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PHY 392S – Physics of Climate, Spring 2011
Problem Set 1, page 1
PHY 392S
PHYSICS OF CLIMATE
Spring Term, 2011
Problem Set #1
DUE:
Monday, February 7, 2011 (in class).
Late penalty = 5% per day, up to 7 days, after which material will not be accepted.
NOTES:
Marks, shown in brackets, will be given for workings, as well as for final answers.
Total marks = 100.
Show all workings and units (preferably SI units).
QUESTIONS:
1.
The figure below shows the annual average radiation budget as a function of latitude.
(a)
Estimate the latitude L
C
where the net radiation crosses over from positive to negative in the
Northern Hemisphere.
Also estimate the value of the net radiation at the North Pole.
Use the two
pieces of information to find the equation of a straight line that approximately describes the net
radiation (in W m
2
) as a function of latitude L between 10
N and the North Pole.
[3 marks]
(b)
The latitude L
C
is where the northward transport of heat by the atmosphere and oceans is at a
maximum in that hemisphere.
Explain why.
[3 marks]
(c)
The rate of meridional (along lines of longitude) heat transport at that latitude equals the total
radiation deficit integrated over the surface area of the Earth from L
C
to the North Pole.
Compute
this value using the equation you obtained in part (a), keeping in mind that a unit change in
latitude is not proportional to a unit of surface area.
[3 marks]
(d)
Convert your result to a power per unit distance (east or west along the line of constant latitude at
L
C
), using units of kilowatts per kilometer. Take the radius of the Earth to be R
E
= 6356 km.
[3 marks]
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