mass conservation

Air conserves its mass in the atmosphere even though the volume may change (by way of compression, expansion due to sensible heating, etc.). This principle is invoked in the continuity equation. The Lagrangian form of the continuity equation expresses a balance between the divergence of the horizontal winds and the rate of change of density following an air parcel. The Eulerian form of the continuity equation expresses a balance between the mass divergence and the local rate of change of density. The Eularian equation states basically that if there is continual convergence of air at the surface (such as in a low-pressure system), that air must rise such that new air can continue to replace the old.