Energy and Human Ambitions on a Finite Planet, 2021a

9 Climate Change 161
(linearly). Is the corresponding temperature trend linear? 85
20. Which of the following are positive vs. negative feedback effects
for climate change as a result of warming, <strong>and</strong> why?
a) warming tundra releases methane trapped in the permafrost
b) more water in the atmosphere creates more clouds <strong>and</strong>
increases the amount of sunlight reflected from Earth
c) an increase in forest fire activity burns lots of carbon-based
material <strong>and</strong> leaves a blackened earth
d) snow covers less of the l<strong>and</strong> each winter as temperatures rise
21. Coal is, <strong>and</strong> always has been, the worst offender of the fossil fuels
in terms of CO 2 emission. Based on the scenarios summarized in
Table 9.5, what is the percentage reduction in final temperature
rise (ΔT) based on emissions out to 2100 (in the case that we hold
steady at today’s fossil fuel levels) if we substitute natural gas for
all uses of coal vs. if we keep things the same?
85: . . . ; same-size steps? A plot might help
elucidate.
Comparing first two scenarios
22. Which of the scenarios in Section 9.3 do you deem to be most
realistic, <strong>and</strong> why? Given this, how much more eventual warming
is likely in store compared to the 1 ◦ C to date?
23. Verify for each panel in Figure 9.15 that the sum of the upper two
arrows in the middle of each panel <strong>and</strong> the difference of the lower
two arrows in the middle match the effective (dashed) arrow at
the right (a total of 8 comparisons).
24. Construct your own panel in the manner of Figure 9.15 corresponding
to the third case in Section 9.3 in which we curtail fossil fuel use
by 2100, resulting in a final equilibrium ΔT of 2.6 ◦ C (thus 290.6 K
ground temperature). Characterize the final equilibrium state,
when net upward radiation equals solar input. After balancing
the books, figure out what the GHG fractional absorption must be
(the number in the “cloud” in Figure 9.15).
25. On a sunny day after a big snowfall, the (low winter) sun might
put 500 W/m 2 onto the ground. Snow reflects most of it, but let’s
say that it absorbs 5% of the incoming energy. How much snow
(ice) will melt in an hour from the absorbed energy if a cubic meter
of snow has a mass of 100 kg?
Tips: Upgoing radiation from the ground
is computed from σT 4 . Verify that you can
match the first or last (equilibrium) panel of
Figure 9.15 by the same technique to know
if you are doing it right.
Hint: It is easiest just to consider a single
square meter of surface <strong>and</strong> figure out what
fraction of a cubic meter (thus what fraction
of a meter-depth) melts. Ignore any effect
of air temperature.
26. If the ocean absorbs an additional 3 W/m 2 of forcing, 86 how long 86: ...3Jdeposited every second in each
would it take to heat the ∼4 km deep column of water directly
square meter
under a particular square meter (thus 4 × 10 6 kg)by1 ◦ C? 87
27. Based on Table 9.7, if we could magically turn off infrared radiation
to space, how long would it take for the sun’s 240 W/m 2 average
to heat the entire ocean by 1 ◦ C? It is fine to assume that the ocean
covers the whole globe, for this limiting-case calculation.
28. Let’s say annual excess energy input from imbalanced radiative
87: Hint: use kcal (4,184 J) <strong>and</strong> solve for
the temperature increase in one year, then
figure out how many years for that to accumulate
to 1 ◦ C.
Hint: multiply by area of Earth <strong>and</strong> seconds
in a year to get Joules of input.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.