The Ups And Downs Of Air Parcels

Let me rewind Meteo 101 back to the time lapse of cumulus clouds building over Mt. Nittany. Without hesitation, the "upshot" of this time lapse is that cumulus clouds build skyward in concert with rising currents of air (I realize that this deduction is not a giant leap, but I want to leave no stone unturned).

Given that cooling is, by far, the most common way to make a cloud, it's logical to assume that cooling results when air moves upward. Let's delve deeper and see if we can prove that our observation is indeed correct.

Weather balloons ascend at rates approaching 6 meters per second (nearly 20 feet in one second). Such rates of upward motion are fast by typical air-parcel standards. Granted, upward velocities in powerful thunderstorms can be very fast, with some "updrafts" approaching 25 meters per second. By comparison, the speed of rising air in the building cumulus clouds shown on the time lapse might be a modest 1 meter per second. In contrast, typical rates of ascent (or descent) by air parcels average only a few centimeters per second (on the order of an inch or two per second), which, compared to the upward zip of helium-filled weather balloons and rising currents in building cumulonimbus clouds, qualifies as a "Sunday driver" (a slowpoke).

When gravity nearly offsets the upwardly directed pressure gradient force, the atmosphere is close to hydrostatic balance. In such a nearly balanced state, the magnitude of up and down motions of air is typically only a few centimeters per second. In other words, most vertical motions are like Sunday drivers.

The reason that the up-and-down motions of air parcels are usually so slow is that the atmosphere, on average, stays close to hydrostatic equilibrium. That's scientific jargon which translates to gravity nearly balancing the large, upward pressure-gradient force. Think about it for a moment. Assuming sea-level pressure is 1000 mb, then the upwardly directed pressure gradient over your favorite beach to 700 mb is approximately 300 mb in just two miles. If that pressure gradient ever existed in the horizontal, then God help us because the winds would easily blow at supersonic speeds! That gives you a hypothetical idea of how large the upward pressure gradient force really is. But, thanks to gravity, the mighty vertical PGF is regularly humbled, keeping upward and downward motions of air gentle and tame most of the time.

Lest you think that air parcels are always "Sunday drivers" in the vertical, I point out that upward speeds in severe thunderstorms that produce large hail can sometimes reach 50 meters per second (over 100 miles an hour). Such behemoth updrafts can suspend embryonic pieces of ice high in the upper cold reaches of a cumulonimbus cloud long enough to allow them to grow into giant hailstones (no relation to Hale Stone).

Such rapid ascent requires air parcels to have very strong positive buoyancy. As an offbeat example of what I mean by "very strong positive buoyancy", you might want to read the harrowing tale of Larry Walters, who, in 1982, tied 45 helium-filled weather balloons to his lawn chair. What happened next qualified him to win the 1997 Darwin Award.

The mighty positive buoyancy that launched Larry and his lawn chair skyward resulted from the large differences in density between the helium-filled balloons and the surrounding air (for a given volume at a temperature of 0 degrees Celsius, "regular air" is at least seven times more dense than pure helium). Of course, regular parcels of air have very little helium in them (in the real atmosphere, helium is a trace gas).

The difference in temperature between an air parcel and its immediate environment governs the buoyancy of the parcel. That's because temperature is related to density (as you recall from an experiment in Lesson 5). The bottom line here is that relatively warm parcel of air has a lower density than the cooler air surrounding it and thus will be positively buoyant (it will have a tendency to rise). As the temperature (density) difference between an air parcel and its immediate environment increases, so does the buoyancy. Think of trying to submerge an inflated beach ball (low density) in a swimming pool (water has a relatively high density). The large positive buoyancy of the beach ball cannot be denied. Try it, if you don't believe me.

By the same token, a relatively cool parcel has a higher density than the warmer air immediately surrounding it and, thus, it is negatively buoyant (in other words, it has a tendency to sink if it was initially at rest somewhere above the ground). For an extreme example of negative buoyancy, think of a rock (high density) thrown into a swimming pool (water has a much lower density than rock). What happens? It sinks like a rock (you should take nothing for granite in Meteo 101).

How high a positively buoyant parcel will rise (or how low a negatively buoyant parcel will sink from higher altitudes) depends, of course, on the density (temperature) of the parcel compared to the density (temperature) of its immediate environment. Thus, it behooves us to determine the rate of temperature change inside a rising (or sinking) air parcel. After all, before we can figure out whether an air parcel is positively or negatively buoyant, we must know the parcel's temperature at any given altitude in relation to the temperature of its immediate environment. Clearly, determining the temperature of the environment at any altitude isn't a problem because we can simply read right off a Skew T / Log P diagram. Determining how the temperature changes inside a rising or sinking air parcel appears to pose the real challenge here.

