Monitoring sites
The geology of Benin is composed of two principal domains that are common in West Africa. Northern and central regions are dominated by crystalline rocks whereas the southern region consists of a coastal sedimentary basin with rocks from Cretaceous to recent ages (Fig. 1). A network of piezometers was established in the 1990s in sedimentary formations in southern Benin by the University of Abomey Calavi and the national society in charge of the water supply of cities (SONEB). More recently, a national network of groundwater monitoring sites was established by the National Directorate of Water (Direction Générale de l’Eau, DG-Eau) in the Ministry of Energy, Oil and Water.
To examine the relationship between rainfall and recharge, monitoring sites with short record duration (i.e. less than 15 years) and excessive gaps in their records were excluded. Three monitoring sites were selected in hydrogeological environments that commonly supply groundwater to inhabitants of Benin and that are common in West Africa: Quaternary sediments at Cococodji; Mio-Pliocene sediments at Allansakomey; and crystalline rocks at Natitingou (Fig. 1). These monitoring sites are appropriate to examine recharge because: (1) monitored water-table depths (WTD) are impacted by neither abstraction nor constructed surfaces; (2) records of WTD are some of the longest available in Benin; and (3) rain gauges are localised in the vicinity of the piezometer. At each piezometer, WTDs have been measured manually since the 1990s (Table 1). Recordings have been carried out by technicians of the DG-Eau and the University of Abomey-Calavi using an electrical probe (i.e. “dipper”). The time-step of the measurements in these long-term records varies from 8 to 22 days on average (Fig. 2).
Table 1 Physical characteristics of monitoring sites in Benin Strong seasonality is observed in groundwater-level fluctuations in monitored aquifers in all three geological contexts and reflects the seasonally humid climates of each monitoring site (Fig. 2). In the south (i.e. Cococodji and Allansakomey sites), rainfall usually occurs between March and October. Mean annual temperature, rainfall and Penman-Monteith reference evapotranspiration (ET0) obtained at three weather stations located in southern Benin between 1980 and 2009 are 32 °C, 1,148 and 1,549 mm, respectively (Achidi et al. 2012a). In central Benin (Natitingou site), the rainy season is slightly shorter (April to October); mean annual rainfall (1,163 mm), mean air temperature (33 °C) and ET0 (1,516 mm year−1) measured at two weather stations for the 1980–2009 period are very similar to that recorded in southern Benin (Achidi et al. 2012a). All sites are situated on surfaces of low relief with mean slopes based on Shuttle Radar Topography Mission data of 1.4% (standard deviation σ = 0.5%), 1.2% (σ = 0.4%) and 2% (σ = 1.9%) at Cococodji, Allansakomey and Natitingou, respectively. All three monitoring sites are in suburban areas that are relatively unaffected by constructed surfaces (i.e. tarmac, concrete) and where soils primarily derive from the underlying geology.
Recharge calculation and groundwater level modelling
Recharge was calculated based on the observed groundwater-level fluctuation (e.g. Scanlon et al. 2002; Healy and Cook 2002; Sibanda et al. 2009; Obuobie et al. 2012; Jassas and Merkel 2014). The water-table fluctuation Method (WTFM) assumes that change in groundwater level is controlled by the balance of recharge R [LT−1] to drainage D [LT−1]:
$$ {R}_t={S}_{\mathrm{y}}.\frac{\Delta _h}{\Delta _t}+{D}_t $$
(1)
where Sy [−] is the specific yield and Δh represents the change in groundwater level [L] through time Δt [T]. To solve Eq. (1), Sy has been estimated from measurements using magnetic resonance sounding (see next section), whereas Dt is estimated based on observed recessions in groundwater levels during dry seasons (i.e. when no rain has occurred over multiple weeks). Recharge Rt was first calculated at a daily time step by linearly interpolating the observed change in groundwater level Δh; monthly and yearly recharge were calculated by summing daily recharge. Relationships between rainfall and recharge were assessed on monthly and annual time steps through the use of regression plots. To assess the influence of daily rainfall on recharge, relationships between rainfall and recharge were systematically assessed by applying a threshold daily rainfall for generating recharge from 1 to 30 mm in increments of 1 mm. Observed relationships Rt = f (rainfallt) were then used to model a daily time series of groundwater level as:
$$ {h}_t={h}_{t-\Delta t}+\frac{R_t-{D}_t}{S_{\mathrm{y}}} $$
(2)
Time-lags between rainfall and recharge (ranging from 0 to 50 days) were then applied to model the time series of groundwater levels; the degree to which the modelled time series represented the observed time series was assessed using the Normalised Root-Mean-Square Error (NRMSE) and the Nash-Sutcliffe Coefficient (NSC):
$$ \mathrm{NRMSE}=\frac{\mathrm{RMSE}}{\overline{h_{\mathrm{observed}}}}\ \mathrm{with}\ \mathrm{RMSE}=\sqrt{\frac{\sum_{i=1}^n{\left({h}_{\mathrm{observed},i}-{h}_{\mathrm{modelled},i}\right)}^2}{n}} $$
(3)
$$ \mathrm{NSC}=1-\frac{\sum_{i=1}^n{\left({h}_{\mathrm{observed},i}-{h}_{\mathrm{modelled},i}\right)}^2}{\sum_{i=1}^n\Big({h}_{\mathrm{observed},i}-{\overline{h_{\mathrm{observed}}\Big)}}^2} $$
(4)
The influence of rainfall on recharge was assessed with the use of annual standard score of rainfall and recharge:
$$ \mathrm{Standard}\ \mathrm{score}=\frac{x-\overline{x}}{\sigma } $$
(5)
where x is the rainfall or the recharge, \( \overline{x} \) and σ are the mean and the standard deviation of the population respectively.
Estimation of specific yield
Estimation of Sy at each of three monitoring stations with long-term groundwater-level records (Fig. 1) was conducted through MRS (Vouillamoz et al. 2012a, 2014). Detailed descriptions of the MRS technique can be found in numerous publications (e.g. Legchenko and Valla 2002; Legchenko 2013). The major advantage of MRS compared to other geophysical methods (e.g. electrical resistivity tomography) is the direct measurement of signals that are generated by sub-surface water itself. One of the primary output parameters obtained from the interpretation of MRS measurements is the variation in depth of the MRS water content θMRS. MRS measurements were conducted at the 3 monitoring sites and Sy was calculated using relationships between θMRS and Sy established in previous studies carried out in several sites of the same geological environment (Table 2). The relationship used to calculate the specific yield in crystalline rock was established in central Benin (at six locations) where the Natitingou site is also located (Vouillamoz et al. 2014). For the monitoring site in Mio-Pliocene sandstone at Allansakomey the relationship used to calculate specific yield was established in the neighbouring Niger at six locations (Boucher et al. 2009) and is expected to be valid for Benin as the geological context is comparable. At Cococodji, the specific yield of Quaternary sands was estimated to be equal to the MRS water content as established in similar beach sands in India (Vouillamoz et al. 2012b). Applied Sy values for Quaternary sands, Mio-Pliocene sandstones and crystalline rocks are 16.2%, 7.1 and 0.4% respectively (Table 2); the low value of Sy obtained at Natitingou is consistent with observations that this quartzite aquifer possesses a very low specific capacity (0.3 m2 day−1). Uncertainty in Sy is estimated from uncertainties in MRS output parameters that are calculated by determining the range of acceptable solutions (i.e. equivalence analysis).
Table 2 Specific yield calculation with the use of MRS water content