Due
Wednesday 7 February 2018

A. __Numerical Problems__

### For questions 1 through 4, use the methodology
summarized in Appendix A of Stull and in the assigned summary sheet on
Structured Problem Solving discussed in class.

### Provide the answers to the following, showing
all steps, on separate sheets.

1. It
is observed that the updrafts in supercell thunderstorms, such as the
thunderstorm that produced the Joplin tornado, are on the order of 40 m s^{-1}.
Convert this to mph. (10 pts)

2.
Convert 5.5^{o}F to its Centigrade equivalent.(10
pts)

3.
Convert -40^{o}C to its Fahrenheit equivalent.(10
pts)

4. It
is observed that when small groups of air molecules, collectively called
"air parcels", are lofted relative to surrounding quiescent air (that
is not moving up or down) that these air parcels cool at a rate of around 5.5^{o}F
for every 1000 feet they rise if water vapor is not condensing. This rate (5.5^{o}F/1000
ft or 5.5^{o}F (1000 ft)^{-1} is called the "dry adiabatic
lapse rate." Convert the dry adiabatic lapse rate to its metric equivalent
(15 pts)

(Answer units: ^{o}C/100m)

B. __Thought
Problems__

### Provide the answers to the following questions.
No calculations are needed.

5. We
will be learning about a powerful "basic" law of nature that is
directly used in the computer modeling of the atmosphere. It is known by various
names, but we will call it the Ideal Gas Law. It is written somewhat
incorrectly below for simplicity's sake:

where
p is pressure, **R is a constant**
(just consider it a number that never changes), T is temperature, and rho (the greek symbol just to the right of the equals sign) is
density.

You can
think of pressure as a measure of the weight of the atmosphere, density as a
measure of how close the air molecules are together, and temperature a measure
of the vibrational activity of the molecules (which humans refer to as
temperature).

(a) Why
is the following statement wrong unless you make an important assumption?

*"...the
warmer the temperature, the higher the pressure..."*(10 pts)

(b)
At sealevel, the average density of the atmosphere is
around 1.225 kg m^{-3}. This can be considered a constant at sealevel, even though there are small variations depending
on certain meteorological situations.

Given
that information is the following statement true *"...the higher the pressure the lower the temperature..."*

Please
say why, given the constraints of the problem.(10 pts)

(c)
Algebraically solve the Ideal Gas Law above for temperature.

Show
all steps. In essence you are simply rewriting the Ideal Gas Law.(15
pts)

6.
Here's a surface weather map.

The
solid lines are called isobars, and connect points on the map that experience
the same atmospheric pressure. The isobars are labeled in whole numbers. You
already know how to decode the temperature information. Although no
calculations are part of this, just be aware that the Ideal Gas Law requires
that the temperatures be in the Kelvin or Absolute scale. For this question,
you don't need to worry about that.

**Now note that weather stations A, B, C, and D are roughly on the
isobar labeled 1020.** No calculations are needed to answer the following question. To
answer it, do not assume that the density is constant, even though scale
analysis shows that density roughly is constant at sea level at the scale of
weather maps.

Question:
Assuming that air density is only determined by the Ideal Gas Law the
conceptual treatment of which is given above, use the equation as written in
your answer for 5 (c) above to decide which of the weather stations above given
as A, B, C, or D, has the air that is most dense.