Chapter 3 - If Hot Air Rises, How Come It's Cold Up Here?


"Daddy, if hot air rises, like my teacher says, how come it's snowing up here when it's raining downtown?" my fifth grader asked. She had asked, as children are wont to do, at the worst possible moment on that drive from town. It was raining in town, elevation 500 feet, but as we ascended the last hill to the farm, elevation 2,500 feet, we were greeted with two inches of fresh, very slippery snow on the road. The world was transformed into a wonderful playground for kids, but the change caused me to make an abrupt transition in driving style. She did pick up on the occasional slip of the wheels on the road and didn't pursue the question until we unloaded the groceries from the trunk.

After we deposited the groceries in the kitchen, we went back outside to look at the snow. I told her that her teacher was right as far as it went, that given two parcels, garbage bag size bits of air side by side, the one with the higher temperature would rise. The parcel of air would expand and cool. The temperature would drop at a known rate of 5.5 degrees F per 1,000 feet of elevation. She said that the thermometer on the side of one of the stores read 40 degrees. We concluded that if the air were forced uphill, our thermometer should read around 29 degrees F. We checked it and it was close.

Making a spot decision as to how far to push it, I decided to go for it as she seemed to be willing to explore at this moment. I asked her if we bundled up a big bag of the 29 degree air and took it to town, what would be the temperature when we got there? She said probably about 40. I congratulated her and told her that she had just figured out the concept of potential temperature from one of my advanced meteorology courses, and she beamed.

Potential temperature is the temperature a parcel of air would have if it were taken to a standard reference level. The teacher was right. It's probably common sense, but dense air can't be above less dense air for more than a few minutes. The atmosphere overturns and there is general upheaval until the density situation is eased with the more dense air on the bottom. When it comes right down to it, buoyancy drives the upward and downward movements of the atmosphere. This means density differences, of the type Archimedes envisioned in his famous bath, drive the clouds. This is hardly surprising but does need to be mentioned.

The trouble with air density is that it is hard to measure. The only relatively inexpensive instrument that I know of to measure atmospheric density is the "Cape Cod" barometer. My grandmother had one, a delicate glass swan that had colored water in it which was forced up and down the neck as the air density changed. Technically, the swan densitometer did measure the density of the air in the room as well as that in the air outside the house, that is, it did before it met with an untimely end on the floor. They are a little delicate to put into a plane and should be reserved for the parlor as they tend to make messes all over the panel as the fluid comes squirting out the nose. Given two samples of air at the same pressure the one with the highest temperature will be the less dense; the teacher didn't get into the way you can compare two parcels at different pressures.

The potential temperature allows you to do it. The temperature of the air at your service ceiling (say 12,000 feet) may be -20 degrees F in winter, but if its potential temperature is higher than that of the air below it, the air won't descend. If you were to force that -20 degree air down to the surface it would warm by compression and the temperature would be 66 degrees warmer than it was up there or 46 degrees Fahrenheit. If the temperature of the air blowing along the runway below were less than 46 degrees the air would be stable. Most of the time, it is. Unstable situations resolve themselves quickly.

No group of people is more aware that the temperature of the air generally decreases as one gains altitude than pilots. It's a fact of aviation life. The big aircraft often have to sit on the hot tarmac in summertime waiting for clearances, but most of us VFR folk do the run-up, make the last minute checklist verifications, and then are off VFR into the wild blue, cool yonder. Those of us who have awaited IFR clearances on a hot summer's day while sitting inside of a un-airconditioned singles have had a lesson in the fundamental fact that the sun drives the weather by heating the air from the bottom. Climbing up through an inversion, which is an increase of temperature with height, can be a hazy or even polluting experience; however, you usually run out of it and then the temperature starts to decrease again, ending up at temperatures well below zero in Class A airspace.

The vertical temperature and dew point temperature structure, perhaps more than any other property of the atmosphere, is the key to determining if you'll be VFR, IFR, or if you will be firmly planted to the ground. It could even determine if your passenger's face could end up on the business end of a doggie bag.

