http://www.atmos.washington.edu/academics/classes/2013Q1/380/HW8.html
Due Friday Mar 7
In this exercise you will learn about equilibrium climat change from doubling CO2 concentration in a global climate model and in an energy balance model. You will learn about radiative forcing and top of atmosphere energy balance. You will learn about the strength of albedo feedback.
Summary:
I. Run the ebm and save some figures and output.
II. Analyze GCM runs already done for you.
Expect to turn in 2-3 typed pages with tables. Include any figures you refer to in your write-up.
0. Begin your assignment with a one-paragraph introduction about what the assignment is about. Probably you will write this last, but make it the first paragraph anyway.
I. Run the ebm
Click here for a pdf description of the ebm
At the very leaset, recognize that an ebm is a simple model with a domain that only varies in latitude. Hence it is zonally and vertically averaged. The surface is the same everywhere and is assumed to have a low heat capacity, like land surface. There is no moisture in the model. If the temperature should fall below -10 degC, the albedo is set to a value appropriate for an ice covered surface. If the temperature is above -10 degC the albedo is appropriate for average conditions over land and ocean with clouds. The model is run to equilibrium.
Make a supdirectory for this exercise's analysis files. If you call it "climsens", something like the following should do the job:
cd /home/disk/p/atms380/$LOGNAME
mkdir climsens
cd climsens
cp /home/disk/p/atms380/ebm/* .
cp /home/disk/p/atms380/scripts/ex8* .
matlab &
a) Run ebm.m in matlab. It should pop up a gui. You will probably have to stretch the window from the lower left corner so it looks like this:
Hit the Run EBM button in the pop-up gui to do a run with the defaults. Examine the figure. In the lowest panel, the total of the vertical fluxes into the column is balanced by the divergence of the northward heat flux into a latitude circle. Recall that at equilibrium, divF= Fin - Fout - Fsurf, where Fout is the outgoing longwave radiation and Fin is the net downward shortwave flux. Note that the surface flux Fsurf is always zero because the model is run to equilibrium (not even sea ice is growing as in HW7 which caused a small flux into the surface ad infinitum). Here it really is zero so we don't bother to plot it. The northward heat flux (F) in the middle panel at each latitude is the integral of the -divF starting at one pole and stopping at each latitude point (it can start from either pole). The northward heat flux is negative where the heat flux is southward.
Notice the discontinuity in Fin in the lowest panel. This is because there is an ice-like albedo poleward of the abrupt change in Fin.
Save some variables for later use by giving the variables unique names. This run has modern CO2 levels so append an "x1" to the name of various variable. Do this in the matlab window where you can type commands:
Tx1=T; Finx1=Fin; Foutx1=Fout; divFx1=divF;
save ebmx1.mat Tx1 Finx1 Foutx1 divFx1 phi
Now rerun the model with A decreased by 2.1 (recall that raising CO2 lowers Fout), which in an ebm is roughly like doubling CO2, and save as before but substitute x2 for x1. Use the up arrow key in matlab to scroll through previous commands and then edit them. This way you can make your life easier when trying to save this stuff.s
Rerun it again with A decreased by another 2.1 and save as before using x4 (as this approximates doubling CO2 again).
Rerun it again with A increased by 2.1 relative to the default (so A=205.4 and save variables as before using xhalf (as this approximates halving CO2 relative to the default).
Be sure your runs had A = 203.3, 201.2, 199.1, and 205.4 by looking at the four figures that you have on your screen. This is critical.
Finally rerun the model with the "No Albedo Feedback" button on and with default A. Note that this is equivalent to the x1 case (no need to save anything). Now lower A as for the x2 case and save as before using the suffix x2noAF.
You can retrieve your run output in matlab using "load ebmx1.mat" (etc). Note that a convenience of using the grid with uniform spacing in sin(phi) is that global means are conveniently computed by taking mean(Tx1), for example, with no weighting needed with latitude.
Numbers smaller than +/-1e-6 are zero to roundoff error, please list them as zero in your table and consider them as zero in your discussion!!!
In your write-up of part I
1) State which runs have icy polar caps as determined by a discontinuity in Fin from high surface albedo. Use sum(Tx1<-10)/length(Tx1) (for example) in matlab to determine the global fraction of ice.
2) Plot the change in T, Fin, Fout, and divF, as a function of latitude for example
plot(phi, Tx1-Txhalf, phi, Tx2-Tx1, phi, Tx2noAF-Tx1, phi, Tx4-Tx2)
and answer:
a) Can Fin change with global warming if there is no change in the albedo? Why?
b) It is easiest to understand what is happening in the model if you first think about two runs that have no ice, or the x2 and x4 runs. You imposed a "radiative forcing" in the outgoing longwave flux when you alter A by LOWERING Fout since Fout=A+BT. The planet responds to the imposed forcing by seeking to return to balance. What is the climate response to the radiative forcing? Hence, what are the consequences to Fout?
c) Now consider the difference between x2 and x1 where there is a change in ice cover. Again you imposed radiative forcing by lowering A. The planet responds to the imposed forcing by seeking to return to balance. What is special about the climate response to the radiative forcing when there is ice? Hence what happens to Fin and Fout? It may help to do parts 3 and 4 first before you begin writing up your discussion to this part.
d) Finally in the difference between x2noAF and x1 you turned off albedo feedback. Is albedo feedback positive or negative? Is the difference between these runs more like x2 versus x4 or x1 versus x2?
3) Compute the global mean value of divF for each run and discuss
4) Make a table like so, using the differences of global means of the variables:
Delta T Delta Fin Delta Fout Delta Icefrac
x1 minus xhalf
x2 minus x1
x2noAF minux x1
x4 minus x2
Keep in mind that Icefrac for the x2noAF case is computed from Tx1 not Tx2noAF so effectively Delta Icefrac for x2noAF minus x1 is zero.
5) Discuss the linearity of the changes in global mean in the table in terms of albedo feedback and the change in ice cover.
II. Analyze similar runs from a GCM that Cecilia ran but unfortunately could not turn of albedo feedback.
In your write-up of part II
1) Run ex8_a in matlab for each of the variable choices and make a table similar to the one above like so (to turn in):
Delta T Delta Fin Delta Fout Delta Icefrac Delta Cloudfrac Delta Precip
x2 minus x1
x4 minus x2
The script ex8_a computes the global means and differences for you. Fig 1 is the climatology and Fig 2 is the difference of climatologies. Fig 3 shows the spatial pattern. In these runs with obliquity set to the modern value, the sea ice does not grow indefinitely, so the top of atmosphere should be pretty close to in flux balance for the individual runs.
2) Discuss the linearity of the changes in these GCM variables in global mean and in their horizontal spatial patterns. Try to understand what is happening with the ice and cloud fraction changes and Fin changes (like is there less ice/more clouds and hence expected changes in Fin?)
3) After running the script for a variable that EBM and GCM have in common, say "T", you can compare GCM and EBM like this (making the EBM results appear dashed):
load ebm ebmx1.mat
load ebm ebmx2.mat
load ebm ebmx4.mat
figure(2); hold on;
plot(phi, Tx2-Tx1, 'b--', phi, Tx4-Tx2,'r--')
hold off;
Run ex8_b to look at TOA energy balance and divF. This time I have included GCM and EBM from my runs for convenience. Again solid lines are GCM and dashed are EBM.
To turn in: Discuss how GCM and EBM compare for T, Fin, Fout and the sum Fin-Fout. Note the good agreement at times between EBM and GCM and poor agreement at other times is evidence of how much the EBM has been tuned to do some things well, in spite of missing physics like water vapor transport and condensation processes.