Contribution to the management of a reservoir dam on the Sebou river (Morocco) using a hydraulic model
The studied reach The Sebou River (600 km) is an important river in Morocco and its waters are solicited for several different uses. The Sebou has an average bottom slope of 10-4, variable geometry and many meanders. The flow is characterised by considerable annual and seasonal variations (Figure 2). The studied reach is situated between the town of Belksiri and the Lalla Aïcha dam. Flow is influenced by the presence of two dams, the Al Wahda upstream and the Lalla Aïcha in the downstream reach. The first dam was constructed on the Ouergha River, which has a torrential regime. The second dam comprises five principal and two secondary radial floodgates and these gates are opened from the bottom. This dam is completely opened during the period of high flows. The maximum flow during this season is 1800 m3/ s. The dam has a catchment area of 2700 km2. The maximum volume of the dam reservoir is 37 Mm3. Its length of influence is about 120 km. During the dry season, the floodgates are partially closed in order to increase the water level upstream. The maximum level upstream of the dam is 6.5 m NGM (the bottom is at -1 m). This situation facilitates the pumping of water for agriculture, allowing the irrigation of 15,600 hectares of rice. A volume of 200 Mm3 of water is mobilised annually, which, before the construction of the dam, was lost to the Atlantic Ocean. The hydraulic model MHS.1 The hydraulic model MHS.1 is based on a modification (essentially the representation of the topography and the outputs) of the DYNHYD5 model. It solves the one dimensional Saint-Venant equations of continuity and momentum (equations 1 and 2). The Manning coefficient used in the momentum equation is evaluated initially by the empirical formula (Formula No. 3) proposed by Chow. The factor n0 is evaluated from granulometric measurements that were carried out from upstream to downstream in the studied reach. The others coefficients were evaluated from observations of the river in aerial photos, from the cross sectional areas and available photos, and from field visits. MHS.1 uses a network called ''Link-Node''. The equations of continuity and momentum, expressed in a finite difference manner, give respectively equations 4 and 5. These equations are solved using a Runge-Kutta procedure. Discretisation of the studied reach The discretisation of the studied reach was performed using aerial photos achieved by the ORMVAG (L'Office Régionale de la Mise en Valeur Agricole du Gharb) in 1983. These photos were taking in a dry period where the river was nearly dry. This situation permitted a good stereoscopic visualisation of the river morphology. The river reach was divided into 529 grids with a length varying between 50 and 900 m. Data on cross sectional areas from the ORMVAG and other sources were used. Near the town of Souk Tlat (Figure 1), we exploited a new technique called ''Numeral photogrammetry'', which allowed us to reconstitute many cross sectional areas. This technique uses principally stereoscopic pairs of aerial photographs and photogrammetry software. The remaining cross sectional areas were evaluated from observations on aerial photos and from field visits. Evaluation of the pumped water One of the important factors that affect flow in the studied reach is the intensive pumping of waters along the river. The pumped water was divided into two types. The first type corresponded to the ten central stations managed by the ORMVAG (Fig. 1). The data of this first type were neither centralised nor easily available. Only the data at the important S2 station were readily available. The second type corresponded to water pumped by individuals and is less quantified than the first type. Two major hypotheses were adopted. First, the pumped flow at the S2 station was assumed to be equal to 25% of the total flow pumped by all the ORMVAG stations. The stations were classified into three classes according to their theoretical capacity (Table 1). This hypothesis allowed the estimation of the unknown pumped flow at the nine other stations. We further assumed that in the neighbourhood of each station, the flow pumped by individuals was equal to the flow pumped by the station. This latter hypothesis was adopted on the basis of a field investigation in a 7 km characteristic reach. Figure 3 shows the evolution of the overall pumped flow evaluated for the months of June and July 1997. These two months were used respectively for the validation and calibration of the model. Calibration and validation of MHS.1 The Manning coefficient, estimated initially by the Chow formula (3), varied along the studied reach. It ranged from 0.02 to 0.04 s/m1 /3, with a mean value of 0.037 s/m1 /3. In the calibration procedure, the Manning coefficient was modified to the same degree along the studied reach because we assumed that the sources of errors involved in its evaluation are identical for all the grids. Along the studied reach, the only available measured data are the water levels at the S2 station and upstream of the dam. The period chosen for the calibration was from 07/01/1997 to 07/30/1997. The upstream boundary (at the Belksiri hydrological station) was given as values of the water level as a function of time (Figure 4). The downstream boundary was given as values of the discharge (flow through the dam gates) as a function of time (Figure 5). Figures 6 and 7 give the results of the calibration (month of July). The Manning coefficient decreased for all the reaches by 0.008 s/m1 /3. These figures show good agreement between the calculated and the observed water level at the S2 station and near the dam. In order to confirm the results of the calibration test, we proceeded with a validation test of the model for the period from 06/04/1997 to 06/30/1997. The results are also satisfactory (Figure 6 and 7, month of June). Figure 8 shows the evolution of the water level on 12/06/1997. The water level profile remains parallel to the bed profile for the zones situated very far from the dam (the downstream end). From the 45th kilometre (between stations S7 and S8, see Figure 1), we begin to detect the effect of the dam, characterised by an increase in the water level (and therefore an increase in depth). Figure 9 show the evolution of stream velocity from the upstream to downstream regions on 12/06/1977. Great variations in velocity can be seen due to the changes in river geometry. Also, these variations tend to decrease downstream, reflecting the effect of the dam. Figure 10 represents the evolution of the water reserve available for the whole reach during the months of June and July. It shows a series of decreases in this variable due to the pumping of water. The reserve reaches very low levels (15 Mm3) compared to its maximal capacity, which is 37 Mm3. Also, there is an interrelationship between the evolution of the reserve, and pumped water and the flow differences between upstream and downstream. The reserve increases when the upstream-downstream flow difference is greater than the pumped flow. Inversely, when the pumped water is greater, the water reserve decreases. Finally, in this study we proposed a mathematical model that can provide the stages at all locations of the studied reach, specifically at the pumping stations. Water reserve availability can also be provided at any moment, allowing rapid interventions when this variable begins to decrease dramatically. However, more measured water levels at different stations could improve the present results. Also, other considerations must be included such as hydroelectric energy production in dams upstream and river characteristics. Thus, a multipurpose model of the river must be used. More hydraulic data can improve the accuracy of the present model.