Definitions

# Air parcel

An air parcel is an imaginary volume of air used by meteorologists to conceptualize the thermodynamic fluid motions of the atmosphere for use in weather forecasting. For mathematical simplicity, an air parcel is usually considered a rigid cube which has limited interactions with surrounding environmental air. The dimensions of this parcel are determined by the atmospheric scale under study.

The importance of the concept of air parcels in meteorology lies in its ability to assist meteorologists in conceptualizing how areas of an atmosphere will feature rising and sinking motions, the magnitude of those motions, and the possibility of ensuing clouds and precipitation. Many older numerical weather prediction models used the conceptual models of air parcels.

### Buoyancy

The primary concern of air parcels for meteorologists is whether they will rise, sink or remain steady. To understand this motion, it is helpful to consider thermodynamic buoyancy equations. One such equation can be derived as follows.

Let the weight of the parcel be $mathrm\left\{V\right\} mathbf\left\{g\right\}$, while the pressure gradient force is $frac\left\{dp\right\}\left\{dz\right\}$. Using the hydrostatic assumption (both terms equal zero) and observing that $rho V frac\left\{dw\right\}\left\{dt\right\}=0$ in this case gives $rho V frac\left\{dw\right\}\left\{dt\right\} = -Vfrac\left\{dp\right\}\left\{dz\right\} -Vrho g$ Allowing for the pressure to be the sum of the environmental and parcel pressure $p = bar\left\{p\right\} +p^prime$ yields the following as the buoyancy equation: $frac\left\{dw\right\}\left\{dt\right\} = -frac\left\{1\right\}\left\{rho\right\}frac\left\{dp^prime\right\}\left\{dz\right\}+g\left(frac\left\{bar\left\{rho\right\}-rho\right\}\left\{rho\right\}\right)$ (where $frac\left\{dw\right\}\left\{dt\right\}$ is the buoyancy and w is the vertical motion $frac\left\{dz\right\}\left\{dt\right\}$).

The first term of this equation details the effects of pressure perturbation, wherein the parcel must literally "push" surrounding air out of the way to move through the environment. This effect tends to retard parcel acceleration, and is an important consideration in thunderstorm updrafts.

From the second term, it is easily seen that if the parcel is denser than its environment (i.e. $p > bar\left\{p\right\}$), it will have a negative buoyancy and will thus sink relative to the environment. The opposite case is also true ($p < bar\left\{p\right\}$ causes rising), while neutral buoyancy is achieved by the two terms being equal. Alternatively, the density can be replaced by the virtual temperature (virtual temperature is necessary because of the density differences between air and water vapor). Basically, an air parcel which is warmer than its environment will rise. Conversely, if it is cooler, it will sink.

In addition to the basic buoyancy equation, there are two other factors which govern parcel movement; precipitation loading, amount of parcel water vapor, and entrainment. If moisture precipitates within the parcel, the amount of precipitation in the parcel versus the amount in the environment will affect the parcel's buoyancy (every drop of precipitation adds extra weight to the parcel). This is described mathematically as a third term in the buoyancy equation $bar\left\{q_c\right\}-\left\{q_c\right\}$. Lastly, if mixing of environmental air with parcel air is considered, the properties of the parcel will change to reflect that of the environment. This process is known as entrainment and is mathematically represented as a coefficient lambda $lambda = frac\left\{1\right\}\left\{m\right\} frac\left\{dm\right\}\left\{dz\right\}$ (m is the mass of air entrained into the parcel).

Combining all the factors yields an equation which suitably expresses the buoyancy of an air parcel $frac\left\{dw\right\}\left\{dt\right\} = -frac\left\{1\right\}\left\{rho\right\}frac\left\{dp^prime\right\}\left\{dz\right\}+ g\left(\left(frac\left\{bar\left\{rho\right\}-rho\right\}\left\{rho\right\}\right)+\left(bar\left\{q_c\right\}-\left\{q_c\right\}\right)\right)-lambda*w^2$

To summarize in simpler terms, there are four major factors which affect the buoyancy of air parcels. Pressure perturbation decelerates parcels because moving parcels have to "push" surrounding air out of the way. Density differences between the air parcel and its environment can accelerate or decelerate the parcel. Precipitation within the parcel can act a drag on upward motions. Lastly, mixing of the parcel air with environmental air acts to decrease buoyancy.

### Applications

When using a Skew-T chart (a Tephigram chart can be used for this as well) to diagnose the atmosphere, meteorologists assume that air interacting with the environment will behave as an air parcel (that individual parcels of air will not significantly interact with the environment). A meteorologist can then trace a parcel up or down the appropriate adiabat to determine the desired variable, which can be temperature, pressure, moisture content, and so forth.

The notion of air parcels is partially confirmed by examining convective plumes within cumulus congestus clouds. Individual columns of rising air can be observed in such clouds. In time lapse photography, areas of convection can be observed, and the individual terms of the buoyancy equation can be observed in action (e.g. warmer air rising, entrainment of environmental air causing decay, etc). The figure on the right demonstrates how a rising air parcel can create a localized cloud in the beginning stages of a thunderstorm.