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20 The Atmosphere

If you don't like the weather in Ithaca, just wait a few minutes. It'll get worse.
— apologies to Mark Twain

20.1 Circulation Around Fronts and Low Pressure Centers

Because the earth is spinning and the air is moving, there are significant Coriolis effects.¹ You'll never understand how weather systems work unless you pay attention to this.

We are accustomed to seeing the rotation of storm systems depicted on the evening news, but you should remember that even a chunk of air that appears absolutely still on the weather map is rotating, because of the rotation of the earth as a whole. Any chunk of air that appears to rotate on the map must be rotating faster or slower than the underlying surface. (In particular, the air in a storm generally rotates faster, not slower.)

Based on their everyday indoor experience, people think they understand how air behaves:

They know that the stream of air from a fan moves in a straight line, with no particular tendency to curve right or left.
They know that once the fan is switched off, the airflow won't last very long or travel very far before being overcome by friction.

However, when we consider the outdoor airflow patterns that Mother Nature creates, the story changes completely. In a chunk of air that is many miles across, a mile thick, and a mile away from the surface, there can be airflow patterns that last for hours or days, because there is so much more inertia and so much less friction. During these hours or days, the earth will rotate quite a bit, so Coriolis effects will be very important.

Note: In this chapter, I will use the § symbol to indicate words that are correct in the northern hemisphere but which need to be reversed in the southern hemisphere. Readers in the northern hemisphere can ignore the § symbol.

20.1.1 Flow Around a Low

Suppose we start out in a situation where there is no wind, and where everything is in equilibrium. We choose the rotating Earth as our reference frame, which is a traditional and sensible choice. In this rotating frame we observe a centrifugal field, as well as the usual gravitational field, but the air has long ago distributed itself so that its pressure is in equilibrium with those fields.

Then suppose the pressure is suddenly changed, so there is a region where the pressure is lower than the aforementioned equilibrium pressure.

In some cases the low pressure region is roughly the same size in every direction, in which case it is called a low pressure center (or simply a low) and is marked with a big ``L'' on weather maps. In other cases, the low pressure region is quite long and skinny, in which case it is called a trough and is marked ``trof'' on the maps. See figure 20.1.

In either case, we have a pressure gradient.² Each air parcel is subjected to an unbalanced force due to the pressure gradient.

Initially, each air parcel moves directly inward, in the direction of the pressure gradient, but whenever it moves it is subject to large sideways Coriolis forces, as shown in figure figure 20.2. Before long, the motion is almost pure counterclockwise§ circulation around the low, as shown in figure 20.3, and this pattern persists throughout most of the life of the low-pressure region. If you face downwind at locations such as the one marked A, the pressure gradient toward the left§ is just balanced by the Coriolis force to the right§, and the wind blows in a straight line parallel to the trough. At locations such as the one marked B, the pressure gradient is stronger than the Coriolis force. The net force deflects the air.

Figure 20.1: Initial Force near a Low Pressure Region

Figure 20.2: Initial Motion near a Low Pressure Region

Figure 20.3: Steady Motion near a Low Pressure Region

Now we must must account for friction (in addition to the other forces just mentioned). The direction of the frictional force will be opposite to the direction of motion. This will reduce the circulatory velocity. This allows the air to gradually spiral inward.

The unsophisticated idea that air should flow from a high pressure region toward a low pressure region is only correct in the very lowest layers of the atmosphere, where friction is dominant. If it weren't for friction, the low would never get filled in. At any reasonable altitude, friction is negligible — so the air aloft just spins around and around the low pressure region.

The astute reader may have noticed a similarity between the air in figure 20.2 and the bean-bag in figure 19.12. In one case, something gets pulled inwards and increases its circulatory motion ``because'' of Coriolis force, and in the other case something gets pulled inwards and increases its circulatory motion ``because'' of conservation of angular momentum. For a bean-bag, you can analyze it either way, and get the same answer. Also for a simple low-pressure center, you can analyze it either way, and get the same answer. For a trough, however, there is no convenient way to apply the conservation argument.

