Regional Innovative Trend Analysis of Annual and Seasonal Discharges of Rivers in Bosnia and Herzegovina

Abstract

Climate change is becoming more pronounced and affecting all environmental components, leading to river flow changes. This study aimed to investigate the annual and seasonal discharge trends for six rivers in Bosnia and Herzegovina in Europe in the period from 1961 to 2020. The trends were analysed using a linear regression (LR) analysis, the Mann–Kendal test (MK), and an innovative trend analysis (ITA). The fewest significant trends were obtained by the LR analysis, followed by the MK test, and the most were obtained by the ITA method. The ITA method identified 76.67% significant negative trends and 13.33% significant positive trends in all data groups. It can be concluded that the discharges in the second part of the observed period (1991–2020) were significantly lower compared to the first part (1961–1990). A more detailed ITA of the flow by data group (low, medium, and high) was also carried out. The results showed the occurrence of increasingly large extremes. Therefore, in the second subperiod, the minimum values were smaller and the maximum values were larger than in the first subperiod. The occurrence of high water levels increases the possibility of floods, and a long dry period can cause problems with the generation of electricity from hydropower plants. For this reason, analysing discharge trends in the future is certainly a justified recommendation.

1. Introduction

An increasing number of changes in meteorological, hydrological, and other environmental parameters have been observed in recent decades as a result of ever more pronounced climate change. For example, increases in average air temperatures and humidity as well as the temperatures of rivers, lakes, oceans, and groundwater have been recorded [1,2,3,4]. Changes in precipitation, infiltration, and evapotranspiration have also been noticed [5,6,7].

In addition to the increase in average values, studies show an increasingly frequent occurrence of extremes [8]. Such changes have an impact on watercourses, and research shows that these changes were particularly pronounced after the 1970s [9,10,11]. The changes are mainly caused by various anthropogenic activities, such as groundwater extraction, land use and land cover, watershed development, urbanization, or dam construction [12,13]. Such changes affect the hydrology of the catchment and its hydrological and hydropower potential [14].

Monitoring discharge trends is one of the fundamental hydrological parameters required for sustainable water resources management [15]. It provides a better understanding of hydroclimatic changes within a watercourse or catchment [16]. For this reason, monitoring and analysing discharge trends are subjects of research by scientists around the world. Various methods are used for this purpose, such as linear regression (LR) analyses [17,18], Spearman’s rho [19,20], and Mann–Kendall (MK) tests [21,22]. Numerical methods have also been used, but they require the knowledge or estimation of a larger number of parameters [23,24,25,26]. Recently, a new trend analysis, the innovative trend analysis (ITA), was introduced by [27]. This method can effectively provide a visual understanding of trends without strict assumptions about serial independence, pre-whitening, data length, and data normality as required in the MK test [28]. The method has found wide application, and it has been used in trend analyses of precipitation, air temperature, winds, and waves [29,30,31,32].

Several authors have used the ITA method to analyse long-term discharge trends. A trend analysis of river flows at 13 hydrological stations in the Lake Issyk-Kul catchment area in Central Asia was performed [33]. The results showed the greater sensitivity of the ITA method compared to the MK test. In addition, a discharge trend analysis in the Wadi Mina catchment (Northwestern Africa) was conducted during the period from 1973 to 2012, in which a decreasing trend was observed at most monitoring stations [34]. The temporal variability of seasonal and annual precipitation was also investigated in the Calabria region in Southern Italy using the MK test and the ITA [35]. Both methods showed a negative trend in annual precipitation in the entire study area. Several studies have also been conducted on the Balkan Peninsula to analyse the discharge trends using the MK test and Sen’s slope [36,37,38,39,40,41]. The impact of climate change on discharge rates in two Croatian rivers was also investigated using different methods: a seasonal MK test, the innovative polygon trend analysis (IPTA) method, innovative visualization for innovative trend analysis (IV-ITA), and Bayesian changepoint detection and time series decomposition (BEAST) algorithms [33]. The seasonal MK analysis revealed significant decreasing trends, whereas the IPTA and IV-ITA results exhibited consistent decreasing trends in most months.

Discharge trends are also becoming a subject of research in Bosnia and Herzegovina [42,43]. In a recent study, the trends were analysed using the MK test, the modified MK test (mMK), and Sen’s slope estimator (SSE) at seven hydrological stations on larger rivers in Bosnia and Herzegovina [44]. The results showed a decreasing trend of annual discharge in all analysed rivers, with clearly negative trends in the summer months (June, July, and August). The analysis of discharge trends in the mentioned area is still in its early stages. Therefore, further research is necessary to better understand the impact of climate change on long-term discharge trends and short-term fluctuations. Understanding the variability of discharge trends is important for assessing water availability and planning in agriculture, irrigation, power generation, and other human activities.

