In this activity, we’ll explore some relatively simple aspects of Earth’s climate system, through the use of several STELLA models. STELLA models are simple computer models that are perfect for learning about the dynamics of systems — how systems change over time. The question of how Earth’s climate system changes over time is of huge importance to all of us, and we’ll make progress towards understanding the dynamics of this system through experimentation with these models. In a sense, you could say that we are playing with these models, and watching how they react to changes; these observations will form the basis of a growing understanding of system dynamics that will then help us understand the dynamics of Earth’s real climate system.
It is a computer program containing numbers, equations, and rules that together form a description of how we think a system works — it is a kind of simplified mathematical representation of a part of the real world. Systems, in the world of STELLA, are composed of a few basic parts that can be seen in the diagram below:
A Reservoir is a model component that stores some quantity — thermal energy in this case.
A Flow adds to or subtracts from a Reservoir — it can be thought of as a pipe with a valve attached to it that controls how much material is added or removed in a given period of time. The cloud symbols at the ends of the flows signify that the material or quantity has a limitless source, or sink.
A Connector is an arrow that establishes a link between different model components — it shows how different parts of the model influence each other. The labeled connector, for instance, tells us that the Energy Lost Flow is dependent on the Temperature of the planet.
A Converter is something that does a conversion or adds information to some other part of the model. In this case, Temperature takes the thermal energy stored in the Reservoir and converts it into temperature.
To construct a STELLA model, you first draw the model components and then link them together. Equations and starting conditions are then added (these are hidden from view in the model) and then the timing is set — telling the computer how long to run the model and how frequently to do the calculations needed to figure out the flow and accumulation of quantities the model is keeping track of. When the system is fully constructed, you can essentially press the ‘on’ button, sit back, and watch what happens.
Our first model is slightly more complicated than the diagram shown above because there are quite a few other parameters that determine how much energy is received and emitted and how the temperature of the Earth relates to the amount of thermal energy stored. The complete model is shown below, with three different sectors of the model highlighted in color:
The Energy In sector (yellow above - albedo, solar constant, surf area, and insolation) controls the amount of insolation absorbed by the planet. The Solar Constant converter is a constant, as the name suggests — 1370 Watts/m2. This is then multiplied by the cross-sectional area of the Earth — this is the area that faces the Sun — giving a result in Watts (which you should recall is a measure of energy flow and is equal to Joules per second). This is then multiplied by (1 – albedo) to give the total amount of energy absorbed by our planet. In the form of an equation, this is:
S is the Solar Constant (1370 W/m2), Ax is the cross-sectional area, and a is the albedo (0.3 for Earth as a whole).
The Energy Out sector (blue above - surf area, LW int, LW slope) of the model controls the amount of energy emitted by the Earth in the form of infrared radiation. This is simply described by the Stefan-Boltzmann Law as being the surface area times the emissivity times the Stefan-Boltzmann constant times the temperature raised to the fourth power:
A is the whole surface area of the Earth, e is the emissivity, s is the Stefan-Boltzmann constant, and T is the temperature of the Earth.
The Temperature sector (brown above - water density, ocean depth, heat capacity, temp) of the model establishes the temperature of the Earth’s surface based on the amount of thermal energy stored in the Earth’s surface. In order to figure out the temperature of something given the amount of thermal energy contained in that object, we have to divide that thermal energy by the product of the mass of the object times the heat capacity of the object. Here is how it looks in the form of an equation (with units added):
Here, E is the thermal energy stored in Earth’s surface [Joules], A is the area of the planet [m2], d is the depth of the oceans involved in short-term climate change [m], ρ is the density of sea water [kg/m3] and Cp is the heat capacity of water [Joules/kg°K]. We assume water to be the main material absorbing, storing, and giving off energy in the climate system since most of Earth’s surface is covered by the oceans. The terms in the denominator of the above fraction will all remain constant during the model’s run through time — they are set at the beginning of the model and can be altered from one run to the next. This means that the only reason the temperature changes is because the energy stored changes.
The model has a few other parts to it, including the initial temperature of the Earth, which determines how much thermal energy is stored in the Earth at the beginning of the model run. There are also some converters that divide the energy received and the energy emitted by the surface area of the Earth to give a measure of the intensity of energy flow, of the flux, in terms of Watts/m2, which is a common form for expressing energy flows in climate science.
