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The Sahelian regions have experienced a drought that has made them vulnerable to hydro-climatic conditions. Strategies have been developed to re duce this vulnerability. The governments of Senegal, Mauritania, Mali and Guinea have created the Organization for the development of the Senegal River (OMVS in french) with the aim of realizing large hydraulic installations. This resulted in the construction of the Diama and Manantali dams in the Senegal River Basin. The first aims to stop the saline intrusion, the second to regulate the flow of the river, to allow the irrigation of agricultural perimeters, and to produce electrical energy. The impoundment of the Diama dam has modified the hydraulic behavior of the estuary. The purpose of this study is to carry out the hydraulic modeling of the estuary of Senegal river downstream of the Diama Dam in transient mode by the HEC-RAS software. Two geometric models were constructed on the basis of a digital terrain model (DTM) using the Arc-GIS and HEC GeoRAS soft wares after processing the collected topographic data. The first geometric model, of which the areas of Senegal river downstream Diama Dam have been represented by cross-section, is one-dimensional. The second one is also one dimensional; in this model, the area of the Senegal River estuary downstream Diama Dam is introduced as water storage zones. The components of these models are the stream sections, lateral links, and storage areas. The flood hydrograph downstream Diama Dam is introduced as conditions at the upstream limits of the models while the tidal is introduced as a downstream condition. After the stability and calibration, the results given by HEC-RAS simulations are the variations of the water levels, the temporal variations of the flow rates for each section, the maximum flow velocities and the propagation times of the flood waves. The analysis and comparisons of these results strongly suggest using HEC-RAS issues as a decision-making tool helping to manage floods during times of crisis.

The Senegal River basin experienced hydroclimatic variability that resulted in drought during the 1970s. The resulting is a significant decrease in water of river flows. To this must be added a strong inter-annual irregularity of these flows. This has made the socio-environmental system much more vulnerable. The strategy adopted to reduce this vulnerability was to carry out large-scale hydraulic improvements: these were the Diama dams on the lower Senegal River and Manantali dams on the Bafing River [

HEC-RAS, Hydrologic Engineering Centers River Analysis System, is software developed by the Hydrologic Engineering Center (HEC) in California. Its purpose is to do hydraulic modeling to simulate flow in streams and channels. It is capable of modeling hydraulic structures such as culverts, weirs, dikes, flood drains and bridges in a section of the river [

This article aims to study the propagation of artificial floods and to analyze the behavior of the Senegal River estuary downstream of the Diama dam using hydrodynamic modeling software HEC-RAS developed by the “Center hydrological engineering, US Army Corps of Engineers”. A 1D simulation is carried out in steady state for different flows corresponding to the water releases at the Diama dam. The main output variables of this analysis are the height of the water surface on the cross sections of the river, the flow velocity and the extent of the flood.

The Senegal River basin is located in the western part of Africa. It extends from latitude 10˚20'N to latitude 17˚00'N approximately and is between the meridians 7˚W and 12˚20'W. It is drained by the 1770 km long river, from the Fouta Djalon massif in Guinea to the Atlantic Ocean. It is the second longest river in West Africa. Its area is 337,000 km^{2}, including 60,000 km^{2} in the national territory of Senegal. Most of the Senegal River Basin has a desert sub-Saharan climate, which has been aggravated by more or less long periods of drought in the 1970s. The estuary of the Senegal River is located in the lower delta of the river, bordering the Atlantic Ocean, 250 km north of Dakar. The estuary faces many environmental problems, the most worrying being coastal erosion and flooding. These last occur during the rainy season, from August to October. They are frequent, recurrent and sometimes very severe, causing a lot of material damage and exceptionally loss of life. Our study area is 50 km long and lies between the mouth of the Senegal River and the Diama Dam and covers an area of about 10,000 km^{2} [

GIS provides a wide range of tools for determining areas affected by floods or for predicting areas likely to be flooded due to high river levels. NTMs are increasingly used for visual and mathematical analysis of topography, landscapes and reliefs, as well as for surface process modeling. A DTM is the most common means of displaying topographic information and even allows the modeling of flows through the topography; a control factor in distributed models of relief processes [

series of cross sections along the stream [

Z + 2 Y 2 + α 2 V 2 2 2 g = Z 1 + Y 1 + α 1 V 1 2 2 g + h e (1)

where: Z_{1} and Z_{2} are the elevations of the main channel inverts, Y_{1} and Y_{2} are the depths of water at each cross section, V_{1} and V_{2} are the average velocities (total discharge/total flow area), α_{1} and α_{2} are the velocity weight coefficients, g is the gravitational acceleration, and h_{e} is the energy head loss between the two cross sections.

