ERTH 535:
Planetary Climate Change
(Spring 2018)
Lab Activity

(5 pts total; due in class Monday, April 30)
Dr. Dave Dempsey
Dept. of Earth & Climate Sci.,

A Simple STELLA Model of the Planetary Heat Budget with a Greenhouse Effect

Note: Unlike previous lab activities, this one will be evaluated for credit.



In class we developed a set of equations describing a simple heat budget and the effective radiative temperature for an earth-like planet. These equations are described in Part I of the handout, "Supplement to Lab Activity #13: A Simple STELLA Model of the Planetary Heat Budget with a Greenhouse Effect". You have been provided with a version of that budget rendered into a numerical model using STELLA modeling software, and a diagram of the model (using STELLA's graphical conventions). (A copy of the model is available via the "Courses" folder on any Mac computer in the Department of Earth & Climate Sciences, in the E535 > Class subfolder. It is in a file called "HeatBdgtModel_Planet.STMX". You should copy this file to the Desktop of your computer. Double-clicking on the file should start the STELLA software, which will open the file for you.)

The STELLA model as it is provided to you treats the earth's surface and atmosphere as a single entity (the planet) with a single temperature. That temperature averages around 255K (–18°C), which is much lower than the average temperature of the earth's surface (about 288K, or 15°C). As you know, the difference is attributable to the greenhouse effect arising from distinctive radiative properties of a handful of gases present in small amounts in the atmosphere (greenhouse gases) and of clouds. The greenhouse effect arises from radiative interactions between the earth's surface and the atmosphere, so capturing its essential behavior requires treating the earth's surface and atmosphere separately, which the simple planetary heat budget model provided to you does not do.

Your task in this lab activity is to (1) extend the STELLA model to treat the earth's surface and atmosphere separately and try to capture the essence, however crudely, of the greenhouse effect; and (2) conduct a couple of simple experiments to investigate how the model (and perhaps the earth) behaves.

You will be given a conceptual diagram of an extended version of the simple STELLA heat budget model above that includes separate (but interacting) budgets for the earth's surface and the atmosphere, in which each is treated as a single layer with a uniform composition (the simplest possible model that has any chance of capturing the essence of the greenhouse effect). The conceptual model uses STELLA's symbolic conventions.


     (1) Part II of the handout, "Supplement to Lab Activity #13: A Simple STELLA Model of the Planetary Heat Budget with a Greenhouse Effect", describes the equations for the extended version of the STELLA model. You should compare these equations to the diagram of the extended model so that you can identify the parts of the model to which each equation applies. Some model components will have values calculated from a quantitative relation between the component and one or more other model components. The remaining model components must be assigned specific values that they retain throughout any given model "run". Assign values to the latter components, justifying your choices when necessary. Use Part II of the handout, "Supplement to Lab Activity #13: A Simple STELLA Model of the Planetary Heat Budget with a Greenhouse Effect", and Figure 3.31 from Lab Activity #5 for guidance.

     (2) [2 pts] For convenience, the model should start with no heat at all in either the atmosphere or the surface layer. Working with your own copy of the model, set up a single graph that plots the temperatures of the earth's surface and the atmosphere plus the effective radiating temperature of the planet as a whole, and run the model for long enough for each temperature to come as close to equilibrium is it can get. (There will be a small annual cycle associated with the variation in distance between the earth and the sun, so it will be at equilibrium only twice a year, at the maximum and minimum in the annual cycle.) This will be the "control" run of the model.

    1. Print a copy of the graph and clearly label each of the three temperature curves with the corresponding final equilibrium temperature (along with anything else that would benefit from a label or a clearer label).

    2. Briefly summarize the evolution of the three temperatures over the period of the model run.

    3. As we found in Lab Activity #4, Part V, the earth's effective radiating temperature at equilibrium, as determined from satellite observations of the global average intensity of longwave infrared radiation that the earth emits to space, is around 255K. How does your model planet's effective radiating temperature compare to the observed value? How does your model's equilibrium surface temperature compare to the observed global average surface temperature?

    4. Is the effective radiative temperature of the planet, as calculated by the model at equilibrium, closer to the equilibrium atmosphere or surface temperature? Explain why.

     (3) [3 pts] Clear the plots from the graph. Now design two experiments in which you change one or more otherwise constant parameters in the model and rerun the model for each experiment. At least one of the two experiments should affect the strength of the greenhouse effect.

    1. For each experimental model run, print a copy of the graph and label it clearly.

    2. Briefly describe each experiment, including the rationale for your choice of the parameter(s) that you chose to modify.

    3. Compare the three temperatures and their evolution to those in your "control" model run in (2) above. Try to account for the differences that you observe.

    4. Turn in your three graphs, descriptions, and analysis with your name on it.

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