➢ Morphological characterization of the Morrison and Lokpoho reservoirs

The morphology of the bottom of the Morrison and Lopkoho dams (Figure 2) was studied using bathymetric surveys. These surveys were carried out using a LOWRANCE Elite 9 Ti echosounder; which is a device for measuring the depth of the sea bed or lake. The depth is deduced from the measurement of the travel time of an acoustic signal reflected by the bottom.

The soundings were taken at a frequency of 455 kHz, to avoid that transmitted signals not to penetrate the silt (Kouassi et al., 2007) . The depths obtained thus represent the distance between the position of the echo sounder transducer and the water-sediment interface. Water travel was conducted using a speedboat in both the longitudinal and transverse directions of the stream. These surveys were carried out over a length of approximately 3855 m for the Morrison Dam and 3815 m for the Lopkoho Dam. The interpolation method used was IDW (Inverse Distance Weighting) with an X and Y space step of 150 m. It is a local deterministic interpolation technique that calculates the value of a point by averaging the values of the points located in the vicinity weighted by the inverse of the distance to the calculated point: the closer the points are, the greater the weighting assigned (Drouin & Saint-Laurent, 2010) .

➢ Establishment of height-volume and height-surface curves

These impoundment contours give the different water volumes and areas for each impoundment contour (Nshimirimana, 2010) . The partial volume V_i between two successive contours is given by (1):

V i = ( S i − 1 + S i ) × H 2 (1)

V_i: Volume of water between the contours i − 1 and i;

H: Height difference between the two contours i − 1 and i, i.e. H_i − H_i−1;

S_i: Surface of the water body corresponding to the curve i (H_i);

S_i−1: Surface of the water level corresponding to the curve i − 1 (H_i−1)

Thus, by applying these relationships for each height of the water body, the area of the water body is determined as a function of its height (Nshimirimana, 2010) . In our study, these calculations were performed using COVADIS software. COVADIS is a software using the graphic interface of Autocad with in the background a calculation process using the usual topographic formulas. It proceeds by modelling the terrain given to it by linear interpolation.

Using the Height-Volume curve of the reservoir (H = f(V)), the Height-Surface curve (H = f(S)) was constructed.

➢ Volume and rate of sediment in the two dams

The 2013 and 2020 bathymetric surveys provided sediments volumes. Thus, the difference between these volumes provides the current sediment volume in the reservoir in 2020. Then the rate (τ) of deposited sediment is calculated by (2) (Kouassi, 2007) :

τ = ( B 2020 B 2013 ) 1 n − 1 (2)

With:

τ: Sediment rate (%)

B: Volume of sediment (m³)

n: Year difference between 2013 and 2020

This study is based on frequency analysis, which consists in determining the probabilities of occurrence and the return periods (forecast). The main objective of this statistical method is to use measurements of past events to estimate future probabilities of occurrence. The frequency analysis is used, in particular, to estimate the magnitude of the temporal event xT to which is associated a return period xT (quantile of return period T or of probability at exceedance T = 1/T (Bobée, 1999) ). The estimate of quantile xT value is obtained by fitting a probability law F(x; θ) to a sample of n observations, x = { x 1 , ⋯ , x n } where θ represent a vector of parameters associated at the probability distribution F. The different steps on frequency analysis are as follows:

➢ Sampling

The sampling of extreme flows concerned the flood (QMAXAN) and low water flows (QMIN) recorded at the hydrometric station Route Korhogo-Badikaha from January to December over the period 1975-2000.

➢ Choice of models

The choice of the frequency model was made on the basis of graphical comparison and numerical comparison criteria (Kouassi et al., 2019) . The graphical method allows one to graphically visualize the goodness of fit of a given law to a sample of data. The best probabilistic models are those whose curve passes through the maximum number of observations and whose Confidence Interval (CI) encompasses the maximum number of observations. This visual acuity-dependent graphical comparison method does not allow for the selection of the appropriate model for fitting the variables under study. Thus, in order to minimize the risk of error in the choice of the best fitting model, a second selection method based on the numerical comparison criteria of the laws must be used. Within the framework of this study, the choice of the frequency model was made by means of two approaches which are the graphic approach and that of the comparison criteria (AIC and BIC). This choice was made among four (04) frequency models (statistical laws) for flood flow series. These are: the general law of extreme values (GEV), the Gumbel law (EV1), the Weibull law (W) and the Lognormal law (LN). For the low-flow sample (minimum flows), the laws competed for are the Exponential law and the Gamma law because the fit of the other laws was negative (Catalogne, 2012) . The maximum likelihood method was used to estimate the parameters of these laws. The application of these laws allows us to assess which one best fits a time series of rainfall and discharge. The ideal distribution is chosen using graphical and numerical criteria. For each sample, the test of independence, stationarity and homogeneity were previously analyzed using HYFRAN software. The HYFRAN-PLUS software allows the fitting of a large number of statistical distributions to a set of data that verify the assumptions of independence, homogeneity and stationarity (see DAS publications). It is designed to clearly present the steps involved in fitting a statistical distribution to a random sample. These steps can be found in Soro (2011) .

