The study area has many piezometers, which are used for groundwater level monitoring and one metrological station to record and describe the climate of Bamako and surrounding areas.

The climate type of the study area is Sudano-Sahelian. The overall annual mean precipitation for the last 30 years (1990-2020) varies from 462.5 mm (year 2017) to 1142.6 mm (year 2008) recorded by the Bamako metrological situation ( Figure 2 ). In the same station and for the area of interest, the highest values of temperature are recorded in April and May while the lowest values in December and January. The mean annual temperature recorded is 35.14˚C.

The Bamako region is located on the southern edge of the large Taoudeni sedimentary basin which extends over most of Mali. It straddles a geological boundary between sedimentary lands and crystalline and/or crystallophyllian terrains. The regions have a granito-gneissic and schistose base (to the south of the agglomeration) covered by a sedimentary cover of sandstone with pelitic intercalations (to the north of the agglomeration).

Geologically, the study area is located in the sandstone plateau unit as defined in ( DNH, 1990 ). The area is mainly constituted by tabular sandstone dated of infra-Cambrian. Milestones and fine to coarse sandstones are the main geological formation and occupy the most area where the study is undertaken. Some geological formations, such as dolerites intrusions, conglomerate, glauconite, and quartzite are associated with the sandstone in Bamako area ( Figure 3 ).

The study area belongs to the 74b hydrogeological unit as specified in ( DNH, 1990 ) and is characterized by two aquifers system: a shallow aquifers system in superficial deposits and a deep fractured aquifer system in fractured or fissured sandstone ( Banton et al., 1991 ) ( Figure 4 ).

To apply the Water Table Fluctuation (WTF) method, fifteen (15) piezometers have been selected in the study area as shown on the map in Figure 1 . These piezometers have been chosen given to the availability of continuous data during the study period.

The monthly average groundwater recharge was estimated using monthly precipitation and groundwater levels data ( Table 1 and Table 2 ) over 24 months i.e. two (02) years (2018 and 2019).

The piezometers used for this study are part of the network of the National Direction of Hydraulic of Mali (DNH-Mali) established for groundwater monitoring. The climate data have been collected from National Meteorological Agency of Bamako.

Among the multiple methods (physical and chemical ( Diouf, 2012 )) that can be used to estimate groundwater recharge, the WTF method is considered to be an attractive method due to its accuracy ( Addisie, 2022 ; Diouf, 2012 ) and because of the ease of use and low cost of the application in the semiarid areas ( Diancoumba et al., 2020 ).

The Water Table Fluctuation method provides an estimate of groundwater recharge by analysis of water level fluctuations in observation wells or piezometers. The method is based on the assumption that a rise in water table elevation measured is due to the addition of recharge across the water table as shown in Figure 5 for the piezometer PZ 300.

This approach is assuming that in dry period, the recharge to the water table is negligible and the groundwater levels decline while, in the rainy season, the recharge rate to the water table is considerable ( Allison, 1988 ). These increases and decreases cause the water table fluctuations ( Figure 6 ). The WTF method is appropriate in fractured aquifer ( György, 1981 ) and requires determining for its application two important parameters: the groundwater level rise ∆h and the Specific yield Sy.

These parameters are linked to each other and to the recharge by the expression indicated below in Equation (1):

$\text{Rt}=\text{Sy}\Delta h/\Delta t$ (1)

where Rt is the recharge, Sy is specific yield, ∆h is the change in water table level (water level rise) and ∆t is the time period.

According to Deg-Allier ( Deg-Allier, 1963 ), the rise in water level due to recharge can be determined by calculating the total level oscillation amplitude if the overall recession regime i.e., the behavior of the aquifer without external recharge is known ( Figure 6 ).

Deg-Allier ( Deg-Allier, 1963 ) also found that the component forming a groundwater hydrograph, including those from a groundwater system, frequently each had a recession ( Figure 6 ) that could be approximated by simple exponential relationships of the from as following in Equation (2):

$h=h_0{\text{e}}^{-at}$ (2)

where h₀ and h are the water level above discharge level at the beginning of the measurement period; and after a certain time (t) respectively and ( $a$) is known as coefficient of recession or discharge coefficient.

