Lecture Notes

Thursday, September 30 and Friday October 1, 2004

Upper Air Data: Lifted air parcels

Objectives

By the end of this class, students should be able to:

define potential temperature and mixing ratio as conserved quantities in adiabatic processes;
identify latent heating as occuring when a lifted air parcel reaches saturation;
use skew-T diagram to identify the potential temperature, the lifting condensation level, the wet-bulb temperature, the level of free convection, lifted index, and equivalent potential temperature

Notes

Parcel Theory

Parcel theory assumes that chunks of the atmosphere can maintain uniform physical properties and not mix with the surrounding atmosphere. This is possible because mixing occurs at relatively small scales. The size of the parcel depends on the scale of the phenomenon studied.

Size Scale Example

0.1-1 km small mesoscale cumulus cloud, thermal

1-100 km large mesoscale thunderstorm, hurricane

100-1000km synoptic scale midlatitude cyclones

Parcel bouyancy

An air parcel is normally in hydrostatic balance, its weight balanced by the vertical pressure gradient force dp/dz exerted by the surrunding atmosphere. A warmer parcel in the same environment occupying the same volume would be lighter. In this case there would be a net bouyant force upward.

Thermodynamics of an ideal gas

The ideal gas law relates the pressure, volume, and temperature of unsaturated air:
The applet below illustrates an ideal gas. The temperature is proportional to the mean kinetic energy of the gas molecules. When the pressure outside the chamber is equal to the pressure exerted by the momentum of the gas molecules inside the chamber, the chamber does not change size.

Changing the pressure outside the chamber can do two things.
- If the temperature is kept constant, increasing (decreasing) the pressure decreases (increases) the volume.
- If the volume is kept constant, increasing (decreasing) the pressure.
Applet courtesy Oklahoma State University.

Adiabatic processes

In reality, simply changing the pressure exerted on an air parcel is an adiabatic process (i.e. it does not alter the mass or heat in a parcel of air). In the case of increased pressure outside the parcel, this means that the parcel will both contract a little and have its temperature increase a little. The increased pressure caused by air molecules pushing harder on the parcel walls will cause the walls to move in, decreasing the volume. The momentum of the wall will be transfered to the molecules inside the parcel, increasing their kinetic energy. The temperature will therefore increase, until the pressure exerted by the molecules inside the parcel walls is equal to that exerted outside the walls.

Therefore, Adiabatic heating (cooling) is associated with compression (expansion) and increasing (decreasing) pressure on the air parcel.

The potential temperature is conserved in adiabatic processes. This means that an air parcel can be compressed and expanded to its original state and retain its temperature.

Vertical displacements of air parcels

Forcing the vertical displacement of an air parcel will lead to a change in pressure exerted on the parcel walls by the surrounding atmosphere. Upward (downward) displacement results in adiabatic expansion and cooling (compression and heating) of the parcel.

The rate of adiabatic cooling or heating for an unsaturated air parcel is constant in a hydrostatic atmosphere (10 K/km). This dry adiabatic lapse rate is represented on tephigrams and skew-T diagrams by dry adiabats.
Potential temperature (theta) is defined as the temperature an air parcel would have if lowered along the dry adiabat to 1000 mb. Potential temperature is constant along a dry adiabat.
If a parcel is saturated with respect to water vapour (i.e. T = Td), adiabatic cooling will lead to water vapour condensing. Adiabatic cooling will be compensated partially by the latent heat of consensation. The parcel will instead be cooled at the moist adiabatic lapse rate (2 to 8 K/km). The moist or pseudo adiabatic lapse rate is represented by moist adiabats on tephigrams and skew-T diagrams.

Lifting a surface air parcel on a skew-T diagram

We define and illustrate qunatities read from skew-t diagrams using the following profile from the Miami sounding station 12Z 28 Sept 2004.

We begin by identifying the temperature, dewpoint, and associated mixing ration of a surface parcel. [Click here for illustration]
- Potential temperature - is found by reading the value of the dry adiabat in Kelvin. Alternatively, it can be found by follwing the dry adiabat from the the plotted temperature to 1000 mb and reading the temperature. Note that potential temperature tends to be higher in the upper atmosphere. [Click here for illustration]
LCL - Lifting condensation level - is found by lifting a surface air parcel until the water vapour inside begins to condense. Unsaturated air parcels conserve their potential temperature (theta) and their water vapour content (mixing ratio) w. To find LCL graphically on tephigram or skew-T diagram, draw lines upward from the surface temperature and surface dewpoint along the dry adiabat and mixing ratio, respectively. They intersect at the LCL. This determines the cloud base. [Click here for illustration]

T_w - Wet bulb temperature - the wet bulb temperature represents the temperature that a moist themometer bulb would have. Evapouration cools the thermometer and increases the water vapour content directly around it to saturated levels. The wet bulb temperature can be found by following the moist adiabat from the LCL to it's original pressure level. A moist thermometer can be used in conjunction with a dry one to determine the dewpoint by determining the wet and dry bulb temperature. [Click here for illustration]
LFC - Level of Free Convection - is found by lifting surface parcel from LCL, and following the moist adiabat up to the ambient temperature profile. At this point, the parcel becomes warmer and more bouyant than it's environment. It will accelerate upwards. Some other lifing mechanism must do work to bring the parcel to this level. [Click here for illustration]
LI - Lifted Index - difference in temperature between atmosphere and lifted parcel:

LI = T - T_lifted

The lifted index is usually calculated for the surface to 500 mb layer, but can be detemined for any layer of the atmosphere. A negative value implies an unstable atmospher prone to convection. [Click here for illustration]
EL - Equilibrium Level - is found by lifing the parcel from the LFC to where it meets with the ambient temperature curve. At this point, the parcel becomes negatively bouyant, and further convective ascent is suppressed. [Click here for illustration]
- Equivalent potential temperature - The potential temperature of a parcel after all water vapour has been condensed from it. This can be read by lifting the parcel until the moist adiabat is parallel with the dry adiabats. This occurs high in the troposphere where there is little if any water vapour present. can also be found by lifting a parcel all the the way to the top of the atmosphere, following the dry adiabat back to 1000 mb, and then reading the temperature. is higher than at a given pressure level. [Click here for illustration]

Assignment
From two of your 3 sounding plots on your skew-t diagram, lift an air parcel from 850, 700, and 500 pressure levels and read the following parameters:

LCL
T_w
LFC
LI (sfc-500 mb only!!!)
EL

Size	Scale	Example
0.1-1 km	small mesoscale	cumulus cloud, thermal
1-100 km	large mesoscale	thunderstorm, hurricane
100-1000km	synoptic scale	midlatitude cyclones