Causal Feedback Discovery using Convergence Cross Mapping on Sea Ice Data

Identifying causal relationships in climate systems remains challenging due to nonlinear, coupled dynamics that limit the effectiveness of linear and stochastic causal discovery approaches. This study benchmarks Convergence Cross Mapping (CCM) against Granger causality, PCMCI, and VarLiNGAM using both synthetic datasets with ground truth causal links and 41 years of Arctic climate data (1979--2021). Unlike stochastic models that rely on autoregressive residual dependence, CCM leverages Takens' state-space reconstruction and delay-embedding to reconstruct attractor manifolds from time series. Cross mapping between reconstructed manifolds exploits deterministic signatures of causation, enabling the detection of weak and bidirectional causal links that linear models fail to resolve. Results demonstrate that CCM achieves higher specificity and fewer false positives on synthetic benchmarks, while maintaining robustness under observational noise and limited sample lengths. On Arctic data, CCM reveals significant causal interactions between sea ice extent and atmospheric variables like specific humidity, longwave radiation, and surface temperature with a $p$-value of $0.009$, supporting ice-albedo feedbacks and moisture-radiation couplings central to Arctic amplification. In contrast, stochastic approaches miss these nonlinear dependencies or infer spurious causal relations. This work establishes CCM as a robust causal inference tool for nonlinear climate dynamics and provides the first systematic benchmarking framework for method selection in climate research.