A nonlinear projection of the tropical Pacific El Niño/La Niña phenomenon onto North American winter (November-March) surface air temperature (SAT) anomalies was performed using a 1-hidden layer feed-forward neural network (NN) model. The first principal component (PC) of the sea surface temperature anomalies (SSTA) over the tropical Pacific is the sole input to the NN model, while the 8 outputs are the best approximations to the 8 leading PCs of the SAT anomalies upon minimizing the mean square error.

Notable nonlinearity of the SAT signal associated with the tropical SSTA is manifested by a curve in the PC phase space – with a parabola-like curve found in the PC1-PC2 plane. During minimum SSTA (strong La Niña), the SAT has negative anomalies over northwest Canada and Alaska, and positive anomalies over the United States (US). During maximum SSTA (strong El Niño), the warm center moves southeastward to the great plains with weak negative SAT anomalies over southeastern US and northern Canada. The nonlinear component of the SAT response to El Niño was estimated by calculating the difference between (a) the SAT anomalies during minimum (maximum) SSTA and (b) twice the SAT anomalies during the half minimum (half maximum) SSTA. The nonlinear pattern shows that regardless of the sign of SSTA, there are positive SAT anomalies (+0.5-1.0°C) over the US and southern Canada, negative anomalies over Alaska and northern Canada. This nonlinear pattern is quite different from the linear regression pattern where SAT has positive anomalies over western Canada and negative anomalies over southeastern US. Polynomial regression analysis shows this nonlinear component to be mainly a quadratic response of the SAT anomalies to the SSTA.