The energy loss term h_{e} in Equation (1) is composed of friction loss h_{f} and form loss h_{o}. Only contraction and expansion losses are considered in the geometric form loss term.

h e = h f + h 0 (2)

To approximate the transverse distribution of flow of the river is divided into strips having similar hydraulic properties in the direction of flow. Each cross section is subdivided into portions that are referred to as subsections [

h f = ( Q K ) 2 (3)

where:

K = ∑ j = 1 J [ 1.49 n j ] ( A 2 + A 1 ) 2 [ R 2 + R 1 2 ] j 0.5 ( L j ) 0.5 (4)

A_{1}, A_{2} are the downstream and the upstream area, respectively of the cross sectional flow normal to the flow direction, J is the total number of subsections, L_{j} is the length of the j^{th} strip between subsections, n is the Manning’s roughness coefficient, Q is the water discharge and R_{1}, R_{2} are the downstream and the upstream hydraulic radius.

Other losses:

Energy losses due to contractions and expansions are computed by the following equation:

h 0 = C L | α 2 V 2 2 2 g − α 1 V 1 2 2 g | (5)

where, C_{L} is the loss coefficient for contraction and expansion. If the quantity within the absolute value notation is negative, flow is contracting, C_{L} is the coefficient for contraction; if is positive, flow is expanding and C_{L} is the coefficient of expansion. In the standard step method for water surface profile computations, calculations proceed from the downstream to upstream based upon the reach’s downstream boundary conditions and starting water surface elevation.

Distribution coverage of the weighted distance can be calculated using the following formula:

L = L l o b Q ¯ l o b + L c h Q ¯ c h + L r o b Q ¯ r o b Q ¯ l o b + Q ¯ c h + Q ¯ r o b (6)

where: L_{l}_{ob}, L_{ch}, L_{rob} are the lengths specified in the flow direction for the left floodplain, main riverbed and right floodplain, Q ¯ l o b , Q ¯ c h , Q ¯ r o b are the arithmetic average of flows between cross-sections for the left floodplain, main riverbed and right floodplain.

This work combines bathymetric data, hydraulic models and GIS (Geographic Information System) tool for the evaluation of flood flows and the delineation of flood prone areas in the Senegal River estuary downstream of the Diama dam. Hec-Ras software uses 1D Saint-Venant coming equations for shallow waters. These equations are deduced from the Navier-Stokes equations by simplifications related to the fluvial model [

Step 1: creation, using the ArcGIS tool, of the Hec-GeoRAS extension, the digital elevation model (DEM) and the aerial images of Google Earth, the geometric data of the Senegal River estuary with the minor and major sections of the estuary bed and cross sections. Hec-GeoRAS is used as the main tool in ArcMap. In the ArcGIS environment, we used Hec-GeoRAS to digitize various vector elements that will allow Hec-RAS to generate the flood model and represent the results. The digitization of these elements is used in the following phases to realize the potential simulation (

· The main channel;

· The left and right banks;

· Cross sections.

Step 2: Apply permanent flow modeling with Hec-RAS 5.0.1, which generates an export file for ArcGIS. Hec-Ras is a software independent of ArcMap but complementary to the analysis processes. The calculation of the hydraulic profiles along the bed of the studied section is fundamental to estimate the water levels during exceptional floods. Overflow levels of the river and areas submerged by water will also be known (

Step 3: Generate water task results: flood surfaces and depth grids. The Hec-Ras modeling allowed to calculate the different flow configurations for the cross sections along the studied section. Water levels, depths, flow velocities and other variables were simulated. The banks, the vegetation, the obstacles and the structures are well identified, which allowed obtain a rather precise geometry of our river. So we created the main axis of the canal.

For a constant flow, we find that the flood covers most of the profiles with large widths downstream. In addition, given the watershed characteristics in terms of geology, geomorphology and vegetation cover, the Manning coefficient retained is 0.03. This is the value of sandy river beds (devoid of gravel and pebbles) with little aquatic vegetation. In the same way, the estuary is characterized by its mixed regime and its weak slopes. The geometry of the canal is defined by 33 cross sections distributed over the 50km of the studied river line (

The unidimensional hydrological modeling of the flood, in the absence of the tide, of the Senegal river estuary downstream of the Diama dam of the present study was carried out using HEC-RAS version 5.0.1 (

of each profile, which is applied to each flow (Q_{1}, Q_{2}, Q_{3} and Q_{4}). We zoomed in on three areas: zone A (

