## 6 Expansion Rate of the Dam  
Figure 15 comprehensively analyzes monthly rainfall patterns from 2010 to 2020, utilizing time series plotting and seasonal decomposition techniques. This approach allows for a nuanced understanding of rainfall dynamics, which is crucial for various domains such as hydrology, agriculture, and climate science. The monthly rainfall data plot presents a high-resolution view of precipitation variability from 2010 to 2020. The graph's oscillating pattern, characterized by pronounced peaks and troughs, vividly illustrates the substantial intra-annual and inter-annual fluctuations in rainfall. Peaks, often exceeding 200 mm, signify months of intense precipitation, likely corresponding to monsoon seasons or tropical storm events. In contrast, the troughs, sometimes approaching 0 mm, indicate periods of minimal rainfall, possibly reflecting dry seasons or drought conditions. This stark variability in monthly rainfall is consistent with findings from regional studies. For instance, [PERSON] et al. analyzed rainfall patterns in Southeast Asia, observing monthly fluctuations between 50 mm and 300 mm, driven by the Asian monsoon system [63]. Similarly, [PERSON] reported extreme monthly variations (0-400 mm) in sub-Saharan Africa, attributed to  
Figure 15: Rainfall event of Kano State, Nigeria, from 2010 to 2020.  
the migration of the Intertropical Convergence Zone (ITCZ). A seasonal decomposition was applied to dissect these complex rainfall dynamics, separating the time series into trend, seasonality, and residual components. Based on the classical decomposition method, this technique assumes that these components combine additively to form the observed data [64]. The trend component reveals a gradual upward trajectory in rainfall over the study period. While subtle, this positive trend suggests a long-term increase in precipitation. Such trends are increasingly observed globally and often linked to climate change. [PERSON] et al. analyzed 55 years of global rainfall data, finding positive trends in over 60% of regions, with rates typically between 10 and 30 mm/decade [63]. Our observed trend aligns with this range, supporting the hypothesis of climate-induced alterations in rainfall patterns. The seasonality component exhibits a remarkably consistent pattern, reflecting the region's well-defined rainfall regime. Each year displays a similar sequence: a steady rise in rainfall beginning around month 3 or 4 (typically March or April), peaking around month 7 or 8 (July or August), followed by a decline back to lower levels. This robust seasonal signature is characteristic of many tropical and subtropical regions. For example, [PERSON] et al. identified nearly identical seasonal patterns in the Western Ghats of India, with rainfall peaking in July-August due to the Indian Summer Monsoon. The amplitude of the seasonal component, varying by approximately 100 mm between peaks and troughs, quantifies the intensity of this annual cycle. Such strong seasonality has profound ecological and agricultural implications [65]. A study by [PERSON] et al. in monsoon-affected regions showed that a 100 mm difference in seasonal rainfall can shift crop yields by 15-20%, emphasizing the importance of understanding these patterns for food security [63]. Lastly, the residual component captures the stochastic variations that are not explained by trend or seasonality. These fluctuations, generally within \(\pm\)60 mm, represent short-term anomalies such as unexpected storms or dry spells. The magnitude of these residuals is not trivial; a 60 mm deviation can significantly impact short-term water availability. [PERSON] et al. found that residual rainfall anomalies of \(\pm\)40 mm in China's Yangtze River basin could alter monthly streamflow by up to 25%, affecting hydroelectric power generation. Moreover, the residual plot shows no clear pattern, suggesting that these fluctuations are mainly random.