To make life easier for the moment, we first assume that ascent takes place without net condensation (and descent occurs in the absence of net evaporation). I make this simplification because net condensation and evaporation involve exchanges in energy. Though we cannot disregard these processes, let's first isolate the effects on temperature that result from dry ascent and descent. Then we'll introduce the complicating factor of moisture.

As an air parcel rises, it moves into an environment of increasingly lower pressure (remember that pressure decreases with increasing altitude). In order to equalize the pressure difference between the the rising parcel and its new environment, air molecules inside the higher-pressure air parcel push out the sides of the parcel. That requires molecules to do work, which results in a loss of kinetic energy. With kinetic energy expended by air molecules to push out the sides of the expanding parcel, the temperature of the air inside the parcel decreases (recall that temperature corresponds to the average kinetic energy of molecules). The energy spent by molecules to push out the sides of the parcel amounts to a flat rate of 5.5 degrees Fahrenheit per 1000 feet of ascent (10 degrees Celsius per 1 kilometer).

In meteorological circles, this rate of decrease in temperature inside rising air parcels goes by the name of "dry adiabatic lapse rate", which, of course, is a mouthful. "Dry" refers to the initial condition that net condensation was not in the picture. "Adiabatic" translates to "without heat", referring to the fact that we did not extract heat energy from the air inside the parcel in order for it to cool. Instead, the mere expansion of the rising parcel's volume led to the temperature decrease as hard-working molecules lost kinetic energy while having to push out the sides of the parcel. "Lapse rate", of course, refers to the pace at which temperature decreases with increasing height above the ground.

I need to drive home an important distinction here, so please take note of my caveat. The dry adiabatic lapse rate applies to air parcels that rise without net condensation taking place. On the other hand, an environmental lapse rate, which corresponds to the temperature sounding over a given city at a given time (12Z or 00Z), applies to the environment in which a rising or sinking air parcel finds itself. Do you see the distinction I'm trying to make here?

The dry adiabatic lapse rate is always positive because the temperature of a rising air parcel decreases with increasing altitude. The dry adibatic lapse rate is always constant. On the other hand, the environmental lapse rate is positive when the temperature of the environment decreases with increasing altitude. But environmental lapse rates can be negative (temperature inversion) or zero (isothermal layer of air). The environmental lapse rate is rarely constant.

On the flipside, sinking parcels of air warm at a rate of 5.5 degrees Fahrenheit per 1000 feet of descent. As a parcel sinks, it moves into an environment with increasingly higher pressure (an alternative way of saying "pressure decreases with increasing height above the ground" is "pressure increases with decreasing height above the ground"). Now air molecules surrounding the parcel perform work as they push the sides of the parcel inward (while trying to equalize pressure between the parcel and the parcel's environment). In turn, air molecules inside the parcel are the beneficiary of the work done by the environment, gaining kinetic energy as the sides compress inward. This gain in kinetic energy results in a temperature increase inside the air parcel.

Let's see how all of this works on a Skew-T / Log P diagram and how meteorologists determine the buoyancy of air parcels. Consider the Skew-T / Log P diagram for Bismarck, North Dakota, at 12Z on June 8, 2001. The light red lines that slant upward to the left are dry adiabats -- their slopes correspond to a temperature decrease of 10 degrees Fahrenheit per 1 kilometer of ascent. Now imagine that there is an air parcel at Point P, whose pressure is about 810 mb and whose temperature is +10 degrees Celsius (the same as it's environment). So, initially, the parcel's buoyancy is "neutral" (no temperature difference between the parcel and its environment). Thus, the parcel has no tendency to rise or sink.

A sample air parcel follows the dry adiabat (blue line) from 810 mb (point P) to 700 mb. By following the dry adiabat, we make the inherent assumption that net condensation does not take place from 810 to 700 mb.
Now suppose we lift the parcel (force it to rise) to 700 mb along the dry adiabat (that is, we assume the rising parcel's temperature decreases at the dry adiabatic lapse rate). Note that the temperature of the parcel at its new position is approximately -2 degrees Celsius (I had to interpolate here). But the temperature of the parcel's new environment at 700 mb is 0 degrees Celsius. To understand how I got 0 degrees Celsius, look just to the right of the lifted parcel's new position (where the dark-red environmental sounding intersects 700 mb). Now note that the zero-degree isotherm conveniently passes through this point of intersection (no interpolation is needed).

Thus, after lifting an air parcel 110 millibars, the parcel's temperature (-2 degrees Celsius) was lower than it's environment (0 degrees Celsius), rendering the parcel negatively buoyant. So, if there were no further lifting, the parcel would naturally sink back toward its original position. We'll discuss the impacts of positive and negative buoyancy on weather in the coming two sections, but I wanted you to see firsthand the mental processes that meteorologists go through when they routinely incorporate Skew-T / Log P diagrams into their forecast.

