Air parcel and its environment

An air parcel is a body of air collected from the atmosphere at a location where we are interested in analyzing its properties. The air surrounding the air parcel is called environment. As an air parcel is collected, its properties is identical to those of the environment. Once the air parcel is moved to a different location, either horizontally or vertically, the properties of the air parcel and its environment may be different. However, the pressure of the air parcel is assumed to adjust immediate to its environmental value.

Upward and downward movement of an air parcel

As an air parcel is moved upward or downward, some of its properties will change. An air parcel is said to be lifted if it is moved upward by some force. But we also use the word lifted in reference to general upward motion of an air parcel.

The following is a list of the thermodynamic parameters of an air parcel:

Pressure

Temperature

Relative humidity

Mixing ratio

Saturation mixing ratio

Vapor pressure

Saturation vapor pressure

Dew point temperature

Potential temperature

Equivalent temperature

Equivalent potential temperature

Wet-bulb temperature

Wet-bulb potential temperature

First we need to know how to find the values of these parameters on a skew T chart. During the lifting of an air parcel, some of the parameters will increase, some decrease, and some stay the same.

You will be working on the following two questions in today's lab.

Which parameter will increase, decrease, or stay the same during unsaturated ascend?

Which parameter will increase, decrease, or stay the same during saturated ascend?

Lifting condensation level (LCL)

During the lifting of a moist but unsaturated air, the temperature will decrease at the dry adiabatic lapse rate but the mixing ratio will stay the same. In other word, the potential temperature and the mixing ratio are conserved. Continuous lifting will cause the parcel to saturate and a cloud will form. The level, usually referenced by its pressure, at which the cloud forms through lifting is the LCL. The LCL depends only on the air parcel of interest, and it does not depends on the properties of the environment.

The LCL level can be found on a skew T chart by first drawing a dry adiabatic line through the temperature of the air parcel. This line shows the change of temperature when an air parcel ascends or descends adiabatically without condensation or evaporation. Next we draw a constant mixing ratio line through the mixing ratio of the air parcel. The intersection of these two lines are the LCL. Inspecting the constant mixing ratio line we can find that the dew-point temperature also decreases when an air parcel is lifted but the rate of decrease is much slower than the dry adiabatic lapse rate.

Question: What is the rate of decrease of the dew point temperature for an air parcel at 1000 mb with a mixing ratio of 15 g/kg.

Lifting of an air parcel beyond the LCL

Since the air parcel is saturated at LCL, lifting beyond LCL will cause condensation and release of the latent heat to warm to air parcel. The path of the air parcel on the skew T chart will follow the saturated adiabatic line. The lapse rate of the saturated adiabatic line varies by the temperature of the air parcel. For a very warm air parcel, the condensation rate and the release of latent heat is large and the lapse rate is small (~5 °c/km). For a cold air parcel, the condensation rate is small and the lapse rate is close to the dry adiabatic lapse rate.

The line we have drawn in this and the last sections give all the thermodynamic parameters of an air parcel when it is lifted upward. If we consider that a cloud is formed by a series of connected air parcels, on after the other, the lines we have drawn represents the parameters of the cloud. Chiefly, we can read the cloud temperature from this line.

Cloud and environment

So far we have lifted an air parcel without comparing its temperature with the environmental temperature. Of special interest during the lifting of an air parcel is the increase of the relative humidity and the production of clouds. If an air parcel is colder and heavier than its environmental air after a small lifting, it is stable and continuous lifting is needed to move it upward. We refer to the upward motion produced by lifting as the forced convection. The clouds produced by forced convection is usually of the stratus type. If an air parcel is warmer and lighter that its environmental air after a small lifting, it is unstable and it will move upward without additional lifting. This upward movement of an air parcel is referred to as the free convection. The clouds produced by free convection is usually of the cumulus type.

