Flood Frequency Analysis in the Catchment of Oued Mazafran in the Northern OF Algeria

GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 FLOOD FREQUENCY ANALYSIS IN THE CATCHMENT OF OUED MAZAFRAN IN THE NORTHERN OF ALGERIA Elkheir SUICI1 , Abdelhalim YAHIAOUI2 ,Yamina EL-MEDDAHI1 1 Hassiba Benbouali University of Chlef, Faculty of Civil Engineering and Architecture, Algeria 2 University of Bouira, Institute of Technology, Algeria E-mail: [email protected] ABSTRACT Extreme flood events are commonly described by several dependent characteristics, such as duration, volume and peak flow. In Algeria and North Africa, flood frequency analysis is conducted as a univariate approach focusing separately on each single of flood characteristics. The analysis of flood in oued Mazafran catchment by the flood frequency analysis is crucial for understanding and managing flood risk, designing infrastructure and planning for floodplain management. To perform flood frequency analysis, the series of the annual maximum flow discharge of Fer a Cheval station is fitted to a probability distribution. Well, several probability distributions can be used to fit this series such as Gumbel, Log Normal, Log Pearson type III, and more. The Choosing a single distribution probability has become an important question in hydrology frequency analysis. Therefore, the use of the decision support system that is based on the heavy tails of distribution probability analysis conducts to the use of subexponential distributions and information Criterion to the Gumbel distribution for this analysis. Keywords: Catchment; Distribution; DSS; Flood; Frequency analysis; Series. 1 INTRUDUCTION Floods are caused by extreme rainfall and their evolution depends on geomorphological characteristics of the catchment and to the urban expansion and its consolidation around rivers. According to the change in climate, the change of flood regime is a major factor that leads to increased exposure to the risk of flooding [1]. In Algeria, floods are considered to be a major natural calamity. The flooding of November 2001 in Algiers, the floods of oued Bechar and oued M’Zab in Ghardaïa October 2008 as examples are an adverse impact on the people and on infrastructure. The phenomena of floods manifest themselves in a catastrophic manner thus constituting a major constraint for economic and social development. Floods are the most destructive and even the most frequent natural disasters and cause significant human and material damage. The oued Mazafran in the north of Algeria is often confronted with floods which can be caused flooding in the surrounding region, the flood of March 1974 caused 52 deaths, destroyed 4570 houses and 13 bridges [2]. The occurrence of extreme precipitation leads to increase in the magnitude and frequency of extreme floods [3]. Estimating of flood can be carried out using methods depending on data resources and time availability [4]. So, the frequency analysis discharge of annual maximum instantaneous or annual maximum peak flow data (QIX) may be used for estimation of the discharge QIXT for return periods T, which is essential for any studies of the hazard and management relation of flooding. Relating the magnitude of extreme events to their frequency of occurrence, through the use of probability distributions, is the principal aim of the frequency analysis [5]. Flood frequency analyses involves computing statistical information of a given annual maximum instantaneous discharge. Frequency distribution is generated gives the likelihood of various discharges as a function of return period. Many distributions may be used for flood frequency analysis. The Gumbel’s distribution, the log-normal distribution and log-Pearson Type III distribution are standard flood frequency distributions used by US Federal agencies such as Federal Emergency Management (FEMA) and US Geological Survey (USGS) can be used to 18 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 estimate design floods with their own advantages and disadvantages [6]. But in hydrology of extremes, several distributions may be used for fitting annual peak flow series [7]. Therefore, a method focusing on the tail of the distribution should be preferred [8], although by the use of the Decision Support System (DSS) [9], which defines the class of distributions prior to a model selection practice with respect to tail behaviour of the time series of data [10]. The DSS conducts finally to the choice of the appropriate distributions for the frequency analysis. 