Before I leave the topic of dry adiabatic ascent and descent, I'd like to show you an application to weather forecasting. On sunny and/or windy afternoons, particularly during the warm season, the temperature profile in the lowest few to several thousand feet tends to parallel dry adiabats on a Skew-T. What's up with that? As an explanation, I offer this animation of the evolution of a temperature sounding on a clear, summer day.

The first image shows the nocturnal inversion (for review, please go back to Atmospheric Controllers of Local Nighttime Temperatures that typically forms on a clear, "calm" night. But once the sun rises and solar heating kicks in (press the button in the upper right corner of the shockwave animation), convective eddies form and mix air upward from the ground and downward from higher up. If you need to review the mixing effects of eddies, I suggest that you study the interactive wind tool in Lesson 4 in the section on the nighttime controllers of temperature. After the sun rises, the bottom line is that the inversion starts to break down and fade as convective eddies driven by solar heating mix cold air near the ground with warmer air higher up (see shockwave animation).

Air mixing upward from the ground cools at the adiabatic lapse rate and air mixing downward from aloft warms at the dry adiabatic lapse rate. It stands to reason, then, that the mixing by eddies would result in the lowest part of the temperature profile of the environment becoming nearly parallel to a dry adiabat in time. Indeed, this transformation from a morning nocturnal inversion to an afternoon (or evening) temperature profile that's parallel to the dry adiabats is exactly what happens during the warm season. It also happens on a windy day, when mechanical eddies form near the ground.

By the way, the lowest layers of the atmosphere where eddies mix air up and down is formally called the planetary boundary layer. Typically, the "PBL" extends from the ground to an altitude of a few or several thousand feet.

Okay, let's now allow water vapor to enter the scientific fray. Recall that water vapor is the highest energy state of the three phases of water. When net condensation occurs and water vapor "shifts down" to the less-energetic water phase (forming, for example, cloud drops), there's a surplus of energy that's made available to the air (the conservation of energy states that energy cannot be created or destroyed, so, as water vapor moves to the lower energy state of water, we must account for the excess energy). This energy makes its presence felt in the form of latent heat ("latent" means "hidden" so the release of latent heat is sort of like finding a crumbled $20 bill in the pocket of an old pair of discarded jeans).

Within a rising, cooling parcel of air that contains ample water vapor, net condensation and the formation of cloud drops leads to a release of latent heat that, in effect, simply slows the parcel's overall cooling. So, instead of the parcel cooling at a rate of 5.5 degrees Fahrenheit per 1000 feet of ascent, it now cools at, say, 3.3 degrees per 1000 feet of ascent -- a cooling rate appropriately called the "moist adiabatic lapse rate".

Unlike the dry adiabatic lapse rate, the moist adiabatic lapse rate is not constant because it primarily depends on the amount of water vapor in the air. For example, the moist adiabatic lapse rate (cooling rate) is smaller over very humid tropical regions where large amounts of water vapor insure large releases of latent heat that, in turn, more markedly slow a rising parcel's cooling rate. There are other examples, but, for practically speaking, 3.3 degrees Fahrenheit per 1000 feet will suffice here as a representative value of the moist adiabatic lapse rate.

Like a hot-air balloon that becomes more positively buoyant as the burner in the gondola heats the air inside the balloon, the release of latent heat during net condensation and the resulting reduced rate of cooling makes air parcels more positively buoyant. To see this on a Skew-T / Log P diagram, let's return to the 12Z sounding at Bismarck, North Dakota, on June 8, 2001. The green dashed lines that gently curve upward to the left are "moist adiabats".

An air parcel undergoing net condensation follows a moist adiabat (blue line) from 810 mb (point P) to 700 mb. For comparison sake, the grey open circle at 700 mb marks the other possible temperature of the lifted parcel, assuming that it underwent "dry ascent". Clearly, the cooling rate associated with "moist ascent" is smaller than the cooling rate associated with dry ascent.

Okay, again imagine a parcel at Point P, but this time, let's assume, for sake of argument, that when we lift the parcel to 700 mb, it cools at the moist adiabatic lapse rate. Following the convenient moist adiabat that runs through Point P, the parcel arrives at 700 mb. Note that its position is different from the one previously determined by following the dry adiabat. At 700 mb, the new temperature of the lifted parcel is about +3 degrees Celsius, making it warmer than its environment and positively buoyant (thus, it would have a tendency to continue rising). Such is the impact that the release of latent heat can have on the positive buoyancy of an air parcel.

