## 6 Expansion Rate of the Dam
However, our linear regression model with noise challenges this notion, demonstrating that a well-designed linear model can outperform sophisticated algorithms. This suggests that, contrary to common belief, the relationship between temporal factors (month, year), type of soil, and soil expansion in this dam's downstream area is predominantly linear. With R2a values (0.989, 0.978) nearly as high as R2, our model achieves top-tier performance without resorting to complex features or interactions. This simplicity enhances reproducibility and reduces computational costs--critical for real-time monitoring systems. The negligible difference between training and testing scores (e.g., R2 of 0.990 vs. 0.989) suggests that our model captures fundamental, stable relationships rather than transient patterns. This stability is crucial for long-term dam safety, where models must remain accurate over decades. The linear model's success implies that soil expansion primarily results from seasonal temperature cycles, potential long-term trends, and the soil-water interaction and mineral composition in this dam's downstream area. The dataset, comprising 132 monthly observations from January 2010 to December 2020, was split into training and testing sets using a time-based approach to maintain the temporal structure of the data. Specifically, we used the first 80% of the time series (January 2010 to August 2018) as the training set and the remaining 20% (September 2018 to December 2020) as the testing set. This approach ensures that our model is evaluated on future data, which is crucial for time series forecasting tasks. We did not use traditional k-fold cross-validation due to the temporal nature of our data. Instead, we employed a time series cross-validation technique called rolling window validation. This method involves training the model on a fixed window of historical data and testing it on a subsequent period, then rolling the window forward and repeating the process. We used a 24-month rolling window with a 12-month forecast horizon, which allowed us to assess the model's performance across different timeframes and seasonal patterns. Regarding potential biases in the dataset, it is essential to note that our data came from a single location (Tiga Dam in Kano State, Nigeria), which may limit the model's generalizability to other geographical areas with different climatic conditions or soil characteristics. Our dataset spans only from 2010 to 2020, which may not capture longer-term climate trends or rare extreme events. We conducted a sensitivity analysis to address these limitations by artificially introducing perturbations to the input data and observing the model's response. This analysis revealed that the model is most sensitive to extreme rainfall events, which were underrepresented in our dataset. Future work should focus on expanding the dataset to include observations from multiple dam sites across different geographical regions and more extended periods. This would enhance the model's robustness and generalizability, providing a more comprehensive tool for predicting soil expansion rates in diverse contexts. These additional details give a more transparent and rigorous description of our methodological approach, addressing the concerns about data splitting, validation, and potential biases in the dataset.