EdGCM - Project 2 - Sensitivity

Global temperature versus solar constant

Goals

Set up and save different simulations
Learn to change one boundary condition for the GCM, solar constant
Determine the climate sensitivity factor, beta

Instructions

1. This project entails making additional simulations with the GCM, changing one of its boundary conditions, the solar flux impinging on the top of the atmosphere. We do this to estimate the "beta" sensitivity factor:

                dTs
(Eq. 1) beta = S---  ,       
                dS

where S is the solar constant and Ts is the global-average surface temperature. Beta tells us how much Ts will change under a fractional change in S.

Your challenges here are

to determine the number and type of simulations to perform in order to estimate S and how S itself may depend on the starting climate, and
to determine how team members might share simulation responsibilities, keeping in mind results from Project 1.

2. You have already completed one 10-year simulation of contemporary climate. Contemporary means that all parameters, such as S, are set to values appropriate for late 20th or early 21st century. First, we should extract relevant information from this run that helps us here:

Solar constant value
Global average temperature for the run

These will be our starting points for further analysis and simulation.

3. Baseline solar constant

This value is provided by EdGCM as part of the simulation set up. We need to find it.

Start EdGCM. In the Run List menu (left side), highlight your simulation for Project 1, which you might have called "Test_Run_1". Then open the "Setup Simulations" from the Window pull-down menu.

Scrolling down the setup window, you should come to a subsection labeled "Forcings". Find the value of the solar luminosity and record it. This is the solar constant for this run.

4. Baseline global-average surface temperature

In Project 1, you plotted the time series of annual-average global temperature. The temperature evolves with time, and we need an estimate of the time average. To do this, we need the numerical values used for the plot. Accessing them differs slightly between the Macintosh and Windows environments.

For both operating systems, if you followed standard installation, then on your desktop is a folder called "EdGCM 4D". If you placed EdGCM codes in another directory, look there for it.
Inside the "EdGCM 4D" folder, open in sequence (each folder is inside the previous) EdGCM2.5/Output/Test_Run_1/diagnostics_Test_Run_1/postprocessing. Substitute the actual name of your simulation for "Test_Run_1". Within this last folder is yet another, called "Test_Run_1_YR1_YR2", where YR1 = year 1 of your run, YR2 = year 2 of your run and again, substitute the actual name of your run for "Test_Run".
- Windows:
  - In the final folder is a set of Excel files. Find the one with SRFAIRTMP (Surface air temperature) as part of its name and open it in Excel.
- Macintosh
  - In the final folder is a set of text files. We want to open the file with SRFAIRTMP (Surface air temperature) in its name, using Excel. Launch Excel.
  - Within Excel, use the "Open" command to open this file. Do not try to open the file simply by clicking on its name. The file most likely will open under text-editing software that will not compute averages for you.
For both operating systems:
- The file contains a column with the complete years simulated and 5 columns of temperatures in degrees C: Global, Land, Ocean, Open Ocean, Ocean Ice. We are concerned here only with the Global temperatures.
- Use the Excel functions to compute the average global temperature for the final 8 years simulated and then record this temperature with the solar constant used for the run. The reason for using 8 is discussed below.

5. Additional simulation

To compute the beta factor, we need to compute Ts(S) for enough cases to allow us to

estimate beta for the present climate and
for two other climates,

by applying a finite-difference approximation to (Eq. 1). This raises some questions: How much can we change S? How many cases do we need to run for each climate?

The EdGCM documentation tells us that we probably should not change S by more than +/- 10%. The EdCGM Setup page actually gives us a setup for a case with S reduced by 2%. However, I suggest starting with only a 1% reduction as our first additional run.

You should give some thought to the second question of how many cases we should run. I think 2 additional climate (giving 3 total) can provide beta for 3 climates, including the control climate, but check with me for guidance if you are not sure how do to this.

6. Reduced solar constant

In the Run List, select the "Sample_Control_Run" case, then push the "Duplicate" button in the "Setup Simulation" panel below the Run List. This creates a duplicate of the run, leaving the original alone.
In the Setup Simulation window, you can see information telling us that the run will be like the standard control run.. You should
- Give the Run ID a name of your choosing
- Change the end date to 31 December 1980 (discussed further below)
- Make the Owner yourself
- Add to the general information in the description window a statement that this run uses a solar constant reduced by 1%
If you scoll down this window, you will see where the solar constant (solar luminosity) is specified. Make this 1% smaller, or 0.99 * 1366.6198 = 1352.9536. We really do not have to go out to 4 digits after the decimal point, of course, but since EdGCM uses solar constant to that level of specification, you might as well.
Run this case.

7. Further simulation

Do the additional simulation needed to get beta for 3 climates.

8. Diagnosis

I had you run your new simulations longer. The reason for this is that we can assume the EdGCM was close to an equilibrium when we started our control case. This would be a "statistical equilibrium" where annual Ts may change from one year to the next, but its time average changes little.

When we change the solar constant, the model may not be close to equilibrium any more. Instead, we must let it adjust to the new equilibrium (let it "spin up").

This figure shows the evolution of global temperature for three runs. The evolution toward the new climate follows an approximate exponential decay. The control simulation was already at quasi-equilibrium, so there is no apparent drift in the temperature.

The 23 years of simulation are to get beyond the spin up stage. We will assume that about 15 years are needed for spin up, so average only over the final 8 years of the simulations with perturbed solar constant.

Note that there is nothing special about choosing 8 years for averages or 15 for spin up. With patience, one could extend these runs further and see how much more spin up is needed, if any. We are assuming here, based on some of my prior experience, that 15 years of spin up and 8 years of averaging are sufficient.

Key question: How can you test my assertion and show limits to its validity?

9. Send to me:

Produce your values of beta as a function of S and turn them in to me. Also give me a plot of multi-year average global Ts as a function of S, as well as a plot showing the evolution of global, annual average Ts versus time.

Finally, answer these questions:

How does your value for beta compare to the estimates presented in the lecture modules (esp. lecture 5)?
Based on your beta values and those in the lectures, do you expect your slope of the Ts vs. S curve to be steeper or flatter than those in the lectures? (Be sure to explain what you mean by "steeper" or "flatter".)
Why do you think beta changes the way it does for the different climates it is computed for?

As before, please put your names in the report and also in the filename, so that I can identify the authors more easily.

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