Figure 3-1 shows a lapse rate as observed on a particular summer afternoon near Gaithersburg, Maryland. This is simply a graph of temperature on the horizontal and height above ground on the vertical axis. The dotted lines are construction lines on the graph which represent the -5.5 degrees F per 1000 feet, a handy way of calculating the potential temperatures.

Notice that there are three layers in this example. The layers are the portions of the sounding where the lines are straight. Look at the lowest 600 feet of the atmospheric temperatures on the graph. Here the temperature is decreasing very rapidly with height, almost 8 degrees Fahrenheit in 600 feet. This is the very unstable boundary layer where the hot air is bubbling up. It is rare to find this kind of layer above the first hundred feet of the atmosphere, and if you hear about a superadiabatic lapse rate, that's what they are talking about. This is the layer where mirages will be found.

If you were standing on the taxiway, your feet would probably give you the first clue, but you could probably see the heat rising off the asphalt. Dogs feel it more than people and usually prefer walking on grass than asphalt on a hot summer's day.

Now let's look at the dotted lines. The dotted lines on figures 3-2 and 3-3 have slopes of -5.5 degrees per thousand feet. They are often called dry adiabats. Think of them as construction lines printed on the graph paper to assist you to do the calculations.

Pick a point along the temperature line. I've picked point "A" which just happens to be at a point where the dry adiabat crosses the sounding. Now, in your imagination, force a sample of air up. Its temperature will decrease at the 5.5 degree rate. This is the potential temperature idea. Then compare it to the real world atmosphere's temperature at the same level (assume the same pressure) depicted by the temperature on the solid black line. Its temperature is higher than its neighbors at the same elevation; therefore, the parcel is less dense than the neighbors. And, like a cork in water it continues to bob upward. (If we were doing this with pressure as the vertical coordinate as meteorologists usually do, it would be exact.)

Now look at point B, somewhere up near 1,300 feet. If you took a parcel of air at 1,300 feet and forced it up a couple of hundred feet, the parcel would be cooler and denser than its surroundings. Released, it would drop back towards 1,300 feet, probably overshoot and might actually descend to 1,150 feet or so. Once it reached its original elevation it would continue on down with its temperature increasing following the slope of the dry adiabatic lapse rate. Below the original position it would be warmer and more buoyant than its neighbors at the new elevation, so the parcel would slow down, stop, and then bob back up, oscillating around its original elevation. This is the inversion, the stable layer of the atmosphere.

Point C is a problem because it's not unstable or not stable. If you were to take a parcel of air at 3,200 feet and pull it up to 3,500 feet, its temperature would be the same as that of its surroundings. Since it would be no more or no less dense than its neighboring parcels, it would not be inclined to move and would stay at that altitude. This is the well mixed layer which some call neutrally stable.

To summarize the way to calculate the stability, break it up into steps.

  1. Pick a point roughly in the middle of the layer you are interested in.
  2. Draw a construction line through the point parallel to the dry adiabatic lapse rate lines.
  3. Calculate the temperature of the parcel at some elevated point.
  4. Compare the parcel temperature to the real temperature at the same elevation. The parcel temperature must be lower, higher or the same.
  5. If the parcel temperature is:

After a short time working with these diagrams, one finds out an unstable atmosphere is a rare event except when very near the ground on a hot sunny day. For the most part, the atmosphere is conditionally stable, that is, it is stable as long as no clouds form. If clouds do form, the heat release from the condensing cloud droplets slows the decrease of temperature to around 3 degrees F per 1,000 feet. On days when the atmosphere has small puffy cumulus around, you can estimate the height of the cloud bases using these ideas. The procedure is often discussed in ground school and is in the NWS book Aviation Weather. But, it can be extended a little more to help out in estimating bumpiness. The trick is to assume the sub-cloud layer is neutrally stable and the sun is heating the ground pretty well. Then assume that a parcel from the ground ascends to cloud base without mixing with the other air. This concept is the lifted condensation level (LCL). It is often taught as a rule of thumb in flight school, but it has some theoretical basis.

