Long-term Climate Regulation

 


OBJECTIVES

The objectives for this lab include improving your skills at modeling, which you will need for your final class project, and developing an understanding of how the Earth’s carbon cycle has changed over time, and how it has affected climate by changing our planetary energy balance. This theme was introduced early in the lectures for the class, and at this point in the semester we are ready to synthesize the two main themes of carbon cycling and Earth's energy balance by combining elements of the carbon cycle lab and the energy balance lab. In terms of the potential applications of such a task, consider that you are employed as a systems analyst at an international company working on providing sustainable, integrated plans for environmental protection and restoration in a large country in, e.g., Africa or S. America or Asia (etc.). Your boss has asked you to explain how the “system” of global temperature, greenhouse gases, and planet energy balance actually operates, and not just in the present but over very long periods of time. You are borrowing from Earth’s history in order to produce a sustainable plan, and your task is to look at millions of years of history and describe how the “system” operates, which is the gateway task needed to develop the environmental protection and restoration plan your company needs.

 

1 Introduction

Earth’s climate has changed through time. There have been ice ages and ice-free periods. Yet, for most of Earth’s 4.5 billion years, the temperature has been hospitable, not too cold nor too hot for life of some kind. The regulation of climate through geologic time has been attributed to interactions between the climate system and the carbon cycle. In this lab, you’ll investigate these interactions and how they have regulated Earth’s climate.

 

Long-term carbon cycle

The carbon cycle describes changes in the fluxes and reservoirs of carbon in the Earth system (Fig. 1). On very long time-scales, millions of years, the primary reservoirs of carbon are the atmosphere, ocean, and rocks (limestone). Carbon moves between these reservoirs through volcanic outgassing, silicate weathering, and limestone sedimentation. The carbon cycle is linked to Earth’s energy balance through atmospheric carbon in the form of CO2, a greenhouse gas.

 

 

Fig. 1. Schematic of the long-term carbon cycle (from Bice, 2001)

 

 

Earth’s energy balance

As you learned in the Energy Balance Lab, the energy balance between incoming shortwave radiation and longwave outgoing radiation determines Earth’s climate (Fig. 2). The net incoming shortwave radiation is influenced by the Sun’s luminosity and Earth’s albedo. The net outgoing longwave radiation is a function of Earth’s temperature (through black-body radiation) and the greenhouse effect. Earth’s climate affects the carbon cycle through temperature, which modifies the rate of silicate weathering and the rate that carbon dioxide is removed from the atmosphere.

 

 

 

Fig. 2. Schematic of the climate system (from Bice, 2001)

 

 

2 Exploring the Long-Term Carbon Cycle

A model of the long-term carbon cycle has already been developed for you. This model was designed by David Bice (2001). Start by opening the Stella model (carboncycle model you must right click and save link as). In its current form, the carbon cycle is not linked to the climate system. This is a good place to start in order to understand how the long-term carbon cycle works without the complicating influence of climate.

 

Model Operation Notes:
1. Check to confirm or change your Run Specs so they are the same as those in Table 1 below. In addition, change “Sim Duration” to at least 5 seconds so you can see how carbon flows through all three stocks in the numerical displays
2. Make Graph 1, which includes the variables ATMOS C, OCEAN C, LIMESTONE. In graph settings, check "Multiscale". Create numeric displays (figure 8 button) with 'full precision' in the formatting option for each of these variables as well. Run the model. The model should be in steady state. Note the different sizes of the carbon reservoirs.
3. Settings: For each numerical display (ATMOS C, OCEAN C, LIMESTONE), insert the display, select one of the variables, and click “Formatting” from the dropdown arrow. Then, under the “Precision” option, change “Auto precision” to “Full precision”. This is the only way you’ll be able to see the changes in the Ocean and Limestone carbon stocks.

 

Note the following abbreviations for this model: ATMOS = atmosphere, C = carbon, DT = delta temperature, SW = short wave, LW = long wave, SURF = surface, SFC = surface, Gt = gigaton, ABS = absorption.

 

Table 1. Carbon model run spec parameters. (Note: DT here is the time step)

Length of Simulation

DT (Myrs)

Integration Method

0 to 10 (Myrs)

0.005

RK2 (Runge-Kutta 2)

 

 

Q 1. The response time is how long the system takes to re-establish steady state after a perturbation. Double the ATMOS C reservoir from 600 Gt C (gigatons of carbon) to 1200 Gt C. Run the model, again graphing ATMOS C, OCEAN C, LIMESTONE. What is the response time of the long-term carbon cycle? Remember that time here is in millions of years. Where did the excess carbon end up? Did it remain in the ATMOS C reservoir? Explain this result using concepts from class. (2.5 points)

 

Q 2.  Return the ATMOS C reservoir to its initial condition so that you can test how the model responds to a temperature perturbation. First, make your own prediction. Next, test your prediction. Increase the external DT converter to 1. This represents a 1 K (1 °C) increase in global temperature. Run the model. Graph ATMOS C, OCEAN C, LIMESTONE. How did the distribution of carbon between reservoirs change after increasing the external DT? Why? Explain your answer in terms of changes in carbon fluxes between reservoirs. You must support your answer with numerical results from the model. (2.5 points)

 

 

3 Exploring the Climate System

A model of the Earth’s energy balance has already been developed for you as well. This model was also designed by David Bice (2001) at Penn State University . Start by opening the Stella model (ebm model you must right click and save link as). This model is slightly, but not much, more complicated than the one that you created in the Earth Energy Balance Lab. Remember in that lab, we determined that our model was insufficient to predict surface temperatures accurately because it did not include an atmosphere. This climate model includes an atmosphere, and estimates longwave fluxes in the atmosphere, as well as at the surface.

