Determination of the ood volume by the aspects of peak ow and ood hydrograph at the level of the city of Biskra, Wadi Biskra watershed, Algeria.

The peak ow of a ood can be determined by several empirical methods. Among these methods, the Gradex method is used in this work to estimate the project ood and the volumes corresponding to the ows. This approach has made it possible to recognize the ow of different frequencies by aspects of the peak ow and the ood hydrograph. The study was based on the maximum annual daily rainfall for a long series of observations (47 years), and on the intensity-duration-frequency (IDF) curves of the four rainfall stations Biskra, T'kout, Djemoura, and El kantara; located in the watershed of Oued Biskra. The application of the Gradex method has allowed to approach the maximum ow of oods at the level of the outlet which is located at the entrance of the city of Biskra; for the rare frequency of occurrence (return periods ranging from 10 to 1000 years).


Introduction
Algeria, like other countries in the world, suffers from water resource management problems. These require a good knowledge of the spatial and temporal variability of the hydrological regime at the scale of catchment areas ( oods and low water levels), in order to achieve a good management of ood risks, whether at the scale of catchment areas or at the scale of alluvial plains. This study focuses on the phenomenon of extreme ood runoff of the Oued Biskra at the level of the city of Biskra. These oods constitute a risk for all the components of the studied watershed. Indeed, the over ows that have occurred in recent years, particularly during the years 2000 and 2010, have caused considerable human losses and material damage (Layan, 2008).

Geographic Context Of The Study Area
The Wilaya of Biskra is located in the South-East of Algeria, it occupies an area of 21671 Km2, its altitude is 128 meters / sea level. (ANAT). The case study and analysis is Biskra, an Algerian Saharan [27] city located at 34°48 North (latitude) and 05°44 East (longitude) [1]. Figure n° 01.
The climate of Biskra is characterized by a very hot and dry summer, the average temperature is 43.5 °C, ( gure 2 (a)), the average relative humidity is 12%, ( gure 2 (b)), and a very cold winter (average minimum temperature of 4 °C, average maximum relative humidity of 89%). Precipitation is rare and does not exceed 31 days per year. Biskra is located in the arid region, according to the aridity index of 'Martonne', [2].
The summer months, June, July, August and until September, are hot months, with average maximum temperatures of 36.5 to 39 °C. On the other hand, the months of November to April are considered cold with average minimum temperatures of 11.7 to 8.4 °C.
Incident solar radiation is very intense and of the order of 7680 Wh/m2, on a horizontal plane during the month of July, ( gure 3(a)), which corresponds to a sunshine duration of 383 hours, ( gure 3(b)), and which can exceed 12 hours per day.
In winter, it reaches its minimum during the month of December for an intensity of 2712 Wh/m2, which corresponds to a sunshine duration of 219 hours/month, or 7 hours/day [3]. All this contributes to the harsh climate of the city of Biskra. (Figure 4 a and b).

Presentation of the Wadi Biskra watershed
Wadi Biskra Limited to Biskra, this sub-basin covers an area of 2787 km², almost all of which belongs to the domain of the runoff slopes. Wadi Biskra is formed by the meeting of the two large wadis El Haï (subbasin of Wadi El Hai), and Wadi Djemoura (sub-basin of Wadi Djemoura), which drain respectively an area of 1788 and 906 km2, whose con uence gives rise to Wadi Biskra (the sub-basin of the complementary Wadi Biskra) covers an area of 93 km2 at an altitude of 200m (Figure 05

Objectives And Methodology
Given the absence of daily ow gauges to facilitate the statistical analysis of ancient oods, the hydrological study was used. This approach aims at the recognition of project oods by the aspects of peak ow and ood hydrograph. The ood study was carried out using the Gradex method to achieve two main objectives; namely the estimation of peak ows (Qp) at the outlet of the studied catchment area for return periods ranging from 10 to 1000 years, and the determination of the shape of the ood hydrograph and the estimation of ood volumes.
The Gradex method, therefore, aims at nding the maximum ood ows for rare to very rare frequencies of occurrence (return time more than 100 years). It is particularly applicable when there is a long series of rainfall in the basin, thus allowing to make the most of all available data.
In general, more rainfall information is often available (Meylan and Musy, 1999). This method was introduced by Guillot and Duband (1967) and has since been used by several authors such as Naghettini et al (1996). Gradex is a very suitable method for watersheds for which ow data are not available (Zemzami et al., 2012).
This method is based on the following assumptions: -the maximum ows sought are only caused by maximum rainfall, uniformly distributed over the basin. Thus, there are no different origins of ood formation.
-The maximum rainfall and the corresponding ow rates follow the same statistical distribution law, called the extremes because of the nature of the phenomenon sought (rare oods). This expresses above all the fact that the asymptotic behaviour of the rainfall and ow distribution laws is identical. Gumbel's law (Gumbel, 1958) is often used for this purpose, and only in this case is the exponential nature of this distribution described by the slope of the observed rainfall adjustment line, measured on a suitable probability diagram. The slope of this line is the gradient of this exponential distribution. The Gradex method was applied according to the following steps: -Gumbel's law adjustment of maximum daily rainfall and determination of Pjmax (T) for T ranging from 2 to 1000 years.
-Choice of a unit hydrograph.
-Calculation of the Rain Gradex over the concentration time Gp(Tc) from the Rain Gradex in 24 hours.
-Calculation of the reference peak ow Qp(T decennial return period) using Caquot's empirical formulas.
-Calculation of the peak ow rates and runoff water levels for each return period using the Gradex method.