Over the years, the LCL has been mentally calculated by pilots to get an idea of the height of convective cloud bases. The concept is often mentioned in the literature by stating that if you take the Fahrenheit temperature - dew point spread and divide by 4, you get the heights of cloud base in thousands of feet. This is sometimes called a "rule of thumb" but is an idea based on a set of rigorous derivations, as long as the assumptions made in the derivation aren't bent much.

It works, sometimes. Let's see how. Figure 3-3 is a temperature versus height diagram of a day when there were small convective clouds around. The temperature is the solid line with the dew point plotted as the dashed line. The dew point also has its adiabatic lapse rate which is a decrease of around one half degree F per thousand feet of upward motion.

If a parcel were warmed by the ground and rose upward the temperature would follow the dry adiabatic lapse rate, or slide along the wide line with an arrowhead. At the same time the dew point decreases about 0.5 degrees per 1,000 feet as indicated by the other arrow. Where the two converge, the temperature and dew point temperature are the same and water vapor starts to condense as dew on dust and sea salt crystals in the air forming clouds.

What happened next? Well, clouds formed and where they formed, they grew a few hundred feet higher, where they ran into the inversion and stopped. After a while they would erode on the top and around the edges. In some spots anyone might call them stratocumuli.

Since most aviation weather reports (SAOs or SAs) give the temperature, dew point, and the height of clouds, you have a way of estimating - if the assumptions are not being met. If the temperature-dew point spread gives the correct base, the assumptions of a well mixed layer probably aren't too bad. If there's wind aloft, expect bumpy weather. If the LCL is much lower or higher than it should be, there's probably a temperature inversion between you and the clouds. You should find a smooth layer somewhere in between.

Figure 3-4 shows the potential temperature calculated from the temperature of Figure 3-1. In the lowest layer the potential temperature of the air a few hundred feet over the runway surface is cooler than the air near the surface of the runway. This is typical for a hot sunny day in summer and can cause the "wet runway" mirage and difficulty in getting the plane to land. Above that level, the potential temperature is at least as warm as the air near the ground, so overturning will not occur unless there is considerable difference between the winds at different elevations.

There is another use of the dry adiabatic lapse rate in aviation, a way of estimating the turbulence potential of powered flight or to help gain altitude for unpowered flight. The Thermal Index was developed by forecasters to assist sailplane enthusiasts to help characterize the day as to the likelihood and height of the thermals. The thermal index is calculated using the early morning sounding data for the temperature at 850 millibars and the temperature at 700 millibars, and the station pressure in millibars and station temperature.

The forecaster also needs to make a forecast of the surface temperature for the time needed. Usually the high for the day is used as this is the time when the thermals, and their seekers, will be at their best. The data and the forecast temperature are all plotted on a graph with a line drawn through the observed points. Figure 3-5 shows the situation for a hypothetical morning in summer.

Starting from the forecast temperature, the forecaster follows the dry adiabatic lapse rate up to the level of interest. Then subtract the value of the temperature on the dry adiabat from the real temperature at the same height. The difference between that temperature and the observed temperature is called the Thermal Index (TI).

I've calculated two Thermal Indices on Figure 3-5. The 850 millibar TI is calculated by finding the temperature at 850 millibars and then continuing over to the temperature at which the dry adiabat coming up from the forecast high for the afternoon intersects the 850 millibar level. Subtracting the two gives a -4. Not too bad a day for thermals. The smaller the stability (the more negative number) the better for overturning. The bigger (more positive) the number the more stable the air.

Continuing up the same dry adiabat to 700 and subtracting that temperature from the observed 700 millibar temperature is the 700 mb TI.

Experience shows that a TI of -3 or less indicates a very good chance of sailplanes reaching the altitude where this temperature difference is found. TIs of -8 or -10 predict very good lift, even in strong winds aloft. At these values, the sailplane would have a long soaring day.

Experience has also shown that wind at the 850 millibar level and the amount of high level cloudiness modifies the thermal index, although not in a simple way. Generally, the faster the wind at 850 millibars (the more wind shear), the less likely the day will be good for thermal production which reaches high levels. Complete high level cloudiness also decreases the potential, although there seems to be little difference between clear at high level and 0.8 of the sky covered with clouds.

