Tue., Sep. 16 notes

Tuesday, Sep. 16, 2014

September 16 is Mexican Independence Day (independence from Spain) so a little Mariachi music from one of my favorite local groups: Calexico and Mariachi Luz de Luna. And the sound was working today so you heard: "World Drifts In" (4:41), "Ballad of Cable Hogue" (3:26), "Cancion del Mariachi" (3:28), "Aires del Mayab" (3:50).

Today was the first of two 1S1P Assignment #1 due dates and reports were collected in class today. It usually takes some time to get all these reports read and graded. We'll get started on them and get them back to you as soon as we can.

Also the first of this semester's Optional Assignments is now available. This is the main way you can earn extra credit in this class. The assignment is due at the start of class next Tuesday (Sep. 23) and should be completed before coming to class.

The Practice Quiz has been graded and was returned in class today. The average score was 64%, a solid D. As you can see below that is typical for the Practice Quiz.

Semester	8 am class	9:30 am class	2 pm class
F14	66	64	----
F13	63	67	-
F12	66		66
F11	65		65
F10	67		60
F09	68		66
F08	65		65

Tropical storm Odile
A few quick comments concerning Tropical Storm Odile which is beginning to affect the weather in Tucson. The light rain showers we were experiencing this morning came from the outer rain bands from the storm.

This photograph of Hurricane Odile was taken after it had made landfall (source of this is photo taken with the NOAA GOES West satellite that was taken at 9:45 am EDT on Monday Sep. 15). The hurricane had weakened and the eye is no longer apparent.

The figure above shows the predicted path of Odile (now a tropical storm). This was issued by the National Hurricane Center earlier this morning. Note the remnants of the storm will pass very close to Tucson. A flash flood watch has been issued for portions of much of Arizona as well as portions of New Mexico, Nevada, and California. The actual path followed by the storm and its moisture may depart significantly from what is being forecast now, but it looks like we may be in for a rainy next couple of days. It is not clear how much rain we will get. Yesterday some of the computer models were predicting 3 to 4 inches of rain, today's model runs show somewhat less, perhaps 1 to 2 inches. These amounts of rain can cause serious flooding.

You can keep track of the latest forecasts at the Tucson office of the National Weather Service.

Hurricane Odile seems to have caused serious damage in Baja California. Here are reports from the BBC, another from USA Today, and a third from The Weather Channel.

We've spent a lot of time (too much?) looking at air pressure and how it changes with altitude. Today we'll consider air density and air temperature.

1. Air density changes with altitude
How does air density change with increasing altitude? You should know the answer to that question. You get out of breath more easily at high altitude than at sea level. Air gets thinner (less dense) at higher altitude. A lungful of air at high altitude just doesn't contain as many oxygen molecules as it does at lower altitude or at sea level.

It would be nice to understand why air density decreases with increasing altitude.

The people pyramid reminds you that there is more weight, more pressure, at the bottom of the atmosphere than there is higher up.

Layers of air are not solid and rigid like in a stack of bricks. Layers of air are more like mattresses stacked on top of each other. Mattresses are compressible, bricks (and people) aren't. Mattresses are also reasonably heavy, the mattress at the bottom of the pile would be squished by the weight of the three mattresses above. This is shown at right. The mattresses higher up aren't compressed as much because there is less weight remaining above. The same is true with layers of air in the atmosphere.

The statement above is at the top of p. 34 in the photocopied ClassNotes. I've redrawn the figure found at the bottom of p. 34 below.

There's a surprising amount of information in this figure and it is worth spending a minute or two looking for it and thinking about it.

1. You can first notice and remember that pressure decreases with increasing altitude. 1000 mb at the bottom decreases to 700 mb at the top of the picture. You should be able to explain why this happens.

2. Each layer of air contains the same amount (mass) of air. This is a fairly subtle point. You can tell because the pressure drops by 100 mb as you move upward through each layer. Pressure depends on weight. So if all the pressure changes are equal, the weights of each of the layers must be the same. Each of the layers must contain the same amount (mass) of air (each layer contains 10% of the air in the atmosphere).

3. The densest air is found at the bottom of the picture. The bottom layer is compressed the most because it is supporting the weight of all of the rest of the atmosphere. It is the thinnest layer in the picture and the layer with the smallest volume. Since each layer has the same amount of air (same mass) and the bottom layer has the smallest volume it must have the highest density. The top layer has the same amount of air but about twice the volume. It therefore has a lower density (half the density of the air at sea level). Density is decreasing with increasing altitude. That's the main point in this figure.

4. Finally pressure is decreasing most rapidly with increasing altitude in the densest air in the bottom layer. This is something we covered a week or two ago and something we'll use again 2 or 3 times later in the semester.

