DIVISION OF
NATURAL SCIENCE

NATS 1750 "The Earth and Its Atmosphere"

Assignment #1

Distributed on ^{th} September, 2006

Due in your Tutorial #4
starting on ^{th}
October, 2006

**NOTE: You must
make and keep a photocopy of your submitted assignment **

**NOTE ALSO**: Marks will be deducted if you do not explain your answers
or do not show all relevant steps in your calculations.

**You may
discuss your assignment in groups but then you must go and do it on your own**

*i.e*., submissions with the same
numerical errors or identical layouts, etc., will be carefully scrutinized by
the markers for illegal collaboration.

SOME INFO YOU MAY NEED:

Stefan-Boltzmann's
Law is E (watt m^{-2})
= 5.7 x 10^{-8} (watt m^{-2} K^{-4}) x T^{4} (K)

Wein's Displacement Law is l_{max} (mm) x T (K) = 3000 (mm K)^{}

p = 3.14; the surface area of
a sphere is 4pR^{2} ; 1 watt = 1 Joule s^{-1}

1.
(*This question deals with increasing CO _{2}
levels and the threat of global warming*)

In
1900 the CO_{2} concentration in air was 0.030 %. In 2000 it was 0.036%.

(a)
By how much has the CO_{2} concentration changed in parts per million (ppm) over the last 100 years?

(b)
Estimated by how much it has been increasing in terms of ppm
per year.

(c)
In 1999 the CO_{2} concentration was 355 ppm. Is this consistent with your answer to (b)
and what does it tell us about the way the CO_{2} is increasing?

2. (*This
question deals with how pressure decreases with height*)

The
surface pressure is 1000 mb and pressure decreases
with height.

(a)
If the pressure halving height is 4.5 km what is the pressure in millibars at 45 km above the surface? Express your answer in scientific notation
with 3 numbers in the digit part, i.e. ?.?? x 10^{?}

(b)
What is the pressure at 45 km in millibars to the
nearest mb?

(c) Is it therefore true to say that the pressure
deceases by about a factor of 10 for every 15 km we go up? Explain your answer.

3. (*This
question deals with radiation from the Sun*)

If the Sun's surface has a radius of R=700,000 km and
its radiation peaks at a wavelength of l_{max} = 0.53 mm calculate, using Wien's Displacement Law and the Stefan-Boltzmann
Law, the total amount of energy it emits in units of watts.

4. (*This
question deals with solar insolation*)

(a) The attached contour plot (Fig 1 below) shows
how the *'insolation'* , *i.e.* the amount of solar radiation measured in units of energy
metre^{-2 }received at the top of the
atmosphere in a 24 hour period, varies with latitude and time of year.

(i) Sketch a graph
with "insolation" as the vertical y-axis
and "month" as the horizontal x-axis showing how the insolation varies throughout the year for the equator (*i.e., *0), and for latitudes of 30, 45 and 90 North. Use the same graph but
different colours or types of lines to distinguish the curves for the different
latitudes.

(ii) What are the yearly
maximum and minimum values of the insolation for each
of the latitudes you have plotted?

(iii) How does the
difference between yearly maximum and yearly minimum insolation
vary with latitude?

(iv) Where and when does the maximum insolation occur?

**N.B.** You do not need to plot a point on your graph for every month - you can
simply sketch the curves by finding when the insolation
had some specific value.

(b) Now look
at the global map (Fig 2 below) showing the variation of solar radiation over
the year at the surface.

(i) Why does more
energy reach the surface over the

(ii) Why is there so little energy (relatively
speaking) at the surface over

(iii) You saw in part (a)
above that at the top of the
Earth's atmosphere there was more insolation
at the pole during the summer solstice than at the equator. Yet this global map
shows that over one year much less energy is received at the poles - give 2
reasons for this.

Figure 1.

Figure 2.