1987 for the 9-month accumulation period (r = 0.94) and the 12-month accumulation period (r = 0.90).

Discussion
Understanding the changes in the intensity of droughts in the past and being able to predict expected changes over different time scales is incredibly important, as precipitationdriven hydrological processes (e.g., evapotranspiration and surface and groundwater discharge) affect all water reserves [86]. In this study, we found that in the analysed period of 1981-2016, there was a relationship between the occurrence of meteorological and hydrological droughts. The strength of this relationship varied. The analysed multi-year period of 1981-2016 showed a high variability, from dry years (SPI ≤ −1.0) to wet years (SPI ≥ 1.0), which can be concluded from the SPI values in various time scales. The driest years included 1982, 1989, 1992, 2003 and 2015. In these years, meteorological droughts covering not only the region of Poland, but parts of Europe, were recorded. Meteorological droughts which have occurred in Europe since the beginning of the 21st century, and were accompanied by heat waves in 2003, 2006, 2010, 2015, are great examples of such phenomena [87][88][89][90][91].
In the studied area, an increase in the intensity of meteorological droughts (downward trend) was observed at only one out of eight meteorological stations. A statistically significant, clear upward trend in SPI drought was identified at two stations. More distinct trends, but opposite in direction, were observed in the case of hydrological droughts recorded at the stations in Łysek and Noć Kalina. The obtained statistics for the Pakość station, calculated in the 12-month accumulation period, point to the rejection of the null hypothesis on the lack of a statistically significant trend. The same direction of changes in the trend was recorded at the Łysek and Pakość stations. This means an increase in the intensity of hydrological droughts. In the longer accumulation period, the occurrence of hydrological droughts at the Łysek station determines the hydrological droughts at the Pakość station.
The strength of the relationship between meteorological droughts and hydrological droughts shows significant variation. This variation is not only the result of the size of the annual sums of precipitation, but also if an increase in air temperature in the analysed area (Figure 2), which leads to an increase in evapotranspiration [92]. Anthropogenic activities related to the operation of a lignite open pit have a significant impact on the analysed area. Some of the water from the mine drainage was directed to the Noteć River above the Noć Kalina station. The amount of water varied in individual years and depended on the location of the exploitation operations. According to Wachowiak [93] relation between the SPI and SRI indices was carried out using the Pearson correlation analysis. The results showed that the strongest correlation between SPI and SRI in the analysed period of 1981-2016 was obtained at the 12-month time scale (r = 0.51) ( Figure  5). In the case of individual years, the highest correlation indicators between hydrological and meteorological droughts varied depending on the length of the accumulation period. The strength of the relationship between SPI and SRI in the catchment area of the Upper Noteć River was higher for long accumulation periods (6 and 9 months), and lower for the short ones (1 and 3 months). The highest correlation values for the 1-month accumulation period were recorded in 1998 (r = 0.76), while for the 3-month accumulation period the highest values were recorded in 1982 (r = 0.83) and 1996 (r = 0.81). For the 6-month accumulation period, the maximum correlation index was recorded in 1987 (r = 0.94) and in 1982 (r = 0.91). High values were obtained in 1987 for the 9-month accumulation period (r = 0.94) and the 12-month accumulation period (r = 0.90).  The Pearson correlation analysis shows that there is a relationship between meteorological and hydrological droughts in the study area. However, it should be emphasized that these results should not be directly interpreted. In the correlation analysis, a nonlinear relationship can be inadequately described or undetected [94]. Non-linear models (polynomial, exponential and logarithmic) for the relationship between meteorological and hydrological droughts were analysed in the research conducted by Salimi et al. [95].
The research on the correlation between droughts conducted by Tokarczyk and Szalińska [44] for catchments with large areas showed that the largest correlations between SPI and SRI occurred for longer periods of accumulation. Similar relationships between meteorological and hydrological droughts were obtained for other catchments in Poland [43]. In the case of the catchment area of the Upper Noteć River, the relationships between meteorological and hydrological conditions are not natural. The flow regime depends on the amount of water discharged in particular periods, and on the retention capacity of lakes, which is particularly noticeable at the Pakość station. The amount of water accumulated in the Pakość reservoir, through which the Noteć flows, is regulated by a water accumulating weir.

Conclusions
The study analysed the trends in meteorological and hydrological drought occurrences in the long-term period of 1981-2016, for the catchment area of the Upper Noteć River. The identification of a meteorological drought was carried out with the use of an SPI, based on monthly precipitation totals from eight meteorological stations. Hydrological drought was determined by means of an SRI for the monthly discharges of the Noteć, which were obtained from three hydrological stations. Non-parametric Mann-Kendall tests and the Sen slope were used to determine trends. The following conclusions might be drawn: -Statistically significant trends, at the significance level of 0.05, were identified at three out of eight meteorological stations, based on the Mann-Kendall test and the Sen slope. -An increase in meteorological drought occurrences was recorded at the Kłodawa station (downward trend), while a decrease in droughts was recorded at the Sompolno and Kołuda Wielka stations. -Hydrological droughts showed an upward trend at the Łysek station, while a decrease in the trend was recorded at the Noć Kalina station, and both were statistically significant. No changes in the trend were found at the Pakość station. - The analysis of the correlation between meteorological and hydrological droughts in individual years showed a strong relationship in dry years e.g., 1982 and 1989. The maximum correlation index was 0.94 and was identified over longer accumulation periods i.e., 6 and 9 months. - The anthropogenic effects related to the operation of an open cast lignite mine may have had an impact on the relationship between droughts.
The example of the catchment area of the Upper Noteć River indicates that the management of water resources requires the use of at least several indicators that will allow an assessment of the actual state of water reserves. Using the SPI to detect meteorological droughts can be used as a drought warning system [96]. In some cases, the value of the SRI depends on the way water is managed within the catchment area. The size of the runoff may be disturbed by anthropogenic factors. Effective water resource management strategies require constant monitoring of water reserves, which should be consulted among various stakeholder groups related in particular to industry, and agriculture.