Spectral correlation analysis between subseasonal-scale precipitation and climate indices in Rio Grande do Sul, Brazil, using FDM and FFT

Abstract This study evaluates the diagnostic capability of the Fourier Decomposition Method (FDM) in comparison with the Fast Fourier Transform (FFT) for diagnosing subseasonal precipitation variability in Rio Grande do Sul (RS), southern Brazil. Time series of 45-day moving averages derived from gridded precipitation estimates from the CHIRPS v2.0 dataset were analyzed across three spatially distinct regional clusters representing different hydroclimatic regimes in the state. Rain gauge observations were used exclusively for validation purposes. The analysis considered large-scale and intraseasonal climate indices, including Niño3.4 (NINO34), the Pacific Decadal Oscillation (PDO), the Madden–Julian Oscillation (MJO),the Southern Annular Mode (SAM/AAO), the Southern Oscillation Index (SOI), the South Atlantic Subtropical High index (SASHI), and sea surface temperature anomalies in the southwestern South Atlantic (SST23). Non-stationarity was assessed using the KPSS test, followed by spectral decomposition using both FFT and FDM within a conservative statistical inference framework. Statistical significance was evaluated using an effective sample size to account for serial autocorrelation and corrected for multiple testing using a false discovery rate approach. Under these stringent conditions, only climate–precipitation relationships that remain statistically supported were retained. The results indicate that spectral reconstruction enhances the detection of multiscale and transient variability relative to fixed-basis approaches, particularly at intraseasonal timescales. Signals associated with large-scale Pacific variability emerge as persistent low-frequency coherence in clusters dominated by synoptic-scale processes, whereas intraseasonal and regional atmospheric influences—linked to the MJO and South Atlantic circulation—are preferentially resolved in specific clusters when FDM is employed. By integrating spatial regionalization with multiscale spectral analysis, this study advances a robustness-based framework for assessing precipitation–climate relationships under non-stationary conditions. The findings underscore the relevance of adaptive spectral methods for regional climate diagnostics and for improving the interpretation of subseasonal precipitation variability in southern Brazil.