The maximum flow observed for the artificial flood (water drop at the Diama Dam) between 2003 and 2011 is of the order of 2000 m^{3}/s. The test of this modelization is carried out on four stations for four different flow rates: PF1 has a flow of 500 m^{3}/s, PF2 a flow of 1000 m^{3}/s, PF3 a flow of 1500 m^{3}/s and PF4 a flow of 2000 m^{3}/s (

We can get information from our simulation on the general profile of the river. The example below, retraces, according to the distance to the starting profile (mouth), the height of water induced by flood flows of 500, 1000, 1500 and 2000 m^{3}/s (

We can also obtain information from our simulation on the water height (W.S.) as a function of flow (Q). We did this simulation on four stations (

Our simulation allows to see also the evolution of the flow velocity (Vel) of the flood as a function of the flow (Q) on four stations (

We also obtained the modeling of the water heights (WS) on different sections across the river for different flow rates (

The bathymetric profiles show irregular bottoms with generally asymmetrical flanks, a phenomenon which is accentuated in the area of the mouth. The profiles are relatively symmetrical and more regular upstream. In the Mermoz area (

The maximum depths of the channel are relatively low towards the mouth (about 6 m) but become strong upstream where they reach 10 m at the Faidherbe bridge and 11.80 m at the immediate downstream of the Diama dam.

In fact, the depths of the channel are very variable over time, in relation to the instability of the bottoms due to the frequent movement of the sand band.

Zone A: This is the area between the Diama Dam and a few kilometers downstream. The artificial flood corresponds to the release of water at this dam. For water releases of flow ranging from 500 m^{3}/s to 2000 m^{3}/s, the simulation shows a sharp increase in the water level (about 2.93 m) in this area causing flooding (

The speed chart produced by Hec-Ras for peak flows (500, 1000, 1500 and 2000 m^{3}/s) confirms this result. In the main channel, the velocities are about 0.77 m/s and 1.52 m/s for the respective flow rates of 500 m^{3}/s and 2000 m^{3}/s respectively. Also, we visualize a difference of the height of water of 3m between these two flows. Flooding in this area occurs whenever the volume of water in the upper parts of the basin exceeds the capacity of the riverbed, the water overflows and flows into the plain (

Zone B: This is the area around the Faidherbe Bridge. This area contains the city of Saint Louis. For the same flows, the simulation shows a sharp increase in the water level (about 4.5 m) in this area causing a flood (

In this area, the main channel has a depth of about 8 m at Mermoz and 10 m at the Faidherbe Bridge. At the Faidherbe Bridge, the velocities are approximately 0.4 m/s and 1 m/s for flow rates of 500 m^{3}/s and 2000 m^{3}/s respectively and the variation of the water height between these flows is 2 m (

Zone C: This zone is located between the Faidherbe bridge and the mouth (

River flow modeling software is sophisticated and increasingly used in natural risk management and mapping by delineating risk areas. The overall results made it possible to locate the flood zones, the speeds, the water heights, etc. These results are reliable and consistent with the morphology of the estuary. The study area has undergone a profound restructuring over the last twenty years. In parallel with increasing awareness of the problem of floods, bridges, dams and rehabilitations of the river and its tributaries have been built. However, only a drop of water at the Diama dam with a flow of 2000 m^{3}/s is required for the water level to increase by 3 m at Diama, 2 m at the Faidherbe Bridge and 1.3 m at the mouth causing flooding of the streets and neighborhoods of the city of Saint-Louis. We also find that the flow velocities also depend on the flow rates of water releases at the Diama dam. For a peak discharge of 2000 m^{3}/s, the flow velocity of the flood is 1.52 m/s at Diama, 1 m/s at Faidherbe Bridge and 4.2 m/s at the mouth. Moreover, this very high speed at the mouth is one of the main causes of fishing pirogue accidents noted in this area since the opening of the unloading channel (new mouth).

To manage flood situations during water releases at the Diama dam, real-time water level monitoring and measurement equipment should be installed upstream of the dam. This model could then be used as a decision tool by the public authorities. It is also important to take into account the storage areas to the left and right of the Diama dam and the development plan simulator to propose for flood protection in the city of Saint Louis.

The authors declare no conflicts of interest regarding the publication of this paper.

Diedhiou, R., Sambou, S., Kane, S., Leye, I., Diatta, S., Sane, M.L. and Ndione, D.M. (2020) Calibration of HEC-RAS Model for One Dimensional Steady Flow Analysis—A Case of Senegal River Estuary Downstream Diama Dam. Open Journal of Modern Hydrology, 10, 45-64. https://doi.org/10.4236/ojmh.2020.103004