I realize that all the crisscrossing lines on a Skew-T / Log P might seem intimidating to beginning students, so, for testing and grading purposes in this course, we'll use a much more simple alternative (you'll want to keep this open) to the Skew-T / Log P diagram. First, you'll notice that this is not a Skew-T / Log P diagram. The vertical axis represents altitude (in meters), not the logarithm of pressure. Moreover, the horizontal axis represents temperature in degrees Fahrenheit, and, isotherms, though not drawn here, are vertical and hence they are not "skewed". So this is a much simpler tool than the Skew-T / Log P.

The dark-red, line represents the environment's temperature sounding derived from radiosonde measurements. Please remember that the default sounding (the one you first see) is the standard atmosphere. To vary the type of sounding, you must select from the pull-down menu at the top of the page. But let's just work with the default sounding for now.

To determine the temperature of the environment at any altitude, simply locate the desired altitude and move your finger horizontally to the left until it intersects the sounding. Then move your finger straight down to the temperature axis and read the appropriate temperature.

Okay, let's simulate the real world and allow for net condensation, so click on the button in the upper right-hand corner of the page. Now grab the parcel and start to slowly lift it. As you begin, notice that a red-dotted line traces the parcel's temperature along a dry adiabat. The green-dotted line traces the dew point, which initially varies little with altitude (the dew-point plot is nearly vertical). Also note that as you slowly lift the parcel, the sliding red indicator at ground level keeps track of the parcel's temperature. Pretty cool, eh?

Your interactive tool should look like this when you're done.

Not very far above the ground, the two lines intersect, marking the point where the parcel's temperature equals the parcel's dew point (the parcel has reached saturation). Thus, a tad more lifting and cooling prompt net condensation to commence. The altitude at which net condensation begins (assuming there's sufficient lifting) is called, appropriately enough, "the Lifting Condensation Level" (or "LCL" for short).

Continue lifting the parcel gradually toward 5000 meters. Now the parcel's temperature follows a moist adaibat, which is the dotted line that gradually curves upward (it's red with a partially green rim). Keep in mind that, as the rising parcel follows the moist adiabat, its temperature is only slightly lower than the dew point. For all practical purposes, however, the two are equal, which is why the red temperature sounding and the green dew-point sounding essentially merge to form the moist adiabat.

By following the moist adiabat, the parcel's temperature now decreases at a slower rate with increasing height than it would have in the absence of net condensation. To see what I mean, note the grayish line that slants upward to the left -- it marks the path that the parcel would have taken had you not clicked the Allow Condensation button. The rate of decrease in temperature with height that corresponds to this grayish line corresponds, of course, to the dry adiabatic lapse rate. Clearly, a parcel would cool more rapidly with height along this path than if it took the moist adiabatic route. And, once more, the release of latent heat during net condensation accounts for the difference between these two cooling rates.

Because temperature (horizontal axis) is expressed in degrees Fahrenheit and because altitude (vertical axis) is expressed in meters on this diagram, the dry adiabatic and moist adiabatic lapse rates become a hybrid of units from the metric and English systems (this really doesn't affect you, but I didn't want the engineering majors to have a coniption). For the record, the dry adiabatic lapse rate now translates to 18 degrees Fahrenheit per kilometer (fast rate of decrease in parcel temperature with altitude) and the moist adiabatic lapse rate translates to approximately 11 degrees Fahrenheit per kilometer (slower rate of decrease in parcel temperature with altitude).

Near the LCL, notice that the green trace of the parcel's dew-point shifts from a nearly vertical orientation (meaning that the dew point stayed relatively constant with height) to one following the moist adiabat (indicating that the parcel's dew point now steadily decreases with increasing altitude). Conceptually, this decrease in dew point with increasing altitude makes sense - it is consistent with dwindling supplies of water vapor (net condensation takes its toll on the amount of water vapor in the parcel).

Keep and eye on the buoyancy meter as you move the parcel up and down.

Did you happen to notice the buoyancy meter as you lifted the parcel? If not, you should probably drag the parcel back to surface and start over. Whenever the temperature of the parcel is less than the temperature of its environment (whenever the red-dotted line lies to the left of the dark-red sounding), the parcel is negatively buoyant. Carefully watch the buoyancy meter to observe the following general result: the colder the parcel is compared to its environment, the more negatively buoyant it is. Conversely, whenever the temperature of the parcel is warmer than its environment (whenever the red-dotted line lies to the right of the dark-red sounding), the parcel is positively buoyant. We will continue this discussion in the next lesson.

Okay, now it's time to practice a bit on your own. I recommend that you experiment with different environmental soundings and different settings of surface temperature and dew point. Find the LCL. Work with the buoyancy meter. Become one with this tool. Interact!

In the next section, I'll reveal more about the mysterious check box on the interactive tool that reads "Dynamic Parcel" (in the upper right-hand corner). I'll also link the concept of parcel buoyancy with a new concept called atmospheric stability. Read on.