Accordingly, in this paper, an analysis of long-term discharge trends on the six rivers in Bosnia and Herzegovina was carried out using an LR analysis, MK test, and the ITA method. The methods used were selected for the following reasons. Namely, the LR analysis is a general method used in trend analyses of various types of data. Therefore, it can be said that it is a general statistical method. The MK test is a method that has been used for many years to analyse trends in hydrological data. In this sense, it is a generally accepted method, and the results obtained are considered relevant. The ITA method, on the other hand, is relatively new. Scientific research has yet to establish a connection between the results of this method and those of other methods. A novelty in the ITA presented in this paper is the determination of an intersection point of the data set. If the trend is not monotonic and there is both a positive and a negative component of the trend in the same data set, it is possible to determine the intersection point. This is a point that lies on the no-trend line. For values below the intersection point, the trend is negative, and for values above it, the trend is positive. For this reason, the method is being applied for the first time for rivers in Bosnia and Herzegovina. The aim of this paper is to evaluate the three methods and identify even the least significant trends to protect and manage water resources. Considering the high sensitivity of the ITA method, the obtained results provide a deeper insight into annual and seasonal discharge trends and represent a significant scientific contribution on a regional scale.

2. Materials and Methods

2.1. The Study Area

Bosnia and Herzegovina is a country located in the central part of the Balkan Peninsula in Southeastern Europe, with an area of 51,209 km². The relief in the central part of the country is predominantly mountainous, while the peri-Pannonian region extends to the north and the sub-Mediterranean region to the south. It is relatively rich in water, with an availability of between 5000 and 10,000 m³ per capita [45]. Hydrologically, it is divided into two basins: the Danube basin (75.7% of the territory) and the Adriatic basin (24.3%) [46]. The research area includes six hydrological stations on six rivers in Bosnia and Herzegovina: Novi Grad on the Una River (NG), Prijedor on the Sana River (PR), Banja Luka on the Vrbas River (BL), Vrbanja on the Vrbanja River (VR), Doboj on the Bosni River (DO), and Grančarevo on the Trebišnjica River (GR) (

Table 1. Details of the hydrological stations [44].

Station	Drainage Area	Elevation	Coordinates	Record Period
	(km2)	(m.a.s.l.)
Novi Grad—Una	8507	116	45°05′–16°38′	1961–2020
Prijedor—Sana	3191	160	44°97′–16°70′	1961–2020
Banja Luka—Vrbas	4588	151	44°45′–17°11′	1961–2020
Vrbanja—Vrbanja	778	166	44°74′–17°27′	1961–2020
Doboj—Bosna	9618	137	44°74′–18°09′	1961–2020
Grančarevo—Trebišnjica	N/A	296	42°43′–18°30′	1961–2020

). The Trebišnjica River belongs to the Adriatic basin, while the other rivers belong to the Danube basin. The river flows, the catchment areas, and the locations of the hydrological stations are shown in Figure 1.

2.2. Experimental Data

Discharges were measured daily at each observed hydrological station in the period from 1961 to 2020, and the data were taken from the Republic Hydrometeorological Institute. At each site, monthly and annual averages were calculated from the total data sum and used in the subsequent analyses.

Table 2. Descriptive statistics of the annual discharges at hydrological stations (1960–2020).

Station	Novi Grad—Una	Prijedor—Sana	Banja Luka—Vrbas	Vrbanja—Vrbanja	Doboj—Bosna	Grančarevo—Trebišnjica
Discharge (m3/s)
Average	217.72	78.99	86.90	15.58	160.09	64.79
Median	211.25	77.84	86.88	15.53	158.12	62.24
Min	101.20	36.09	40.49	2.69	68.80	34.21
Max	359.47	116.50	141.88	28.05	315.83	127.93
First quartile	188.01	69.50	74.32	13.72	126.69	50.83
Third quartile	245.15	91.56	98.90	17.57	189.00	76.50
St. dev.	45.81	17.40	20.18	4.77	44.65	17.49
Skewness	0.24	−0.09	0.24	−0.18	0.58	0.73
Kurtosis	0.68	−0.22	0.27	0.74	1.38	1.43

shows some statistical data on the discharges of each river. Given the temperate continental climate in the north and the mountainous climate types in the central areas, the highest discharges are recorded in the April–May period and the lowest in the August–September period at all sites.

2.3. Linear Regression

Linear regression analysis can be used to analyse the change in the trend of meteorological time series on a large time scale and is represented by the following linear function:

$$y=\alpha x+b+\epsilon$$

(1)

where a is the slope of a linear function (linear trend), b is the intercept, and ε is an error term. There are several implicit assumptions in this method [47]: (1) the error term ε is a random variable; (2) for all x values, the variance of ε is the same; (3) x is the explanatory variable, referred to as the independent variable, and it is a deterministic variable; and (4) y, referred to as the dependent variable, is a random variable. The t-test determined the significance of the trend as follows:

$$t=r·\sqrt{{\displaystyle \frac{df}{1-r^2}}}$$

(2)

where df is the degree of freedom, and r is the correlation coefficient. The t-values obtained are compared with the critical t_α value for the significance levels of 95% and 99%. Given the above, the hypothesis H0 is set that there is no significant trend:

$$H0:t<t_{\alpha (95\%)}$$

(3)

$$H0:t<t_{\alpha (99\%)}$$

(4)

