Parcel Theory

It is common knowledge that warm air rises. While it is correctly understood that warm air rises because it is lighter than cooler air, a more fundamental process explains the cause of rising warm air.

Warm air has lower density as compared to cooler air; as the temperature increases, the density of the air decreases. However, even air that is of a lower density will not begin to rise by itself.

Isaac Newton's first law of motion is that the velocity of an object will remain constant unless another force is exerted on that object. The more common way of saying this is “an object at rest stays at rest and an object in motion stays in motion unless acted upon by an outside force.” This is why decreasing the density alone is not sufficient enough to cause air to rise. There must be another force exerting on the less dense air for it to begin its upward motion.

 

Diagram depicting the parcel theory. Gravity is shown as a large arrow pointing down. Two "cooler, more dense" air masses have arrow below pointing down and then outward at ground level. A "warmer, less dense" air mass has arrows pointing up.

That force is gravity. Gravity pulls cooler, denser air toward the earth's surface. As the denser air reaches the Earth's surface, it spreads and undercuts the less dense air which, in turn, forces the less dense air into motion, causing it to rise.

This is how hot air ballooning works. A flame is used to heat the air inside of the balloon making it less dense. Outside of the balloon, the cooler, denser air is pulled down by gravity and undercutting the warmer, less dense air trapped inside the balloon, causing it to lift.

This is also why thunderstorms often form along weather fronts. A front represents the boundary where cooler, more dense air undercuts less dense, warmer air and forces it up into the atmosphere, forming the storms.

In meteorology, we often treat “pockets of air” in a similar way to ballooning. We call these pockets of air "parcels". A parcel is a bubble of air of no definite size that retains its shape and general characteristics as it rises or sinks in the atmosphere.

The theory behind the parcel has several assumptions.

  • A stable atmosphere is one in which the rising parcel becomes cooler than the surrounding environment, slowing or ending its rise (left image). In an unstable atmosphere, the temperature of the parcel is higher than the surrounding environment and, as such, remains buoyant and will continue to rise (right image).

In both cases, the parcel's rate of cooling remains fixed and we generally assume the ratio of moist air to dry air in the parcel remains constant as it rises (or sinks) in the atmosphere. Therefore, stability/instability is based upon the vertical temperature profile of the atmosphere.

  • We also assume there is no outside source of heating added to the parcel.
  • A parcel that is unsaturated (relative humidity less than 100%) will cool (or lapses) at a rate of 9.8°C per 1,000 meters (5.5°F/1,000 feet) until the relative humidity becomes 100% (the air becomes saturated).
  • A saturated parcel (100% relative humidity) cools at a slower rate. This is because the process of water vapor condensing into a liquid releases heat. The released heat is added to the air within the parcel, slowing the rate of cooling.
Two columns of atmosphere with a scale of decreasing temperatures the farther from the ground. "Stable" shows bubbles of air, each with slightly lower temperatures than the air column at each high. "Unstable" shows bubbles of air slightly warmer then their corresponding surrounding temperature.

Because of many different influences on a parcel of rising air, the above assumptions will not be 100% true at all times. However, the parcel theory, while an over-simplification of real-world processes in the atmosphere, is still a good way of understanding the major factors in how the atmosphere produces the weather.

Buoyancy: Positive and Negative Energy

Looking at parcels helps determine the stability of the atmosphere.

As an unsaturated parcel rises, it will cool at the fixed rate of 9.8°C per 1,000 meters (5.5°F/1,000 feet). If the temperature of the rising parcel decreases to less than the surrounding atmosphere (due to its cooling), the parcel will become denser than the surrounding environment and gravity will slow, or even reverse, the rise. This is called negative energy and means the atmosphere at that level is “stable”.

If the temperature of the rising parcel remains higher than the surrounding atmosphere (despite its cooling), the parcel remains less dense than the surrounding environment and will continue to rise. This is called positive energy and means the atmosphere at that level is “unstable”.