A. Parcel Theory

One way of helping meteorologists assess the risk for buoyant updrafts is to use so-called parcel theory, in which one air parcel at the surface is assumed to have the same temperature and dewpoint of the environment at the surface, and is lifted relative to the environmental air.

Parcel theory has its limitations, since it is difficult to define how large or small a parcel really is and what mechanisms exist that selectively lift the small parcel and not the entire atmospheric layer. In addition, parcel theory fails to accomodate the fact that considerable entrainment of surrounding air occurs as buoyant plumes develop. However, parcel theory has been shown to be successful in explaining thunderstorm development. Hence, we will use it in this presentation.

B. How Temperature Differences Develop Between the Rising Air Parcel and the Surrounding Air at the same Elevation

An air parcel that is lofted, must, according to the scaled First Law of Thermodynamics, cool at the dry adiabatic rate. The temperature of the surrounding, undisturbed environmental air will be that as depicted by the Environmental Lapse Rate (ELR) on an atmospheric sounding. Depending upon the ELR, the rising air parcel may find itself warmer, colder or at the same temperature as the surrounding air at the same elvation.

When an air parcel is lifted and finds itself colder than the surrounding air at the same elevation, the atmosphere is said to be absolutely stable. The atmosphere can be thought to exist between this extreme and the absolutely unstable state, in which the air parcel, upon forced lifting, finds itself warmer than the air around it at the same elevation. The reasoning behind this terminology will be apparent as you read on here.

The methodology you will learn consists of "lifting" (by drawing lines on a thermodynamic diagram) a surface parcel to the point at which it has a relative humidity of 100% (the Lifting Condensation Level--LCL); this lifting initially occurs at the dry adiabatic rate. If the parcel remains cooler than its surroundings, the state is an absolutely stable one. If the air parcel becomes warmer than its surroundings, the point at which it becomes warmer is called the Level of Free Convection (LFC). In an absolutely unstable state, the LFC is at the ground.

Lifting Condensation Level )LCL) -- the level at which the lofting air parcel becomes saturated due to expansional cooling. Procedurally, the elevation at which the mixing ratio line extended from the surface dew point intersects the dry adiabat extended from the surface temperature. Above this level, the air parcel, if lofted, must cool at the wet adiabatic rate.

Level of Free Convection (LFC) -- the elevation above which a lofting air parcel becomes warmer than the air surrounding it at the same elevation. As long as the air parcel is warmer than its surroundings, it will accelerate upwards, and that acceleration will be directly proportional to how warm the air parcel is relative to its surroundings (usually shaded in red).

It is important to keep in mind that the dry adiabatic lapse rate is a constant. Thus, a rising air parcel, whether an in unstable or stable state, will cool at exactly the same rate. But because the Environmental Lapse Rate (the vertical temperature change in the environment) DOES change dramatically over even a several hour period, a rising air parcel (whose temperature at 500 mb is, say, -10C) may find, in one instance, that it is colder than the surrounding air at the same elevation and, in another instance, that it is warmer than the surrounding air at the same elevation.

 In reality, when thunderstorms occur, most often the atmosphere is conditionally unstable. In this situation, the Environmental Lapse Rate lies between the dry adiabatic and wet adiabatic rates. The air parcel must be force-lifted to an elevated LFC (this is the "condition") at which time, further lifting will bring the parcel into a situation in which it finds itself warmer than its surroundings.

B. How to determine stability from an evaluation of a sounding plot

The ability to use soundings is absolutely critical in operational meteorology and physical oceanography. One of the most common uses of soundings plotted on thermodynamic diagrams is to determine the stability of the atmosphere. Dave Dempsey has given you the background to understand the physical interpretation of what is happening when air parcels are lofted. I will show you how to evaluate this on a thermodynamic diagram.

The first step in evaluating atmospheric stability is to determine the elevation at which saturation will occur. As mentioned above, this is called the LCL and is a good estimate for the elevation at which you will have a cloud base.

