Understanding the co-variability between the El Niño–Southern Oscillation (ENSO) and its background in the tropical Pacific is critical for projecting future ENSO. The difficulty is rooted in a circular logic that the background state routinely defined by multi-decadal mean modulates, and is modulated by, ENSO. This circularity arises due to the asymmetry between El Nino and La Nina, resulting in a non-zero mean, referred to as the ENSO rectification effect. Here, we develop a novel method based on Box–Cox normalization to define the tropical Pacific background and its associated anomalies, which removes the ENSO rectification effect and is referred to as the normalized mean state. The normalized mean state accurately quantifies ENSO-related anomalies, ENSO asymmetry and the ENSO rectification effect. It is evident in both observations and model simulations that the normalized mean state has a clear asymmetric impact on the amplitude of ENSO. A warm background weakens El Niño but strengthens La Niña through two key processes: the nonlinear response of precipitation to SST and oceanic zonal advection feedback. The normalized mean state successfully solves the circular reasoning fallacy resulting from ENSO asymmetry and offers a new framework to study ENSO and tropical climate dynamics with far-reaching impacts on global climate.

ENSO rectification effect,ENSO asymmetry,Climate background state,Interaction between ENSO and mean-state