A Mathematical Characterization of Seasonal Rainfall Trends in Sylhet, Bangladesh using Fourier-Based Spectral Decomposition

Understanding the cyclical patterns of rainfall is crucial for water resource management, agricultural planning and flood mitigation in a climatically vulnerable region like Sylhet, Bangladesh. This study employs spectral analysis via the Fast Fourier Transform (FFT) to identify dominant periodicities in the monthly rainfall time series of Sylhet from 1956 to 2018. The monthly data was aggregated into annual and seasonal series to examine inter-annual and seasonal variability. The FFT analysis revealed a dominant and highly significant annual cycle (12-month period) as the primary mode of variability, confirming the strong influence of the South Asian monsoon. Furthermore, significant peaks were identified at periods corresponding to approximately 6 months (semi-annual cycle), 2.33 years and a broader band around 3.5-7 years, which may be linked to quasi-periodic climate phenomena such as the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). The results underscore the utility of FFT for deciphering complex climatic signals and provide a quantitative basis for improving predictive models and developing adaptive strategies for this flood-prone region.