Volcanic Eruptions Reorganize Climate Teleconnections: Detection via Riemannian Covariance Fingerprinting

Standard detection and attribution of volcanic forcing targets spatial temperature anomalies. We show that the covariance structure of climate variability carries an independent volcanic fingerprint. Applying tangent‐space regression on the symmetric positive definite manifold SPD(8) to 40 years of eight teleconnection indices, we detect volcanic aerosol forcing at (block‐permutation surrogates; observed coefficient above the null mean), robust across window sizes, lags, and surrogate block sizes. A decomposition splits each fingerprint into trace (energy‐budget) and traceless (teleconnection‐reorganization) components. All three forcings are reorganization‐dominated ( volcanic, 0.026 anthropogenic, 0.091 solar), but at the limited effective sample size these values lie within the null spread and are not individually significant; we present the decomposition as a physically motivated diagnostic, not a demonstrated inter‐forcing contrast. A single‐member CMIP6 test recovers a known forcing signal but cannot calibrate false positives at this sample size.