Friday Sep. 14, 2012
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Three songs from the Fleet Foxes (I like the way they sound in a
big room like ILC 150). You heard "White Winter Hymnal",
"Tiger Mountain
Peasant Song", and "Mykonos".
A take home Optional
Assignment was collected today and an In-class Optional Assignment
was handed out in class and collected at the end of class. If you
weren't in class and would like to download the in-class assignment,
answer the questions, and turn it in at the start of class next Monday
you can earn at least partial credit.
Here's another way of trying to
understand why warm air rises and cold air sinks - Archimedes
Law. It's a perhaps simpler way of understanding the
topics. A bottle of water can help you to visualize the law.
A gallon of
water weighs about 8 pounds (lbs). I would want to carry a gallon
of water on a hike unless I really thought I would need it.
If you submerge the gallon jug of water in a swimming pool, the
jug
becomes, for all intents and purposes, weightless. That seems
kind of amazing. Archimedes'
Law (see figure below, from p. 53a in the photocopied ClassNotes)
explains why this is true.
Archimedes first of all tells you
that the surrounding fluid will exert an upward pointing bouyant force
on the submerged water bottle. That's why the submerged jug can
become weightless.
Archimedes law also tells you how to figure
out how strong the bouyant force will be. In this
case the 1 gallon bottle will displace 1 gallon of
pool water. One
gallon of pool
water weighs 8 pounds. The upward bouyant force will be 8 pounds,
the same as the downward force. The two
forces are equal and opposite.
What Archimedes law doesn't really tell you is what causes the
upward
bouyant
force. If you're really on top of this material you will
recognize that it is really
just another name for the
pressure difference force that we covered on Wednesday (higher pressure
pushing
up on the bottle and low pressure at the top pushing down, resulting in
a net upward force).
Now we imagine pouring out all the water and filling the 1 gallon
jug
with air. Air is about 1000 times less dense than water; compared
to water, the jug
will weigh practically nothing.
If you
submerge the jug of air in a
pool
it will displace 1 gallon of
water
and experience an 8 pound upward bouyant force again. Since there
is no downward force the jug will float.
One gallon of sand (which is about 1.5 times denser than water)
jug weighs 12 pounds (I checked this out because I like to try to give
you accurate information).
The jug of sand will sink because
the downward force is greater
than
the upward force.
You can sum
all
of this up by saying anything that is less dense
than
water will float in water, anything that is more dense than water will
sink in water.
Most types of wood will float. Most rocks won't
(pumice for example often floats).
The same reasoning applies to air in the atmosphere.
Air that is less dense (warmer)
than the air around it will
rise.
Air that is more dense (colder) than the air around it will sink.
Here's a little more
information
about
Archimedes that I didn't mention in
class.
There's a colorful demonstration that shows how small differences
in density
can determine whether an object floats or sinks.
A can of regular Pepsi (actually it
was Cherry Pepsi) was
placed in a beaker of water.
The
can
sank. A can of Diet Pepsi on the other hand floated.
Both cans are made of aluminum which has a density almost three
times
higher than water; aluminum by itself would sink. The drink
itself is largely water. The
regular soda also has a lot of high-fructose
corn
syrup, the diet soda
doesn't. The mixture of water and corn syrup has a density
greater than plain
water. There is also a little air (or perhaps carbon dioxide gas)
in each can.
The average density of the can of regular soda (water & corn
syrup
+
aluminum + air) ends up being slightly greater than the density of
water. The average density of the can of diet soda (water +
aluminum + air) is slightly less than the density of water.
I sometimes repeat the "demonstration" with a can of Pabst Blue
Ribbon
beer. This also floats because the beer doesn't contain any corn
syrup
(I don't think).
In some respects people in swimming pools are like cans of regular
and
diet soda. Some people float (they're a little less dense than
water), other people sink (slightly more dense than water).
We had time to start a big new topic - weather maps and some of
what you can learn from them.
We began by learning how
weather data are
entered onto surface weather maps.
Much of our weather is produced by relatively large
(synoptic scale)
weather systems - systems that might cover several states or a
significant fraction of
the continental US. To be able to identify and characterize these
weather systems you must first collect weather data (temperature,
pressure, wind direction and speed, dew point, cloud cover, etc) from
stations across the country and plot the data on a map. The large
amount of data requires that the information be plotted in a clear and
compact way. The station model notation is what meterologists
use.
We
worked through this material one step at a time (refer to p. 36 in
the photocopied ClassNotes). The figures below were
borrowed from a previous semester or were redrawn and may differ
somewhat from what was drawn in class.
The center circle is filled in to indicate the portion
of
the sky
covered with clouds (estimated to the nearest 1/8th of the sky) using
the code at the top of the figure (which you can quickly figure
out). 3/8ths of the sky is covered
with clouds in the example above.
Then symbols are
used
to
identify
the
actual types of high, middle, and low altitude clouds observed in the
sky. Later in the semester we will learn the names of the 10
basic cloud types. Six of them are sketched above and symbols for
them are shown. Purple represents high altitude in this
picture. Clouds found at high altitude are composed of ice
crystals. Low altitude clouds are green in the figure.
They're warmer than freezing are composed of just water droplets.
The middle altitude clouds in blue are surprising. They're
composed of both ice crystals and water droplets that have been cooled
below freezing but haven't frozen.
A complete list of cloud symbols was on a handout distributed in class
(a copy can be found here
) You do not, of
course, need to remember all of the cloud symbols.
