The Nouhao sub-basin, covering an area of 4050 km² [21] , is a tributary of the main Nakanbé basin. It is located in the central-eastern region of Burkina Faso (see Figure 1 ), between latitudes 12˚35' and 10˚55' north and longitudes 1˚00' west and 0˚45' east. Climatically, the sub-basin lies in the Sudano Sahelian zone, characterized by a six-month dry season from November to May and a rainy season from May to October [22] . Rainfall ranges from 850 mm in the north to 950 mm in the south. The sub-basin’s hydrographic network is dominated by the Nouhao river, as well as several secondary and tertiary tributaries. Flooding of these tributaries, the main ones being Masra, Kouroko, Koulounda, Koukougo, Kiniguerlo, Ouaré, and Sablogo [23] , generally occurs between August and September. In addition, the Nouhao sub-basin has no permanent watercourses, the majority being temporary.

The climatic data used in this study come from the archives of the National Meteorological Agency of Burkina Faso (ANAM). These include monthly rainfall time series from three rainfall stations (Dialgaye, Ouargaye, Sangha) and one climate station (Tenkodogo). All the chronicles cover the same period from 1981 to 2022. However, there is missing data in the chronicles, amounting to 5% or less. Given that the gaps are non-consecutive and the number of missing values is 5% or fewer, the missing values were replaced by the average of the surrounding values or the average of the entire series. The processing and analysis of these data were carried out using various tools and methods.

1) Nicholson Index

The Nicholson index measures the difference between observed precipitation and the long-term average, thus making it possible to characterize dry, surplus, or normal periods. This index is expressed as a centered and reduced variable and is calculated using the following formula (Equation (1)) [24] [25] :

$I_i=\frac{X_i-X_m}{\sigma }$ (1)

with

$I_i$: rainfall index,

$X_i$: rainfall for year i (in mm),

$X_m$: average interannual rainfall over the study period (in mm),

$\sigma$: standard deviation of interannual rainfall over the study period.

2) 2nd-Order Hanning Low-Pass Filter (Weighted Moving Averages)

To smooth the monthly and annual rainfall series from the various stations in the Nouhao sub-basin, we used a Hanning low-pass filter of order 2. This weighted moving average method eliminates seasonal variations, making the interannual fluctuation in more visible. Seasonal variations are eliminated by weighting the annual rainfall totals using the following equations [26] :

${X^{\prime }}_{\left(t\right)}=0.06X_{\left(t-2\right)}+0.25X_{\left(t-1\right)}+0.38X_{\left(t\right)}+0.25X_{\left(t+1\right)}+0.06X_{\left(t+2\right)}$ (2)

pour $3\le t\le \left(n-t\right)$

where:

${X^{\prime }}_{\left(t\right)}$ is the total rainfall for term t, $X_{\left(t-2\right)}$ and $X_{\left(t-1\right)}$ are the observed rainfall totals of the two terms immediately preceding term t and $X_{\left(t+1\right)}$and $X_{\left(t+2\right)}$ are the observed rainfall totals of the two terms immediately following term t.

The weighted rainfall totals of the first two terms ${X^{\prime }}_{\left(1\right)}$, ${X^{\prime }}_{\left(2\right)}$ and the last two terms ${X^{\prime }}_{\left(n-1\right)}$, ${X^{\prime }}_{\left(n\right)}$ of the series are calculated using the following expressions with n the series size:

${X^{\prime }}_{\left(1\right)}=0.54X_{\left(1\right)}+0.46X_{\left(2\right)}$ (3)

${X^{\prime }}_{\left(2\right)}=0.25X_{\left(1\right)}+0.50X_{\left(2\right)}+0.25X_{\left(3\right)}$ (4)

${X^{\prime }}_{\left(n-1\right)}=0.25X_{\left(n-2\right)}+0.50X_{\left(n-1\right)}+0.25X_{\left(n\right)}$ (5)

${X^{\prime }}_{\left(n\right)}=0.54X_{\left(n\right)}+0.46X_{\left(n-1\right)}$ (6)

Centered and reduced indices of the weighted annual heights obtained are then calculated to better distinguish between periods of rainfall deficit and surplus.

A break is defined as a change in the probability distribution of observed variables within a time series. The Pettitt test is an effective non-parametric test for identifying such breaks in climatic and hydrological series [4] [27] . It is based on the comparison of subseries before and after a possible breakpoint t, determined according to the difference in distributions between these two subseries [28] - [30] . The Pettitt statistic $U_{t,N}$ is defined by Equation (7):

$U_{t,N}={\displaystyle {\sum }_{i=1}^t{\displaystyle {\sum }_{t+1}^N{D}_{ij}}}$ (7)

where $D_{ij}=\mathrm{sgn}\left(x_i-x_j\right)$ ; with $\mathrm{sgn}\left(Z\right)=1$ if $Z>0$; $\mathrm{sgn}\left(Z\right)=0$ if $Z=0$ and $\mathrm{sgn}\left(Z\right)=-1$ if $Z<0$.

