Storms propagate over the ocean and create moving patches of strong winds that generate swell systems. Here, we describe the dynamics of wave generation under a moving storm by using a simple parametric model of wave development, forced by a temporally- and spatially-varying moving wind field. This framework reveals how surface winds under moving storms determine the origin and amplitude of swell events. Swell systems are expected to originate from locations different than the moving high-wind forcing regions. This is confirmed by a physically-informed optimization method that back-triangulates the common source locations of swell using their dispersion slopes, simultaneously measured at five wave-buoy locations. Hence, the parametric moving fetch model forced with reanalysis winds can predict the displacement between the highest winds and the observed swell source area when forced with reanalysis winds. The model further shows that the storm's peak wind speed is the key factor determining swell energy since it determines surface wind gradients that lead to the spatial convergence of wave energy into a much smaller area than the wind fetch. This spatial wave energy convergence implies enhanced wave energy dissipation in this focusing area, slightly displaced from the maximum wind locations. <br />This analysis provides an improved understanding of fetches for extra-tropical swell systems and may help to identify biases in swell forecast models, air-sea fluxes, and upper-ocean mixing estimations.