A Physically Interpretable Spatial PDE Framework for El Niño Supports a Near-Critical Response-Mode Interpretation

Abstract

The recharge oscillator (RO) captures the core ENSO feedback loop in two physically transparent equations but collapses the basin into lumped variables, whereas coupled models of intermediate and higher complexity resolve spatial structure at the cost of less direct operator-level attribution. Here we recast the RO as a spatially explicit strip model: a minimal three-field linear partial differential equation (PDE) framework, evolved directly from RO dynamics, that retains identifiable states and operators (eastern-Pacific SST, western recharge memory, and eastern thermocline adjustment) while resolving basin-scale spatial modes. The framework remains physically interpretable and analytically tractable. Global stability analysis reveals an intrinsic oscillatory branch, a Hopf-type onset of oscillatory instability, and parameter-selective access to oscillations, mainly governed by western memory diffusion and damping. Resolvent analysis, stochastic simulations, and matched model-observation diagnostics yield consistent interannual frequencies and coherent basin-scale modes. A rolling observation-derived linear system built from the same observables remains predominantly stable, indicating that, within this linear, seasonally averaged operator setting, historical ENSO is better interpreted as a near-critical response mode than as a persistent intrinsic global instability. The framework can provide an interpretable basis for ENSO diagnosis, prediction, and physics-informed learning.