You can get the temperature forecasts from the The Forecast Winds and Temperature Aloft (FD) product which can be obtained from a computer briefing, or, you can ask for while you're getting a regular briefing. You can use them and the public forecasts to get a rough idea of the thermal activity which affects sailplanes. The temperatures in the FD are in degrees Celsius.

Table 3-2 is a sample FD Winds (winds aloft forecast) which came over a computer briefing. The report for EMI, the one closest to my home showed

 

3000

6000

9000

EMI

2612

18

2815

10

2918

07

Outside my house, the temperature was 62 F. Making a quick conversions, 18 Degrees C is 64 F, 10 C is 48 F, and 7 C is 40 F. The public forecast was for "... partly cloudy and highs in the upper 80's." The forecast for the upper 80's means the high for the day will probably be between 87 and 89.

Plotting these data on figure 3-6 and drawing in straight lines between the dots gives you a temperature sounding of sorts.

Draw a dry adiabatic line (one with a slope of -5.5 deg F per 1,000 feet) through the high for the day, 88 deg F at the surface.

Go up the dry adiabatic lapse rate from the high for the day and the Thermal Index is negative all the way. It approaches zero at 9,000 feet so the bumpiness should stay with you until you climb beyond that altitude; however, it should decrease with height in the case shown.

The vast majority of people are relatively unaware of the general decrease of temperature with height except when planning summer vacations. The cooling effect of altitude is the reason why some people go to the mountains for the summer vacations. While most of us in the lowlands stay inside with the air conditioners on, air conditioners are still a rarity in the mountains near the East Coast. Up in the mountains where the air temperature is lower, people like to get outside for a walk, and enjoy the stars.

Not a small contribution to those vacation decisions is the fact that the dew point temperature is trapped below the temperature. Since the dew point is the temperature at which dew forms (technically over a flat layer of pure water), as the temperature falls so must the dew point. For me, days with dew points greater than 60, of which we have many in summer, are very uncomfortable. A day with temperatures in the 90s and dew points in the 50s is a fine day. When the dewpoint gets over 70, I suffer. But, I also like plenty of trees around, and water to drink, and rain to cool down a hot summer's day. So, I stay around and put up with the 70+ degree dew points.


There is another temperature, the wet bulb temperature, which is important for flying because the temperature of falling rain or snow is close to the wet bulb temperature. The wet bulb temperature is read from the thermometer on the sling psychrometer which is covered with a wet sock after it is whirled around for a few minutes. This does a reasonable simulation of a falling raindrop.

For a number of reasons, the sling psychrometer is rarely used anymore. The psychrometers usually have mercury thermometers and occasionally, in the line of duty, the thermometers break spreading mercury into the environment. Further, the readings are sometimes compromised by salts which are left behind as tap water evaporates. I've also been told that swinging one of these looks "uncool" and "nerdy" by some of the students. As a consequence, the wet bulb temperatures are usually calculated from the air and dew point temperatures. It's about half way between the air and the dew point. If the temperature is 50 F and the dew point is 40 F, the wet bulb temperature is about 45 F. The temperature of a rain drop falling through this air will probably be about 45 F.

There have been more than a few times when I've seen snow falling when the temperature is above freezing. The last time, the wife said that the thermometer which was reading 34 degrees F must be wrong, so I called our local AWOS-2. The temperature at the airport was 35 degrees but the dew point was 25. Splitting the difference, I figured the wet bulb temperature to be about 30 F, and the temperature of the snow was probably still below freezing. I didn't tell her the thermometer was probably all right, I just resolved to put off buying a new one.

In winter, the wet bulb temperature variation with height helps determine the altitude where falling snow will change over to rain. While knowledge of the altitude of melting snow is not a big concern to the general public, the possibility of enough sticky stuff being ingested into the jet engines to choke off airflow has been discussed on more than one occasion by the NTSB.

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