NOTE: the stability we talked about in the last lecture refer to a thin layer of the atmosphere. The lapse rate of the layer can be considered as constant and the air is either unsaturated or saturated. In this section, an air parcel is lifted starting from a point of interest upward through the atmosphere. Its stability, or the potential for continuous upward motion, does not depends on the local lapse rate, but on the path the parcel is going through.

Level of free convection and the equilibrium level

Since the air parcel is saturated at LCL, the air parcel will follow the moist adiabatic lapse rate above that level. In a conditionally unstable atmosphere, the moist adiabatic lapse rate is smaller than the lapse rate of the sounding, reducing the temperature difference between the air parcel and the environment. At some point the parcel temperature may exceed the environmental temperature, and the air parcel will gain positive buoyancy. The level of transition from the negative buoyancy to positive buoyancy is the level of free convection (LFC), above which the free convection starts. Because the upper levels of the atmosphere is more stable and it is capped by the very stable tropopause, further upward motion will cause the air parcel to be again colder than the environment. The level of transition from positive buoyancy to negative buoyancy is called the equilibrium level (EL).

On a skew T chart, he area bounded by the sounding and the parcel temperature profile between the starting points of the parcel and the LFC is called the negative area because the air parcel is colder than its environment. The area bounded by the sounding and the parcel temperature profile between the LFC and EL is called the positive area because the parcel temperature is warmer than the environment. The area bounded by the sounding and the parcel temperature profile above EL is again called the negative area because the parcel is colder than the environment.

Potential for convective clouds

The potential for convective cloud formation can be determined by a comparison of the sounding and the cloud temperature profile formed by lifting of an air parcel from the low level. Between the starting point of the air parcel and the LCL, the air parcel is unsaturated and is colder than its environment and lifting is needed to maintain the forced convection. Condensation and clouds start to form at LCL, which is the base of the clouds. Between LCL and LFC, the air parcel is saturated but it is still colder than the environment. Could is of the stratus form and continuous lifting is needed to maintain the cloud. Above LFC, the air parcel is warmer than the environment and free convection and cumulus clouds will form. The cumulus clouds can attain great vertical velocity, which could produce severe weather, as will be discussed later this quarter.

Vertical equation of motion

The vertical velocity of a cumulus cloud can be estimated using the original vertical equation of motion before using the hydrostatic approximation:

Separate the pressure and the density into the mean (the environmental value) and the deviation (the cloud value subtract the environmental value),

The vertical equation can be approximated by

Assume , and the environment is in hydrostatic balance

the vertical equation can be written as

Use the equation of state for the parcel and the environment (with bar)

the vertical equation of motion can be written as

Cloud vertical velocity

The vertical velocity at any level above the LFC can be estimated using the vertical equation of motion. First use

The equation of motion can now be written as:

or

Divide the hydrostatic approximation

by the equation of state

we get

or

The vertical velocity equation now can be written as:

Integrate from LFC (level 1) to any level (level 2), we get

is usually small and can be neglected. Since is the area between the sounding and the cloud temperature profile, this area is proportional to the vertical velocity of the cloud. The maximum cloud vertical velocity is computed if we set level 2 at the EL. Since a cloud will attain its maximum vertical velocity at the EL, its momentum will carry it further upward to a greater height beyond the equilibrium level. This is called the over shooting. Some of the clouds can reach as high as 70,000 feet even thought the tropopause is around 30,000 feet. The maximum over shooting can be estimated by integrate the above equation beyond EL until equals zero. On a skew T chart, the maximum overshooting can be estimated by equating the negative area above EL to the positive area between LFC and EL.

NOTE:

In all these discussions, the effect of entrainment, the pressure perturbation, and weight of the liquid water are all ignored. They all contribute to a downward force and will reduce the cloud speed.

Convective available potential energy

CAPE is half the square of the cloud vertical velocity at EL. It represents the kinetic energy of the convection.

Convective inhibition

CI represents the negative energy we have to over come to reach the LFC. In order for a cloud to form, we have to over come CI. Under a condition of large CI, there may not be enough force to lift the air parcel passing the LFC. A convective cloud will not form in this case no matter how large a CAPE is.