2. Principle of the mercury barometer

One of the more impressive seesaws (teeter totters) that I've seen (source of this image). If you understand how this works you'll be able to figure out how barometers function.

A mercury barometer is used to measure atmospheric pressure and is really just a balance that can be used to weigh the atmosphere.

The instrument in the left figure above ( a u-shaped glass tube filled with a liquid of some kind) is actually called a manometer and can be used to measure pressure difference. The two ends of the tube are open so that air can get inside and air pressure can press on the liquid. Given that the liquid levels on the two sides of the manometer are equal, what could you say about P_L and P_R?

The liquid can slosh back and forth just like the pans on a balance can move up and down. A manometer really behaves just like a pan balance (pictured above at right) or a teeter totter (seesaw). Because the two pans are in balance, the two columns of air have the same weight. P_L and P_R are equal (but note that you don't really know what either pressure is, just that they are equal).

Now the situation is a little different, the liquid levels are no longer equal. You probably realize that the air pressure on the left, P_L, is a little higher than the air pressure on the right, P_R. P_L is now being balanced by P_R + P acting together. P is the pressure produced by the weight of the extra fluid on the right hand side of the manometer (the fluid that lies above the dotted line). The height of the column of extra liquid provides a measure of the difference between P_L and P_R.

Next we will just go and close off the right hand side of the manometer.

Air pressure can't get into the right tube any more. Now at the level of the dotted line the balance is between P_air and P (pressure by the extra liquid on the right). If P_air changes, the height of the right column, h, will change. You now have a barometer, an instrument that can measure and monitor the atmospheric pressure.

Barometers like this are usually filled with mercury. Mercury is a liquid. You need a liquid that can slosh back and forth in response to changes in air pressure. Mercury is also very dense which means the barometer won't need to be as tall as if you used something like water. A water barometer would need to be over 30 feet tall. With mercury you will need only a 30 inch tall column to balance the weight of the atmosphere at sea level under normal conditions (remember the 30 inches of mercury pressure units mentioned earlier). Mercury also has a low rate of evaporation so you don't have much mercury gas at the top of the right tube (there's some gas, it doesn't produce much pressure, but it would be hazardous you if you were to start to breath it).

Here is a more conventional barometer design. The bowl of mercury is usually covered in such a way that it can sense changes in pressure but is sealed to keep poisonous mercury vapor from filling a room.

Average and extreme sea level pressure values

Average sea level atmospheric pressure is about 1000 mb. The figure above (p. 30 in the photocopied Class Notes) gives 1013.25 mb but 1000 mb is close enough in this class. The actual pressure can be higher or lower than this average value and usually falls between 950 mb and 1050 mb.

The figure also includes record high and low pressure values. Record high sea level pressure values occur during cold weather. The TV weather forecast will often associate hot weather with high pressure. They are generally referring to upper level high pressure (high pressure at some level above the ground) rather than surface pressure. The 1085 mb pressure value measured in Mongolia wasn't shown in class because there is some concern about its accuracy. The problem is that the pressure was measured at over 5000 feet altitude and a calculation was needed to figure out what the pressure would have been if the location were at sea level. That calculation can introduce uncertainty. But you don't really need to be concerned with all that, I just wanted to give you an idea of how high sea level pressure can get.

Most of the record low pressure values have all been set by intense hurricanes. Hurricane Wilma in 2005 set a new record low sea level pressure reading for the Atlantic, 882 mb. Hurricane Katrina had a pressure of 902 mb. The following table lists some of the information on hurricane strength from p. 146a in the photocopied ClassNotes. 2005 was a very unusual year, 3 of the 10 strongest N. Atlantic hurricanes ever occurred in 2005.

Most Intense North Atlantic Hurricanes	Most Intense Hurricanes to hit the US Mainland
Wilma (2005) 882 mb Gilbert (1988) 888 mb 1935 Labor Day 892 mb Rita (2005) 895 mb Allen (1980) 899 Katrina (2005) 902	1935 Labor Day 892 mb Camille (1969) 909 mb Katrina (2005) 920 mb Andrew (1992) 922 mb 1886 Indianola (Tx) 925 mb

The 850 mb sea level pressure wasn't shown in class either. It was measured in 2003 inside a strong tornado in Manchester, South Dakota (F4 refers to the Fujita scale rating, F5 is the highest level on the scale). This is very difficult (and very dangerous) thing to try to do. Not only must the instruments be built to survive a tornado but they must also be placed on the ground ahead of an approaching tornado and the tornado must then pass over the instruments (also the person placing the instrument needs to get out of the way of the approaching tornado).