In any case, please do not get the idea that the air spins around a low partly because of conservation of angular momentum and partly because of the Coriolis force. Those are just two ways of looking at the same thing; they are not cumulative.

20.1.2 Fronts and Troughs

As mentioned above, whenever the wind is blowing in a more-or-less straight line, there must low pressure on the left§ to balance the Coriolis force to the right§ (assuming you are facing downwind). In particular, the classic cold front wind pattern (shown in figure 20.4) is associated with a trough, (as shown in figure 20.5). The force generated by the low pressure is the only thing that could set up the characteristic frontal flow pattern.

Figure 20.4: Wind Near a Front

Figure 20.5: Pressure Near a Front

Figure 20.6: Temperature Near a Front

The wind shift is what defines the existence of the front. Air flows one way on one side of the front, and the other way on the other side (as shown in figure 20.4).

Usually the front is oriented approximately north/south, and the whole system is being carried west-to-east by the prevailing westerlies. In this case, we have the classic cold front scenario, as shown in figure 20.4, figure 20.5, and figure 20.6. Ahead of the front, warm moist air flows in from the south§. Behind the front, the cold dry air flows in from the north§. Therefore the temperature drops when the front passes. In between cold fronts, there is typically a non-frontal gradual warming trend, with light winds.

You can use wind patterns to your advantage when you fly cross-country. If there is a front or a pressure center near your route, explore the winds aloft forecasts. Start by choosing a route that keeps the low pressure to your left§. By adjusting your altitude and/or route you can often find a substantial tailwind (or at least a substantially decreased headwind).

Note: by ancient tradition, meteorologists name winds by the direction from whence they come. A south wind (or southerly wind) blows from south to north. Almost everything else is named the other way. An aircraft on a southerly heading is flying toward the south. Physicists and mathematicians name all vectors by the direction toward which they point. To avoid confusion, it is better to say ``wind from the south'' rather than ``south wind''.

A warm front is in many ways the same as a cold front. It is certainly not the opposite of a cold front. In particular, it is also a trough, and has the same cyclonic flow pattern.

A warm front typically results when a piece of normal cold front gets caught and spun backwards by the east-to-west flow just north§ of a strong low pressure center, as shown in figure 20.7. That is, near the low pressure center, the wind circulating around the center is stronger than the overall west-to-east drift of the whole system.

Figure 20.7: Warm Front

If a warm front passes a given point, a cold front must have passed through a day or so earlier. The converse does not hold — cold front passage does not mean you should expect a warm front a day or so later. More commonly, the pressure is more-or-less equally low along most of the trough. There will be no warm front, and the cold front will be followed by fair weather until the next cold front.

Low pressure — including cold fronts and warm fronts — is associated with bad weather for a simple reason. The low pressure was created by an updraft that removed some of the air, carrying it up to the stratosphere. The air cools adiabatically as it rises. When it cools to its dew point, clouds and precipitation result. The latent heat of condensation makes the air warmer than its surroundings, strengthening the updraft.

Ascending air Þ low pressure at the surface
Ascending air Þ clouds

The return flow down from the stratosphere (high pressure, very dry descending air, and no clouds) generally occurs over a wide area, not concentrated into any sort of front. There is no sudden wind shift, and no sudden change in temperature. This is not considered ``significant weather'' and is not marked on the charts at all.

20.2 Pressure and Winds Aloft

Air shrinks when it gets cold. This simple idea has some important consequences. It affects your altimeter, as will be discussed in section 20.2.3. It also explains some basic facts about the winds aloft, which we will discuss now.

20.2.1 Thermal Gradient Wind

Most non-pilots are not very aware of the winds aloft. Any pilot who has every flown westbound in the winter is keenly aware of some basic facts:

The winds aloft tend to come from the west.
They are much stronger in the winter.
They get stronger and stronger as altitude increases.

A typical situation is shown in figure 20.8. In January, the average temperature in Vero Beach, Florida, is about 15 Centigrade (59 Fahrenheit), while the average temperature in Oshkosh, Wisconsin is about -10 Centigrade (14 Fahrenheit). Imagine a day where surface winds are very weak, and the sea-level barometric pressure is the same everywhere, namely 1013 millibars (29.92 inches of mercury).

