In the Northern Hemisphere, relatively low pressure appears over the polar region and high pressure at mid-latitudes during the positive phase of the Arctic Oscillation (AO); and the reverse pattern appears during the negative phase of the AO. AO is one major dominator of the climate over the Euro-Atlantic region, as well as the North American region. The anomaly patterns of North American winter surface air temperature (SAT) and precipitation associated with the AO are examined in this study by using a feed-forward neural network (NN) model with 1 hidden layer. The NN model has a single input, the AO index [which is the leading principal component (PC) of the sea level pressure (SLP) anomalies over the Northern Hemisphere (poleward of 20°N)], and the output layer has 7 neurons, which are trained to have minimum mean square error (MSE) relative to the 7 leading PCs of the SAT anomalies by optimizing the model parameters. For precipitation, 11 precipitation PCs are used instead.

The SAT (or precipitation) anomalies associated with AO detected by the NN model can be presented by a curve in the SAT (or precipitation) PC phase space, while the linear projection shows a straight line. The linear projection can only give strictly antisymmetric atmospheric patterns during opposite phases of the AO, while the NN projection shows non-antisymmetric spatial patterns during extreme positive and negative AO phases, suggesting considerable nonlinear association between AO and North American winter climate.

Subtracting the linear response from the NN projection yields the nonlinear component of the atmospheric response, which is mainly a quadratic function of the AO index, indicating that regardless of the sign of the AO index, cooler than normal conditions appear over USA and southwestern Canada, with warmer conditions over other regions of the continent; while wetter than normal conditions appear over southeastern USA and Mexico, Alaska and northern Canada, with drier conditions over other areas of the continent. Intriguingly, the nonlinear response in the SAT and precipitation fields did not appear to be directly caused by changes in the large-scale circulation associated with AO, since neither the 500 mb geopotential height nor the sea level pressure displayed significant nonlinear response to AO.