2 STUDY AREA AND DATA SETS The study has been conducted on the catchment of oued Mazafran (Figure 1) situated in the North of Algeria about 50 km from the west of Algiers between 2°15’and 3°00’ of East longitude and 36°15’ and 36°45’ of North latitude. The area of the catchment is 1893 km2 and its perimeter is 315 km, about 60 % of the catchment is mountainous. The catchment is elongated with a 131 km of length and 14.5 km of width. The stream of oued Mazafran is the junction of three main streams, oued Bou Roumi, oued Djer and oued Chiffa, where the risk of flooding is significant, which needs to be monitored during rainfall as it has become stronger and more intense in recent years [2, 11]. The catchment of oued Mazafran (Figure 1) is characterised by a Mediterranean climate, semi-arid to arid, characterized by dry and hot summers and cold and humid winters. The rainfall is abundant but irregular; the catchment receives annually between 600 mm and 900 mm of precipitation [2], causing significant flooding especially in the stream of oued Mazafran. Figure 1. The catchment of oued Mazafran The hydrometric data set used in this study were provided by the National Agency of Hydraulics Resources (ANRH) of Algiers, it consists of the time series of annual maximum instantaneous discharge (QIX) recorded at Fer à Cheval gauge station for the periods 1969/1970 to 1987/1988, 1990/1991 to 1994/1995 and 1997/1998 to 2011/2012 (Figure 2). The number of element in the time series is 42, with a mean of 269.25 m3/s and standard deviation of 179.62 m3/s, the min and max values are respectively 18 m3/s and 861 m3/s. 19 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 Figure 2. Annual instantaneous maximum discharge at Fer à Cheval gauge station By the use of Wald-Wolfowitz test [12], Mann-Whitney test [13], Mann-Kendall test [14, 15] and Grubbs test [16], the series of QIX is independent, homogeneous, stationery and with no outlying values (Table 1). So, it may be used for frequency analysis study. Table 1. Sampling tests of the annual instantaneous maximum discharge series Type of the test Calculated Value Critical Value Wald-Wolfowitz test for independence at 5% 1.860 1.960 Mann-Whitney test for homogeneity at 5% 1.698 1.960 Mann-Kendall test for stationarity at 5% 1.170 1.960 Grubbs test for outliers at 1% 3.294 3.404 3 MATERIALS AND METHODS 3.1 The use of decision support system The estimation of the event QIXT requires the knowledge of the nature of the distribution of the population of the annual instantaneous maximum discharge QIX. So, a number of distributions probabilities may be used to fit a series of QIX. Thus, the use of the Decision Support System (DSS) [9, 17] may conduct to the choice of the class of distributions prior to a model selection practice with respect to tail behaviour of the series of data [10]. The DSS is based on the study of the tail behaviour of extreme event distributions by two classifications and four graphical criteria. The first graphic is the log–log plot, well the series of QIX is fitted to Zips or Pareto distribution [18], well its probability density function is given by: ( ) α IX IX Q Q Q α QXP −         − == minmin 1 (1) Where, α is the only parameter (tail) and Qmin is the minimum value existed in the population of QIX, α may be estimated by the maximum likelihood method [19, 20] as: 20 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 1min 1 ln  = =+  n IXi i n Q Q (2) Hence, Qmin is obtained as a function of α by: min 1 11 exp ln 1  =  = − +  −   n IX i i QQ n (3) To estimate the value of α [21, 22], let’s considering the discrete probability density function of Pareto given by [23]: ( ) ( ) αζ k kXP α− == (4) Where, ( )  is the Riemann Zeta function [25], which is given by: ( ) 1 1    = mm (5) The estimation of α by maximum likelihood method gives: ( ) ( ) 1 1ln 5.29   = = − = −  n IXi i Q n (6) ( )  , is the derivative of the Riemann Zeta function. The value of the ratio ( ) ( )      can be generated on most modern mathematical and engineering calculation programs [24]. So, ,17.1=α from the equation (3), Qmin is calculated and is equal to 0.55 m3.s-1. Thus, the series of QIX may be fitted to Zips or Pareto distribution (Figure 3). Figure 3. Log-Log plot for the regularly varying distributions 21 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 According to the Log-Log plot (Figure 3) of the fitting the series of QIX to Pareto distribution, the DSS conduct to consider that the distributions for frequency analysis of