A robust assessment of the Bjerknes-Wyrtki-Jin indices for ENSO growth rate and periodicity

Quantifying coupled ocean-atmosphere feedback processes for El Niño-Southern Oscillation (ENSO) is important for advancing our modeling and prediction of this most active interannual climatic variability of great broad global impacts. The Bjerknes stability and Wyrtki periodicity indices formulated basing on Recharge-Oscillator framework serve as a useful tool bench mark for quantitative assessment of the sources of ENSO's linear stability and periodicity. Here we have refined the formulation of these indices in the following aspects: (1) use the mixed-layer full heat budget with two new processes (nonlinear advective dynamic heating and sub-grid scale processes); (2) optimize thermocline feedback parameterization by considering the contribution of vertical mixing on temperature anomaly at the bottom of the mixed layer; (3) include both Ekman and geostrophic components for the mixed-layer equatorial zonal and meridional currents and upwelling anomalies. Using eight ocean reanalysis products, we found that these refinements have improved the representation of ENSO feedbacks. For the ensemble mean of reanalysis, these indices yield an ENSO growth rate about year^-1 and a period in about 4 year range, indicating that ENSO linear coupled dynamics are very close to criticality. Potential applications for this formulation for assessing the ENSO simulation of climate models will be addressed as well.