To determine this elevation, you will need to make the assumption that one air parcel at the surface, with a temperature and dew point identical to that shown at the base of the sounding is lofted relative to the atmospheric environment, which itself is NOT experiencing any vertical motion. Next you will need to consider the elevation at which this lofting decreases the temperature of this air parcel so much that its saturation mixing ratio equals the actual mixing ratio (explained in class). The Midland, TX sounding for 12 UTC 3/27/09 is given below as an example. The right hand panel shows you how to determine the LCL; there's a simple procedure outlined there.

This is the "cookbook" summary of the initial procedure. I caution you to be careful about "cookbook" summaries and rules of thumb. Unless you know why these steps work, and how they relate to what you discussed in Dave Dempsey's portion of the course, you are liable to quickly forget, and get confused.

1. Extend the saturation mixing ratio line upon which the surface dew point temperature lies upward;
2. Extend the dry adiabat passing through the surface temperature upwards;
3. Where Line 1 and Line 2 intersect, the lofted air parcel's relative humidity will be 100%.

Above the LCL, the air parcel will cool at the wet adiabatic rate. You can see that the ascent curve now parallels the wet adiabats above the LCL on the diagrams above. In this case, note that the lofting air parcel always stays cooler than the air surrounding it at the same elevation. This is an example of an Absolutely Stable sounding (discussed in class). In this case, a temperature inversion in the ELR makes it quite evident why the lofted air parcel becomes so much cooler than the air surrounding it, as it lofts.

Let's examine another sounding from 12 UTC 3/27/09, this time from Lake Charles, LA, shown below. You'll note on the left hand panel, that the LCL is going to be very near the ground. I haven't drawn in the saturation mixing ratio line nor the dry adiabat emanating from the surface conditions for this case, but the LCL will be virtually near the ground.

Note that as the air parcel then cools at the wet adiabatic rate as it continues to loft, at some point, for this sounding, its temperature becomes the same as the surrounding air again. This is called the Level of Free Convection, because above this level the air parcel will "freely" convect (will be buoyant).

C. Above the LFC and the Meaning of Buoyancy

The gas law predicts that at a given pressure elevation, an air parcel that is cold relative to its suroundings will be more dense (and heavier) than its surroundings. The gas law also predicts that at a given pressure elevation, an air parcel that is warm relative to its surroundings will be less dense (and lighter) than its surroundings.

Some basic equations show the importance of this concept. Substitution of the Gas Law into the vertical Equation of Motion for a forced lifted air parcel, yields a relationship which gives the acceleration experienced by an air parcel that is either warm or cold relative to the surrounding air at the same pressure elevation. The NWS index called "Lifted Index" is embedded in the convective acceleration equation just given.

Integrating this equation through the depth of the unstable layer (from the LFC to the EL), gives the Convective Available Potential Energy (CAPE). The CAPE can then be related (by integration) to the vertical velocity at the top of the unstable layer (EL). (See the Handout/Reading 3 on Calculating CAPE). On soundings, the portion of the parcel ascent curve for which the parcel is warmer (i.e., has CAPE) than its surroundings is often colored red, and for which it is colder than its surroundings (CIN or CINH) is colored blue. See the figure below for an example of how this appears on the Lake Charles sounding.

Convective Available Potential Area (CAPE) -- a direct measure of how buoyant (unstable) the lofting air parcel will be above the LFC. It really is a measure of how much warmer the air parcel is than its surroundings for every level from the LFC to the spot at which the air parcel's ascent curve recrosses the environmental lapse rate (sounding) for the day (normally shaded in red).

Convective Inhibition Energy (CIN) -- a direct measure of how resistant an air parcel will be to lofting and is related to how cold the air parcel is relative to its surroundings. CIN has the same units as CAPE, but is negative. If the atmosphere is conditionallly unstable, some mechanism must be present to force lift the air parcel through the area of CIN (normally shaded in blue).

