Parameterizing the nonlinear feedback on ENSO from tropical instability waves (TIWs) by nonlinear eddy thermal diffusivity

As the dominant form of mesoscale variability in the equatorial eastern Pacific, Tropical Instability Waves (TIWs) are known to interact with the El Niño and Southern Oscillation (ENSO) in complex ways. TIWs activity is modulated by the ENSO state and also provide significant feedback on ENSO via nonlinear dynamic heating (NDH), acting as a source of asymmetry between the El Niño and La Niña phases. In this work, we show that the interannual variability of TIWs-induced heat flux and NDH can be approximately expressed in terms of the mean meridional temperature gradient as TIWs tend to transport heat downgradient of the temperature anomalies along the Sea Surface Temperature (SST) front. The TIWs-induced NDH can be quantified as an asymmetric negative feedback on ENSO by a nonlinear thermal eddy diffusivity which depends on the background TIWs pattern and the ENSO-related linear and nonlinear processes. This proposed parameterization scheme can capture well the direct ENSO modulation on TIWs activity, the combination effect arising from the nonlinear interaction between ENSO and the cold tongue annual cycle, and associated ENSO nonlinearity. This parameterization scheme is effectively tested using four ocean reanalysis datasets with different horizontal resolutions that exhibit contrasted patterns of TIWs activity. This scheme may be useful for assessing the TIWs-induced feedback on ENSO in mechanistic ENSO models to better understand the dynamics of ENSO complexity.