M.S. Applied Data Science - Capstone Chronicles 2025

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interval coverage within their 95% confidence bands, indicating well ‑ calibrated uncertainty quantification. Figure 8 Manganese Forecast in (next 10 Years)

The forecast captures the strong seasonality evident in historical data, with recurring spikes near 130,000 µg/L. Negative troughs (down to –60,000 µg/L) reflect model uncertainty at low baseline levels; in practice, forecasts should be truncated at zero to maintain physical plausibility. The model also reproduces the timing of peaks, indicating that SARIMAX effectively learns the annual cycles and persistence in manganese concentrations. The Manganese forecast shows a clear seasonal pattern of pronounced spikes each summer, consistent with our historical observations of lower river flows and greater geogenic release during dry months. Over the next decade, the model projects those summer peaks to continue rising modestly (from a median of ~100 µg/L to ~150 µg/L by 2035), while winter troughs remain near detection limits. The widening confidence bands around peak months reflect the high variability seen in past extreme events; several systems exceeded 3,000 µg/L historically which underscores the need for targeted summer monitoring and potential source ‐ water blending or treatment upgrades before each dry season.

From a regulatory standpoint (secondary MCL = 50 µg/L), the forecast suggests that average manganese concentrations will remain above the aesthetic standard in many counties unless mitigations are implemented. The model’s ability to replicate both long ‐ term drift and recurring spikes provides a valuable decision ‐ support tool for water managers to plan capital improvements proactively rather than reacting to episodic exceedances. Figure 9 Manganese Forecast in the next 10 years

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