|Worksheet #21 : The Climate Machine, ATOC 3600 : November 9, 2000
1. Explain the balance implied by the Earth's radiative balance. What terms are involved? On what properties of the Earth/solar system do the terms depend?
The Earth's radiative balance states that the amount of sunlight absorbed by the Earth equals the amount of longwave radiation it emits. The amount of sunlight absorbed by the Earth depends on the strength of the Sun, the distance from the Sun to the Earth, and the reflective properties of the Earth as determined by cloud amount, snow/ice amount, and other radiative properties of the surface and atmosphere. The amount of longwave radiation emitted by Earth is impacted by Earth's surface temperature, cloud amount/height, the mean atmospheric temperature (among other Earth properties).
2. Is the strength of sunlight reaching the Earth constant over time? What solar phenomena can alter the strength of sunlight reaching the Earth? Do they lead to increased or decreased solar intensity?
The strength of sunlight reaching Earth is not constant over time. From season to season the intensity is altered by the distance of the Earth from the Sun. The 11-year sunspot cycle also modulates the intensity of sunlight reaching the Earth due to the presence of plages. In periods when sunspots are frequent, the intensity of sunlight reaching the Earth increases. On very long timescales its also known that the Sun is becoming more and more intense, increasing by about 10% every billion years.
3. In the simple climate model developed in class, what basic balance was assumed? If the intensity of the Sun is doubled in the model, what impact does this have on the Earth's temperature?
A balance was assumed between the amount of radiation absorbed by the Earth and the amount of longwave radiation emitted by the Earth. We solved for Te = [Fs*(1-albedo)/(sigma*4)]1/4. So if Fs is doubled, Te increases by 21/4 or approximately 20%.
4. What is meant by the greenhouse effect? What is the most important greenhouse gas? List two others.
The greenhouse effect pertains to the fact that the amount of radiation that leaves a planet is often less than that emitted by the surface and hence some energy is "trapped" in the atmosphere and/or oceans. On Earth, the most important greenhouse gas is water vapor. CO2 and CH4 are two other important gases.
5. A friend of yours claims that the seasons are controlled by how far the Earth is from the Sun. Prove to your friend that this is not the case by calculating the relative importance of the seasonal change in distance from the Sun to the Earth versus the change in tilt of the Earth in determining the change intensity of sunlight at Boulder (40oN). Note: the distance of the Sun to the Earth in (boreal) winter is 147 106 km and in summer is 152 106 km and the tilt of the Earth is 23.5o.
One can calculate the reduction in solar radiation at Earth based on the inverse square law. In winter the Earth receives Fs/(147 x 106)2 W m-2and in summer the Earth receives Fs / 152x106)2 W m-2, where Fs is some solar constant. The ratio between the strength of sunlight during the summer and winter is thus 0.92 based on the changing distance from the Sun. This corresponds to an 8% change. However, in winter the angle of the Sun relative to vertical at Boulder is (40+23.5) as we are tilted away from the Sun. During summer, the angle is (40-23.5). If we then resolve the component of sunlight that is perpendicular to the surface we get the cos(63.5deg) in winter and the cos(16.5deg) in summer time. The ratio of summer intensity to winter intensity is thus 0.95/0.45 or a 115% increase during summer.