The data used in this study are those from 5 piezometric stations located around the Upper Cretaceous recharge zone at its outlet at Athiémé. These data are available from 2007 and cover the period 2007 to 2020, with a few gaps that have been filled ( Figure 3 ).

The strong correlation between piezometric data ( Figure 4 ) made it easy to fill in the data using analytical linear correlation. This analytical linear correlation between two series is expressed by the equations:

$\{\begin{array}{l}y-\bar{y}=r\frac{{\sigma }_y}{{\sigma }_x}\left(x-\bar{x}\right)\\ x-\bar{x}=r\frac{{\sigma }_x}{{\sigma }_y}\left(y-\bar{y}\right)\end{array}$ (1)

with

$\{\begin{array}{l}{\sigma }_x=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{n-1}}\\ {\sigma }_y=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\bar{y}\right)}^2}{n-1}}\end{array}n\le 30$ (2)

$\{\begin{array}{l}{\sigma }_x=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\bar{x}\right)}^2}{n}}\\ {\sigma }_y=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-\bar{y}\right)}^2}{n}}\end{array}n>30$ (3)

${\sigma }_x$ and ${\sigma }_y$ are the respective standard deviations of the series for the reference station and the station under study, and

$\{\begin{array}{l}\bar{x}=\frac{1}{n}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}{x}_i\\ \bar{y}=\frac{1}{n}\underset{i=1}{\overset{n}{{\displaystyle \sum }}}{y}_i\end{array}$ (4)

$\bar{x}$ and $\bar{y}$ are the respective averages of the series for the reference station and the station under study.

Two static tests have been used to study the temporal stability of data series. These are the Pettitt test [18] and the LEE and HEGHINIAN test [19] .

1) Bayesian procedure by Lee and Heghinian [19]

Lee & Heghinian’s [19] method aims to confirm or refute the hypothesis of a change in the mean of the series. It is a parametric approach whose application to a series requires a normal distribution of values. The null hypothesis is that there is no break in the series. The procedure is based on the following assumption:

Let $\left\{X_i\right\}$ be a series of independent normal random variables with constant variance ${\sigma }^2$

$X_i=\{\begin{array}{ll}\mu +{\epsilon }_i\hfill & i=1,2,\cdots ,\tau \hfill \\ \mu +\delta +{\epsilon }_i\hfill & i=\tau +1,\cdots ,n\hfill \end{array}$ (5)

Lee & Heghinian’s method proposes to determine the a posteriori probability distribution of these two parameters. To do this, we give ourselves a priori distribution of the independent parameters τ, μ, δ and σ and, in particular, we assume that the date of rupture follows a uniform probability, i.e., there is exactly as much chance of it occurring at one time or another.

Bayes’ formula can be used to update this distribution in the light of observed results: the new “a posteriori” distribution is calculated using the formulae.

- Subsequent distribution of τ

$P\left(\tau |x\right)=\frac{\sqrt{\frac{n}{\tau \left(n-\tau \right)}}}{\sqrt{R{\left(\tau \right)}^{n-2}}}$ (6)

- Subsequent distribution of τ

$P\left(\delta |x\right)={\displaystyle {\sum }_{\tau =1}^{n}P\left(\delta |x\right)P\left(\tau |x\right)}$ (7)

with

$R\left(\tau \right)=\frac{{{\displaystyle \sum }}_{i=1}^{\tau }{\left(x_i-{\bar{x}}_{\tau }\right)}^2+{{\displaystyle \sum }}_{i=\tau +1}^n{\left(x_i-{\bar{x}}_{n-\tau }\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-{\bar{x}}_{\tau }\right)}^2}$ (8)

$\begin{array}{l}{\bar{x}}_{n-\tau }=\frac{1}{n-\tau }{\displaystyle {\sum }_{i=\tau +1}^n{x}_i}\\ {\bar{x}}_n=\frac{1}{n}{\displaystyle {\sum }_{i=\tau +1}^n{x}_i}\end{array}$ (9)

$P\left(\delta |x\right)$ follows a Student distribution with (n − 2) degrees of freedom and mean $\left({\bar{x}}_{\tau }-{\bar{x}}_{n-\tau }\right)$ and variance $Var=\frac{nR\left(\tau \right){{\displaystyle \sum }}_{i=1}^{\tau }{\left(x_i-{\bar{x}}_{\tau }\right)}^2}{\left(n-2\right)\tau \left(n-\tau \right)}$.