In addition, an alternative hypothesis H1 is put forward, which proves the existence of a significant trend:

$$H1:t>t_{\alpha (95\%)}$$

(5)

$$H1:t>t_{\alpha (99\%)}$$

(6)

2.4. Mann–Kendal (MK) Test

The Mann–Kendall (MK) test [48,49] is a rank-based non-parametric test to detect significant trends in meteorological and hydrological time series data [44,50,51]. The MK trend test statistic S is calculated as follows:

$$S=\sum _{k=1}^{n-1}\sum _{j=k+1}^{n}sign\left(x_j-x_k\right)$$

(7)

where x_j is the rank of the j-th event; x_k is the rank of the k-th event; n is the number of events; and the sign (x_j − x_k) is measured as follows:

$$sign\left(x\right)=\left\{\begin{array}{ccc}+1& if& \left(x_j-x_k\right)>0\\ 0& if& \left(x_j-x_k\right)=0\\ -1& if& \left(x_j-x_k\right)<0\end{array}\right.$$

(8)

The variance of statistic S was estimated as follows:

$$var\left(S\right)={\displaystyle \frac{n\left(n-1\right)\left(2n+5\right)-\sum _{i=t}^p{t}_i(t_i-1)(2t_i+5)}{18}}$$

(9)

where n is the number of data points; p is the number of connected groups; and t_i is the number of ties of extent.

After calculating the variance of the data series, the standardized statistic Zc value is calculated using the following formula:

$$Z_c=\left\{\begin{array}{ccc}{\displaystyle \frac{S-1}{\sqrt{var\left(S\right)}}}& if& S>0\\ 0& if& S=0\\ {\displaystyle \frac{S+1}{\sqrt{var\left(S\right)}}}& if& S<0\end{array}\right.$$

(10)

The standardized statistical value Z_c follows the standard normal distribution (Z), with a variance of one (σ² = 1) and a mean value of zero (μ = 0). The null hypothesis H0 assumes that the river discharge observations show no trend, while the alternative hypothesis H1 assumes that the river discharge data series shows a significant trend. Under the two-sided condition, H0 and H1 are as follows:

$$H0:\left|Z_c\right|<Z_{\alpha \left(95\%\right)}=1.96$$

(11)

$$H0:\left|Z_c\right|<Z_{\alpha \left(99\%\right)}=2.58$$

(12)

$$H1:\left|Z_c\right|>Z_{\alpha \left(95\%\right)}=1.96$$

(13)

$$H1:\left|Z_c\right|>Z_{\alpha \left(99\%\right)}=2.58$$

(14)

where Z_α is the critical value at the 95% or 99% significance level. A negative/positive value of Z_c indicates a downward/upward trend in the observed data.

2.5. Innovative Trend Analysis (ITA)

The ITA method’s basis is dividing the original time series into two sub-series. The two sub-series are sorted in ascending order, with the first half-series (X_i = 1, 2, …, n/2) on the horizontal axis (X-axis) and the second half-series (X_j = n/2 + 1, n/2 + 2, …, n) on the vertical axis (Y-axis) of the Cartesian coordinate system (Figure 2). The 1:1 (45°) line divides the diagram into two equal parts and implies no trend, but any plot above/below this line implies increasing/decreasing trends [27]. The closer the scatter points are to the 1:1 line (45°), the weaker the trend slope and vice versa. In the case of non-monotonic trends (composition of different trends in the time series), the variation range of each sub-series can be divided into several groups: low, medium, and high. The choice of quantitative group boundaries varies from case to case, and such a diagram provides a visual overview of the trend’s nature [52].

The intersection point is introduced to the proposed methodology in this paper. This is the point that lies on the no-trend line for non-monotonic trends and marks the point of trend change (Figure 2). Below this value, the trend is negative, and above it, it is positive. It can be determined by fitting a line (linear regression) to the scatter points of the ITA data set. In this way, one intersection point is found. If there are multiple trends, it is possible to fit the curve and obtain more intersection points. However, this requires a suitable data set, which is not the case for the observed parameter. This method does not require restrictive assumptions, as is the case when using the MK test and Spearman’s rho rho test [53]. The ITA method is valid regardless of the sample size, the serial correlation structure of the time series, and non-normal probability distribution functions [52].

The significance test was performed at the α significance levels of 95% and 99%. The straight-line trend slope s was calculated using the following equation [52]:

$$s={\displaystyle \frac{2(\overline{y_2}-\overline{y_1})}{n}}$$

(15)

where s is the straight-line slope of the trend line represented by the ITA method; $\overline{y_2}$ and $\overline{y_1}$ are the arithmetic means of the first and second halves of the dependent variable; and n is the number of years of data.

The standard deviation of the sampling slope is calculated using the following expression:

$${\sigma }_s={\displaystyle \frac{2\sqrt{2}}{n\sqrt{n}}}\sigma \sqrt{1-r}$$

(16)

where ${\sigma }_s$ is the standard deviation of the sampling slope; σ is the standard deviation of the entire time series; and r is the correlation coefficient between the ascending sorted arithmetic means of the two halves.

