The study area covers a surface of 9 km² [5]. According to the Senegalese National Agency for Statistics and Demography (ANSD) population projections report, the total population of Yeumbeul Nord (YN) was 200,318 in 2019 [6]. It represents one of the most populous arrondissement communes in Senegal. YN is located in the suburbs of Dakar in the department of Pikine more precisely in the Niayes arrondissement between 17˚20' - 17˚22' west longitude and 14˚46' - 14˚48' north longitude (Figure 1). The “Niayes” are dune depressions in which the water table of the Quaternary sands outcrops or sub crops. Figure 1 illustrates the location of the study area.

Located in the Niayes depression zone, the YN lake system is formed by three closed depressions (Thiouroure, Warouwaye and Wouye) and regenerates. Urban sprawl occurs on an area with a hydromorphic profile [7].

Lake Warouwaye is located in the inter-dune depressions and receives runoff from several sub-watersheds. The characteristics of the lake are shown in Table 1.

With the expansion of urbanization (Figure 2), this lake is experiencing filling problems threatening its hydrological and ecological functions. A large part of this reserve has become fragile and exposed to various environmental problems.

The lake’s water level has decreased from about 54 to 25 ha between 2013 and 2020. It is increasingly overgrown with aquatic vegetation and causes nuisance to the riparian populations (garbage dumps and wildlife shelters). Even for bathymetric study purposes, this lake is difficult to access [9].

YN is one of the last wetlands in the Dakar region where natural areas are rare. In the context of a significant decrease in rainfall during the 1970 [1], the decrease in the water table has led to a drying up of the Niayes. However, a progressive reduction in the surface area of the lake was noted, mainly due to the expansion of the built-up area. The vegetation that used to predominate in the area has been greatly degraded.

Currently, the built-up area is expanding into the wetland depressions as almost all of the available space around the lakes is occupied. The densification of the road network leads to a fragmentation of the ecosystem. The extension of the road network, for example, encourages the occupation of low-lying areas without prior development. As a result, urbanization has strongly amplified the consequences of the great drought on wetlands [1]. The development of buildings and road infrastructure is the main factor in the disappearance of wetlands and the modification of their hydrological system.

Another environmental risk is that the wetlands have long been considered unhealthy and unproductive. The majority of the population considers the Niayes to be cumbersome, mainly due to the presence of mosquitoes, and uses it as a garbage dump. Household waste and rubble usually deposited along the lakeshore can be washed in by runoff.

All these anthropogenic factors threaten the preservation of these ecosystems, already weakened by the advancing urban front. Photo 1 and Photo 2 illustrate the degradation of this area with a poorly developed outlet and abandoned houses in the low-pressure areas.

A 30-year series (1990-2019) of annual rainfall (Figure 3) was used as rainfall data. This series is likely to give a representative mean value for the Dakar/Yoff station.

Flooding in YN often occurs during the rainy season, beginning in July and ending in October with a peak during August [10].

The rainfall data for the area are obtained after exploitation of the Master Drainage Plan (MDP) [11] in which the authors used the work of Brunet-Moret (1963) for the current ORSTOM IRD. These studies are based on the analysis of rainfall records and rain gauge recordings and aim to establish Intensity-Duration-Frequency (IDF) curves for various recurrence periods over the entire Senegalese territory. In order to exploit the Intensity-Duration graphs of the

Brunet-Moret study, the MDP recalculated the daily rainfall of the Dakar region for different return periods (Table 2).

Several equations can be used to describe adaptive IDF curves, capable of taking into account climate trends. In the sub-region and in Senegal, the Montana formula remains the most widely used. It describes the relationship between the intensity, duration and frequency of rainfall. It is expressed as follows (Equation (1)).

I = a t − b (1)

With, I: average intensity in mm/h; t: rain duration in min; a and b: adjustment coefficients of Montana’s law defined for a return period T (years).

Figure 4 below shows that the decadal IDF curve shows a break and thus allows us to determine the values of Montana coefficients.

In the calculations, the formula defined previously (Equation (1)) gives two expressions of the intensity of the showers. Indeed, the graph allows to see the accuracy of the evolution of the intensity as a function of time.

Pour T = 10   years     { I = 9.0038 t − 0.522     for   t < 1   h I = 42.232 t − 0.846     for   t > 1   h (2)

· The concentration time by the Desbordes method is expressed by Equation (3).

T c = 5.3 0.8 ⋅ S 0.3 ⋅ P − 0.38 ⋅ C − 0.45 (3)

With:

Tc: concentration time in min; S: surface in Ha; P: Slope in % and C: Runoff

coefficient.

· The runoff coefficient of a given surface is the ratio of the volume of water that runoff to the volume of water falling on it. In the context of our study area, which is urbanized, the coefficient is defined as the ratio of the impervious surface to the total surface of the watershed (land use) and the type of soil (Table 3).

For the site, we note a diversity of occupation mode and soil type.

For the choice of the method of calculation of the flows, we studied the validity of the various existing methods of estimation compared to the characteristics of the zone and the catchment areas obtained. The rational method is used to estimate the flows to be drained to the retention basins that are the Warouwaye and Thiouroure lakes. This method uses a model of transformation of rain, described by its intensity considered as uniform in time, into a maximum instantaneous flow at the outlet. The rational method allows the calculation of each sizing flow of the drainage network starting at the head of the basin. This flow is given by Equation (4):

Q = 0.278 × C × I × A (4)

With, Q: Maximum flow at the outlet expressed in m³/s; C: Runoff coefficient;I: Rainfall intensity expressed in mm/h; A: Watershed area in Km².