Figure 20.8: Thermal Gradient Wind

The pressure above Vero Beach will decrease with altitude. According to the International Standard Atmosphere (ISA), we expect the pressure to be 697 millibars at 10,000 feet.

Of course the pressure above Oshkosh will decrease with altitude, too, but it will not exactly follow the ISA, because the air is 25 centigrade colder than standard. Air shrinks when it gets cold. In the figure, I have drawn a stack of ten boxes at each site. Each box at VRB contains the same number of air molecules as the corresponding box at OSH.³ The pile of boxes is shorter at OSH than it is at VRB.

The fact that the OSH air column has shrunk (while the VRB air column has not) produces a big effect on the winds aloft. As we mentioned above, the pressure at VRB is 697 millibars at 10,000 feet. In contrast, the pressure at OSH is 672 millibars at the same altitude — a difference of 25 millibars.

This puts a huge force on the air. This force produces a motion, namely a wind of 28 knots out of the west. (Once again, during most of the life of this pressure pattern, the pressure gradient toward the left§ is just balanced by the Coriolis force to the right§, assuming you are facing downwind.) This is the average wind at 10,000 feet, everywhere between VRB and OSH.

More generally, suppose surface pressures are reasonably uniform (which usually the case) and temperatures are not uniform (which is usually the case, especially in winter). If you have low temperature on your left§ and high temperature on your right§, you will have a tailwind aloft. The higher you go, the stronger the wind. This is called thermal gradient wind.

The wind speed will be proportional to the temperature gradient. Above a large airmass with uniform temperature, there will be no thermal gradient wind. But if there is a front between a warm airmass and a cold airmass, there will be a large temperature change over a short distance, and this can lead to truly enormous winds aloft.

In July, OSH warms up considerably, to about 20 centigrade, while VRB only warms up slightly, to about 25 centigrade. This is why the thermal gradient winds are typically much weaker in summer than in winter — only about 5 knots on the average at 10,000 feet.

In reality, the temperature change from Florida to Wisconsin does not occur perfectly smoothly; there may be large regions of relatively uniform temperature separated by rather abrupt temperature gradients — cold fronts or warm fronts. Above the uniform regions the thermal gradient winds will be weak, while above the fronts they will be much stronger.

For simplicity, the foregoing discussion assumed the sea-level pressure was the same everywhere. It also assumed that the temperature profile above any given point was determined by the surface temperature and the ``standard atmosphere'' lapse rate. You don't need to worry about such details; as a pilot you don't need to calculate your own winds-aloft forecasts. The purpose here is to make the official forecasts less surprising, less confusing, and easier to remember.

20.2.2 Altimetry

An aircraft altimeter does not really measure altitude. It really measures pressure, which is related to altitude, but it's not quite the same thing.

In order to get an estimate of the altitude, the altimeter depends on a two-step process. First, the altimeter has a knob whereby you can adjust things to account for how the local weather raises or lowers the atmospheric pressure. You should make this adjustment on the runway before takeoff, and for extended flights you should get updated settings via radio. If you neglect this, you could find yourself at a too-low altitude, if you fly to a region where the barometric pressure is lower. The mnemonic is: ``High to low, look out below''.

Altimeters are not perfect. Even if the altimeter and airplane were inspected yesterday, and found to be within tolerances,

±: The altimeter could be off by 30 feet when it reads 2500 (according to the tolerances in FAR 43 Appendix E).
-: If the airplane is moving at 100 knots, the indicated altitude could be off by another 30 feet, due to nonidealities in the arrangement of the static port (FAR 23.1325).
-: If the airplane is descending at 750 FPM, the altimeter could be off by an additional 70 feet, due to friction in the mechanism (FAR 43 Appendix E).
-: There could be 30 feet of hysteresis, if you have recently descended from a very high altitude (FAR 43 Appendix E).
-: Wind flowing over a nice airfoil-shaped hill can produce low pressure there. A 35-knot wind could produce a 50-foot altimetry error. See section 3.4.1.

