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