The lower and upper confidence limits CL of the trend slope at the α level of significance are calculated by applying the following equation:

$${CL}_{1-\alpha }=0\pm s_{cri}·{\sigma }_s$$

(17)

where CL_1−α is the upper and lower confidence limits at α level of significance; σ_s is the standard deviation of sampling slope; and s is the slope value.

In view of the methodology presented, the null hypothesis H0 is established, which means that there is no significant trend in the observed time series at the significance level α:

$$H0:\left|s\right|<\left|{CL}_{1-\alpha (95\%)}\right|$$

(18)

$$H0:\left|s\right|<\left|{CL}_{1-\alpha (99\%)}\right|$$

(19)

Conversely, an alternative hypothesis H1 is also set up, which confirms the existence of a trend in the observed time series at the significance level α:

$$H1:\left|s\right|>\left|{CL}_{1-\alpha (95\%)}\right|$$

(20)

$$H1:\left|s\right|>\left|{CL}_{1-\alpha (99\%)}\right|$$

(21)

A positive (negative) value of s indicates an increasing/decreasing trend in the time series [47,52].

3. Results

Based on discharges from six hydrological monitoring stations at different locations in Bosnia and Herzegovina, the annual and seasonal trends (winter, spring, summer, and autumn) in the period from 1961 to 2020 were determined using a LR, the MK test, and the ITA method.

3.1. Annual Discharge Trends

The results of the linear trend analysis show that the general annual discharge trends during the observed period are negative at all sites. For this reason, the values of the slope s are negative (

Table 3. Analysis of linear trend (slope a) and MK test (Z_c value) of annual and seasonal river discharge in the study area (1961–2020).

Station	Annual		Winter		Spring		Summer		Autumn
	LT	MK	LT	MK	LT	MK	LT	MK	LT	MK
Novi Grad—Una	−0.37 →	−1.29 →	−0.22 →	−0.53 →	−0.68 →	−1.29 →	−0.31 →	−1.96 ↘	−0.28 →	0.09 →
Prijedor—Sana	−0.23 →	−1.87 →	−0.05 →	−0.22 →	−0.39 →	−1.75 ↘	−0.25 →	−2.80 ↓	−0.24 →	−0.70 →
Banja Luka—Vrbas	−0.10 →	−0.86 →	−0.10 →	−0.15 →	−0.12 →	−0.73 →	0.06 →	−0.26 →	−0.25 →	−0.48 →
Vrbanja—Vrbanja	−0.07 ↘	−2.32 ↘	−0.13 ↘	−1.82 ↘	−0.04 →	−0.90 →	−0.04 →	−2.32 ↘	−0.09 →	−1.92 →
Doboj—Bosna	−0.80 ↘	−2.76 ↓	−0.97 →	−1.63 →	−0.80 →	−1.72 ↘	−0.36 →	−1.83 ↘	−1.10 ↘	−2.00 ↘
Grančarevo—Trebišnjica	−0.23 →	−2.24 ↓	−0.16 →	−0.79 →	−0.42 ↘	−2.80 ↓	−0.15 →	−3.61 ↓	−0.17 →	−0.82 →

→ (blue arow)—No trend; ↘ (orange arow)—Negative trend at 95% significance level (p < 0.05); ↓ (red arow)—Negative trend at 99% significance level (p < 0.01).

). However, no trend at the 99% significance level was detected, while a trend at the 95% significance level was detected at the Vrbanja and Doboj stations. No significant trend was found at the other locations using this method.

The MK test shows a better sensitivity to trend changes than the LR analysis. The results indicate a negative trend at all locations; however, the significance test fails at three measuring stations: Novi Grad, Prijedor, and Banja Luka. At two sites (Vrbanja and Grančarevo), a trend was found at the 95% significance level, and at one (Doboj), a trend was found at the 99% significance level (Table 3).

After the LR and MK tests, the annual river discharge trends were determined by applying the ITA method (

Table 4. Analysis of ITA (slope s) of annual river discharges in the study area (1961–2020).

Station	Slope (s)	Standard Deviation (σ)	Correlation (r)	Slope Standard Deviation (σs)	CL (95%)	CL (99%)
Novi Grad—Una	−0.261 ↓	45.805	0.935	0.071	±0.140	±0.184
Prijedor—Sana	−0.174 ↓	17.396	0.988	0.012	±0.023	±0.030
Banja Luka—Vrbas	−0.101 ↓	20.180	0.989	0.013	±0.025	±0.033
Vrbanja—Vrbanja	−0.058 ↓	4.766	0.971	0.005	±0.010	±0.013
Doboj—Bosna	−0.398 ↓	44.650	0.944	0.064	±0.126	±0.165
Grančarevo—Trebišnjica	−0.244 ↓	17.488	0.892	0.035	±0.069	±0.090

↓ (red arow)—Negative trend at 99% significance level (p < 0.01).

). The results indicate a higher sensitivity of this method compared to the LR and MK tests, which would be advantageous for analysing hidden fluctuation trends. Indeed, a negative trend at the 99% significance level was found at all sites. Therefore, the null hypothesis H0 is rejected, and the alternative hypothesis H1, regarding the existence of a significant negative trend at the 99% significance level, is accepted.

