Long-term Climate Regulation

 

1 Introduction

Earthís climate has changed through time. There have been ice ages and ice-free periods. Yet, for most of Earthís 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, youíll investigate these interactions and how they have regulated Earthís 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 Earthís 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)

 

 

Earthís energy balance

As you learned in the Energy Balance Lab, the energy balance between incoming shortwave radiation and longwave outgoing radiation determines Earthís climate (Fig. 2). The net incoming shortwave radiation is influenced by the Sunís luminosity and Earthís albedo. The net outgoing longwave radiation is a function of Earthís temperature (through black-body radiation) and the greenhouse effect. Earthís 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.

 

Check to confirm or change your Run Specs so they are the same as those in Table 1 below. Open Graph 1, which includes the variables ATMOS C, OCEAN C, LIMESTONE. Run the model. The model should be in steady state. Note the different sizes of the carbon reservoirs.

 

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

10 (Myrs)

0.005

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 įC) increase in global temperature. Run the model. Graph ATMOS C, OCEAN C, LIMESTONE. How did the distribution of carbon between reservoirs change? Why? Explain your answer in terms of changes in carbon fluxes between reservoirs, and support it with numerical results from the model. (2.5 points)

 

 

3 Exploring the Climate System

A model of the Earthís 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

10 (yrs)

0.01

Runge-Kutta 2

 

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. Letís perturb the system by changing the Solar Input, the percent of Sunís radiation received by Earth. This experiment isnít entirely unrealistic. Remember that Sunís 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

0.00į

99

 

98

 

97

 

95

 

80

 

 

Return Solar Input from your model to 100.

 

4. Climate Regulation by Carbon Cycling

Now, itís 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) Using the dynamite tool, blast away 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) Ė 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, weíre essentially running the climate system on a slightly shorter time scale. This trick isnít 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

20 (Myrs)

0.005

Runge-Kutta 2

 

 

Q 4. Letís 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 Earthís 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

0.00į

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.