A Bayesian CUSUM Framework for Integrated Breakpoint Detection, Outlier Reconstruction, and Missing-Value Estimation in Climate Time Series Homogenization

Abstract Homogenization of climate time series is essential for reliable climate change assessment, yet distinguishing structural breakpoints from transient anomalies remains challenging when outliers and missing observations coexist with artificial shifts. Existing homogenization methods mainly focus on breakpoint detection, whereas the combined effects of structural breaks, outliers, and missing observations have received comparatively little attention.This study proposes a Bayesian Cumulative Sum (BYS-CUSUM) framework that integrates breakpoint verification, outlier identification, missing-value reconstruction, and homogenization within a unified probabilistic workflow. Candidate breakpoints are first identified using the CUSUM algorithm applied to regression residuals derived from neighboring reference stations. Bayesian inference is then used to estimate breakpoint locations and shift magnitudes while quantifying their uncertainty. Outliers are identified from the same residuals, and both detected outliers and missing observations are reconstructed using the regression model before breakpoint adjustments are applied.The proposed framework was evaluated against RHtestsV4 and Climatol using four synthetic benchmark scenarios with progressively increasing breakpoint complexity, outlier contamination, and missing observations. While all methods performed similarly under ideal conditions, the benchmark methods became increasingly vulnerable as contamination increased. Climatol frequently missed subtle breakpoints, whereas RHtestsV4 produced false or displaced detections. In contrast, BYS-CUSUM consistently achieved more accurate breakpoint localization and superior reconstruction of contaminated observations, reducing the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) by up to 83% and 82%, respectively.These results demonstrate that BYS-CUSUM provides a robust and effective framework for climate time series homogenization under realistic observational conditions.