2) Pettitt test [18]

This is a non-parametric test based on ranks (Pettitt, 1979). The sign function is defined as follows:

$Signe:\text{IR}\to \left\{-1,0,1\right\};\{\begin{array}{l}signe\left(x\right)=1,\forall x>0\\ signe\left(x\right)=-1,\forall x<0\\ signe\left(0\right)=0\end{array}$ (10)

Let $u\left(t\right)={\displaystyle {\sum }_{i=1}^t{\displaystyle {\sum }_{j=t+1}^{n}signe\left(x_i-x_j\right)}}$ and $T=MAX\left\{\left|u\left(t\right)\right|,t=1,\cdots ,n\right\}$ (11)

Let p be the probability that the test statistic T on the observed series exceeds the value k:

$p=P\left(T\ge k\right)\approx 2\exp \left(\frac{-6k^2}{n^3+n^2}\right)$ (12)

if $p<\alpha$ then the null hypothesis is rejected at the α level considered.

Analysis of curves A, B, C and D in Figure 5 shows that all piezometers installed around the recharge zone of the Cretaceous aquifer show a downward trend in static level. Analysis of the linear trends expressed in % per year under the assumption of a slope equal to 0 in Student’s t-test shows that this downward trend in the static level of each of the piezometers is significant or non-significant. In fact, the trend is qualified as significant if the probability p of the t-test applied to the regression slope is less than 0.05 or 5%, whereas it is not significant when it exceeds the 0.05 threshold. The drop in static level at the Djacotomè and Dogbo piezometers is insignificant. At Toviklin, however, the drop is statically significant ( Figure 6 ). It is 2.30 m/year at Djacotomè ( Figure 6(A) ), 1.2 m/year at Dogbo ( Figure 6(B) ) and 5.1 m/year at Toviklin ( Figure 6(C) ). At Aplahoué, the trend is towards a non-significant rise of 0.4 m/year ( Figure 6(D) ). This upward trend

in the static level of the Volly-Latadji piezometer at Aplahoué is in contradiction with the others. This contradiction stems from the rise in the static level in this piezometer from the year 2014 onwards, which has continued to the present day ( Figure 7 ). Even though the latter is located in the vicinity of the Cretaceous aquifer recharge zone [17] , there is no match between its operation and that of the others from 2014 to date. It is not representative of the hydrodynamic functioning of the aquifer. Figure 8 clearly illustrates the downward trend in static levels in the piezometers of the Upper Cretaceous aquifer over the study period (2007-2020). This figure, which spatializes the difference between maximum and minimum static levels in the piezometers over the study period, shows that all Cretaceous piezometers experienced a drop in static level. This drop ranged from 6.3 m in the north-west and south-west to 8.3 m in the centre-east of the aquifer. The maximum value was recorded in the Toviklin localities, where the Djikémè piezometer registered a maximum value of 8.3 m. The lowest values were recorded in Dogbo and Aplahoué, where the average was 6.3 m. On the aquifer, the average drop recorded was of the order of 7 m. This translates into an average increase of 7 m in the water column of the aquifer’s water resources.