Available Data
The present study was based on the annual maximum daily rainfall and the Intensity-Duration-Frequency (IDF) curves of the seven stations located in the Oued Biskra watershed (see Table 01).
The Montana coe cients are necessary for the application of certain formulas related to the Gradex method (Musy, 1998). The parameters (a and b) adopted for the estimation of the point ow are obtained from the curves (IDF) of the meteorological stations of Biskra, Batna, T'kout, Menaa, Djemoura, Bouzina and El kantara. ( g.06).
The watershed concerned by this study was delimited by the Arc gis software. The geometric characteristics (area, length of the talweg, maximum gradient...) of the upstream part of the Oued Biskra watershed are represented in the table below (Table.2).

Concentration Time
The concentration time Tc of the water on a watershed is de ned as the maximum amount of time required for a drop of water to travel the hydrological path from a point as far as possible from the outlet to reach the outlet.
Theoretically, Tc is estimated to be the duration between the end of net rainfall and the end of runoff. In practice, the concentration time can be deduced from eld measurements or can be estimated with the help of formulas that are usually empirical.
In this study we calculated the concentration time by three empirical formulas : The values adopted are the averages of the results of the three formulas. (Table 3).
Among the results obtained in Table 3; we opt for the result derived from the law of Giandotti because it is the formula, which takes into account the majority of the geomantic parameters of the watershed.
Tc wadi El Hai=15 hours and 11,47 hour s for wadi Djemoura. The sub-basin of the complementary Biskra wadi has a concentration time ; 9,62 hours.

Application And Discussion Estimation Of Gradex
To estimate the Gradex, different approaches are possible. When the observation series is long (>30 years) the simplest and most e cient is to directly adjust the maximum annual rainfall to a Gumbel's law. When the series is shorter, it is often preferable to work on rainfall above a threshold (number of rains above the threshold adjusted to a sh law, height of this rainfall adjusted to a Fuller's law (Laborde, 2000).
It is generally accepted that about 15 years of observations provide a relatively reliable estimate of Gradex. This way of estimating Gradex makes it possible to extrapolate precipitation to return periods of several thousand years (Duband, 1982).

Extreme Rainfall Heights
In this study, the daily maximum rainfall was adjusted from meteorological stations in the Wadi Biskra catchment area; for a fairly long series of observations (47 years) using Gumbel's law, this adjustment made it possible to estimate rainfall values for different return frequencies (Fig. 7). Moreover, this Gradex presents a constancy regardless of the period over which the maximum rainfall is taken.
The graphs obtained by the Gradex method for the Biskra Wadi Watershed and its sub-basins are presented in Fig. 08.

Flood Hydrograph
This method consists of plotting the curve from two parabolic equations, one for the rising ood and the other for the falling ood (Sghara, 2013). Figure 09 shows the ood hydrographs for the Biskra Wadi and its catchment areas.

Results And Discussion
Based on the results obtained, we have concluded that the Gradex method is the most optimal method for determining the maximum ow rates for the Biskra Wadi basin.
The ood hydrographs established for the Biskra wadi watershed and its sub-basins allow to see the evolution of oods in time.
Finally, a more or less varied evaluation made it possible to x the values of the oods crossing the study zone which will allow us to make the dimensioning and the hydraulic calculation of the protection work of this center against the risks of oods.
The knowledge of the threshold ow a allowed us to draw synthetic single frequency hydrographs, which are essential elements for the input of hydrodynamic models in order to determine the ood hazard characterized by a return period T. It was found that the station of Biskra (which controls the large basin of Wadi Biskra) is characterized by a very important quantile for large return periods, followed by the station of Wadi El Hai, then the station of Wadi Djemoura and nally the station of Tkout (which controls the complementary Wadi Biskra).

Conclusion
The hydrology study conducted by applying the Gradex method resulted in a ow rate ranging from 9y-è3 to 2396 m3/s for periods ranging from 10 to 1000 years. These results constitute a useful document for hydraulic modeling that allows the calculation of ow pro les and ood propagation in rivers.
Indeed, the hydrological study constitutes the foundation on which all river hydraulic modelling is built, allowing ood forecasting and hydrological risk management in ood plains.
The ood hydrographs established for the Wadi Biskra watershed and its sub-basins allow to see the evolution of oods over time.
Tr(Finally, a more or less varied evaluation allowed us to x the values of the oods crossing the study area which will allow us to make the dimensioning and the hydraulic calculation of the protection work of this center against the risks of oods. Tables   Table. 1Coordinates