# Regional Flood Frequency Analysis of the Sava River in South-Eastern Europe

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}), see for example [28]. In the spring of 2014, Croatia, Bosnia and Herzegovina, and Serbia, were impacted by a flood event unparalleled in the hydrological records of the region [45,46]. The major cause of this flood was a Vb-type cyclonic weather system [5] that remained stationary over South-eastern Europe for several days causing rainfall accumulations of up to 300 mm in three days [45,47]. In Serbia alone, these floods affected the territories of 24 municipalities and caused EUR 1.525 billion in damages [48]. Before the 2014 event, there were other widespread floods such as in 1933, 1937, 1940, 1947, 1964, 1974 and 2007 [49]. The most remarkable of these occurred in 1974, when historical record water levels and discharges were exceeded at all stations downstream of the Drina River confluence. These extremes were exceeded by the 2014 flood event.

## 2. Research Area

^{2}, is the largest river catchment in South-eastern Europe and the second-largest sub-basin of the Danube River basin (Figure 1). It is shared by Slovenia, Croatia, Bosnia and Herzegovina, and Serbia; and a small part of 0.2% of the basin lies within Albania [50]. The Sava River originates in Slovenia, where two mountainous streams, Sava Dolinka and Sava Bohinjka, merge together near the town of Radovljica. The main tributaries of the Sava River are in downstream order the rivers Kolpa, Una, Vrbas, Bosna, Drina and Kolubara. Between the Una and the Drina, the majority of water comes from the south. Una, Vrbas, Bosna and Drina jointly contribute a discharge of 1149 m

^{3}/s to the Sava River, which is as much as 68% of the flow of the Sava at its confluence with the Danube [51]. Drina is the largest tributary with 371 m

^{3}/s or 22% of the flow of the Sava at its confluence with the Danube [51]. The length of the Sava River is 945 km to its confluence with the Danube River in Belgrade. Around 8 million people live in the Sava River basin [36].

## 3. Data

## 4. Methods

#### 4.1. L-Moments Estimation for RFFA

_{r}represents the rth-order PWM, while F

_{X}(x) is the CDF of X. Further, $b$

_{i}for i = 0, 1, 2, 3, represents the unbiased sample estimators of the first four PWM as described by Hosking and Wallis [43]:

_{(j)}indicates the ranked AMS values, that is, X

_{(n)}is the largest and X

_{(1)}is the smallest value. Furthermore, the first four L-moments [43] are given as follows:

_{1}), scale (λ

_{2}), shape (λ

_{3}) and kurtosis (λ

_{4}) of the distribution functions, a fact that is particularly useful in RFFA. Lastly, the L-moments ratios are calculated as follows [43]:

_{i}is the record length at site i; τ

^{(i)}, τ

_{3}

^{(i)}, τ

_{4}

^{(i)}are the sample values of LCv, LCs and LCk at site i, respectively; and ${\tau}^{R}$, ${\tau}_{3}^{R}$, ${\tau}_{4}^{R}$ are the regional sample averages of LCv, LCs and LCk, respectively. For a region to be considered as homogeneous, the test statistic values, V

_{i}, for i = 1, 2, 3, should all be less than unity. If 1 ≤ V

_{i}< 2, then a region is possibly homogeneous and if V

_{i}≥ 2, then the region can be assumed as heterogeneous [31,73].

_{4}is the regional sample standard deviation of the LCk values [31]. The test is performed by means of a comparison with a quantile of the standard normal distribution. We adopted a significance level of 5%, this means, a candidate distribution is considered suitable if $\left|Z\right|<1.96$.

_{(j)}, j = 1, …, n, be the size-sorted AMS values (as in Section 4.1); and the empirical CDF, F

_{n}(x), be defined as the number of X

_{(j)}≤ x divided by n; then F

_{n}(x) is a step-like curve in dependence on X

_{(j)}, which goes from 0 to 1 and makes steps of size 1/n at each X

_{(j)}value. The smaller the distance is between a certain theoretical candidate distribution, F

_{theo}(x), the better the fit. The distance can be measured by means of the differences,

^{−1}is used to correct for the number of employed parameters, p, of a theoretical distribution. (That means, it is “easier” to fit a distribution with many parameters to data than with few, and Ockham’s Razor [56] indicates to prefer descriptions with fewer parameters.)

#### 4.2. Trend Estimation

## 5. Results and Discussion

#### 5.1. Regional Flood Frequency Analysis

#### 5.2. Trend Analysis

#### 5.3. Homogeneity Assessment and Regional Flood Frequency Analysis

_{1}, V

_{2}and V

_{3}(Table 4) indicate that after Hosking and Wallis [43] we can consider the Sava River basin as acceptably homogeneous. Since all measures are less than unity, no further inspection of the data or of the cross-correlation between sites was necessary. That means, that the AMS data from the Sava River basin can be meaningfully applied for RFFA and also for a subsequent quantile estimation for gauged and ungauged rivers within the basin.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Mathematical Formulas for the Distribution Functions

_{X}(x), where

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**Figure 1.**Sava River basin (red line), major rivers (blue lines), locations of the six selected gauging stations (black dots) and political borders with country names (grey) in ISO 3166-1 alpha-3 code. Inset is the position of study region within Europe.

