A weak coupling between the rotational and orbital angular momenta of Mars has been postulated to produce a ‘coupling term acceleration’ (CTA) that accelerates the wind field and is asynchronous with the seasonal cycle of solar forcing (Shirley, 2017). This paper presents the first GCM simulations of a fully interactive dust cycle with the CTA included, enabling storm sizes, onset times and locations to be predicted. The inclusion of the CTA greatly augments interannual variability in the occurrence and timing of GDS, with the nature of the storm season strongly linked to the phasing and amplitude of the orbit-spin coupling. This dramatically improves the model's skill at predicting GDS and non-GDS Mars Years (MY) compared to a GCM without CTA forcing. The model is clearly wrong in only 4 out of 22 well-observed storm seasons and is able to capture the general onset time of most observed storms as well as some onset locations.In years when the CTA forcing has large positive amplitudes around perihelion, GDS with onset near perihelion occur due to a net strengthening of the single-cell Hadley circulation at this time, while earlier (or later) GDS are likely produced by more localized constructive interference between the CTA and tidal/topographic flows at a time of peak forcing amplitudes. The latter may be more sensitive to errors in the assumed surface dust availability, which may explain why a late GDS observed in MY 10 is not predicted. Depletion of surface dust in source regions by GDS in prior years may have prevented a GDS from occurring in the real MY 17, when a large GDS is incorrectly predicted. Early GDS are observed but not predicted in two MYs (12 and 25) with large negative CTA forcing amplitudes around perihelion, which may be associated with a lack of water cycle coupling in these simulations. Other missing physical processes, imperfect dust parameterizations or parameter values, the assumption of unlimited surface dust availability, or the wrong CTA strength may account for other mismatches.A GDS is predicted close to perihelion in the current storm season, MY34 (2018), with a smaller GDS predicted later next Mars year, MY35 (2020). The CTA forcing in MY 34 is very similar to that of MY 21, in which a GDS is correctly predicted by the model.