ERTH 535: Planetary Climate Change (Spring 2018) Problem #4 (10 pts total) (Due Monday, April 2)

Background:
The greenhouse effect works because "greenhouse" gases such as water vapor, carbon dioxide, and some other, much less abundant gases, plus clouds, absorb most of the longwave IR radiation emitted by the earth's surface and emit radiative energy themselves, partly out to space but partly downward to the earth's surface, which absorbs it. For the heat budget of the earth's surface to be roughly balanced (as we observe it to be in the long run, approximately), this additional source of energy (beyond what would exist without greenhouse gases and clouds) requires that the surface to be warmer than it would be otherwise, so that that the surface emits enough radiative energy (and hence loses enough heat) to balance the heat gained by absorption of both solar radiation and longwave infrared radiation emitted downward by the atmosphere.

The Earth's Long-Term, Global Average Surface Temperature without Greenhouse Gases and Clouds

Consider Figure 3.31 in Lab Activity #5: "Long-Term Average Heat Budgets for the Earth's Atmosphere and Surface", which shows a complete, long-term, global average energy budget diagram for the earth's atmosphere and surface. Suppose that all gases that absorb terrestrial radiation (notably water vapor and carbon dioxide, but other, less important ones, too, such as ozone) were removed from the atmosphere. Removing water vapor would also mean that no clouds could be present, either, which would reduce the atmosphere's (and hence the earth's) albedo. There would be other changes as well, such as less absorption of solar radiation in the atmosphere.

1. [6 pts] Estimate the size of the various terms in the heat budgets for the atmosphere and the earth's surface under these conditions, assuming that the budgets balance. (You can simply list them by name with their new values, or you can sketch a budget diagram and label them on the diagram.) For each term, explain your reasoning.

To keep things simpler, make the following assumptions:
1. the albedo of the earth's surface that you estimated in Question 2(c) in Lab Activity #5 remains the same;
2. the sensible heat flux from the surface into the atmosphere is zero (for reasons that I can explain in person if you want, though you might figure it out yourself!); and
3. since there is no water vapor (or clouds) in the revised atmosphere, the latent heat flux from the surface into the atmosphere (due to evaporation and sublimation) is zero.

2. [1.5 pts] Based on your revised budget in (a), use the global, long-term average radiative emission flux from the surface to estimate the corresponding effective radiating temperature of the surface. (You'll need to invoke the Stefan-Boltzmann relation. Be sure to convert the emission flux from a percentage figure into an actual energy flux, assuming that the global, long-term average insolation on horizontal surfaces at the top of the atmosphere is 341.3 W/m2, calculated using My World GIS's incoming solar radiation data for 1987.)

3. [0.5 pts.] Based on your revised budget in (a), what is the effective radiating temperature of the planet as a whole? If it is different from today's value (based on Figure 3.31 in Lab Activity #5), explain why.

4. [2 pts] Compare your answer to (b) above to the global, long-term average surface temperature (which from 1951-81 averaged about 288K, or about 15°C, or about 59°F; in 2017 it was about 0.9°C or 1.6°F higher). Based on the Stefan-Boltzmann Law, the assumption of a balanced budget, and the main terms in the budget for the earth's surface with and without greenhouse gases (and clouds), what, at root, accounts for the difference?

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