Exercises: Greenhouse Gases, Albedo, and Feedback Loops

Name three greenhouse gases. For each one, give one natural source or one human source.

Define albedo. Which surface has a higher albedo: fresh snow or the open ocean? Explain what this implies about how much sunlight each surface absorbs.

Name the three Milankovitch cycles. For each one, state what part of Earth's orbit or orientation changes (use eccentricity, axial tilt, and precession).

The average solar energy arriving at the top of the atmosphere (solar constant) is $1{,}361\ \text{W/m}^2$ on a surface facing the Sun. Because Earth is a sphere, the average over the whole planet is one-fourth of this. Earth's albedo is 0.30.

1. Calculate the average absorbed solar energy per square meter, $\frac{S(1-\alpha)}{4}$.

2. Without any greenhouse effect, Earth's average surface temperature would be about $-18\,^\circ\text{C}$. The actual average is about $15\,^\circ\text{C}$. Calculate the difference.

3. Explain how greenhouse gases cause this difference.

Albedo values for several surfaces:

Sunlight reaches each surface at $1{,}000\ \text{W/m}^2$.

1. Calculate the energy absorbed per square meter by fresh snow and by open ocean.

2. Calculate how much more energy a square meter absorbs when sea ice (assume albedo 0.85) melts and becomes open ocean.

3. Explain what this means for the warming of the Arctic.

Classify each of the following as a positive (amplifying) or negative (stabilizing) feedback loop, and justify each answer:

1. Warming melts Arctic sea ice, which lowers albedo, which causes more warming.

2. Warmer air holds more water vapor, a greenhouse gas, which causes more warming.

3. Higher atmospheric CO$_2$ increases plant growth, which removes more CO$_2$ from the air.

4. Warming thaws permafrost, which releases methane, which causes more warming.

Earth's axial tilt (obliquity) varies between about $22.1^\circ$ and $24.5^\circ$ with a period of about 41,000 years. Since about 1850, atmospheric CO$_2$ has risen from roughly 280 ppm to roughly 420 ppm, over about 175 years.

1. Calculate the percent increase in CO$_2$.

2. Explain how a larger tilt changes the contrast between summer and winter at high latitudes, and how this could influence the growth or melting of ice sheets.

3. Explain why a small change in solar energy from orbital cycles is not enough by itself to explain the size of past ice-age cycles, and identify at least two feedback loops that amplify it.

4. Compare the time scale of Milankovitch cycles with the time scale of recent CO$_2$ increase, and state what this comparison implies about the cause of current warming.

A class models the greenhouse effect with two identical clear bottles under a lamp. Bottle A contains air. Bottle B contains air with extra CO$_2$ produced by mixing vinegar and baking soda in a separate container and transferring the gas. A thermometer in each bottle is read before the lamp turns on and after 20 minutes.

1. Calculate the temperature change in each bottle and the difference between them.

2. Use the model to explain how greenhouse gases trap thermal energy.

3. Identify at least two ways the model differs from Earth's real atmosphere.

4. Suggest one change that would make the experiment more reliable.