The hardest thing you'll ever learn is ... climate modelling

Credit: pixabay

1.
a) where is the final ice-edge? pass
b) what are the mean temperature and mean albedo? 15C and 0.31
c) what are the approximate temperatures at the pole and the equator? -15C and 0C
d) does this look like the real Earth? No, these temperatures are lower than the real Earth

2.
a) what is the mean temperature and albedo in the absence of heat transport? 9C and 0.34
b) at what K value does the model become completely ice-free? pass
c) what are the implications of this sensitivity to K with regard to variations in poleward heat transports (e.g. variations in the Gulf stream)? Is this realistic? pass

3.
a) By reducing the “Fraction of Solar Constant” in Run 1 determine the value at which the Earth becomes completed ice-covered. 0.88
b) Set the initial ice-edge to 0o (i.e. “Snowball Earth'”) and increase the solar constant from the value found in (a). At which value does the ice-sheet completely melt? 1.2
c) Set the initial ice-edge to 90o (i.e. ice-free Earth) and reduce the solar constant from the value found in (b). At which value does the ice begin to reappear? 0.88
d) Sketch phase diagrams of mean albedo versus fractional solar constant, and mean temperature versus fractional solar constant. Initialise Run 1 and Run 2 with ice-edges at 0o and 90o, and increase the solar constant values from 0.8 to 1.2 in steps of 0.05. Fill in the mean values of temperature and albedo in the workspace table at the bottom of the “Graphs” sheet. This will produce phase space diagrams below the table. Wow, a big jump (+60C) in temperature between 1.15 solar constant and 1.2
e) Given that the Sun was fainter in the past, what do these diagrams “predict” the current Earth state should be? What missing processes might resolve this “faint young Sun paradox”? The Earth should be cooler than it is. The missing process is the warming effect of CO2.

4.
a) What is the impact of doubling CO2 on global temperature and albedo? Mean temperature increases by 3.44604C and albedo decreases by 0.009162
b) Why does this differ from the T2x input parameter? Because this input parameter assumes 0 albedo
c) The global mean temperature is given by : = [ {1 - <>} – A] / B where =1370 fS / 4 is the mean incident solar radiation, <> is the mean albedo, and B=2.17 W m-2 oC-1. Derive a relation between the increment to the mean temperature due to albedo changes, Tsnow , and the albedo change itself, . Does this fit with the answers given in (a) and (b) above? pass
d) Now try 4xCO2 in Run 1. How large are the mean temperature and mean albedo changes in going from 2xCO2 to 4xCO2? Why are they lower than in (a)? Mean temperature increases by 2.00086 and albedo decreases by 0.000005.