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Interannual sea surface height (SSH) forecasts are subject to several sources of uncertainty. Methods relying on statistical forecasts have proven useful in assessing predictability and associated uncertainty due to both initial conditions and boundary conditions. In this study, the interannual predictability of SSH dynamics in the North Atlantic is investigated using the output from a 150 year long control simulation based on HadGEM3, a coupled climate model at eddy-permitting resolution. Linear inverse modeling (LIM) is used to create a statistical model for the evolution of monthly-mean SSH anomalies. The forecasts based on the LIM model demonstrate skill on interannanual timescales O(1-2 years). Forecast skill is found to be largest in both the subtropical and subpolar gyres, with decreased skill in the Gulf Stream extension region. The SSH initial conditions involving a tripolar anomaly off Cape Hatteras lead to a maximum growth in SSH about 20 months later. At this time, there is a meridional shift in the 0 m-SSH contour on the order of 0.5 degrees-1.5 degrees-latitude, coupled with a change in SSH along the US East Coast. To complement the LIM-based study, interannual SSH predictability is also quantified using the system's average predictability time (APT). The APT analysis extracted large-scale SSH patterns which displayed predictability on timescales longer than 2 years. These patterns are responsible for changes in SSH on the order of 10 cm along the US East Coast, driven by variations in Ekman velocity. Our results shed light on the timescales of SSH predictability in the North Atlantic. In addition, the diagnosed optimal initial conditions and predictable patterns could improve interannual forecasts of the Gulf Stream's characteristics and coastal SSH.