series of QIX may be either exponential distribution (Class E) or sub-exponential distributions (Class D). To discriminate between these two classes of distributions it has to use the mean excess function (Figure 4) [26]. Figure 4. Excess mean function plot The mean excess function has a positive slope. So, the sub-exponential distributions of the class D may be used for the analysis of the series of QIX. Thus, the confirmation of this decision may be done by the generalized Hill ratio plot (Figure 5) [27] or with the method based on statistic of Jackson (Figure 6) [28]. Figure 5. Generalized Hill ration plot 22 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 Figure 6. Statistic of Jackson plot The Generalized Hill ratio plot (Figure 5) shows that there is a tendency to an oblique mean stability according to the majority of the points and the statistic of Jackson plot is irregular and is diverges from 2. Therefore, those plots [9] confirm the use of the sub-exponential distributions of the class D for the frequency analysis of the series of QIX. 3.2 Fitting of the series of QIX The sub-exponential distributions applied in the frequency analysis in hydrology of extremes are Gumbel, Gamma, Pearson Type III and Halphen B distributions. Those distributions are used for the frequency analysis of the series of QIX of oued Mazafran. 3.2.1 Case of Gumbel distribution The Gumbel distribution is given by its cumulative distribution function: ( ) exp exp  −   = − −     IX IX Qm FQ a (7) m and a are the location and scale parameters. By the use of the probability weighted method (PWM) [29], the estimation of a and m are respectively equal to 143.90 m3.s-1 and 186.20 m3.s-1 (Figure 7). 3.2.2 Case of Gamma distribution The Gamma distribution with the scale parameter a and the shape parameter k is given by the following probability density function: ( ) ( ) 1 1exp −     =−         k IX IX IX QQ fQ a k a a (8) 23 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 Where, ( ) . is the Gamma function [30]. By the method of moments, a =.119.83 m3.s-1 and k.=.2.25 (Figure 8). Figure 7. Fitting to Gumbel distribution (PWM) Figure 8. Fitting to Gamma distribution (MM) 3.2.3 Case of Pearson Type III distribution The Pearson Type III distribution with location parameter m, scale parameter a and the shape parameter k, is given by its density probability function: 24 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 ( ) ( ) 1 1exp − −−     =−         k IX IX IX Q m Q m fQ a k a a (9) The method of moments (MM) gives, the estimate of a, m and k as -120.65 m3.s-1, 186.20 m3.s-1 and 4.71 (Figure 9). 3.2.4 Case of Halphen B distribution The Halphen B distribution with scale parameter a, and two shape parameters k and υ. The probability density function of Halphen B is given by: ( ) ( ) 2 1 2 22 2exp    − = − +   IX IX IX IX Q Q Q f Q k a ef k a a (10) Where, ( ) . υ ef , is the Halphen’s exponential factorial function [31]. The estimation of the parameters a, k and υ by the method of the maximum likelihood (MLE) are a = 373.43 m3.s-1, k.=.0.44 and υ = 0.59 (Figure 10). Figure 9. Fitting to Pearson Type III (MM) 25 GeoScience Engineering Vol. 70 (2024), No. 2 geoscience.cz pp. 17–29, ISSN 1802-5420 DOI 10.35180/gse-2024-0109 Figure 10. Fitting to Halphen Type B (ML) 4 RESULTS AND DISCUSSION Goodness-of-fit test of the used distributions (Table 2) may be done by the probability plot correlation coefficient (PPCC) [32, 33], root mean square deviation (RMSD) [34] and the test of Kolmogorov–Smirnov (KS-test) [35]. The values of PPCC and RMSD assess the fitted distribution at a site by summarizing the deviations between observed discharges and computed discharges. The KS-test is a nonparametric test, the computation of Dob as the maximum of the difference between cumulative observed frequencies Fi and the theoretical distribution F (QIX): ( ) max=− ob i IXi D F F Q (11) Dob must be lower than the critical values Dn, α, where α the significance level and n is the sample size. When n is over 35, Dn, α is calculated for α = 1% and α = 5% by: , 1% 1.63 0.252== n Dn (12) , 5% 1.36 0.210== n Dn (13) According to obtaining results (Table 2), all the observed Kolmogorov–Smirnov values are less than 0.21 except for the Halphen B distribution. The PPCC values are close to 1 and the values of RMSD are less than 1. Moreover, the comparison of the fittings of the four distributions shown in Figure 11, conducts to accept all the distributions for prediction of the probable maximum instantaneous discharges.