The first item could be off in either direction, but the other items will almost certainly be off in the bad direction when you are descending. Also, if the airplane has been in service for a few months since the last inspection, the calibration could have drifted a bit. All in all, it would be perfectly plausible to find that your altimeter was off by 50 feet when parked on the ground, and off by 200 feet in descending flight over hilly terrain.

20.2.3 High Altimeter due to Low Temperature

The altimeter measures a pressure and converts it to a so-called altitude. The conversion is based on the assumption that the actual atmospheric pressure varies with altitude the same way the the standard atmosphere would. The pressure decreases by roughly 3.5% per thousand feet, more or less, depending on temperature.

The problem is that the instrument does not account for nonstandard temperature. Therefore if you set the altimeter to indicate correctly on the runway at a cold place, it will be inaccurate in flight. It will indicate that you are higher than you really are. This could get you into trouble if you are relying on the altimeter for terrain clearance. The mnemonic is HALT — High Altimeter because of Low Temperature.

As an example: Suppose you are flying an instrument approach into Saranac Lake, NY, according to the FAA-approved ``Localizer Runway 23'' procedure. The airport elevation is 1663 feet. You obtain an altimeter setting from the airport by radio, since you want your altimeter to be as accurate as possible when you reach the runway.

You also learn that the surface temperature is -32 Centigrade, which is rather cold but not unheard-of at this location. That means the atmosphere is about 45 C colder than the standard atmosphere. That in turn means the air has shrunk by about 16%. Throughout the approach, you will be too low by an amount that is 16% of your height above the airport.

The procedure calls for crossing the outer marker at 3600 MSL and then descending to 2820 MSL, which is the Minimum Descent Altitude. That means that on final approach, you are supposed to be 1157 feet above the airport. If you blindly trust your altimeter, you will be 1157 ``shrunken feet'' above the airport, which is only about 980 real feet. You will be 180 real feet (210 shrunken feet) lower than you think. To put that number in perspective, remember that localizer approaches are designed to provide only 250 feet of obstacle clearance.⁴

You must combine this HALT error with the ordinary altimetry errors discussed in section 20.2.2. The combination means you could be 400 feet lower than what the altimeter indicates — well below the protected airspace. You could hit the trees on Blue Hill, 3.9 nm northeast of the airport.

Indeed, you may be wondering why there haven't been lots of crashes already -- especially since the Minimum Descent Altitude used to be lower (1117 feet, until mid-year 2001). Possible explanations include:

Most people use the ILS approach instead of the localizer approach. That provides electronic vertical guidance that isn't affected by temperature.
In winter, the real atmosphere usually has a smaller lapse rate than the standard atmosphere, especially at the lower altitudes, so the errors are usually less than what simple theory would suggest.
The FAA has overestimated the height of the trees. They routinely assume there will be small structures and trees rising 200 feet above the land surface, but the trees on Blue Hill are probably closer to 100 feet. This is helpful, but we shouldn't rely on it. The trees are still growing, and other trees in the vicinity are over 150 feet tall. Furthermore, if somebody built a 190-foot tower atop Blue Hill, the FAA would not change the Minimum Descent Altitude for this procedure, and there would be problems for sure.
The new 1157-foot Minimum Descent Altitude is about 40 feet higher than what you would expect just based on the height of the hill. I'm told this represents an allowance for the effect of wind blowing over hilly terrain as mentioned above.

Even if people don't ``usually'' crash, we still need to do something to increase the margin for error.

There is an obvious way to improve the situation: In cold weather, you need to apply temperature compensation to all critical obstacle-clearance altitudes.

You can do an approximate calculation in your head: If it's cold, add 10%. If it's really, really cold, add 20%. Approximate compensation is a whole lot better than no compensation.

The percentages here are applied to the height above the field, or, more precisely, to the height above the station that is giving you your altimeter setting. In the present example, 20% of 1157 is about 230. Add that to 2820 to get 3050, which is the number you want to see on your altimeter during final approach. Note that this number, 3050, represents a peculiar mixture: 1663 real feet plus 1387 shrunken feet.

