NATS 1750 "The Earth and Its Atmosphere"


Assignment #1


Distributed on Wednesday 20th September, 2006

Due in your Tutorial #4 starting on Wednesday 18th 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.



Stefan-Boltzmann's Law is E (watt m-2) = 5.7 x 10-8 (watt m-2 K-4) x T4 (K)

Wein's Displacement Law is lmax (mm) x T (K) = 3000 (mm K)

p = 3.14; the surface area of a sphere is 4pR2 ; 1 watt = 1 Joule s-1


N.B. Your tutorial leaders will show you how to do these questions with different numbers


1. (This question deals with increasing CO2 levels and the threat of global warming)


In 1900 the CO2 concentration in air was 0.030 %.  In 2000 it was 0.036%.


(a) By how much has the CO2 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 CO2 concentration was 355 ppm.  Is this consistent with your answer to (b) and what does it tell us about the way the CO2 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 lmax = 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 Sahara and the SW USA than at the Equator?

 (ii) Why is there so little energy (relatively speaking) at the surface over Amazonia compared to other longitudes?

(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.