The decreasing trend in the annual discharge at the stations indicates that the data points mostly fall below the 1:1 line (45°) in the Cartesian coordinate system (Figure 3). Indeed, it is clear that, at all sites, the centroidal point is below the 1:1 line, indicating a general downward trend. To provide more detailed visual insights, the discharge scale is divided into three groups: low, medium, and high. It can be observed that the annual discharges in the low group for the second part of the observed time series (1991–2020) are lower than those in the first part (1961–1990) at almost all sites. Exceptions were recorded at the Banja Luka and Grančarevo stations, where several data points are above the 1:1 line. Even at these stations, a negative trend was generally recorded in the low data group. A similar observation was also noticed in the medium data group. The scatter points in this group are mainly below the 1:1 line. That means that the general discharge trends are also negative. Likewise, there are exceptions at some locations (e.g., the Doboj and Grančarevo stations). It is important to note that the differences between the flow in this group’s first and second halves are smaller than in the low data group. Hence, the scatter points are closer to the 1:1 line. In contrast, higher discharges were recorded in the high data group, especially in the second part of the time series. The blue dashed line in the graphs in Figure 3 indicates a higher slope than the 1:1 line, and where the two lines intersect generally marks the boundary between a negative and positive trend. Therefore, a positive trend is expected for flows greater than the intersection points, and a negative trend is expected for flows less than the intersection point.

3.2. Seasonal Winter Discharge Trends

The results of the LR analysis show that the trends in the winter period are generally negative. However, a trend at the 95% significance level was only observed at the Vrbanja site, while the trends at the other sites could not be considered significant (Table 3). The results of the MK test also agree with the LR analysis. The trend was confirmed at the 95% significance level at the Vrbanja site, while no significant trend was found at the other sites. The results of the ITA method show a significantly higher sensitivity. At four measuring stations (Banja Luka, Vrbanja, Doboj—Bosna, and Grančarevo), a negative trend was observed at the 99% significance level, while at one station, a negative trend was found at the 95% significance level (Novi Grad) (

Table 5. Analysis of ITA (slope s) of winter river discharges in the study area (1961–2020).

Station	Slope (s)	Standard Deviation (σ)	Correlation (r)	Slope Standard Deviation (σs)	CL (95%)	CL (99%)
Novi Grad—Una	−0.212 ↘	91.270	0.964	0.106	±0.208	±0.273
Prijedor—Sana	−0.032 →	35.066	0.942	0.052	±0.101	±0.133
Banja Luka—Vrbas	−0.135 ↓	34.607	0.962	0.041	±0.081	±0.106
Vrbanja—Vrbanja	−0.122 ↓	8.882	0.967	0.010	±0.019	±0.025
Doboj—Bosna	−0.601 ↓	74.393	0.976	0.069	±0.136	±0.179
Grančarevo—Trebišnjica	−0.376 ↓	42.224	0.972	0.043	±0.084	±0.111

→ (blue arow)—No trend; ↘ (orange arow)—Negative trend at 95% significance level (p < 0.05); ↓ (red arow)—Negative trend at 99% significance level (p < 0.01).

). At those sites, the alternative hypothesis H1, which posits the presence of a negative trend, is accepted. At the Prijedor monitoring station, the hypothesis about the absence of a trend (H0) is accepted, since the value of the slope s is smaller than the critical value CL_1−α. Looking at the results by groups, at some monitoring stations, a negative trend is observed in the low data group and a positive trend in the high data group (Novi Grad, Vrbanja, and Grančarevo). At other locations, the situation is reversed (Banja Luka and Doboj) (Figure 4).

3.3. Seasonal Spring Discharge Trends

The results of the LR analysis in spring show a negative trend at the 95% significance level at the Grančarevo monitoring station (Table 3). At other locations, it is not possible to determine a significant trend with this analysis. As expected, the MK test shows a higher sensitivity than the LR analysis. Therefore, a trend at the 99% significance level was observed at the Grančarevo monitoring station, and a trend at the 95% significance level was found at two other locations (Prijedor and Doboj). At the remaining three locations (Novi Grad, Banja Luka, and Vrbanja), no significant trend was found (Table 3). On the other hand, the ITA method confirms a negative trend at the 99% significance level at all locations (

Table 6. Analysis of ITA (slope s) of spring river discharges in the study area (1961–2020).

Station	Slope (s)	Standard Deviation (σ)	Correlation (r)	Slope Standard Deviation (σs)	CL (95%)	CL (99%)
Novi Grad—Una	−0.643 ↓	78.054	0.977	0.073	±0.142	±0.187
Prijedor—Sana	−0.443 ↓	31.593	0.959	0.039	±0.077	±0.101
Banja Luka—Vrbas	−0.199 ↓	37.039	0.959	0.046	±0.090	±0.118
Vrbanja—Vrbanja	−0.030 ↓	9.009	0.979	0.008	±0.015	±0.020
Doboj—Bosna	−0.566 ↓	70.453	0.986	0.050	±0.098	±0.129
Grančarevo—Trebišnjica	−0.475 ↓	22.956	0.983	0.018	±0.036	±0.047

↓ (red arow)—Negative trend at 99% significance level (p < 0.01).

