Environmental Physics - Radiative forcing effect on greenhouse effect

  • #1
ProbablySid
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Homework Statement:
To mitigate climate change, a large-scale afforestation project is commenced. The project aims to create a radiative forcing of ##\Delta Q = -1.0 Wm^{-2}## over 50 years by the removal of ##CO_{2}## through photosynthesis. Before the project is undertaken, a typical value of the outgoing longwave radiation (OLR) for the region is ##160 Wm^{-2}## and the average surface temperature is ##292 K##. After complete afforestation (of 50 years), the OLR reduces to ##145 Wm^{-2}##.

i) (a) Estimate the Greenhouse Effect, ##G##, for the region before planting begins.
(b) The total feedback parameter, ##\gamma##, for the region is found to be ##2.1 Wm^{-2}K^{-1}##. Assuming that the forcing target associated with the afforestation earlier is met, estimate what the surface temperature change will be due to the plant growth, hence calculate ##G## for the region after afforestation.
Relevant Equations:
##G=\sigma T^{4}_{s} - OLR## where ##T_{s}## is the average surface temperature, ##G## is the Greenhouse Effect, and ##OLR## is the outgoing longwave radiation. ##\sigma## is the Stefan-Boltzmann Constant.

##\gamma = \frac{-Q_{ext}}{\Delta T_{s}}## where ##\gamma## is the total climate feedback parameter, ##Q_{ext}## is the applied radiative forcing, and ##\Delta T_{s}## is the resulting change in temperature. I think this equation is relevant for (b).
I think part (a) is simple enough. Here is what I have done.
(a) ##G=\sigma T^{4}_{s} - OLR##
$$ =\sigma (294)^{4} - 160 = 254 Wm^-{2} $$

Part (b) is where I am confused. I think I'm supposed to apply the second relevant equation, in order to get the change in average surface temperature due to the radiative forcing. Thus,

(b) $$\gamma = \frac{-Q_{ext}}{\Delta T_{s}} \longrightarrow 2.1 = -\frac{-1}{\Delta T_{s}} \longrightarrow \Delta T_{s} = +0.48 K$$
So now the temperature has increased from ##292 K## to ##292.48 K## as a result of the radiative forcing.
Thus,
##G = \sigma (294.48)^{4} - 145 = 272 Wm^{-2}##

but doesn't this imply afforestation has actually increased the Greenhouse effect? I would not expect this to be the case, which leads me to believe I may have done part (b) incorrectly. Any help/pointers would be greatly appreciated. This is my first time posting on this website, so I hope I have got the hang of the LaTeX. If it's easier to read, I've also attached an image of my working out.
image_2022-06-06_012327750.png
Thank you very much.
 

Answers and Replies

  • #2
Steve4Physics
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Not familiar with this material but is it possible that the problem is simply due to confusion with names/sign-convention?

You have written:
##\Delta Q = -1.0 Wm^{-2}## and
##\gamma = \frac{-Q_{ext}}{\Delta T_{s}}##
Then you treat ##\Delta Q## and ##Q_{ext}## as if they are the same thing.

But perhaps ##Q_{ext}## is intended to be a positive quantity here - so ##Q_{ext} = -\Delta Q = 1.0 Wm^{-2}##.

Please note that's just an uninformed guess. If you check on your definitions of ##\Delta Q## and ##Q_{ext}## you should be able to tell.
 
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