The effect of deep convection parameterization on the jet stream above the cold front of an explosive extratropical cyclone is investigated in the global numerical weather prediction model ARPEGE, operational at Météo-France. Two hindcast simulations differing only in the deep convection scheme used are systematically compared with each other, with (re)-analysis datasets and with NAWDEX airborne observations. The deep convection representation has an important effect on the vertical structure of the jet stream above the cold front at one-day lead time. The simulation with the less active scheme shows a deeper jet stream, associated with a stronger potential vorticity (PV) gradient in the jet core in middle troposphere. This is due to a larger deepening of the dynamical tropopause on the cold-air side of the jet and a higher PV destruction on the warm-air side, near 600 hPa. To better understand the origin of this stronger PV gradient, Lagrangian backward trajectories are computed. On the cold-air side of the jet, numerous trajectories undergo a rapid ascent from the boundary layer to the mid levels in the simulation with the less active deep convection scheme, whereas they stay at mid levels in the other simulation. This ascent explains the higher PV noted on that side of the jet in the simulation with the less active deep convection scheme. These ascending air masses form mid-level ice clouds that are not observed in the microphysical retrievals from airborne radar-lidar measurements. On the warm-air side of the jet, in the warm conveyor belt (WCB) ascending region, the Lagrangian trajectories with the less active deep convection scheme undergo a higher PV destruction due to a stronger heating occurring in the lower and middle troposphere. In contrast, in the simulation with the most active deep convection scheme, both the heating and PV destruction extend further up in the upper troposphere.