For better accuracy, you can use the following equation. The indicated altitude you want to see is:

A_i = F + (A_r-F)

288.15 - l F

273.15 + T_f

(20.1)

where F is the field elevation, A_r is the true altitude you want to fly (so A_r-F is the height above the field, in real feet), l is the standard lapse rate (2 ^°C per thousand feet), T_f is the temperature at the field, 273.15 is the conversion from Centigrade to absolute temperature (Kelvin), and 15 C = 288.15 K is the sea-level temperature of the standard atmosphere.

You might want to do this for a range of temperatures, and tabulate the results. An example is shown in table 20.1. Make a row for each of the critical altitudes, not just the Minimum Descent Altitude. Then, for each flight, find the column that applies to the current conditions and pencil-in each number where it belongs on the approach plate.

Field Temperature, ^°C	12	0	-10	-20	-30	-40
South Sector	6600	6820	7000	7220	7440	7700
Northeast Sector	5100	5240	5380	5540	5680	5860
Northwest Sector	4100	4200	4300	4400	4520	4640
Procedure Turn	4800	4940	5060	5200	5340	5500
Crossing Outer Marker	3600	3680	3760	3840	3940	4020
Minimum Descent Alt	2820	2860	2920	2960	3020	3080

Table 20.1: Saranac Lake Critical Altimeter Readings

It is dangerously easy to get complacent about the temperature compensation. You could live in New Jersey for years without needing to think about it -- but then you could fly to Saranac Lake in a couple of hours, and get a nasty surprise.

The HALT corrrection is important whenever temperatures are below standard and your height above the terrain is a small fraction of your height above the station that gave you your altimeter setting. This can happen in a couple of ways:

When flying an instrument approach, you might need to apply 200 feet of compensation; this might make the difference between crashing and not crashing.
When flying over tall mountains, you might need to apply a great deal of compensation; 12,000 shrunken feet might not be enough to get you over a 10,000-foot mountain.

20.3 Prevailing Winds and Seasonal Winds

A parcel of air will have less density if it has

a higher temperature,
a higher dewpoint, and/or
a lower pressure.

If a parcel of air is less dense than the surrounding air, it will be subject to an upward force.⁵

20.3.1 Primary Circulation Patterns

As everyone knows, the tropics are hotter and more humid than the polar regions. Therefore there tends to be permanently rising air at the equator, and permanently sinking air at both poles.⁶ This explains why equatorial regions are known for having a great deal of cloudy, rainy weather, and why the polar regions have remarkably clear skies.

You might think that the air would rise at the equator, travel to the poles at high altitude, descend at the poles, and travel back to the equator at low altitude. The actual situation is a bit more complicated, more like what is shown in figure 20.9. In each hemisphere, there are actually three giant cells of circulation. Roughly speaking, there is rising air at the equator, descending air at 25 degrees latitude, rising air at 55 degrees latitude, and descending air at the poles. This helps explain why there are great deserts near latitude 25 degrees in several parts of the world.

Figure 20.9: Primary Circulation Cells

The three cells are named as follows: the Hadley cell (after the person who first surmised that such things existed, 250 years ago), the Ferrel cell, and the polar cell. The whole picture is called the tricellular theory. It correctly describes some interesting features of the real-world situation, but there are other features that it does not describe correctly, so it shouldn't be taken overly-seriously.

You may be wondering why there are three cells in each hemisphere, as opposed to one, or five, or some other number. The answer has to do with the size of the earth (24,000 miles in circumference), its speed of rotation, the thickness of the atmosphere (a few miles), the viscosity of the air, the brightness of the sun, and so forth. I don't know how to prove that three is the right answer — so let's just take it as an observed fact.

Low pressure near 55 degrees coupled with high pressure near 25 degrees creates a force pushing the air towards the north§ in the temperate regions. The air responds to this force with motion in the perpendicular direction, namely from west to east. As shown in figure 20.10, these are the prevailing westerlies that are familiar to people who live in these areas.

According to the same logic, low pressure near the equator coupled with high pressure near 25 degrees creates a force toward the equator. The air responds to this force with motion in the perpendicular direction, namely eastward. These are the famous trade winds, which are typically found at low latitudes in each hemisphere, as shown in figure 20.10.

