A nonlinear projection of the tropical Pacific El Niño/La Niña phenomenon onto Northern Hemisphere winter (November-March) 500mb geopotential height (Z500) 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 10 outputs are the best approximations to the 10 leading PCs of the Z500 anomalies upon minimizing the mean square error.

Considerable nonlinearity of the Z500 signal associated with the tropical SSTA is manifested by a curve in the PC phase space – with parabola-like curves found in the PC1-PC2 and PC1-PC3 planes. During minimum SSTA (strong La Niña), the Z500 anomaly pattern is a negative Pacific-North America (PNA) pattern. During maximum SSTA (strong El Niño), the Z500 anomaly pattern is a positive PNA pattern but with the anomaly centers shifted eastward by about 30-40^o, and with increased magnitude. The nonlinear component of the Z500 response to El Niño was estimated by calculating the difference between (a) the Z500 anomalies during minimum (maximum) SSTA and (b) twice the Z500 anomalies during the half minimum (half maximum) SSTA. The nonlinear pattern shows that regardless of the sign of the SSTA, there are Z500 anomalies over the central-eastern North America, north Atlantic and western Europe, and negative anomalies over the western coast of North America and eastern Europe, strengthening the positive phase of PNA teleconnection and the North Atlantic Oscillation (NAO). Unlike the linear response which shows strongest Z500 anomalies in the North Pacific and North American regions, the nonlinear response has strongest anomalies in the northeast Atlantic and European regions. Polynomial regression analysis also shows this nonlinear component to be mainly a quadratic response of the Z500 anomalies to the SSTA.