Introduction
Dams are designed based on the assumption of stationarity and recoverability to an equilibrium state. However, growing evidence shows that climatic and managerial pressures violate this assumption, leading to non‑stationary behavior. In recent literature, "stationarity failure" refers to the collapse of structural relationships among inflow, storage, and outflow – a condition where the system loses its ability to return to a previous equilibrium. The Sefidrud Dam (nominal capacity ~310 MCM) is a strategic infrastructure in the Sefidrud basin, playing a vital role in agricultural water supply, flood control, and hydropower generation. It has faced concurrent pressures from droughts, altered runoff patterns, and increasing downstream demands. Previous studies have been mostly univariate (e.g., trend analysis of inflow or water level alone), neglecting the closed "inflow–storage–outflow" cycle as a coherent dynamic system. This study focuses on four operational variables to seek quantitative evidence of stationarity failure at the Sefidrud Dam using a 16‑year daily dataset and an integrated multi‑method approach.
Methodology
Daily data of four variables – inflow (IFR), reservoir storage volume (RSV), reservoir water level (RWL), and total outflow (OFR) – were collected from the Sefidrud Dam monitoring network over 16 water years (from October 2009 to September 2025). After outlier screening and removal of days with missing values, the final dataset comprised 5,792 valid days. To detect structural and behavioral changes, a comprehensive analytical framework was applied: (1) Pettitt non‑parametric test for abrupt change‑point detection in the mean of time series; (2) Mann–Kendall test coupled with Sen's slope estimator to assess monotonic long‑term trends; (3) STL (Seasonal‑Trend decomposition using Loess) to separate trend, seasonal, and residual components; (4) rolling window correlation (365‑day window) to examine the temporal evolution of pairwise relationships (IFR–RSV, RSV–OFR, IFR–OFR); (5) continuous wavelet transform (CWT) using the Morlet wavelet (cmor1.5‑1.0) on the RSV time series to identify shifts in dominant oscillation scales. Additionally, a sensitivity test was performed by removing irrigation months (May to September) and re‑running trend analyses on the remaining data to assess whether seasonal agricultural releases were the primary driver of observed changes. All computations and visualizations were carried out in Python using libraries pymannkendall, statsmodels, and pywt
Results and Discussion
Descriptive statistics showed that IFR and OFR had very high coefficients of variation (149% and 162%, respectively), indicating strong daily fluctuations and right‑skewed distributions, while the CV of water level was only about 4%, reflecting the reservoir's regulatory role. Reservoir storage volume (RSV) exhibited an intermediate behavior, with its CV increasing from ~18% in early years to ~30% in later years – an early sign of weakening storage stability. The Pettitt test identified a significant structural break (p < 0.001) for all four variables around water year 2015–2016. Mean RSV decreased from 278.1 MCM before the break to 174.6 MCM after the break, a drop of 37.2%. The Mann–Kendall test indicated significant downward trends for all variables (p < 0.05), but Sen's slope values for IFR and OFR were negligible, whereas the slope for RSV was -0.0483 MCM/day. Annual inflow volumes remained roughly constant (~50 MCM/year) across the two periods, confirming that storage decline was not caused by systematic inflow reduction. STL decomposition revealed that the trend component of RSV dropped sharply after 2015–2016, while the seasonal component remained stable throughout – indicating that the changes were non‑seasonal and structural in nature. Rolling correlation analysis showed that the correlation between IFR and RSV fell from about 0.68 in the early period to 0.22 after the break (collapse of the inflow–storage linkage), whereas the correlation between RSV and OFR increased from 0.41 to 0.79. This concurrent shift demonstrates a transition from an inflow‑driven operational regime to a storage‑driven regime, where release decisions increasingly depend on available storage rather than on incoming flows. Daily storage changes (ΔS) after the break exhibited larger interquartile range and negative skewness, indicating more frequent and rapid reservoir drawdowns. Continuous wavelet transform (CWT) revealed a striking shift: before 2015–2016, most wavelet power was concentrated at the annual scale (~365 days), reflecting long‑term planning and seasonal cycles. After the break, power shifted markedly toward shorter scales of 60–120 days, indicating dominance of reactive, short‑term decision‑making. The sensitivity test – removing irrigation months – showed that the downward trend of RSV remained statistically significant (p < 0.001) with only a slight reduction in Sen's slope, proving that seasonal agricultural releases were not the primary cause of the structural failure. Taken together, these multiple lines of quantitative evidence confirm that after water year 2015–2016 the Sefidrud Dam is no longer in a recoverable steady state and has experienced "stationarity failure."
Conclusion
This study provides convergent quantitative evidence – a ~37% storage decline, collapse of inflow–storage correlation, increased short‑term fluctuations, and a wavelet spectral shift from annual to 60–120‑day scales – demonstrating stationarity failure at the Sefidrud Dam. Annual inflow reduction played no decisive role; instead, endogenous system pressures (operational patterns, rising demand, managerial constraints) are the main drivers. The integrated analytical framework (change‑point test, trend analysis, STL, rolling correlation, and wavelet analysis) can serve as a general tool for dynamic health monitoring and early regime‑shift detection in other reservoir systems. Based on the findings, it is recommended to: (1) dynamically update reservoir performance curves to match the post‑failure regime; (2) integrate continuous wavelet analysis into early warning systems as a leading indicator of instability; (3) employ data‑driven and machine learning models (e.g., LSTM with SHAP) to restore or strengthen the functional inflow–storage linkage. Ultimately, this study highlights that dam performance assessment should not be limited to water deficit indicators or inflow trends; rather, "system dynamic health" and the stability of internal control linkages must be placed at the center of management and decision‑making.