After plotting the water levels above discharge level in semilogarithmic paper (when water level is plotted to the log scale and time to the arithmetic scale), the recession curves plot as nearly as straight lines ( Figure 6 ). In the log system with base 10, the formula is a follow ( Korkmaz, 1988 ) (Equation (3)).

$\log h=\log h_0-0.4343at$ (3)

According to ( Johansson, 1987 ), the shape of the recession curves is function of parameters such as water yielding properties of the aquifer material, the transmissivity and the geometry.

For this study, the water levels have been measured monthly during 24 months through 15 piezometers. The oscillations amplitude due to infiltration have been calculated using recession curve displacement as indicated in Figure 7 .

Specific yield (Sy) is defined as the volume of water released from storage by an unconfined aquifer per unit surface area of aquifer per unit decline of the water table ( Freeze & Cherry, 1979 ; Johansson, 1987 ). This parameter depends on the nature of the aquifer material and is related to the porosity through the Equation (4) according to Jacob Bear ( Bear, 2012 ).

$\text{η}=\text{Sy}+\text{Sr}$ (4)

where:

η: porosity;

Sr: specific retention.

According to Sophocleous ( Sophocleous, 1985 ), the specific yield is a crucial parameter for groundwater recharge calculation and its value varies according to the type of the aquifer material ( Johnson, 1967 ; Sophocleous, 1985 ). To get an accurate value of the specific yield authors have developed many methods such as aquifer tests ( Banton et al., 1991 ; Lv et al., 2021 ; Machiwal et al., 2017 ), water budget methods ( Alex Thomas & Pankaj Kumar, 2021 ), volume balance methods ( Walker et al., 2019 ), geophysical methods ( Frohlich & Kelly, 1988 ), and laboratory methods ( Islam et al., 2016 ; Lerner et al., 1990 ). The use of multiple methods aims to find out which of them gives the best value of Sy. According to many authors, the laboratory methods are considered as more reliable than all the other methods. They highly recommended to use the Sy value from literature when laboratory measurement values of specific yield are not available ( Sinha & Sharma, 1988 ). They also recommended the use of same value of Sy for regions with the same geological and climatic conditions.

Many studies have been conducted in many parts of the world and near the study area to determine the value of specific yield in consolidated sandstone aquifers. Authors like Sinha and Sharma ( Nygren et al., 2020 ) found that the value of Sy varies from 0.01 to 0.08 in sandstones in India. Values of specific yield have been determined by Touré ( Toure et al., 2016 ) in Kléla basin and Koda basin which are all located in the same climatic and geological conditions as the study area. He found that the Sy ranged from 0.011 - 0.081, with a mean value of 0.042.

Seasonal cycles have influences on groundwater levels in such factors as recharge from precipitation, evapotranspiration, and discharge from wells and show a seasonal pattern of fluctuations ( Nygren et al., 2020 ). The degree of correlation between fluctuations of groundwater level and fluctuation of total precipitation (Pt) in wet period furnishes a clue as to the freeness of the connection between recharge (water levels) and total precipitation ( Figure 5 ) (Pt) in wet period ( Korkmaz, 1988 ).

In this study and as applied by ( Korkmaz, 1988 ) and ( Blarasin et al., 2016 ), the estimated recharge was obtained by a direct estimation using recovery of the groundwater level (∆h) and total precipitation (Pt) during wet period ( Figure 4 ). The line regression ( Korkmaz, 1988 ) is Equation (5):

$\Delta h=a+b\text{Pt}$ (5)

where ∆h is recovery of groundwater level, and Pt is total precipitation during the wet period, a and b are the regression coefficients.

To estimate the recharge, water level fluctuations curves have been established ( Figure 8 ) for each piezometer form which the amplitudes of oscillation were calculated. The global recharge was calculated as the average of the values obtained from the piezometers in month time step.