One unit of time in this model is equal to a year, but the program will actually calculate the energy flows and the temperature every 0.01 years.
Now that you have seen how the model is constructed, let’s explore it by doing some experiments. Here is the link to the model [2].
What will happen to the temperature of the Earth if we run the model for 30 years with the following initial conditions:
Initial Temp = 0°C
Albedo = 0.3 (this will not change over time)
Emissivity = 1.0 (this will not change over time)
Ocean Depth = 100 m (this will not change over time)
Solar Constant = 1370 W/m2
These are the values you see when you first launch the model.
Once you are done answering the questions below, enter your answers into the Module 3 Lab Submission (Practice) to check your answers. If you didn’t do as well as you'd hoped, review the course materials, including the instructional videos, or post questions to the Yammer group to ask for clarification of a particular topic or concept. After that, open the Module 3 Lab Submission (Graded) and complete the graded version of the lab. The graded lab mostly includes questions similar to the practice lab, but has some additional questions.
Download this lab as a Word document: Lab 3: Climate Modeling [4] (Please download required files below.)
Use this Model for Questions 1 - 4. [5] Please Note: The model in the videos below may look slightly different than the model linked here. Both models, however, function the same.
How will changing the initial temperature affect the model? We saw that when we started with an initial temperature (remember that this is the global average temp.) of 0°, the model ended up with a temperature of about -18°C. What will happen if we start with a different initial temperature? Change the initial temperature to 1, then run the model and take note of the ending temperature by placing your cursor over the curve at the right-hand side (where the time is 30 years) and then click and you should see the little box that tells you the position of your cursor. You should round this temperature to the nearest whole number. Select your answer from the following:
A. 10°
B. -8°C
C. -18°C
D. -33°C
Click on the Restore all Devices button when you are done, before going on to the next question.
What will happen to our climate model if we change the albedo? Recall that a low albedo represents a dark-colored planet that absorbs lots of solar energy, while a higher albedo (it can only go up to 1.0) represents a light-colored planet that reflects lots of solar energy. Change the albedo to 0.5, then run the model and find the ending temperature, and select your answer from the following:
A. about -38(plus or minus 1)
B. about 2 (plus or minus 1)
C. about -1 (plus or minus 1)
D. about -16 (plus or minus 1)
Click on the Restore all Devices button when you are done, before going on to the next question.
Next, we will see what happens when we change the emissivity. Recall that if the emissivity is 1.0, the planet has no greenhouse effect and as the emissivity gets smaller, it represents a stronger greenhouse effect — so, how will this change our climate model? Change the emissivity to 0.3, then run the model and find the ending temperature, and select your answer from the following:
A. about -18 (plus or minus 1)
B. about 47 (plus or minus 1)
C. about 16 (plus or minus 1)
D. about 71 (plus or minus 1)
Click on the Restore all Devices button when you are done, before going on to the next question.
The solar constant is not really constant for any length of time. For instance, it was only 70% as bright early in Earth’s history, and it undergoes smaller, more rapid fluctuations (and much smaller) in association with the 11-year sunspot cycle. Let’s see how the temperature of the planet reacts to changes in the solar constant. First, we need to run a “control” version of our model, as is shown in the video above. Set the model up with the following parameters:
Initial Temp = 15°C
Albedo = 0.3
Emissivity = 0.6147 (enter the value manually in the box)
Ocean Depth = 100 m
Solar Constant — alter graph as shown in the video. Note the lines in the Solar Constant graph do not line up exactly with numbers. To get the exact number (1372) click on the Solar Constant Plot, then on Graph and enter the value at X=15 Y-1372.
Record the peak temperature (should be 15.04 deg C) and the time lag (should be 1.7 years).
What we are going to look at now is how the ocean depth affects the way the model responds to this spike in the solar constant. In our control, the ocean depth is 100 m — this means that only the upper 100 m of the oceans are involved in exchanging heat with the atmosphere on a timescale of a few decades. If the oceans were mixing faster, this depth would be greater, and if they were mixing more slowly, the depth would be less. Change the ocean depth to 50 m. Then run the model and note the peak value of the temperature and estimate the lag time, for comparison with the control version. Select your answer from the following:
A. Peak temp > control; lag time > control
B. Peak temp < control; lag time > control
C. Peak temp > control; lag time < control
D. Peak temp < control; lag time < control
Use this Model for Question 5. [6] Please Note: The model in the videos below may look slightly different than the model linked here. Both models, however, function the same.