). For this reason, the alternative hypothesis H1 is accepted for the seasonal spring trend at all sites. Looking at the discharges by group, a negative trend in the low data group and a positive trend in the high data group were observed at four monitoring stations (Novi Grad, Banja Luka, Vrbanja, and Doboj). At the other two measuring stations (Prijedor and Grančarevo), a negative trend was observed in the low, medium, and high data groups (Figure 5).

3.4. Seasonal Summer Discharge Trends

The LR analysis shows that no statistically significant trend was observed at any location during the summer period (Table 3). The MK test shows a trend with a significance level of 99% at two sites (Prijedor and Grančarevo) and 95% at three sites (Novi Grad, Vrbanja, and Doboj). The MK test detected no significant trend at the Banja Luka measuring station. The results of the ITA method also indicate a general negative trend at all locations. However, this method was unable to determine a statistically significant trend at the Banja Luka and Doboj sites. For this reason, the hypothesis H0 (no trend) was established for the Banja Luka station. At the Novi Grad station, a negative trend was observed at the 95% significance level, and at three monitoring stations (Prijedor, Vrbanja, and Grančarevo), a negative trend was identified at the 99% significance level. At those locations, the alternative hypothesis H1 is accepted (

Table 7. Analysis of ITA (slope s) of summer river discharges in the study area (1961–2020).

Station	Slope (s)	Standard Deviation (σ)	Correlation (r)	Slope Standard Deviation (σs)	CL (5%)	CL (1%)
Novi Grad—Una	−0.190 ↘	55.129	0.919	0.096	±0.187	±0.247
Prijedor—Sana	−0.204 ↓	22.041	0.971	0.023	±0.045	±0.059
Banja Luka—Vrbas	−0.019 →	20.876	0.862	0.047	±0.092	±0.122
Vrbanja—Vrbanja	−0.039 ↓	6.528	0.911	0.012	±0.023	±0.031
Doboj—Bosna	−0.109 →	51.380	0.963	0.060	±0.118	±0.155
Grančarevo—Trebišnjica	−0.147 ↓	9.716	0.959	0.012	±0.023	±0.031

→ (blue arow)—No trend; ↘ (orange arow)—Negative trend at 95% significance level (p < 0.05); ↓ (red arow)—Negative trend at 99% significance level (p < 0.01).

). During the summer period, a negative trend was observed in the low data group, while a positive trend was noted in the high data group at all sites. This becomes clear when looking at the slopes of the blue dashed lines in Figure 6, which are higher than the 1:1 no-trend line.

3.5. Seasonal Autumn Discharge Trends

The results of the LR analysis in the autumn indicate only a negative trend at the 95% significance level at the Doboj measuring station. At the other locations, it is not possible to determine significant trends using this method (Table 3). The results of the MK test show identical trends, indicating a significant finding at the 95% significance level (Table 2) at the same monitoring station (Doboj). At three measuring stations (Prijedor, Banja Luka, and Grančarevo), detecting significant trends is impossible even with the ITA method. At those locations, the H0 hypothesis is accepted. At the other three measuring stations, a significant trend was found at the 99% significance level, confirming the alternative hypothesis H1. It should be noted that a positive trend was recorded for the Novi Grad station, presenting the only significant positive trend in the seasonal analyses (

Table 8. Analysis of ITA (slope s) of autumn river discharges in the study area (1961–2020).

Station	Slope (s)	Standard Deviation (σ)	Correlation (r)	Slope Standard Deviation (σs)	CL (5%)	CL (1%)
Novi Grad—Una	0.516 ↑	89.965	0.941	0.132	±0.260	±0.342
Prijedor—Sana	−0.016 →	33.498	0.934	0.052	±0.102	±0.135
Banja Luka—Vrbas	−0.021 →	30.303	0.895	0.060	±0.117	±0.154
Vrbanja—Vrbanja	−0.040 ↓	6.211	0.971	0.006	±0.013	±0.017
Doboj—Bosna	−0.317 ↓	69.860	0.946	0.098	±0.193	±0.254
Grančarevo—Trebišnjica	0.019 →	36.916	0.972	0.038	±0.074	±0.098

→ (blue arow)—No trend; ↓ (red arow)—Negative trend at 99% significance level (p < 0.01); ↑ (green arow)—Positive trend at 99% significance level (p < 0.01).

). Examining the position of the scatter points by group, it can be generally observed that they are positioned below the 1:1 trend line in the low data group and above it in the medium and high data groups (Figure 7).

3.6. Comparison of Trend Analysis Methods

In this section of the paper, a comparative analysis of the results obtained using the LR analysis, the MK test, and the ITA method is presented. At all locations and in all data sets (annual, winter, spring, summer, and autumn data), either no trend or a negative significant trend was found. The one exception is in the autumn period at the Novi Grad station, where the only significant positive trend was recorded. Out of a total of 30 data sets, the LR method identified five significant trends at the 95% significance level, including 8.33% significant negative trends. The MK test revealed eight trends at the 95% significance level and five at the 99% significance level (43.33% significant negative trends). The ITA method revealed two trends at the 95% significance level and 22 at the 99% significance level (76.67% significant negative trends and 3.33% significant positive trends) (

Table 9. Comparison of LR, MK test, and ITA methods.