The value of CAPE obtained from each sounding can then be plotted on a map to help us visualize where the atmosphere is most potentially unstable. Take a look at the kind of chart available to meteorologists to visualize potential instability. In this case, this is a 36 hour forecast of CAPE and CINH.

 Examine also the 36 hour forecast fields of Precipitable Water, Lifted Index, Dew Point Temperature and the Day 2 Convective Outlook covering the same period. If you are skeptical about looking at forecast products, you can do the same thing for current data by using many sources of interactive websites that allow you to ACTIVELY overlay real-time data. See this one used by the Storm Prediciton Center: Model/Real Time Data Composite Page Thought and In-class Discussion Question: There seems to be a correspondence between each of these fields. First, describe the correspondence; and, second, account for it. (Use 5 second rule...which is, think before you answer.)

 The CAPE, or Positive Buoyancy, is the area on a Skew-T/ln P diagram encompassed by the parcel curve on the right and the sounding on the left from LFC to EL, and in which the air parcel is warmer than its surroundings. It is usually indicated by red shading or + signs. The units of CAPE are Joules/kg, units of energy. CAPE represents the potential energy available to the air parcel to be converted to kinetic energy in a buoyant updraft.

D. Below the LFC

In a conditionally unstable state, the air parcel must be force lifted through a layer in which the air parcel is relatively cold compared to its surroundings to its LFC. If the equation used to calculate CAPE yields a negative number, then the acceleration due to buoyancy is negative (directed downward). This is because the air parcel is denser than its surroundings. The resulting calculation yields negative CAPE or Convective Inhibition Energy (CINH). This represents the work that must be expended in order to bring the air parcel to the LFC. It is usually represented by blue shading or - signs on a Skew-T/ln P diagram.

E. Midland TX Sounding, 1200 UTC 4/13/99

The sounding for Midland TX for 1200 UTC 4/13/99 is a good example of a conditionally unstable sounding. The sounding is deceptive and the indices calculated from it should be used with caution.

For example, the difference in temperature between the environment and the surface lifted parcel at 500 mb (Te -Tp)500 known as the Lifted Index (LI). Tables that relate LI to thunderstorm risk show that an LI of -4 or less are associated with soundings capable of supporting severe thunderstorm development.

This may be true if the instability in the sounding "is realized." In the case of the Midland sounding above, the LI -4.4 merely expresses a potential for instability which would NOT be realized given the need for force-lifting to the 600 mb level (nearly 10000 feet). Typical mechanisms for force-lifting of air parcels do not contribute more than around 50-100 mb of lift.

E. Midland Sounding Altered for Afternoon Heating

The Midland sounding can be altered to estimate how much surface warming would be needed to eliminate the stable layer near the ground. The assumptions in this method are that surface heating will affect the ground temperature the most, with decreasing effects upwards.

The "convective temperature" is that temperature to which the surface parcel must be warmed in order to eliminate the elevated inversion that occurs typically in the so-called "Loaded Gun" sounding. There are two procedures that must be followed in order to determine this. The first procedure is followed if the saturation mixing ratio that passes through the surface dew point intersects the actual environmental lapse rate (temperature sounding) at or above the top of the inversion layer, and the second is followed if the saturation mixing ratio that passes through the surface dew point temperature passes beneath the inversion layer.