➢ Comparison criteria

The aim of these criteria is to find a compromise between a sufficient parameterization to fit a probability distribution to the observations and the least complex parameterization possible. To be able to compare probabilistic models by comparison criteria, we set equal a priori probabilities for all distributions. Then, we specify a return period (T). Thus, the a posteriori probability is calculated from the a priori probability (Soro, 2011) . The Akaike Information Criterion (AIC) (3) and the Bayesian Information Criterion (BIC) (4) are also calculated. The best probabilistic model is the one with low AIC and BIC values and the highest posterior probability (Soro, 2011) . The BIC and AIC criteria are calculated as follows:

Akaike Information Criterion (AIC)

AIC = 2 log ( l ) + 2 k log ( n ) (3)

With l: likelihood; k: number of parameters; n: sample size

Bayesian information criterion (BIC)

BIC = − 2 log ( l ) + 2 k (4)

With l: likelihood; k: number of parameters

o Model validation test

Once the fitting model is chosen, it must be subjected to a series of tests to verify its fit to the chosen sample. In this study, the chi-square test ( χ 2 ) was used.

The HYFRAN (Hydrological Frequency Analysis) software developed by INRS-EAU of Canada was used to implement the frequency analysis.

Figure 3 and Figure 4 show the bathymetric maps of the Morrison and Lokpoho impoundment. These maps were made using bathymetric surveys conducted in February 2020. For the Morrison reservoir (Figure 3), the 292.23 m water level was used as the reference level. The maximum depth sounded is 11.98 m and the area of the bathymetric survey is 472.92 hectares as of 20/02/2020. The bottom of the reservoir is characterized by a morphology disturbed by abrupt slope variations in the project area. These slopes reach 24˚ in places.

For the Lokpoho impoundment (Figure 4), the bottom is slightly less rugged. On this bathymetric map, there is a main north-south flow channel leading to the water intake. Depths vary gradually from place to place from upstream to the dike. The depths are less important and reach 8.82 m. The 296.97 m water level was chosen as the reference level and the area of the bathymetric survey is 312.93 hectares as of 21/02/2020. The bottom of the reservoir is also characterized by a morphology disturbed by abrupt slope variations in the project area. These slopes reach 80˚ in places.

Figure 5 shows respectively the evolution of the volume of water and the average surface area of the reservoirs as a function of water depths. These curves show a logarithmic curve with a height of 292.23 m and 296.97 m respectively for Morrison and Lokpoho. For the Morrison reservoir, this water level corresponds to an area of 32.000 m² (Figure 5(a)) and a volume of 11,656,735.5 m³ on 20/02/2020 (Figure 5(b)).

And for the Lokpoho reservoir, this water level corresponds to a surface of 27,000 m² and a volume of 4,354,531.5 m³ on 21/12/2020.

The sediment levels in the two impoundments between 2013 and 2020 are recorded in Table 1. Analysis of the results shows that the sediment rate in Morrison impoundment is lower than that in Lokpoho. Indeed, for the Morrison reservoir, sediments volume varies from 875,900 m³ in 2013 to 1,013,058.96 m³ in 2020 or a sedimentation rate of 2.1%. For Lopkoho reservoir, the results of sediments volume in 2013 is 508,000 m³ and in 2020, this volume is estimated at 599,740,543.3 m³ or a sedimentation rate of 2.4%.

The maximum daily flows recorded at the Korhogo-Badikaha station follow the GEV and Gumbel laws (Figure 6). Indeed, the observations are all within the Confidence Interval and, moreover, remarkably close to the curve representing the probabilistic models mentioned above. These results are confirmed by those in Table 2, which present the ranking of the probability laws fitted to the annual maximum flow series of the Korhogo-Badikaha road station.

At the level of the low water flows, among the competing laws, only the Gamma and Exponential laws were able to fit the observations (Figure 7). Thus, the comparison of the two laws by the BIC and AIC criteria show that the Gamma law comes first with 58.24% chance that the sample comes from this law (Table 3). The criteria of BIC (58.57) and AIC (51.06) are lower than those of the Exponential law.

Table 4 summarizes the quantiles of minimum and maximum flows estimated according to the laws that came first in the adjustment. It can be seen that flood and low-flow rates increase with return periods. Confidence intervals are also estimated to evaluate the uncertainty associated with the estimates.