**Figure 3.**L-moments ratio diagram for the six selected gauging stations (1961–2020) in the Sava River basin.

**Figure 4.**FFA results: CDFs of empirical data and fitted candidate distributions for the six selected gauging stations in the Sava River basin ((

**a**), Radovljica; (

**b**), Čatež; (

**c**), Zagreb; (

**d**), Jasenovac; (

**e**), Županja; (

**f**), S. Mitrovica).

**Figure 5.**Estimated at-site return levels with 95% confidence bounds for GEV for the six selected gauging stations in the Sava River basin ((

**a**), Radovljica; (

**b**), Čatež; (

**c**), Zagreb; (

**d**), Jasenovac; (

**e**), Županja; (

**f**), S. Mitrovica).

**Figure 6.**Estimated return discharge levels for different return periods for the six selected gauging stations in the Sava River basin.

Station | Country | Elevation (m a.s.l.) | Location (River-km) | Basin Area (km^{2}) |
---|---|---|---|---|

Radovljica | Slovenia | 408 | 901 | 908 |

Čatež | Slovenia | 137 | 737 | 10186 |

Zagreb | Croatia | 112 | 664 | 12450 |

Jasenovac | Croatia | 87 | 501 | 38953 |

Županja | Croatia | 76 | 262 | 62891 |

S. Mitrovica | Serbia | 72 | 139 | 87966 |

**Table 2.**Descriptive statistics for the AMS data from the six gauging stations on the Sava River; STD, standard deviation.

Station | n | Mean (m ^{3}/s) | Median (m ^{3}/s) | Maximum * (m ^{3}/s) | STD (m ^{3}/s) | Skewness ^{†} | Kurtosis ^{†} |
---|---|---|---|---|---|---|---|

Radovljica | 60 | 445 | 433 | 809 | 149 | 0.60 | −0.39 |

Čatež | 60 | 1744 | 1727 | 3811 | 588 | 0.95 | 1.49 |

Zagreb | 60 | 1664 | 1643 | 3005 | 441 | 0.59 | 0.07 |

Jasenovac ^{‡} | 56 | 2078 | 2089 | 2814 | 302 | 0.36 | −0.69 |

Županja | 60 | 2915 | 2843 | 5317 | 573 | 1.26 | 3.66 |

S. Mitrovica | 60 | 4027 | 3823 | 6420 | 910 | 0.56 | 0.49 |

^{†}a normal distribution has skewness zero (dimensionless) and kurtosis zero (dimensionless);

^{‡}missing years (1992–1995) are due to the civil war in former Yugoslavia.

Station | $\mathit{b}$ * |
---|---|

Radovljica | 0.5 ± 1.1 |

Čatež | 3.3 ± 4.6 |

Zagreb | 1.9 ± 4.5 |

Jasenovac | 3.1 ± 2.4 |

Županja | −0.7 ± 4.2 |

S. Mitrovica | −9.6 ± 6.4 |

^{3}/s per year.

${\mathit{\tau}}^{\mathit{R}}$ | ${\mathit{\tau}}_{3}^{\mathit{R}}$ | ${\mathit{\tau}}_{4}^{\mathit{R}}$ | ${\mathit{V}}_{1}$ | ${\mathit{V}}_{2}$ | ${\mathit{V}}_{3}$ |
---|---|---|---|---|---|

0.14 | 0.13 | 0.14 | 0.04 | 0.07 | 0.077 |

**Table 5.**Results of goodness-of-distributional-fit measures u (Equation (18); dimensionless) of candidate distributions to observed station data.

Distribution | Radovljica | Čatež | Zagreb | Jasenovac | Županja | S. Mitrovica |
---|---|---|---|---|---|---|

GEV | 0.3580 | 0.3516 | 0.3576 | 0.3280 | 0.3516 | 0.3575 |

GLO | 0.3664 | 0.3607 | 0.3754 | 0.3674 | 0.3607 | 0.3785 |

Gumbel | 0.3597 | 0.3611 | 0.3589 | 0.3399 | 0.3621 | 0.3612 |

LNIII | 0.3575 | 0.3518 | 0.3578 | 0.3575 | 0.3515 | 0.3580 |

LPIII | 0.3827 | 0.3598 | 0.3697 | 0.3798 | 0.3498 | 0.3666 |

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**MDPI and ACS Style**

Leščešen, I.; Šraj, M.; Basarin, B.; Pavić, D.; Mesaroš, M.; Mudelsee, M.
Regional Flood Frequency Analysis of the Sava River in South-Eastern Europe. *Sustainability* **2022**, *14*, 9282.
https://doi.org/10.3390/su14159282

**AMA Style**

Leščešen I, Šraj M, Basarin B, Pavić D, Mesaroš M, Mudelsee M.
Regional Flood Frequency Analysis of the Sava River in South-Eastern Europe. *Sustainability*. 2022; 14(15):9282.
https://doi.org/10.3390/su14159282

**Chicago/Turabian Style**

Leščešen, Igor, Mojca Šraj, Biljana Basarin, Dragoslav Pavić, Minučer Mesaroš, and Manfred Mudelsee.
2022. "Regional Flood Frequency Analysis of the Sava River in South-Eastern Europe" *Sustainability* 14, no. 15: 9282.
https://doi.org/10.3390/su14159282