Simple coupled midlatitude climate models

A set of simple analytical models is presented and evaluated for interannua l to decadal coupled ocean-atmosphere modes at midlatitudes. The atmosphere and ocean are each in Sverdrup balance at these long timescales. The atmos phere's temperature response to heating determines the spatial phase relati on between SST and sea level pressure (SLP) anomalies. Vertical advection b alancing heating produces high (low) SLP lying east of warm (cold) SST anom alies, as observed in the Antarctic circumpolar wave (ACW), the decadal Nor th Pacific mode, and the interannual North Atlantic mode. Zonal advection i n an atmosphere with a rigid lid produces low SLP east of warm SST. However , if an ad hoc equivalent barotropic atmospheric response is assumed, high SLP lies east of warm SST. Relaxation to heating produces behavior like the observed North Atlantic decadal pattern, with low SLP over warm SST. Merid ional advection in the atmosphere cannot produce the observed SST/SLP patte rns. The dominant balance in the oceans temperature equation determines the phas e speed of the modes. The coupled mode is nondispersive in all models exami ned here, indicating the need for additional processes. For modes with an S ST-SLP offset as observed in the ACW and North Pacific, Ekman convergence a cting as a heat source causes eastward propagation relative to the mean oce an flow. Sverdrup response to Ekman convergence, acting on the mean meridio nal temperature gradient, causes westward propagation relative to the mean ocean Row. When the ocean temperature adjusts through surface heat flux alo ne, the mode is advected by the mean ocean flow and is damped. Relaxation to heating in the atmosphere, when operating with Sverdrup respo nse in the ocean, produces the only complete solution presented here that e xhibits growth, with an a-folding timescale of order (100 days). This solut ion appears appropriate for the North Atlantic decadal mode. In Northern Hemisphere basins, with meridional boundaries, the: same sets o f dynamics create the observed SST-SLP phase relation. An additional factor is the creation of SST anomalies through variations in the western boundar y current strengths, which are related to the zonally integrated wind stres s curl over the whole basin. If barotropic and hence fast adjustment is ass umed, the resulting positive feedback can maintain or strengthen the couple d anomalies in the North Pacific and interannual North Atlantic modes.