You can experience much lower pressure values than shown above (roughly 700 mb) by just driving up to Mt. Lemmon. What makes hurricanes so intense is the pressure gradient, i.e. how quickly pressure changes with distance (horizontal distance). Pressure can drop from near average values (1000 mb) at the edges of the storm to the low values shown above at the center of the storm. This large pressure gradient is what causes the strong winds found in a hurricane.

Here is the announcement from the National Hurricane Center when Hurricane Odile had made landfall Sunday evening.

HURRICANE ODILE TROPICAL CYCLONE UPDATE
NWS NATIONAL HURRICANE CENTER MIAMI FL       EP152014
1000 PM PDT SUN SEP 14 2014

...ODILE MAKES LANDFALL NEAR CABO SAN LUCAS...

SATELLITE IMAGERY INDICATES THAT THE CENTER OF ODILE MADE LANDFALL
AT ABOUT 945 PM PDT...0445 UTC...NEAR CABO SAN LUCAS MEXICO. THE
ESTIMATED INTENSITY OF ODILE AT LANDFALL WAS 125 MPH...205 KM/H...
CATEGORY THREE ON THE SAFFIR-SIMPSON HURRICANE WIND SCALE.

AN AUTOMATED OBSERVING STATION NEAR CABO SAN LUCAS RECENTLY
REPORTED A SUSTAINED WIND OF 89 MPH...144 KM/H...WITH A GUST TO 116
MPH...187 KM/H.  THE STATION HAS ALSO REPORTED A MINIMUM PRESSURE OF
959 MB... 28.32 INCHES.

A WEATHER STATION NEAR SANTA ROSA MEXICO HAS RECENTLY REPORTED A
WIND GUST TO 87 MPH...140 KM/H.

earlier in the day on Sunday the center pressure in Odile had dropped to as low as 922 mb and the sustained winds were 125 MPH.

3. Air temperature changes with altitude, troposphere & stratosphere
What happens to air temperature with increasing altitude. Again our personal experience is that it decreases with increasing altitude. It is colder at the top of Mt. Lemmon than it is here in the Tucson valley.

That is true up to an altitude of about 10 km (about 30,000 ft.). People were very surprised in the early 1900s when they used balloons to carry instruments above 10 km and found that temperature stopped decreased and even began to increase with increasing altitude.

Measurements of air temperature at high altitude in unmanned balloons lead to the discovery of the stratosphere in about 1900 (the information above is on p. 31 in the ClassNotes).

The figures below are more clearly drawn versions of what was done in class.

The atmosphere can be split into layers depending on whether temperature is increasing or decreasing with increasing altitude. The two lowest layers are shown in the figure above. There are additional layers (the mesosphere and the thermosphere) above 50 km but we won't worry about them in this class.

1. We live in the troposphere. The troposphere is found, on average, between 0 and about 10 km altitude, and is where temperature usually decreases with increasing altitude. [the troposphere is usually a little higher in the tropics and lower at polar latitudes]

The troposphere can be stable or unstable (tropo means "to turn over" and refers to the fact that air can move up and down in the troposphere). The troposphere contains most of the water vapor in the atmosphere (the water vapor comes from evaporation of ocean water and then gets mixed throughout the troposphere by up and down air motions) and is where most of the clouds and weather occurs.

2a. The thunderstorm shown in the figure with its strong updrafts and downdrafts indicates unstable conditions. When the thunderstorm reaches the top of the troposphere, it runs into the bottom of the stratosphere which is a very stable layer. The air can't continue to rise into the stratosphere so the cloud flattens out and forms an anvil (anvil is the name given to the flat top of the thunderstorm). The flat anvil top is something that you can go outside and see and often marks the top of the troposphere.

ISS016-E-027426

ISS015-E_27038

ISS007-E-13020

Here are several images of thunderstorms and anvil clouds taken from above, from the International Space Station (all 3 images courtesy of the Image Science and Analysis Laboratory, NASA Johnson Space Flight Center, www.eol.jsc.nasa.gov).

This photo of Mt. Everest was selected as the Picture of the Day on Wikipedia for Dec. 22, 2007.
Photo credit: Luca Galluzi www.galluzi.it

2b. The summit of Mt. Everest is a little over 29,000 ft. tall and is close to the average height of the top of the troposphere.

2c.   Cruising altitude in a passenger jet is usually between 30,000 and 40,000, near or just above the top of the troposphere, and at the bottom of the stratosphere. The next time you're in an airplane try to look up at the sky above. There's less air and less scattering of light. As a result the sky is a darker purple color not blue. If you get high enough the sky would eventually become black.

3. Temperature remains constant between 10 and 20 km and then increases with increasing altitude between 20 and 50 km. These two sections form the stratosphere. The stratosphere is a very stable air layer. Increasing temperature with increasing altitude is called an inversion. This is what makes the stratosphere so stable.