Figure 20.10: Primary Prevailing Winds

In days of old, sailing-ship captains would use the trade winds to travel in one direction and use the prevailing westerlies to travel in the other direction. The regions in between, where there was sunny weather but no prevailing wind, were named the horse latitudes. The region near the equator where there was cloudy weather and no prevailing wind was called the doldrums.

The boundaries of these great circulatory cells move with the sun. That is, they are found in more northerly positions in July and in more southerly positions in January. In certain locales, this can produce a tremendous seasonal shift in the prevailing wind, which is called a monsoon.⁷

20.3.2 Continental / Oceanic Patterns

Now let us add a couple more facts:

The sun is not very effective at heating the air, especially dry air. Normally, the sun heats the surface of the planet, then the air gains heat from the surface — partly by simple contact, and partly by absorbing energy-rich water vapor that evaporates from the surface.
When we change from winter to summer, solar heating warms the dry land much more quickly than the ocean.⁸ This is because the ocean is constantly being stirred. To heat up the land, you need only heat up the top few inches of soil. To heat up the ocean, you need to heat up several feet of water.

As a consequence, in temperate latitudes, we find that in summer, the land is hotter than the ocean (other things, such as latitude, being constant), whereas in winter the land is colder than the ocean.

This dissimilar heating of land and water creates huge areas of low pressure, rising air, and cyclonic flow over the oceans in winter, along with a huge area of high pressure and descending air over Siberia. Conversely there are huge areas of high pressure, descending air, and anticyclonic flow over the oceans in summer.

These continental / oceanic patterns are superimposed on the primary circulation patterns. In some parts of the world, one or the other is dominant. In other parts of the world, there is a day-by-day struggle between them.

20.4 Summary

Very near the surface (where friction dominates), air flows from high pressure to low pressure, just as water flows downhill. Meanwhile, in the other 99% of the atmosphere (where Coriolis effects dominate) the motion tends to be perpendicular to the applied force. The air flows clockwise§ around a high pressure center and counterclockwise§ around a low pressure center, cold front, or warm front.

Although trying to figure out all the details of the atmosphere from first principles is definitely not worth the trouble, it is comforting to know that the main features of the wind patterns make sense. They do not arise by magic; they arise as consequences of ordinary physical processes like thermal expansion and the Coriolis effect.

If you really want to know what the winds are doing at 10,000 feet, get the latest 700 millibar constant pressure analysis chart and have a look. These charts used to be nearly impossible for general-aviation pilots to obtain, but the situation is improving. Now you can get them by computer network or fax. On a trip of any length, this is well worth the trouble when you think of the time and fuel you can save by finding a good tailwind.

A few rules of thumb: eastbound in the winter, fly high. Westbound in the winter, fly lower. In the summer, it doesn't matter nearly as much. In general, try to keep low pressure to your left§ and high pressure to your right§.

1: The origin of the Coriolis effect is discussed in section 19.3.
2: In general, a gradient has to do with how steeply something changes from place to place.
3: The bottom box starts at sea level at both sites. We ignore the fact that OSH is actually 808 feet above sea level. The fact that the ground ``sticks up'' into the bottom box doesn't change the essence of the argument. This is consistent with the notion that you adjust your altimeter to read 808 (not zero) on the ground at OSH.
4: The idea to get you down as low as possible, to maximize your ability to get below the cloud ceiling so you can find the airport in bad weather.
5: It would be simpler, but less accurate, to say ``hot air rises''. For one thing, if all the air is hot, none of it will rise. Secondly, it is important to keep in mind that an upward force is not necessarily the same as upward motion.
6: Although there is, as expected, somewhat low pressure at the equator (and very low density, when you take humidity into account), there is not any noticeable high pressure at the poles. In fact, there is phenomenally low pressure at the south pole. I have no idea why this is. Sorry.
7: Many people take the word ``monsoon'' to mean ``lots of rain'', but that's not the only (or even the primary) meaning. It comes from an Arabic word meaning ``season'', hence ``seasonal wind''. Now in parts of India and various other places, one of the seasonal winds comes from the ocean, bringing lots of rain.
8: A similar thing happens, on a smaller scale, when we change from night to day.

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