Antarctic Ice Core Harmonic Analysis

A harmonic analysis of Antarctic ice core proxy temperature, CO₂ and CH₄ data is presented spanning 350,000 years. Using a greedy algorithm to select periodic components, the analysis initially obtained 59 periods for temperature but subsequently refined this to 55 periods after removing four components (22,150, 9,000, 8,000, and 4,540 years) that exhibited high correlations in the normalized covariance matrix. This refinement ensures stable, well- conditioned parameter estimates while maintaining excellent fits: R² = 0.952 for temperature and R² = 0.964 for CO₂ (truncated at 1850 CE), R² = 0.873 for CH₄ . The algorithm independently recovers the canonical Milankovitch orbital periods (approximately 100,000, 41,000, and 23,000 years) without prior specification, validating both the methodology and the orbital pacing of ice ages (Milankovitch, 1941). Phase analysis reveals that CO₂ consistently lags temperature by 600–4,000 years at orbital timescales, supporting the hypothesis that temperature drives CO₂ through ocean degassing rather than the reverse. Examination of the Last Interglacial (Eemian) reveals a striking asymmetry: CO₂ remained elevated at 275–280 ppm for approximately 13,000 years while temperature declined by 7°C. An R² analysis clearly reveals the Mid-Pleistocene Transition and justifies limiting the input to the fit. The modern CO₂ spike, which departs dramatically from the 350,000-year orbital envelope, is clearly anomalous relative to the harmonic structure of the paleoclimate record.