*2.5. Data Analysis*

We calculated the rainfall variability in terms of (1) the daily and seasonal amounts, (2) number of rainy days, and (3) total seasonal amounts. We recorded the start and end dates of the rainy season (onset and cessation dates). We used natural neighbor kriging interpolation in QGIS to describe the seasonal rainfall patterns and analyse the spatial rainfall variability. We calculated the variation coefficient of daily and seasonal rainfall amounts and for the number of events.

We determined the probability of an event covering the entire study site (P100) and the probability of covering at least half of the study site (P50) using daily rainfall events for both seasons:

$$P100 = \frac{\text{Number of rainfall events recorded by all 38rain gauge stations}}{\text{Total number of rainfall events per season}} \tag{1}$$

$$\text{P50} = \frac{\text{Number of rainfall events recorded by at least half of the 38 rain gauge stations}}{\text{Total number of rainfall events per season}} \tag{2}$$

Using *Statgraphics Centurion XVII software* (Statgraphics Technologies, Inc., The Plains, VA, USA), we also performed an analysis of variance (ANOVA) of daily rainfall for both seasons. We used the Kruskal–Wallis test to compare the medians when there were some significant non-normalities in the daily rainfall data [27].

We performed a kriging analysis for each daily rainfall event for both seasons using QGIS. From kriging maps, we performed a variogram cloud analysis using the variogram cloud tool in QGIS for every daily rainfall event to determine their variance related to distances between rain gauges (Appendix A). We modified the approach from [12], who used a defined set of transects from a kriging map of daily rainfall and assigned the mean differences of rainfall along transects to the distances between gauges. The variogram cloud analysis was used to determine the variance, semivariance, and covariance of the rainfall in all directions (360 degrees) by applying the moment of inertia to the data. We performed a regression analysis for the rainfall differences and their distances (Appendix B). Then, we calculated the correlation coefficients for maximum rainfall differences and their associated distances.

We used the Statgraphics Centurion XVII software to map the seasonal yield of pearl millet. Then, we determined the relationships between rainfall variability and pearl millet yield variability among farmers using a simple linear regression model.

We individually tested how both variables (rainfall (mm) and number of events) influence the yield for both seasons. We used the R-squared statistic to indicate how the fitted linear model explains the influence of rainfall and events on pearl millet yield.

We determined the effect of soil type at the study sites on yield variability by performing an ANOVA, comparing the average yields in different soils. We analyzed the effects of tied ridges compared to flat cultivation. We checked the within variation by computing the coefficients of variation (CVs).

## **3. Results**