4.   A kilometer is one thousand meters. Since 1 meter is about 3 feet, 10 km is about 30,000 feet. There are 5280 feet in a mile so this is about 6 miles (about is usually close enough in this class).

5.    The ozone layer is found in the stratosphere. Peak ozone concentrations occur near 25 km altitude.

Here's the same picture drawn again (for clarity) with some additional information. We need to explain why when temperature decreases all the way up to the top of the troposphere, it can start increasing again in the stratosphere.

6. Sunlight is a mixture of ultraviolet (7%), visible (44%, colored green in the picture above) and infrared light (49%, colored red). We can see the visible light.

6a. On average about 50% of the sunlight arriving at the top of the atmosphere passes through the atmosphere and is absorbed at the ground (20% is absorbed by gases in the air, 30% is reflected back into space). This warms the ground. The air in contact with the ground is warmer than air just above. As you get further and further from the warm ground, the air is colder and colder. This explains why air temperature decreases with increasing altitude in the troposphere.

5b. How do you explain increasing temperature with increasing altitude in the stratosphere?

Absorption of ultraviolet light by ozone warms the air in the stratosphere and explains why the air can warm (oxygen also absorbs UV light). The air in the stratosphere is much less dense (thinner) than in the troposphere. So even though there is not very much UV light in sunlight, it doesn't take as much energy to warm this thin air as it would to warm denser air closer to the ground.

7. That's a manned balloon; Auguste Piccard and Paul Kipfer are inside. They were the first men to travel into the stratosphere (see pps 31 & 32 in the photocopied Class Notes). It really was quite a daring trip at the time, and they very nearly didn't survive it.

4. The great age of stratospheric exploration

Pages 31 and 32 in the ClassNotes list some of the significant events in the early study and exploration of the atmosphere. A few of them are included below.

Note the mercury barometer was invented in 1643.

The earliest balloon trips into the upper atmosphere were in unheated and unpressurized gondolas. Climbers have made it to the summit of Mt. Everest without carrying supplementary oxygen but it is difficult and requires acclimation. You can't acclimate to conditions above 25,000 ft and can't remain up there very long - it's referred to as the "death zone." (Read "Into Thin Air" by Jon Krakauer if you'd like to get some idea of what it's like trying to climb Mt. Everest)

Note the clothing that Capt. Grey had to wear to try to stay warm. All of his trips were in an open, unpressurized gondola.

Source of the image below

I believe this is the gondola flown into the stratosphere by Auguste Piccard and Paul Kipfer is shown above (source). The figure caption is in German so I am not sure that is the case.

Auguste Piccard is shown in the figure at left. The gondola he took into the stratosphere is shown at right. Note how one side is black and the other white. By turning the gondola they could control the temperature inside (pointing the black side toward the sun would warm the gondola, turning the white side would allow the gondola to cool off).

We watched about 10 minutes of video describing Piccard's first trip into the stratosphere (they very nearly didn't make it back down alive).

You might have heard about Felix Baumgartner and the Red Bull Stratos balloon (or seen the GoPro commercial during a recent Super Bowl). On Oct. 14, 2012 he reached an altitude of nearly 128,000 feet (39 km or 24 miles) and then jumped. He reached a speed of 843 MPH on the way down (Mach 1.25 or 1.25 times the speed of sound).

Here's a short video (1:25) that''s the one I showed in class. It shows portions of his jump. If you have time you should really watch the longer version (9:32). Baumgartner began to spin during the descent but was able get out of it. He came very close to blacking out.

That was about all the time we had today. I have a couple more videos that I would like to show at some point.

Jacques Piccard, Auguste's son, would later travel with Lt. Don Walsh of the US Navy to a depth of about 35,800 feet in the ocean in the Mariana Trench (Auguste participated in some of the test descents to 10,000 ft). They did that in the Bathyscaph Trieste (shown below) on Jan. 23, 1960 (source of the image). I'll try to show a short video of one of their test dives (to 10,000 ft.)

Here's a National Geographic video describing film director James Cameron's much more recent dive to the Challenger Deep in the Mariana Trench on Mar. 12, 2012 (2:16). (note mention of the 16,000 psi pressure on the submersible at the bottom of the ocean)

Bertrand Piccard, Jacques' son (Auguste's grandson) was part of the first two man team to circle the globe non-stop in the Breitling Orbiter 3 balloon (Mar. 20, 1999). Brian Jones was the second team member (source of the left image above, source of the right image). I've got a pretty good video summary of their trip. Here are three online videos of the event: short summary (1:40), longer summary (6:15 with music only, no commentary)

and a full documentary (54:06).