## Energy Balance and Climate

### Class #3 (Mon., Jan 24)

#### PDF version

## Reading:

### Required Reading (everyone):

- Understanding the Forecast, Ch. 2–3, pp. 9–23.

### Reading Notes:

**Note:** **There is an error in Table 3.1 on p. 23 of Understanding the Forecast:** The observed temperature of the earth
(\(T_{\text{observed}}\)) is 288 K, not 295 K.

As you read *Understanding the Forecast*, focus on pp. 13–23 . You need to understand the calculations of the “bare-rock” model on pp. 19–23. The intermediate steps are not as important as two equations:
\[
F_{\text{out}} = F_{\text{in}}\quad\text{at equilibrium,}
\]
and equation (3.1), which describes the bare-rock model:
\[
T_{\text{earth}} =
\sqrt[4]{\frac{(1-\alpha)I_{\text{in}}}{4\epsilon\sigma}}
\]
(Helpful hint: to take a fourth root easily with your calculator, just press the square root key twice.)

Questions to think about (**not** to write up and turn in):

What is blackbody radiation? What is a “blackbody” anyway?

Why is it that the sun gives off visible light, but the earth does not?

When the earth absorbs energy from sunlight, where does the energy go initially? Where is the final destination of that energy?

What is the Stefan-Boltzmann equation, and why is it important?

What does the Stefan-Boltzmann equation tell us would happen if the sun got hotter? What would happen if the Earth got hotter?

Study table 3.1 on p. 23 of

*Understanding the Forecast*(ignore the column “\(T_{\text{1 layer}}\)” because we don’t get to that until later in the chapter.):- Why is the sunlight brighter on Venus than on Earth, and dimmer on Mars?
- Why is the “bare-rock” temperature of Venus lower than Earth, even though it gets more sunlight?
- Why do you suppose the actual observed temperature at the surface of Venus is so much hotter than the “bare rock” temperature?

At the top of p. 20, why does Archer write, \(F_{\text{out}} = F_{\text{in}}\)? What would happen if \(F_{\text{out}} \ne F_{\text{in}}\)

Without getting bogged down in the details of the numbers, why are the areas used to calculate the incoming and outgoing energy fluxes different? (Figures 3.1 and 3.2 explain this)

If the sun got 5% brighter, approximately how many degrees warmer would the earth become?