A typical way of forcing air parcels upwards is along a boundary, such as a cold front or warm front. A cold front effectively bulldozes the warm air ahead of it, forcing it upwards. The case is reversed along a warm front: the warmer (less dense) air is forced over the wedge of cold air, which is being slowly pushed forward by the warm air (see figures below). The cold front can be a large (synoptic) scale front, or the boundary of cool air flowing out of an already existing thunderstorm (outflow boundary).
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The cold front pushes forward like a bulldozer or a wedge, forcing the warm, moist air ahead of it upwards. This upward motion helps initiate convection.