Convective clouds such as cumulus and cumulonimbus develop in unstable air due to the buoyancy force. In the context of cloud formation, buoyancy mainly refers to air parcels that are warmer and/or more moist than the surrounding environmental air, and hence rise upwards.

In this chapter, we start by describing the basic equations of the reference state to describe the motion of air, the Navier–Stokes equation, from which the concept of buoyancy can be derived. We also discuss the meaning of stability and instability in the atmosphere in the vertical, horizontal, or slantwise directions. To this end, we introduce the concept of lapse rates, including the dry adiabatic lapse rate and saturated adiabatic lapse rate. When discussing vertical and horizontal air motions, we introduce key concepts, like the hydrostatic equation, the gradient wind, the geostrophic wind, the cyclostrophic wind, and the thermal wind, respectively.