 #1
ProbablySid
 4
 3
 Homework Statement:

To mitigate climate change, a largescale 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 StefanBoltzmann 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.
Thank you very much.
(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.