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A capping inversion is an elevated inversion layer that caps a convective planetary boundary layer, thus inhibiting significant convection.
The boundary layer
The boundary layer is the part of the atmosphere which is closest to the ground. Normally, the sun heats the ground, which in turn heats the air just above it. Thermals form when this warm air rises into the relatively colder air (warm air is less dense than cold air), a process described as convection. Then, this active boundary layer can be called the convective planetary boundary layer. A convective layer such as this has the potential for cloud formation because condensation occurs as the warm air rises and cools. For further information see the separate article on the planetary boundary layer.
An inversion occurs when the normal temperature (warm air below, cold air above) profile is reversed, creating a stable configuration of dense, cold air sitting below lighter, warm air. An elevated inversion layer is a region of warm air above a region of cold air, but higher in the atmosphere (typically several thousand feet above the surface). There are two primary causes of an elevated inversion layer. Sinking air aloft (subsidence) will warm as it is compressed at higher pressure. Warm advection aloft, warmer air moving over a region, can also produce an elevated inversion layer.
A capping inversion occurs when there is a planetary boundary layer with a normal temperature profile (temperatures decreasing with height) and a layer above that is an inversion layer (temperature increasing with height). Rising parcels of air will now become cooler than the surrounding air and no longer buoyant. Cloud formation from the lower layer is "capped" by the inversion layer. If the capping inversion layer or "cap" is too strong, it will prevent thunderstorms from developing. A strong cap can result in foggy conditions. Although initially a stable situation, a capping inversion can allow the buildup of heat and moisture at low levels, potential fuel for thunderstorms later.
If the capping inversion is weakened or destroyed by solar heating during the day or a change in weather patterns, then convection, often strong, can develop.