Despite its limitations, the rational method provides good results.

The runoff coefficient used is that of the drained areas. It corresponds to the ratio of the impervious surface to the total surface of the watershed.

The Epaswmm software was used for the simulations that allow to appreciate the hydrological behavior of the Warouwaye Lake according to different rainfalls of 10 years return period in order to appreciate the contributions of water at risk of flooding following the overflow of the lake.

· Project rain

Five (5) project rains was used for the simulations, including four short rains of intense duration (15 min, 30 min, 60 min and 120 min) over a period of 4 hours and one long Kieffer-type rain of 24 hours duration.

The project rainfall is summarized in Table 4 below.

· Kinematic wave runoff model

It is a conceptual model that represents the watershed as a rectangular channel with a free surface.

The inflow Q_e(t) corresponds to the excess precipitation (precipitation-infil- tration-evaporation-interception by vegetation or depressions on the surface of the BV) (Figure 5).

The outflow Q_s(t) is calculated at each time step using the Manning-Strickler formula from the characteristics of the channel (width and roughness) and the height h(t) of the water flowing in the channel [14].

Q s ( t ) = S H ( t ) ⋅ R H ( t ) 2 / 3 ⋅ p (5)

S H ( t ) = B ⋅ h ( t ) (6)

R H ( t ) = B ⋅ h ( t ) B + 2 h ( t ) (7)

With, SH: represents the surface area of the watershed; RH: is the hydraulic

radius; h(t): is the height of the water runoff; p: is the slope of the watershed.

Examination of the digital terrain model (DTM) highlights the elevations of the area, the hydrographic network and the drained watersheds. The contour lines and the variation in the coastline of the resulting area are shown in Figure 6.

Elevations are low in the YN area, but are lower at the lakes. This suggests that the lakes are a natural depression or outlet for runoff. Lake Warouwaye is 0 m high (source: Google Earth).

After generating the direction of water flow, we were able to obtain different sub-watersheds represented in Figure 7.

Following the delimitation of the watersheds, we were able to observe the flow of two main rivers that drain the waters of YN, but also those of Djidah Thiaroye Kao, Medina Gounass, the northern part of South Yeumbeul, Wakhinane Nimzatt, and which have as their outlet the lakes Warouwaye and Wouye. In this study, we will focus on the catchment areas that have Lake Warouwaye as their outlet in order to study the risk of overflow from the latter, which is located within North Yeumbeul. The Warouwaye (BVW) and Thiouroure (BVT) watersheds cover an area of 1124 ha and their characteristics are presented in Table 5.

All of the watersheds in this area are considered small watersheds because they are less than 10 km² in size. Thus, the Gravelius compactness index of each

of these watersheds is 2.08 for BVW (very long watershed) and 1.6 for BVT (watershed 6 times longer than wide).

The discharge at the outlet of the two watersheds estimated by the rational method is given in Table 6.

The normal water surface of the lake is 24.56 hectares with a maximum depth of 1 m. The total volume of the normal water body of Lake Warouwaye is 245,600 m³, but due to dysfunctions caused by natural causes such as wind deposits, the invasion of aquatic plants, and also to numerous causes of anthropogenic origin, the lake can only retain 122,425 m³ of the total runoff volume.

In the following, we will present and comment on the simulation results of

four (4) Desbordes-type and one (1) Kiefer-type project rainfall events.

· Intense short duration DESBORDES type rainfall

The actual rainfall events causing disruptions in storm water systems generally consist of a relatively short period of intense rainfall within a rain sequence of a few hours. Desbordes therefore proposed to choose a particular form of project rainfall by reasoning not in relation to the physical phenomenon, but in relation to the elements to which the runoff model (used after the rainfall model) was the most sensitive. This sensitivity analysis, conducted from the linear reservoir model, showed that a simple double triangular shape provided hydrograph shapes and maximum flow values that were not very sensitive to errors on the main parameter of the runoff model.

The passage of each of these rains caused overflows (red curve) at the level of the lake with variable volumes of water largely higher than the capacity of the lake.

Figures 8-11 represent the curves of volumes entering the lake versus time and maximum storage capacity (122,425 m³).

For all these different rainfall events of the Desbordes 4-hour type with intense durations of 15, 30, 60, 120 minutes, the quantity of water received by the lake is always greater than the maximum storage capacity (122,425 m³).

· For a 24-hour KEIFER-type rainfall of long duration

This project rainfall was proposed by Keifer and Chu (1957). It consists in transforming directly the IDF curves (represented by the classical Montana formula) into hyetograms. This method leads to an excessive overestimation of the peak flows generating a flood wave in the hydrological system (runoff-network) never observed in situ.

The passage of this rain caused the greatest overflow of the lake with a volume of 1,063,020 m³ greater than the storage capacity (122,425 m³), i.e. an overflow of 939,330 m³. Figure 12 gives us the variation curve of the volume entering the lake compared to the maximum capacity.

Table 7 presented below permit us to summarize the results of the system-wide simulations.

Therefore, Lake Warouwaye has a transit limit of a certain occurrence that is tested by the simulated passage of different types of project rainfall, causing overflow of runoff water to the nearby residential areas.

One of the consequences of this hydrological dysfunction is the recurrence of floods, in the face of which the Senegalese government has displayed a firm political will to definitively curb this phenomenon.