This analysis was made possible by Pettitt’s break detection tests and the LEE and HEGHINIAN test. A break is defined as a change in the probability distribution of a time series at a given, usually unknown, point in time [20] . The results of the detection tests are summarized in Table 1 . Analysis of the results shows that 4 piezometric stations all experienced a break in 2013. This break, which is significant (1% < Péttit test value < 5%), reveals two sub-periods over the study period: the sub-period before 2013 (2007-2013) and the sub-period after 2014 (2014 to 2020). Thus, the 2013 to 2020 sub-period shows a static level deficit at all piezometric stations. As a result, water levels in wells and boreholes rose by 23% in Toviklin, 10% in Dogbo and Klouékanmè and 11% in Djacotomè. On the other hand, no break occurred in the data measured at Aplahoué. The absence of a break at this piezometer confirms our analysis that it does not represent the hydrodynamic functioning of the Upper Cretaceous nappe. Furthermore, given the aquifer’s geographical position, we should expect an increase in water resources in the area in general. The aquifer is located in the lower Mono River valley in Benin, with its outlet at Athiémé. At this point, the Mono drains a watershed of 21,500 km² (86%), with a specific flow rate of 5.34 l/s/km² [9] . This outlet is located after the confluence of the main tributaries (Ogou, Anié, Amou and Kra) of the Mono River in Benin [9] . Spatialization of static piezometric maxima over the study period ( Figure 9 ) shows that the Cretaceous nappe in the northeast and south experienced the highest static water levels over the period 2007-2020. Indeed, maximum static water levels in the Upper Cretaceous reservoir were recorded in the south at Dogbo (43 m) and in the northeast at Klouékanmè (40 m). These static levels were recorded in 2007. As for static levels in the Upper Cretaceous aquifer at year break (2013) ( Figure 10 ), static levels in the aquifer reservoir at this date range from 11 m to 36 m. The lowest values are recorded in the Centre-East of the aquifer and in the North-West in the Aplahoué and Toviklin wells and boreholes, where the Volly-Latadji and Djikème piezometers recorded the lowest values since their installation. In the north-west, for example, the static level is 16 m in Azovè and Kissamè. At the Volly-Latadji piezometer in the extreme north of the Cretaceous, in the Aplahoué localities, the level is 11 m ( Figure 10 ). In the south-east

Cretaceous, static levels measured in wells and boreholes fall from 21 m at Avèdji, to 13 m in the Toviklin localities and 12 m at the Djikème piezometer. These results show that the central-eastern and north-western parts of the aquifer received more water that year.

The climatic assessment carried out in the Benin sub-basin of the Mono River by Amoussou [9] and by Nakou et al. [16] revealed two important months in the basin. June is the month of maximum infiltration of water into the sub-basin’s underground reservoirs, and February is the month of maximum depletion of the sub-basin’s groundwater reserves. The Upper Cretaceous aquifer, which outcrops the Benin River sub-basin to the northeast where its recharge zone is located, reҫoit rainwater by infiltration [17] . Maps A, B, C and D in Figure 11 respectively spatialize the static levels in the aquifer’s piezometers during the month of June in 2009, 2010, 2011 and 2012. Map E in the same figure shows the drop in static levels from June 2009 to June 2012. Analysis of maps A, B, C and D reveals a similar trend in static levels in piezometers in the Upper Cretaceous aquifer. Over the months of June 2009 and 2011, static levels in the Cretaceous aquifer ranged from 12 m in the north-west and centre-east to 40 m in the south and north-east of the aquifer, with an average of 29.50 m over the entire aquifer. In 2010, static levels during the month of greatest infiltration in the Cretaceous aquifer ranged from 13 m in the northwest and central-east to 41 m in the south and northeast, with an average of 29 m over the entire aquifer. The month of June 2012 recorded 12 m in the North-West and Centre-East and 39 m in the South and North-East of the aquifer, with an average of 27.40 m over the entire aquifer. There was a 2.1 m drop in the static water level over the average (difference between 29.50 m and 27.40 m) during this short period. This phenomenon is illustrated on map E of the same figure ( Figure 11 ). This map, which depicts the drop in static levels in piezometers in the Upper Cretaceous aquifer from June 2009 to June 2012, shows the significance of the phenomenon in the aquifer. Indeed, this 2.1 m drop in static level reflects a 2.1 m increase in water resource levels in the aquifer over this period. This increase in water resources (rise in piezometric levels) is much more pronounced in the extreme north-east of the aquifer. This zone has seen more infiltration during the Upper Cretaceous.