 

Check to confirm that your Run Specs are the same as those in Table 2 below. Graph SFC TEMP (Surface Temperature). Run the model. The model should be in steady state.

 

Table 2. Climate model run spec parameters. (Note: DT here is the time step)

Length of Simulation

DT (yrs)

Integration Method

0 to 10 (yrs)

0.01

RK2

 

Q 3. Our primary goal in this lab is to investigate climate-carbon cycle interactions. To begin, explore how the climate system responds to perturbations in the absence of the carbon cycle. Let’s perturb the system by changing the Solar Input, the percent of Sun’s radiation received by Earth. This experiment isn’t entirely unrealistic. Remember that Sun’s luminosity has increased with time at a rate of 1% per 100 million years. Run the model (a new run each time) trying values of 99, 98, 97, 95, 80. Set your numeric value tool to display SFC DT, and set the precision to 0.00 (two decimal points). Record this value in the table below. Summarize in words what the table means. (2.5 points)

 

Solar Input

SFC DT

100

0.00°

99

 

98

 

97

 

95

 

80

 

 

***Return Solar Input from your model to 100 before the next step.***

 

4. Climate Regulation by Carbon Cycling

Now, it’s time to link our carbon cycle model and our energy balance model. This requires a fair amount of manipulation in Stella, excellent practice for you to hone your modeling skills. 

 

Start by copying and pasting the entire energy balance model into the window with your carbon cycle model using the tools in the Edit menu. Note: Put the Energy Balance model that we give you in this lab into the Carbon Cycle model (not the reverse). Hint: Use Edit -> Select All, then Edit -> Copy. Hint: before pasting, click in the far corner of your model space so that your models don't overlap. 

 

To link the models, you need to make a few modifications:

(1) Delete the SFC DT and external DT converters from the carbon cycle model.

 

(2) Create a radiative forcing converter and connect it to the LW SPACE flow. Also connect the relative atmos C converter to the radiative forcing converter. Double click on the new radiative forcing converter and add the following equation:

 

5.35*LN((relative_atmos_C + 0.0000000000001)/280)

 

This equation defines the relationship between CO2 and radiative forcing. The relationship is logarithmic. As atmospheric CO2 increases, the radiative forcing increases by a smaller and smaller amount.

 

(3) Double click on the relative_atmos C converter. Modify the equation by multiplying by 280 (the pre-industrial concentration of CO2). It should read:

 

(ATMOS_C/600)*280

 

(4) Modify the LW SPACE equation to include the radiative forcing from the carbon cycle model, and multiply this term by 10 (see explanation in step 6). The equation should be:

 

(60*((ATMOS_TEMP/255)^4) – radiative_forcing)*10

 

(5) Rename SFC DT_1 to SFC DT. Connect the SFC DT converter to weathering.  

 

(6) And, finally, multiply the SW ATMOS, SW SURF, LW ATMOS, LW SURF, and the SFC LW SPACE flows by 10 (put the existing equation in parentheses " ( ) " first!). This is a little sleight of hand. The energy balance model and the carbon cycle model operate on very different time scales (years versus millions of years). As far as the carbon cycle is concerned, the atmosphere responds immediately. However, Stella requires that the models operate on the same, long time scale. By multiplying the energy balance fluxes by 10, we’re essentially running the climate system on a slightly shorter time scale. This trick isn’t perfect, but will work as long as our focus is the steady state answers.

 

Fig. 3. Schematic of the climate-geochemical model in Stella.

 

Check to confirm that your Run Specs are the same as those in Table 3. Also make sure that you returned the Solar Input to 100. Run the climate-geochemical model. Graph SFC TEMP. The model should have a steady state temperature of 288 K.

 

Table 3. Model run spec parameters

Length of Simulation

DT (Myrs)

Integration Method

0 to 20 (Myrs)

0.005

RK2

 

 

Q 4. Let’s compare solutions from our climate model (energy balance model) with our climate-geochemical model. As above, perturb the system by changing the Solar Input. Again use values of 99, 98, 97, 95, 80. Record the change in Earth’s surface temperature (SFC DT) in a table. Compare the solutions using the climate model (energy balance model) and the coupled climate-geochemical model. Explain why the solutions are different. Specifically address how climate-carbon cycle interactions affect the final global average temperature. (Hint: Remember that this lab focuses on the long-term carbon cycle). (2.5 points)

 

 

Solar Input

SFC DT

100

0.00°

99

 

98

 

97

 

95

 

80

 

 

Lab Assignment:

Turn in a Word document on Canvas that includes answers to all 4 questions and include the 2 tables. Make sure to number and label your tables.