A forcing-aware Jacobian framework for coupled climate subsystems

Post-1979 monthly climate records are short, externally forced, and nonstationary; a fully endogenous Jacobian is not identifiable on such data. This paper targets instead the driver- unexplained, window-averaged linear drift of a diagnostic state. The pipeline is fully repro- ducible and executable: (i) declared drivers are screened on trend-only standardized levels using a dependence-aware multiple-testing rule (so removal is noncircular); (ii) trend and retained drivers are removed jointly using one window-level ridge, preserving forced structure; (iii) two derivative residuals are constructed on the same level residuals, and cadence consistency is en- forced in the same induced norm as the solve; (iv) each drift column is estimated by a masked ridge whose penalty matches the window ridge (αmask = αeff(W)), and whose support is fixed by a structural mask; (v) an overlap-preserving block bootstrap is run per operator and per window with deterministic seeding; (vi) operator outputs are normalized to each operator’s own 10th-percentile bootstrap baseline before the cross-operator minimum is taken. All algorithmic levers (ridge rules, cadence tests, admissibility guards, bootstrap resampling, and mask semantics) are fully specified. A slow-drift triangular-array argument shows the masked ridge targets the window-averaged operator at rate Op(T−1/2) under stated conditions. Complete algebra, cadence tests, admissibility rules, masked solves, baseline normalization, pseudocode, and JSON/CSV schemas are in the Supplementary Information.