Multi-Scale Analysis Based on Wavelet Transform of Reservoir and River Total Phosphorus Correlation and Determination of Monitoring Time Scales

Total phosphorus (TP) dynamics between reservoirs and inflowing rivers critically affect eutrophication risks, but their multi-scale interactions remain insufficiently quantified. This study applied wavelet transform analysis to 8-year TP time series data from the Shanxi Reservoir and its inflowing rivers. Key findings include the following: (1) Morlet wavelet decomposition revealed dominant 8–16-month cycles for reservoir TP, contrasting with 4–8-month cycles in river TP; (2) wavelet coherence analysis identified a 90° phase lag (2–4 months delay) between reservoir and river TP at the 8–16-month scale; and (3) the time–frequency localization capability quantified rapid responses—reservoir TP reacted within 2 months to abrupt river TP increases, showing stronger intensity. Multi-resolution analysis further distinguished the driving mechanisms: interannual cycles (>12 months) governed reservoir TP variations, while seasonal cycles (<8 months) controlled river TP fluctuations. The study demonstrated wavelet analysis’ dual strengths: resolving scale-specific interactions through multi-scale decomposition and quantifying transient responses via phase coherence metrics. The 90° phase shift exposes hysteresis in TP transport, and the 2-month response threshold defines critical intervention timing. An adaptive monitoring framework is proposed as follows: ≤8-month sampling under stable conditions and 2-month intervals during TP surges, providing a time–frequency decision tool for precise reservoir water quality management.