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A tangent linear adjoint for a low-resolution dynamical model of the atmosphere is used to derive the optimal forcing perturbations for all state variables such that after a specified lead time the model response has a given projection, in terms of an energy norm, on the pattern associated with the 51-yr trend in the Northern Hemisphere winter tropospheric circulation, 1948/49–1998/99. A feature of the derived forcing sensitivity is a Rossby wave–like feature that emanates from the western tropical Pacific and is associated with the deepening of the Aleutian low, whereas an annular pattern in the forcing sensitivity in the uppermost model level is shown to be associated with the pattern of the trend over the Euro-Atlantic/Asian sectors, including the upward trend in the North Atlantic Oscillation index. The authors argue that the Rossby wave–type feature is consistent with studies that have argued a role for the upward trend in tropical sea surface temperature during the 51-yr period. On the other hand, the authors interpret the annular pattern in the forcing sensitivity as being consistent with studies that have argued that the trend over the Euro-Atlantic sector was associated with influences from the stratosphere. In particular, a nonlinear model driven by the optimal forcing perturbation applied only to the top model level is successful at reproducing the trend pattern with the correct amplitude in the Euro-Atlantic sector, but implies a trend over the North Pacific toward a weaker Aleutian low, contrary to what was observed but similar to the spatial pattern associated with the northern annular mode. These results show that the adjoint approach can shed light on previous apparently different interpretations of the trend. The study also presents a successful application of a tangent linear adjoint model to a climate problem

Interpreting the Atmospheric Circulation Trend during the Last Half of the Twentieth Century: Application of an Adjoint Model