|
http://www.atmos.washington.edu/academics/classes/2013Q1/380/HW9.html Due Friday Mar 14 |
|
In this exercise you will learn about climate feedbacks and determine if they differ with different types of forcings. One type of forcing is the familiar doubling CO2. The other is a volcanic aerosol forcing or you can think of it as geoengineering via "Solar Radiation Management" or (SRM). Summary: I. Run the EBM and compute climate feedbacks. In the EBM SRM is accomplished by simply lowering the solar constant. II. Analyze equilibrium GCM runs already done for you, compute their feedbacks, and discuss the results. In the GCM (which is CCSM3 here, so not the same as last week) SRM is accomplished by adding volcanic aerosol to the stratosphere. I. Run the EBM cd /home/disk/p/atms380/$LOGNAME/climsens matlab & Run the ebm.m for a default case and compute the "radiative forcing" that would come from reducing the solar constant by 1% by typing at the matlab prompt deltaQ99 = -0.01*mean(S.*(1-alb)) Tx1=T; Finx1=(1-alb).*S; Foutx1=A+B*T; divFx1=divF; % rename the data for later use Run a 2XCO2 case by lower A by 2.1 Tx2=T; Finx2=(1-alb).*S; Foutx2=A+B*T; divFx2=divF; % rename the data for later use Return A to 203.3 and run a case with Q/Qo = 0.99 T99=T; Fin99=(1-alb).*S; Fout99=A+B*T; divF99=divF; % rename the data for later use deltaQx2=2.1; Run a combination "geoengineered" case with A lowered by 2.1 and run a case with Q/Qo = 0.99 Tgeo=T; Fingeo=(1-alb).*S; Foutgeo=A+B*T; divFgeo=divF; % rename the data for later use save hw9_ebmresults.mat % this will make it easy to retrieve the data later if you wish Next we will compute the feedback parameters. In class, we computed lambda from the partial derivative with respect to temperature of (Fout-Fin). We also broke lambda into a longwave and shortwave components with lambda_LW=partial derivative with respect to temperature of Fout and lambda_LW=partial derivative with respect to temperature of Fin. These derivitaves can be estimated from the EBM using a perturbation approach (see some notes about how). First for the doubling of CO2: deltaT=mean(Tx2)-mean(Tx1) deltaFout=mean(Foutx2)-mean(Foutx1) deltaFin=mean(Finx2)-mean(Finx1) lambda_LW = (deltaQx2 + deltaFout)/deltaT % note deltaQx2 appears in the LW feedback lambda_SW = (-deltaFin)/deltaT lambda_total = deltaQx2/deltaT Now for the reduced solar constant case. deltaT=mean(T99)-mean(Tx1) deltaFout=mean(Fout99)-mean(Foutx1) deltaFin=mean(Fin99)-mean(Finx1) lambda_LW = (deltaFout)/deltaT lambda_SW = (deltaQ99-deltaFin)/deltaT % note deltaQ99 appears in the SW feedback lambda_total = deltaQ99/deltaT Now for the geoengineered case. deltaT=mean(Tgeo)-mean(Tx1) deltaFout=mean(Foutgeo)-mean(Foutx1) deltaFin=mean(Fingeo)-mean(Finx1) lambda_LW = (deltaQx2+deltaFout)/deltaT % note deltaQx2 appears in the LW feedback lambda_SW = (deltaQ99-deltaFin)/deltaT % note deltaQ99 appears in the SW feedback lambda_total = (deltaQx2+deltaQ99)/deltaT The deltaQ's must be in the various lambda equations because they were imposed in the model. In other words deltaFout in the double CO2 case is due to the temperature change and the imposed forcing. So to find how Fout changes with T, we must add deltaQ2 to deltaFout and divide by deltaT. Make a table like so for the EBM (to turn in): Delta Q Delta T lambda_LW lambda_SW lambda_total 99% sun doubling CO2 geoengineered Remember all these lambda's have the opposite sign of their actual feedback. The signed feedback, or capital lambda, is just the opposite sign of each variable. Turn in: 1) In class we showed that lambda without ice-albedo feedback is the parameter B for the EBM. Note that lambda_LW equals B and explain why. 2) For the first two cases, discuss the extent to which the lambda's are the same. Try to understand the changes in terms of what is happening with the albedo. 