CLIMATE
Simple Earth Climate Model
Problem Set
Problem 1: Reality Check. Our Simple Earth Climate Model assumes that solar radiation has a
wavelength that allows it to pass through our atmosphere, while the wavelength of Earth’s radiation
does not. Find the maximum wavelength () of solar and Earth’s radiation using Wien’s Displacement
Law and confirm this assumption. Wien’s Displacement Law is:
where b is Wien’s Displacement Constant, T is the temperature, and
is the wavelength of the EM
wave. In equating these two equations, Note that the spread of λ values of the EM radiation around the
λmax for a particular object will create a graph characteristic to black body radiation.
Problem 2: Four cubes of identical size and mass are made of the following:
- Aluminum painted white
- Aluminum painted black
- Concrete painted white
- Concrete painted black
A. These blocks are left for several hours in boiling water. Which one(s) has(have) the highest
temperature? Lowest temperature? Or are they all at the same temperature?
B. These blocks are left for several hours in boiling water. Immediately after being pulled out,
which one(s) feel(s) the hottest to your touch? Coolest? Or do they feel like they are at the same
temperature?
Problem 3: During the Ice Ages, Earth was covered in ice. As a result, a much higher percentage of solar
power was reflected back out of Earth’s atmosphere without ever warming the planet as compared to
today. Calculate the effect this change in albedo had on Earth’s surface temperature. Is this an example
of positive or negative feedback?
Problem 4:
A. State in 10 words or less (no equations!) the essential physical properties of greenhouse gases
that cause them to warm the surface of the earth more than it would be warmed otherwise.
(Note: “they trap the heat” is too vague an answer).
B. It has been suggested that the Earth’s recent warming trend may be due to variations in solar
power output (which varies by about 0.1% over the 11-year sunspot cycle, and may have risen
as much as 0.2% over the last few centuries). What fractional change in the Sun’s output would
result in a rise in the Earth’s mean surface temperature of 1°C? Express your answer as a
percentage.
Physics and Astronomy Outreach Program at the University of British Columbia
C. It has been proposed that we can lower the Earth’s mean surface temperature by pumping
sulphates into the upper atmosphere, thus changing the Earth’s albedo. Our albedo is currently
0.30; what would it have to be to reduce the Earth’s mean surface temperature by 1°C?
Problem 5: The mean temperature of Earth is 287.5K. If the sun's brightness (i.e. power output)
increased by 4%, what would the earth's mean temperature become, assuming everything else stayed
the same (which it wouldn't)?
Problem 6:
How much does our
atmosphere affect Earth’s surface
temperature? If Earth’s atmosphere
increased in layers, would our planet
eventually be inhabitable? Let us look
at Venus, an uninhabitable planet.
Venus' mean surface temperature is
actually hotter than Mercury's midafternoon temperature, despite being
nearly twice as far from the Sun.
Explain this difference, and determine
how many layers of atmosphere Venus
has have to to account for this
temperature.
Problem 7:
A. How much power, in calories per day, must a human consume in the form of food in order to
maintain an energy balance between the power radiated by the body and the surroundings?
Note that the temperature of human skin is 33°C, and for the sake of the question assume the
person is in a white room.
B. How much power, in calories per day, must you consume in the form of food in order to
maintain an energy balance between the power radiated by the body and the surroundings?
Physics and Astronomy Outreach Program at the University of British Columbia
Use the Mosteller Formula below to calculate your own body surface area (BSA). Note that the
temperature of human skin is 33°C.
C. A person’s basal metabolic rate (BMR) can be used to calculate your total daily energy
expenditure (TDEE). Using the BMR formulae below,
calculate your BMR. Using you BMR, find your total daily energy expenditure in calories using
the Harris Benedict Equation
assuming little or no exercise. Compare your TDEE to the value you obtained in 3B). Do these
values correspond?
References
BMI Calculator. BMR Formula (online). http://www.bmi-calculator.net/bmr-calculator/bmrformula.php [May 22, 2009].
BMI Calculator. Harris Benedict Equation (online). http://www.bmi-calculator.net/bmrcalculator/harris-benedict-equation/ [May 22, 2009].
Mosteller, R.D. Simplified Calculation of Body Surface Area. New England Journal of Medicine 317(17):
p. 1098, 1987.
Claire Wheeler 2009/06/08
Physics and Astronomy Outreach Program at the University of British Columbia