Station	Annual			Winter			Spring			Summer			Autumn
	LR	MK	ITA	LT	MK	ITA	LT	MK	ITA	LT	MK	ITA	LT	MK	ITA
Novi Grad—Una	→	→	↓	→	→	↘	→	→	↓	→	↘	↘	→	→	↑
Prijedor—Sana	→	→	↓	→	→	→	→	↘	↓	→	↓	↓	→	→	→
Banja Luka—Vrbas	→	→	↓	→	→	↓	→	→	↓	→	→	→	→	→	→
Vrbanja—Vrbanja	↘	↘	↓	↘	↘	↓	→	→	↓	→	↘	↓	→	→	↓
Doboj—Bosna	↘	↓	↓	→	→	↓	→	↘	↓	→	↘	→	↘	↘	↓
Grančarevo—Trebišnjica	→	↓	↓	→	→	↓	↘	↓	↓	→	↓	↓	→	→	→

→ (blue arow)—No significant trend; ↘ (orange arow)—Trend at 95% significance level (p < 0.05); ↓ (red arow)—Trend at 99% significance level (p < 0.01); ↑ (green arow)—Positive trend at 99% significance level (p < 0.01).

). The MK test confirmed all significant trends detected by the LR analysis, and the ITA method confirmed all significant trends detected by the MK test. Trends that were not deemed significant by the ITA method were also not significant in the MK test or the LR analysis. Accordingly, the LR analysis was found to be the least sensitive, followed by the MK test, and the ITA method was the most sensitive (Figure 8).

3.7. Trends in ITA Low, Medium, and High Data Groups

To gain more detailed insights into the trend movement in the low, medium, and high data groups, a trend analysis was performed for each group using the ITA method, which proved to be the most sensitive. Of the total 90 data sets (annual and seasonal), a negative trend at the 99% significance level was found in 46 data sets, and a negative trend at the 95% significance level was found in five data sets. No trend was found in 18 data sets (

Table 10. Results of the ITA method for annual and seasonal flows in the low, medium, and high data groups.

Station	Annual			Winter			Spring			Summer			Autumn
	ITA			ITA			ITA			ITA			ITA
	L	M	H	L	M	H	L	M	H	L	M	H	L	M	H
Novi Grad—Una	↓	↓	↑	↓	↓	↑	↓	↓	↗	↓	↑	↗	↓	↑	↘
Prijedor—Sana	↓	↓	→	↘	→	↓	↓	↓	↘	↓	→	↗	→	↑	↓
Banja Luka—Vrbas	↓	↓	↑	→	↓	↓	↓	↘	→	→	→	↗	→	↑	↓
Vrbanja—Vrbanja	↓	↓	↗	↓	↓	↓	↓	→	↑	↓	↑	↗	↓	→	↓
Doboj—Bosna	↓	↓	↑	→	↓	↓	↓	↓	→	↓	→	↗	↓	→	↓
Grančarevo—Trebišnjica	↘	↓	↑	↓	↓	↑	↓	↓	↓	↓	↓	→	→	→	↑

→ (blue arow)—No trend; ↘ (orange arow)—Negative trend at 95% significance level (p < 0.05); ↓ (red arow)—Negative trend at 99% significance level (p < 0.01); ↗ Positive trend at 95% significance level (p < 0.05); ↑ Positive trend at 99% significance level (p < 0.01); L—low; M—medium; H—high.

). Positive trends were also identified in this analysis. Thus, a positive trend was found at the 99% significance level in 13 data sets and at the 95% significance level in seven data sets. The analysis of the results showed that the low data group mainly exhibits negative trends. The medium data group also showed mostly negative trends, except in summer and autumn, when positive trends were recorded at some locations. The high data group recorded the most positive trends, except in the autumn period when the trends were primarily negative. These results provide detailed information on the annual and seasonal discharge patterns of the observed sites by assessing the low, medium, and high data groups.

4. Discussion

Rivers are products of nature. Therefore, rivers directly reflect the interaction between different factors of climatic characteristics in a catchment area, such as air temperature and precipitation. Nowadays, climatic factors are changing rapidly due to increasing anthropogenic influences, which directly affect the amount of water in the riverbeds. Therefore, the measurement of river flows and their changes over time is the focus of numerous scientific and professional studies. To obtain the most accurate results, methods are constantly being developed and improved. For this reason, a very sensitive ITA method was used in this work. The results obtained represent an improvement over the previous research carried out in the observed area [44].

The results from 1961 to 2020 at all six monitoring stations indicate a significant negative trend in annual discharges from 1961 to 2020. This leads to our conclusion on the changes in climatic factors at the beginning and end of the observation period. From a territorial perspective, the catchment areas of the observed rivers encompass approximately two-thirds of Bosnia and Herzegovina’s territory, indicating that climate changes have a regional character. These results align with numerous local, regional, and global scientific studies [54,55,56].

