Weather and Climate Prediction Exercise 6
http://www.atmos.washington.edu/academics/classes/2011Q1/380/HW6.html
Due Friday Feb 18

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.

Summary:

I. Run the ebm and save some figures and output.

II. Analyze GCM runs already done for you.



I. Run the ebm

Click here for a pdf description of the ebm

Make a supdirectory for this exercise's analysis files. Maybe you would like to call it "climsens". Go to that directory and copy the ebm files and analysis files to your directory for this exercise. Start matlab

cd /home/disk/p/atms380/$LOGNAME/camruns
mkdir climsens
cd climsens
cp /home/disk/p/atms380/ebm/*   .
cp
/home/disk/p/atms380/scripts/analyze_ex6* .
matlab &

  a) Run ebm.m in the matlab window by typing "ebm". It should pop up a gui. You will probably have to resize the window to see all the buttons. Do a run with the defaults and give the variables unique names like (in the matlab interactive environment):

Tx1=T;  Finx1=(1-alb).*S; Foutx1=A+B*T; divFx1=divF;       %(the .* is necessary)
save ebmx1.mat Tx1 Finx1 Foutx1 divF 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.

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/print as before using xhalf (as this approximates halving CO2 relative to the default).

Finally rerun the model with the "No Albedo Feedback" button on and with default A. Note that this equivalent to the x1 case (no need to save anything). Now lower A as for the x2 case and save as before using x2noAF.

Make a table like so (to turn in):

                                     Delta T      Delta Fin    Delta Fout      Delta divF
x1 minus xhalf
x2 minus x1
x2noAF minux x1
x4 minus x2

You can retrieve your run output using load ebmx1.mat (etc). Note that a convenience of using a grid in the varialbe x=sin(phi) is that global means are conveniently computed by taking mean(T) with no weighting needed with latitude. (Numbers smaller than +/-1e-12 are zero to roundoff error, please list them as zero in your table!!!)

Also plot the change in zonal mean T, Fin, Fout, and divF, for example
plot(phi, Tx1-Txhalf, phi, Tx2-Tx1, phi, Tx2noAF-Tx1, phi, Tx4-Tx2)

Turn in: Discuss the linearity of the changes in global mean values and in the zonal means (provide plots of zonal means). Try to understand the changes in terms of what is happening with the albedo.




II. Analyze GCM

  Run analyze_ex6_a in matlab for each of variable choices and make a table similar to the one above like so (to turn in):

                          Delta T  Delta Fin  Delta Fout   Delta Cloudfrac   Delta Icefrac   Delta Precip
x2 minus x1
x4 minus x2

 
To turn in: Discuss the linearity of the changes in these 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?)

After running the script for variable "T" you can compare GCM and EBM like this:

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;

To turn in: Discuss how GCM and EBM compare for T, Fin and Fout

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