Once a break in the time series has been identified, it is useful to calculate the average variation in rainfall before and after the break. This enables us to assess the rainfall deficit or surplus between two sub-periods. The variation is calculated using the following formula (Equation (8)) [27] - [31] :

$D=\frac{{\bar{x}}_j}{{\bar{x}}_i}-1$ (8)

with ${\bar{x}}_j$ the average over the period after the break and ${\bar{x}}_i$ the average over the period before the break, $D$ is the hydro-climatic deficit.

This is a non-parametric test used to assess the existence of a trend and to test the significance of trends and breaks in stationarity in the rainfall and hydrometric series in the study area [32] . The null hypothesis H0 states that there is no trend (data are independent and identically distributed).

The $U_{\text{MK}}$ statistic is calculated as follows (Equation (9)):

$U_{\text{MK}}=\frac{S}{\sqrt{Var\left(S\right)}}$ (9)

$S={\displaystyle {\sum }_{i=1}^{n-1}{\displaystyle {\sum }_{j=i+1}^n\mathrm{sgn}\left(x_j-x_i\right)}}$ (10)

$\mathrm{sgn}\left(x\right)=\{\begin{array}{ll}1,\hfill & x>0\hfill \\ 0,\hfill & x=0\hfill \\ -1,\hfill & x<0\hfill \end{array}$ (11)

The $Var\left(S\right)$ is given by Equation (12):

$Var\left(S\right)=\frac{n\left(n-1\right)\left(2n+5\right)-{\displaystyle {\sum }_{i=1}^n{t}_{i}i\left(i-1\right)\left(2i+5\right)}}{18}$ (12)

where $S$ is the sum of the signs of the differences between the values in the series and $Var\left(S\right)$ is the variance of $S$. The p-value is used to test the significance of the trend. If $U_{\text{MK}}$ is positive, the trend is upward; if $U_{\text{MK}}$ is negative, the trend is downward.

The sen’s slope method [33] was used to quantify the magnitude of the trend. The slope $\beta$ is calculated using the following formula (Equation (13)):

$\beta =\left[\frac{X_j-X_i}{j-i}\right]$. (13)

for $i<j$

where $X_j$ and $X_i$ are the values of the series at times $j$ and $i$, respectively.

Figure 2 illustrates the evolution of these indices, highlighted by the Nicholson index and the Hanning low-pass filter of order 2 (weighted moving average). Variations in these indices identify wet, normal, and dry periods.

Between 1981 and 2003, Dialgaye recorded a rainfall deficit, with a particularly marked anomaly in 1984 (−1.83). However, 1989 and 1994 were characterized by abundant rainfall, with indices of 1.59 and 2.81 respectively. From 2004 onwards, the trend is reversed and a rainfall surplus is observed, although dry years such as 2011 and 2018 show anomalies of −1.26 and −1.46.

For Tenkodogo, the period from 1981 to 2004 is also characterized by a deficit. However, between 2005 and 2022, the alternation between drought and humidity is marked by particularly rainy years, notably 1991, 1998, 2007, 2008, 2009, 2016, 2018 and 2020. The most negative anomalies were recorded in 1984, 1993, 2002 and 2004.

In Ouargaye, from 1981 to 1990, a deficit was also observed, with an anomaly of -2 in 1984. From 1990 to 2022, there was a similar alternation between dry and wet years, with indices of 1.85 in 1994 and 2.10 in 1998.

Finally, in Sangha, the period from 1981 to 1990 shows indices close to normal. However, from 1991 to 2022, there is significant variation between wet and dry years, with a notable drought in 2010 (−2.32) and excess rainfall in 2018 (2.19).

The results obtained using Pettitt’s method, presented in Table 1 , enabled us to identify breaks in the stations’ rainfall series. These breaks occurred on distinct dates: in 2003 for Dialgaye, in 2004 for Tenkodogo, and in 1990 for Sangha and Ouargaye. Of these stations, only Tenkodogo shows a statistically significant change (p-value < 0.05), while the others show no significant change (p-value > 0.05). This suggests that the variations observed at these stations are random.

Test: Statistically significant change, *P < 0.05.

