An ADIABATIC process deals with the changing temperature of a parcel of air due to the air rising adiabatically or sinking adiabatically. An adiabatic process assumes no heat, mass or momentum pass across the air parcel boundary. The DIABATIC process on the other hand is any temperature change of air not related to its adiabatic vertical displacement.

Air that rises will cool adiabatically. Air that sinks will warm adiabatically. Diabatic temperature changes on the other hand can occur in the form of diabatic heating or diabatic cooling. The prime contributor to diabatic heating is the sun. Warm soils (via sun's radiation) can also produce diabatic heating. The sun's energy warms the earth's surface and thus warms parcels of air near the surface even though they are not rising or sinking. The atmosphere absorbs some of the sun's energy before it gets to the surface. A good example is the ozone layer. Some of the sun's shortwave energy is absorbed by the ozone layer and thus warms it. Examples of diabatic cooling include evaporative cooling and the emission of longwave energy from the earth's surface.

Often, adiabatic and diabatic temperature changes occur at the same time (First example: evaporational cooling of air in the mid-levels of the atmosphere causes it to become more dense and fall to the earth's surface; The air cools diabatically through evaporational cooling then warms adiabatically as it sinks to the surface; a parcel of air could be experiencing evaporational cooling at the same time it is sinking and warming adiabatically, the cooling and warming at the same time will try to offset each other). The key concept is that the temperature change of a parcel of air due to diabatic heating/cooling is INDEPENDENT from the temperature change caused by adiabatic heating or cooling. Temperature changes due to diabatic heating or cooling by themselves do not necessarily depend on if the parcel is rising or sinking. (Second example: The sun warms a parcel of air near the earth's surface diabatically; This parcel then becomes less dense and rises and therefore cools adiabatically).

Diabatic temperature change also occurs when parcels of air are not able to obey the adiabatic assumption. In situations with turbulence (very common in the PBL) heat, mass and momentum will cross the parcel boundary.

Condensational warming is a diabatic process, but due to its extreme importance to convection and thermodynamic instability it has been given the name of the moist adiabatic lapse rate. Notice that the terminology calls heating due to condensation adiabatic! Actually, there are two separate phenomena occurring at the same time. One phenomenon is the parcel of air cooling at the DALR. The second phenomenon is the parcel warming through latent heat release of condensation. These two processes partially offset each other. Since the DALR is greater than the rate of warming due to latent heat release, the saturated parcel still cools as it rises. However, it cools at a lesser rate than it would if it were unsaturated. The moist adiabatic lapse rate is a combination of adiabatic cooling and diabatic heating due to condensation. Understanding adiabatic and diabatic heating/cooling will help you gain a grasp on why temperature changes in the atmosphere the way they do.