Global Environmental Problems

Spring 2006

Problem Set #7

Due: 29 March

1.

In chapter II of Harte, read problem 13 ("How Hot Is Planet Earth?") and do exercise 1.

EXTRA CREDIT: exercises 3 and 4.

2.

In the class notes we introduced a very simple two-box (atmosphere and surface) model of the Earth's climate, in which the average surface temperature is given by:

where a is the albedo (0.3), e is the fraction of infrared energy absorbed by the atmosphere (0.75), W is the average solar flux at earth orbit (1370 W/m²), and s is a constant (5.67×10^–8 W/m²K⁴). Find the change in surface temperature associated with the following:

A.

Solar flux increases by 4 W/m².

This is the highest estimate of the increase from 1700 to the present; the best estimate is four times smaller.

B.

The Earth’s albedo decreases by 0.01 (i.e., from 0.30 to 0.29).

A decrease of this magnitude could result from melting of polar and glacial ice, northward movement of boreal forests (replacing snow with snowy forests), or decrease in cloud cover.

C.

An increase in e from 0.75 to 0.77.

An increase of this magnitude is roughly equal to the effect of doubling the CO₂ concentration.

3.

As noted in class, a doubling of the CO₂ concentration would result in a “radiative forcing” of about 3.7 W/m²—that is, emission of infrared energy to space would decrease by 3.7 W/m² if the CO₂ concentration was doubled very quickly. For comparison, estimate the radiative forcing from the following:

A.

Solar output increases by 0.1 percent. (This is the variation over the 11-year sunspot cycle.)

HINT: How would the energy flow into the climate system (currently 240 W/m²) change?

B.

The Earth’s average albedo increases by 0.01 (from 0.30 to 0.31).

C.

A quadrupling of the CO₂ concentration (e.g., from 275 to 1100 ppm).