The results of the seasonal trends are, to some extent, consistent with the annual trends, and in most cases, significant negative trends were recorded. Nevertheless, the results deviate from the general yearly pattern. For example, in winter, at the four stations (Prijedor, Banja Luka, Vrbanja, and Doboj), the maximum discharges are lower in the second subperiod. Similar results were also observed at three measuring stations in autumn (Prijedor, Banja Luka, and Vrbanja). From this, it can be concluded that the maximum discharges in winter and autumn are usually lower in the second subperiod and generally higher in spring and summer. In the second subperiod, the minimum discharges are lower in almost all cases (except in winter). The mean flows in the second subperiod are also usually lower in winter, spring, and summer and slightly higher in autumn.

If we examine the results by data group (low, medium, and high), we conclude that the most significant reduction in discharges occurs in the low data group, with a slightly smaller reduction in the medium data group. In contrast, the annual flows in the high data group are generally higher in the second subperiod (1991–2020). Thus, the results obtained by the data group indicate the occurrence of increasingly severe extremes in recent years, making them extremely important from a practical point of view. Namely, these results provide the first visual insight that could potentially improve the situation at hand. The measures that should be applied still need to be considered and evaluated. Still, it is generally clear that extremes are more significant in a quantitative sense, and the period of their occurrence is becoming shorter. In this sense, the occurrence of extremes could have negative consequences in economic terms, as well as in terms of the potential number of human casualties. Therefore, increasingly large and prolonged extremes, such as droughts and floods, can be expected. According to Vidmar et al. [57], the catastrophic floods in 2014 affected more than 50% of the territory of BH, while the total damage was estimated at around two billion EUR. Similar phenomena are also observed in neighbouring countries, so the observed area is not an exception in this respect but is subject to the same general rule.

A comparative analysis of the methods used confirms previous research on the sensitivity of the ITA method [34]. This method detected twice as many significant trends as the MK test and ten times as many as the LR analysis. For this reason, the statistical processing of trends using innovative new methods is becoming increasingly important compared to traditional techniques. Indeed, it is essential to evaluate the trend in different hydrological data sets, as they are the first and irrefutable evidence of a change in the climatic characteristics of a given area. Further research will be needed to analyse the factors influencing climate change in more detail, as the results obtained do not allow for such conclusions, which is a limitation of the performed trend analyses. For the protection of natural resources, as well as for predictions of minimum and maximum values, they are of exceptional interest to the local community and scientists. In the future, it is recommended that research be conducted to obtain accurate forecasts of the likelihood and severity of floods, as well as the potential consequences for hydropower management, due to increasingly pronounced dry periods. Measures to mitigate the impact of extreme events have yet to be determined. In the long term, they are certainly reducing anthropogenic effects on the environment as a whole, and in the short term, specific measures in terms of regulating watercourses can limit the occurrence of extreme events to within acceptable limits.

5. Conclusions

In this study, the discharge trends at six hydrological monitoring stations in Bosnia and Herzegovina in 1961–2020 were observed using an LR, the MK test, and ITA methods. It was found that the ITA method has the highest sensitivity. This is because this method revealed many significant trends that could not be detected with the LR and MK trend tests. Therefore, it can be generally concluded that the ITA method is helpful to analyse many hidden trends of changes in time series of flow data in the research area.

The most important conclusions are presented below:

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The LR analysis revealed the fewest significant trend changes of the three methods examined, with two annual negative trends (p < 0.05) and three seasonal negative trends (p < 0.05), representing 16.67% of the total number of trends examined. With this method, no trend at the 99% significance level was observed in any of the data sets;

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The MK test showed a significantly higher sensitivity, so this method recorded eight negative trends at the 95% significance level (26.67%) and five negative trends at the 99% significance level (16.67%). Thus, of the total number of records, 43.33% showed negative trends;

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The ITA method showed the highest sensitivity to trend changes in the observed data sets, and thus, all annual negative trends were recorded at the 99% significance level. In terms of seasonal trends, two negative trends were detected at the 95% significance level, 21 negative trends at the 99% significance level, and one positive trend at the 99% significance level. This accounts for approximately 80% of the significant trends identified. Looking at the results by group (low, medium, and high), the ITA method recorded a total of 47 negative trends at the 99% significance level (52.22%) and 13 at the 95% significance level (14.44%). Grouping the data in this way yielded seven positive trends at the 95% significance level (7.78%) and thirteen at the 99% significance level (14.44%).

The results of this study provide essential insights into the discharge trends in the observed area and represent a significant step towards sustainable water management planning in Bosnia and Herzegovina. The observed decline in discharge trends could have undesirable consequences for electricity generation in the short term, as a substantial proportion of the country’s electricity is generated in hydropower plants. In addition, the negative consequences of climate change are exacerbating the increase in maximum discharges, leading to more frequent flooding problems that could become even more severe. However, to confirm this, further trend analyses and investigations into the influence of extremes on these phenomena must be carried out. Therefore, continued scientific research in this direction is to be expected.