3) A stable climate has on average negative feedback, in which case lambda_total should be positive. This would mean for a given imposed forcing, the climate change acts to eliminate the forcing. The EBM tries to elimate an imposed forcing by warming so the product B*deltaT cancels the imposed forcing plus whatever warming ocurs from ice changes. The lambda_total in the geoengineered case is negative! This was a surprise to me at first. However, the run certainly did not blow up! It is weird that a negative imposed forcing caused warming. Here the negative lambda_total demonstrates a limitation of the definition of lamba in terms of global mean quanitites. This run shows how climate science is still a research problem. Just think, you could become famous for discovering how feedbacks ought to be computed. At the matlab command line, type "plot(phi,Tgeo-Tx1)". Discuss the latitudinal distribution in terms of how you think the feedbacks vary spatially. Hint: there are only two feedbacks, longwave feedback controlled by B, which is spatially uniform, and shortwave feedback controlled by ice-albedo, which depends on temperature. II. Analyze the GCM, click on the links to see a bunch of figures Double CO2 Alone Volcanic Aerosol Forcing Alone Both Forcings Together or Geoengineered First spend some time just looking at whatever interests you in the myriad of figures provided. The sets I find most useful are 1 Tables, 3 Line plots, 4 Vertical contour plots, and 5 Horizontal Contour plots. The figures and web sites are made automatically using a diagnostics package provided by NCAR. Some of the figures are turned off for various reasons --- just hit back if you find a missing figure. In the links above, the first item in the list you are offered is "Tables". Select it and then again select "global" "ANN", which brings you to a large table of data. The variables in CAM that correspond to the names that we use in class are as follows: Fin = FSNT which stands for Flux Shortwave Net absorbed Top of atmosphere Fout = FLNT which stands for Flux Longwave Net outgoing Top of atmosphere T = TS which stands for Surface Temperature FLNT and FSNT are "all sky" quantities, which means they are averages of cloudy and clear sky areas. FLNTC and FSNTC are just these quantities for the clear part of the grid cell. The difference gives you the cloudy sky part of the grid cell. Note that for doubling CO2, Delta FSNT is 1.079 W/m2 and Delta FSNTC is 2.342 W/m2. This tells you that the clear sky increase in absorbed shortwave radiation is much higher than when clouds are overhead. The clouds also are changing (fewer low clouds/more high clouds). Hence the cloud presence obscures the change in surface ice loss somewhat and moderate the positive ice albedo feedback. The cloud changes themselves also change the albedo from the top of atmosphere and hence muddy FSNT. Note that we think deltaQ = 3.7 W/m2 in CAM for doubling CO2 and -3.7 W/m2 for adding volcanic aerosols. Just as for the EBM, the radiative forcing from volcanic aerosol figures into the lambda_SW while the radiative forcing from doubling CO2 figures into lambda_LW. Use the instructions in part I above as a guide. Be sure that lambda_LW+lambda_SW=lambda_total and lambda_total and lambda_LW > 0 and lambda_SW < 0. Make a table like so for the GCM, leaving off the lambda's for the geoengineered case since the error in deltaQ cause highly inaccurate lambda's for the GCM when delta T is very small: Delta Q Delta T lambda_LW lambda_SW lambda_total volcanic aerosol doubling CO2 geoengineered 0.0 0.09 - - - To turn in: A) Discuss the extent to which the lambda's are the same. Can you make sense of why they differ? B) Set 3 "Line Plots" (zonal mean annual mean plots) are useful for determining where the action is in latitude. Just look at the change from doubling CO2 on the annual mean. Discuss the distribution of Delta TS and how it relates to Delta FLNTC. C) Where is there an increase in low and medium to high clouds? Discuss how the change in medium to high clouds corresponds to changes in FLNT by looking at the Line Plots for FLNT and FLNTC. D) Discuss how the change in clouds corresponds to changes in FSNT by looking at the set 3 Line Plots for FSNT and FSNTC. You don't need to repeat the discussion about clouds obscuring surface ice changes. Instead discuss how the cloud changes themselves affect FSNT. E) For something different... What is the percent change in global mean annual mean total precipitation (PRECT in the table under set 1) for (i) doubling CO2 and (ii) adding volcanic aerosol forcing? Also include the percent change normalized by the global mean temperature change in (i) and (ii).
|
| Return to Homepage |