A simple approach to quantifying the noise-ENSO interaction. Part I: deducing the state-dependency of the windstress forcing using monthly mean data

Stochastic forcing has been used conceptually to explain ENSO irregularity. More recently, the concept of state-dependent stochastic forcing has also been explored to further explain a number of ENSO properties. Here we propose a method using monthly mean data to isolate "the stochastic part" in the zonal windstress anomalies as the residual after both the linear and low-order nonlinear parts of the deterministic ENSO signal are removed. We then further use a conditional variance approach to quantify the ENSO state-dependency in this stochastic forcing represented by this windstress residual. This methodology of isolation and quantification of state-dependent stochastic forcing is demonstrated and validated in a conceptual model and then applied to examine reanalysis and two coupled model data sets. The stochastic windstress forcing term is shown to be dependent on the ENSO state both in the reanalysis and the model data. Both of the coupled model simulations examined here have a stronger the state-dependence than in the reanalysis data. These results also reveal a threshold dependence on SST for the windstress stochastic forcing of ENSO, likely due to the nonlinearity in atmospheric convection.