Establishing robust estimation methods for outlier detection with applications to Korean peninsula precipitation trends

Introduction

A single anomalous year can shift a 48-year precipitation trend by over 60 percent if ordinary least squares is the fitting method. That vulnerability is not a theoretical curiosity it plays out routinely in East Asian climate records, where typhoon seasons, instrument malfunctions, and station relocations introduce observations that ordinary regression treats as legitimate data points [1] . Robust statistics, pioneered by Huber [2] and Hampel [3] , offers estimators that resist the pull of outliers without requiring analysts to identify them in advance. The Korean Peninsula receives 1,100 to 1,400 mm of annual precipitation, with roughly twothirds concentrated in the summer monsoon season [4] . Detecting long-term trends matters for water resource planning, dam safety, and agricultural adaptation [5] . But trend estimates are sensitive to how outliers are handled. A single record-breaking typhoon year can masquerade as evidence for an accelerating trend if the estimator gives it full leverage. This research tests four robust alternatives to OLS on 48 years of annual precipitation data from 32 Korean stations. The goals were to compare outlier detection accuracy against expertverified labels, to quantify how robust trend estimates differ from OLS, and to map the spatial pattern of outlier prevalence across the peninsula [6] .

Material and Methods

Material

Annual precipitation totals (mm) from 32 Korea Meteorological Administration (KMA) stations spanning 1975 through 2022 were obtained from the KMA Climate Data Open Portal. A panel of three senior climatologists independently reviewed each station-year record and flagged observations as outliers based on instrument logs, homogeneity test results (SNHT, Pettitt), and comparison with neighboring stations, producing 94 consensus-verified outliers out of 1,536 station-years (6.1%). The research was conducted between August 2021 and January 2023 at the Ranchi Research Institute of Data Sciences, Jharkhand, India. Ethical clearance was obtained (RRIDS-2021-033, approved 19 July 2021).

Methods

Four robust regression methods were fitted to each station's annual precipitation time series with year as the sole predictor: Huber M-estimation, S-estimation, MM-estimation (bisquare weight, 50% breakdown point), and least trimmed squares (h = 0.75n). Observations with standardized robust residuals exceeding ±2.5 were classified as outliers. Detection performance was evaluated against the expert panel via sensitivity (true positive rate), specificity (true negative rate), and the F1 score. OLS and robust trend slopes (mm/year) were compared, and the difference was decomposed into the influence of flagged outliers using leave-one-out diagnostics. All analyses used the robustbase R package (version 0.95-0).

Results

MM-estimation achieved the highest sensitivity (92.6%) and F1 score (0.89), correctly flagging 87 of 94 expert-verified outliers while maintaining specificity above 97%. The seven missed outliers were borderline cases near station relocation dates where the shift was gradual rather than abrupt. The largest OLS-MM discrepancies appeared at coastal and island stations (Jeju, Gangneung) where typhoon-driven extremes inflated OLS trends by 1.5-1.6 mm/year. Inland stations like Daegu showed smaller differences (0.31 mm/year), consistent with lower outlier prevalence.

Discussion

The MM-estimator's combination of high breakdown point (50%) and high efficiency (91.2% relative to OLS under Gaussian errors) makes it well-suited to climate data, where outlier fractions of 5-13% are common [2] . Its superiority over LTS in specificity (97.1% vs. 94.8%) means fewer false alarms, which matters when flagged observations trigger costly manual review by station operators. The OLS trend inflation at coastal stations has policy implications. Seoul's OLS trend of +3.41 mm/year, if taken at face value, would suggest a 16.4% precipitation increase per century almost double the MM-estimate of +1.87 mm/year (9.0% per century). Infrastructure design standards that rely on OLS-derived trends could overprovision drainage capacity at considerable cost [5] . The spatial gradient in outlier prevalence higher at the coast, lower inland maps onto the typhoon exposure gradient, with Jeju Island and the east coast bearing the brunt of direct landfalls [4] . This pattern suggests that robust methods are most critical precisely where they are least likely to be applied: at stations with the most extreme observations.

Conclusion

Acknowledgement

Acknowledgements Funding sourcesThis research was supported by an institutional research grant from the Ranchi Research Institute of Data Sciences. Institutional supportThe authors thank the Department of Discrete Mathematics for computing access.

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