Small barbs at the end of the straight
line give the wind speed in knots. Each long barb is worth 10
knots, the short barb is 5 knots.
Knots are nautical miles per hour. One nautical mile per hour is
1.15 statute miles per hour. We won't worry about the distinction
in this class, we will just consider one knot to be the same as one
mile per hour.
Here are four more examples.
What is the wind direction and wind speed in each case. Click here
for
the answers.
The air temperature and the dew point temperature are probably the
easiest data to decode.
The air temperature in this example
was 64o
F
(this is
plotted above and to the left of the center circle). The dew
point
temperature was 39o F and is plotted below and to the left
of the center circle. The box at lower left reminds you that dew
points range from the mid 20s to the mid 40s during much of the year in
Tucson.
Dew
points rise into the upper 50s and 60s during the summer thunderstorm
season (dew points are in the 70s in many parts of the country in the
summer). Dew points are in the 20s, 10s, and may even drop below
0 during dry periods in Tucson.
And maybe the most interesting part.
A symbol representing the weather
that is currently
occurring is plotted to the left of the center circle (in between the
temperature and the dew point). Some of
the common weather
symbols are
shown. There are about 100 different
weather symbols that you can choose
from (click here
if you didn't get a copy of the handout distributed in class today).
There's no way I could expect you to remember all of those weather
symbols.
The pressure data is usually the most confusing and most difficult
data to decode.
The sea level pressure is shown above and to the right
of
the center
circle. Decoding this data is a little "trickier" because some
information is missing. We'll look at this in more detail
momentarily.
Pressure change data (how the pressure has changed during
the preceding
3 hours)
is shown to the right of the center circle. We didn't discuss
this in class. You must
remember to add a decimal point. Pressure changes are usually
pretty small.
Here's what you need to know about the pressure data.
Meteorologists hope to map out small horizontal pressure
changes on
surface weather maps (that produce wind and storms). Pressure
changes much more quickly when
moving in a vertical direction. The pressure measurements are all
corrected to sea level altitude to remove the effects of
altitude. If this were not done large differences in pressure at
different cities at different altitudes would completely hide the
smaller horizontal changes.
In the example above, a station
pressure value of 927.3 mb was measured in Tucson. Since Tucson
is about 750 meters above sea level, a 75 mb correction is added to the
station pressure (1 mb for every 10 meters of altitude). The sea
level pressure estimate for Tucson is 927.3 + 75 = 1002.3 mb.
This sea level pressure estimate is the number that gets plotted on the
surface weather map.
Do you need to remember all the
details above and be able to calculate the exact correction
needed? No. You
should
remember that a correction for altitude is needed.
And the correction needs to be added to the station pressure.
I.e. the sea-level pressure is higher than the station pressure.
The calculation above is shown in a picture below
Here are some examples of coding
and decoding the pressure data.
First of all we'll take some sea
level pressure values and show
what needs to be done before the data is plotted on the surface weather
map. These should be the same numbers that we used in
class.
To save room, the leading 9 or 10
on the sea level pressure
value and
the decimal
point are removed before plotting the data on the map. For
example the 10 and the decimal pt in
1002.3 mb would
be removed; 023
would be plotted on the weather map (to the upper right of the center
circle). Some additional examples are shown above.
You'll mostly have to go the other way - read data off a map and
figure out what the sea level pressure is. This is illustrated
below.
When reading pressure values off a
map you must remember to
add a 9 or
10 and a decimal point. For example
118 could be either 911.8 or 1011.8 mb. You
pick the value that
falls closest to 1000 mb average sea level pressure. (so 1011.8
mb would be the correct
value, 911.8 mb would be too low).
Another
important piece of information on a surface map is the time the
observations were collected. We didn't have time
for this in class. Time on a
surface map is converted to a universally agreed upon time zone called
Universal Time (or Greenwich Mean Time, or Zulu time).
That is the time at 0 degrees longitude, the Prime Meridian.
There is a 7 hour time
zone difference between Tucson and Universal Time (this
never changes because Tucson stays on Mountain
Standard Time year round). You must add 7
hours to the time in Tucson to obtain Universal Time.
Here are several examples of conversions between MST and UT
to convert from MST (Mountain Standard Time) to UT (Universal Time)
10:20 am MST:
add the 7
hour time zone correction ---> 10:20
+ 7:00 = 17:20 UT (5:20 pm in Greenwich)
2:45 pm MST :
first convert to the 24 hour clock
by adding 12 hours 2:45 pm MST + 12:00 = 14:45 MST
add the 7 hour time zone
correction ---> 14:45 + 7:00 = 21:45 UT (7:45 pm in England)
7:45 pm MST:
convert to the 24 hour clock by
adding 12 hours 7:45 pm MST + 12:00 = 19:45 MST
add the 7 hour time zone correction ---> 19:45 + 7:00 = 26:45 UT
since this is greater than 24:00 (past midnight) we'll subtract 24
hours 26:45 UT - 24:00 = 02:45 am the next day
to convert from UT to MST
18Z:
subtract the 7 hour time
zone
correction ---> 18:00 - 7:00 = 11:00 am MST
02Z:
if we subtract the 7 hour time
zone correction we will get a negative
number.
So we will first add 24:00 to 02:00 UT then subtract 7 hours
02:00
+
24:00
=
26:00
26:00 - 7:00 = 19:00 MST on the previous day
2 hours past midnight in Greenwich is 7 pm the previous day in
Tucson