The results of non-seasonal Mann-Kendall trend test, presented in Table 2 , confirm the findings of the breakpoint test. At the Tenkodogo station, rainfall shows an upward trend, which is statistically significant at the 95% confidence level. In contrast, the Dialgaye, Ouargaye, and Sangha stations show no significant trend. Although these annual rainfall series show a general upward trend, this is not statistically significant at the 95% level, suggesting that the variations observed could be attributed to random fluctuations.

Test: Statistically significant change, *P < 0.05.

In this section, we present the spatial variability of rainfall in the Nouhao sub-basin over the decades 1981-1990 ( Figure 3 ), 1991-2000 ( Figure 4 ), 2001-2010 ( Figure 5 ), and 2011-2020 ( Figure 6 ).

Between 1981 and 2020, isohyets show significant variations, reflecting climatic fluctuations.

During the decade 1981-1990 (Figure 3), high rainfall (>900 mm) was limited to the southeast, while the north and center received less than 750 mm. During the 1991-2000 decade ( Figure 4 ), there was a general retreat of isohyets towards

the southeast, with a notable reduction in areas receiving 850 mm and 900 mm of rain, marking an increase in aridity, particularly in the northwest where 650 mm and 700 mm isohyets appeared. Between 2001 and 2010 ( Figure 5 ), a slight upturn in precipitation is perceptible, with the 750 mm isohyets moving northwards and the 850 mm covering more of the central areas, while the 900 mm widens in the southeast, and a new 1000 mm isohyet emerges in the extreme southeast. Finally, during 2011-2020 ( Figure 6 ), stability dominated in the north-west with 650 mm and 700 mm, while 750 mm and 850 mm remain in the central and south-eastern zones. The 900 mm are maintained in the extreme southeast, and new isohyets, 1100 mm, reflect an extension of very wet zones in this region, confirming a trend towards localized high rainfall.

The index method has enabled us to accurately identify the years and periods of rainfall deficits and surpluses. The rainfall regime of the Nouhao sub-basin experienced alternating dry and wet periods between 1981 and 1990, with a general upward trend in annual precipitation. The analysis of the annual rainfall indices revealed a dry period from 1981 to 1990. This result corroborates previous studies in this sub-basin [34] , which highlight the decline in rainfall starting in the 1980s. This decrease in rainfall was also reported in the central-northern region of the country [35] . Similar findings have been made in Côte d’Ivoire [16] and Senegal [14] [15] . During the dry period, one particularly dry year stands out in each of the studied stations. This was the year 1984, which is part of the major droughts that affected West Africa [17] [18] . The observed rainfall fluctuations indicate a return of precipitation to the basin starting in the 1990s, which aligns with other studies conducted in the central-northern region of Burkina Faso [10] .

Analysis of the results of the Pettitt test applied to the time series shows that the null hypothesis, postulating the absence of a break, was rejected at the 90% confidence level at the Sangha, Ouargaye, and Dialgaye stations. However, only the Tenkodogo station showed a significant break (p-value < 0.05 in 2004). The Pettitt test allows for the identification of a significant break with an overshoot thresholdwhen the observation period is long enough [35] . Secondary breaks were observed in 1990 in Sangha and Ouargaye, and in 2003 in Dialgaye. These breaks signal the start of an increase in rainfall in the basin. These results are in line with those provided by the index method. This trend is also corroborated by the calculation of the average variation in rainfall based on the break years identified. This calculation indicates a surplus of 12% at Dialgaye, 16% at Sangha, 13% at Ouargaye and 21% at Tenkodogo, with an overall average of 16%. These results are similar to those of [35] . These authors also obtained recent break years (1990, 2000), resulting in an increase in rainfall with an average surplus of 13%.

Analysis of ten-year averages for precipitation in the Nouhao sub-basin reveals significant variations, including a shift in isohyets. Between 1991 and 2000, a significant increase in precipitation was observed, particularly in the southeast, where levels reached up to 1050 mm. This decade marks a return to wetter conditions compared with the previous period, with an extension of the wet zone, particularly in the southeast, and a slight increase in precipitation in the central and northwestern zones. However, between 2001 and 2010, although the south-east remains the wettest zone, precipitation there decreased slightly, while the central and north-west zones experienced a modest increase. Between 2011 and 2020, a notable drop in precipitation is observed in the central and north-western zones, while the south-east experienced a slight decrease. A study of the spatial dynamics of future precipitation in this sub-basin [20] , shows a latitudinal shift in annual precipitation totals from northwest to southeast under the RCP 4.5 scenario, corroborating the trend observed in our analysis. This concordance suggests that the southeastward shift of isohyets could continue, or even increase, in the coming decades, underlining the need to integrate these dynamics into planning of adaptation strategies to climate impacts in the region.