 Procedure 1: The method involves finding the saturation mixing ratio line that intersects the morning surface dewpoint temperature. Highlight that line and draw it upward until it intersects the main sounding, at or above the inversion layer. This intersection is known as the Convective Condensation Level (CCL). The convective condensation level (CCL) is the elevation at which a convective cloud base is found when surface air parcels are heated to the convective temperature, termed the convective temperaturre, the lowest temperature to which the surface air must be heated to make the sounding absolutely unstable. The CCL is sort of a combined LCL and LFC. The convective temperature is the temperature to which the surface parcels must be warmed in order to eliminate the inversion, and to make the sounding, essentially, absolutely unstable. The blue area is related to the CIN but in this context represents the amount of heating that is needed to make the sounding absolutely unstable. If the red area exceeds the size of the blue area the sounding is said to be "potentially unstable". Procedure 2: But what if the saturation mixing ratio line passing through the surface dew point temperature does not intersect the sounding above the inversion layer? See box to right. Draw the saturation mixing ratio that passes through the surface dew point. Draw the wet adiabat that passes through the nose of the inversion and extend to the intersection point with the saturation mixing raio line highlighted in (1) (this is the CCL). From the CCL come down the dry adiabat to the surface. This is the CT. Extend the wet adiabat found in (2) to the new EL. The new CAPE is found from the nose of the inversion to the EL.

Continuation of Procedure 1: From the CCL, a line should be drawn to the surface pressure at Midland. The intersection of this line with the surface gives the so-called Convective Temperature, the temperature to which the surface air must be warmed in order to eliminate the surface stable layer. In this case, the Convective Temperature is 30C.

Next, one accepts this sounding temporarily as a reasonable estimate of the one which may occur by late afternoon. We now may use parcel theory once again.

Force lift a surface air parcel upwards and you will see that it becomes saturated at the CCL. Also, at the CCL it becomes warmer than its surroundings.

Continuing the drawing, we can develop a new CAPE area and a new EL. The region between the ascending parcel curve BENEATH the CCL and the original sounding is analagous to CINH, since it represents the amount of energy ( or work to be done) to be expended in order to heat the bottom of the sounding.

In this case, the CAPE has nearly doubled to over 2500 J/kg. If the CAPE>CINH the sounding is said to be potentially unstable and thunderstorms can be expected. The LI has decreased from -4.4 to -8 Also, in this case, insertion of the CAPE into the formula for vertical velocity at the EL yields a value >60 m/s, or over 120 mph, for the strength of the convective updraft.

Such buoyancy and updraft strength can support GIANT hail (>2" in diameter). In addition, the wind profile (note the wind profile on the right which shows a wind VEERING with height and increasing in speed very rapidly with height in the lowest part of the troposphere) is favorable for storm rotation (supercell formation). The relationship of the wind profile to rotating thunderstorms is a topic for future discussion.

Relate the Area Forecast Discussion (AFD) from Midland (script "disc KMAF" in our lab), to the discussion above.

Satellite and Radar Imagery

AREA FORECAST DISCUSSION
NATIONAL WEATHER SERVICE MIDLAND TX
930 AM CDT TUE APR 13 1999

LATEST VIS LOOP/SFC OBS SHOW PAC FRONT JUST ENTERING CWA AND GOOD
HEATING AHEAD OF FRONT...FOR A BUSY DAY AHEAD. DEWPOINTS AHEAD OF FRONT
LOOK MORE LIKE E TX COASTAL DEWPOINTS ON A DRY DAY...W/MOST IN THE
60S. 12Z KMAF RADAT WAS SATURATED FM H8-SFC AND VERY
UNSTABLE...W/LI OF -8...CAPE OF 2800 J/KG...AND ZILCH CIN. EVEN
MEAN PARCEL LIFTING YEILDS -6 LI/S AND LITTLE CAPE REDUCTION. IN
EITHER SCENARIO...HODOGRAPHS FAVOR ROTATION. SPARKS ALREADY FLYING
N OR CWA ALONG FRONT...AND EXPECT CONVECTION TO EITHER TRAIN S ALONG
FRONT...OR ALL AT ONCE AS FRONT MEETS DRYLINE HEAD-ON. ONLY CHANGES
ARE UPDATES FOR CLOUD COVER FOR TXZ058-059-067...AND MENTION OF
POSSIBLE SEVERE THERE. WZIS.

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