Now, we’re ready to try something more challenging and more realistic. In the real world, the surface temperature has a big impact on the albedo — when it gets very cold, snow and ice will form and increase the albedo. So, there is a feedback in the system — a temperature change will cause an albedo change, which will cause a temperature change, and so forth. To explore this feedback, we need to work with an altered version of the model [7], where we have defined the relationship between albedo and temperature as follows:
This graph implies that there is a kind of threshold temperature of about -10 to -15°C, at which point the whole planet becomes frozen. The suggestion is that even with a very cold global temperature of 0 °C, the equatorial region might be relatively ice-free and would thus have a low albedo, but as the temperature gets colder, even the tropics become covered by snow and ice. Once that happens, the planetary albedo changes only slightly. Likewise, at higher temperatures, the albedo decreases only slightly since there is so little snow and ice to remove.
This important to understand what this model includes — a link between planetary temperature and planetary albedo. As the temperature changes, so the albedo changes, and as the albedo changes, so the insolation changes, and as the insolation changes, so the temperature changes — this is a feedback mechanism. Feedback mechanisms are very important components of many systems, and our climate system is full of them.
By definition, feedback mechanisms are triggered by a change in a system — if it is in steady state, the feedbacks may not do much. In the above graph, you may notice that at a temperature of 15°C (our steady state temperature), the albedo is 0.3, which is the albedo of our steady state model. So, if we run the model with an initial temperature of 15 °C, and an unchanging solar constant of 1370, our system will be in a steady state and we will not see the consequences of this feedback. But, if we impose a change on the system, things will happen.
The change we will impose involves the greenhouse effect. The model includes something called the CO2 Multiplier. When this has a value of 1, it gives us a CO2 concentration of 380 ppm, which is the default value that gives us a temperature of 15°C. If we change it to 2, we then have 760 ppm and a stronger greenhouse, which leads to warming. If we change it to 0.5, we then have 190 ppm and a weaker greenhouse, thus cooling.
You will be given a value for the CO2 Multiplier; enter that into the model and run it with the Albedo Switch in the off position (see the video) and note the ending temperature. Then turn the Albedo Switch on, which activates the feedback mechanism, and run the model again, noting the ending temperature. The difference between these two temperatures is what you need for your answer. For example, if you set the CO2 Multiplier to 3 and run the model with the Albedo Switch turned off, you see an ending temperature of 18.17°C, and then with the switch turned on, the ending temperature is 24.86°C, so the temperature difference due to the albedo feedback is +6.69°C — this is the answer you would select.
What is the temperature difference due to the albedo feedback? Choose the answer that most closely matches your result. Be sure to study page 3 of the graph pad to get your results.
A. about -5°C
B. about +11°C
C. about +18°C
D. about -20°C
Causes of Climate Change
Use this Model for Questions 6-7. [8] Please Note: The model in the videos below may look slightly different than the model linked here. Both models, however, function the same.
Things that can cause the climate to change are sometimes called climate forcings. It is generally agreed upon that on relatively short time scales like the last 1000 years, there are 4 main forcings — solar variability, volcanic eruptions (whose erupted particles and gases block sunlight), aerosols (tiny particles suspended in the air) from pollution, and greenhouse gases (CO2 is the main one). Solar variability and volcanic eruptions are obviously natural climate forcings, while aerosols and greenhouse gases are anthropogenic, meaning they are related to human activities. The history of these forcings is shown in the figure below.
Volcanoes, by spewing ash and sulfate gases into the atmosphere block sunlight and thus have a cooling effect. This history is based on the human records of eruptions in recent times and ash deposits preserved in ice cores (which we can date because they have annual layers — we count backward from the present) and sediment cores for older times. Note that although the volcanoes have a strong cooling effect, the history consists of very brief events. The solar variability comes from actual measurements in recent times and further back in time, on the abundance of an isotope of Beryllium, whose production in the atmosphere is a function of solar intensity — this isotope falls to the ground and is preserved in ice cores. The greenhouse gas forcing record is based on actual measurements in recent times and ice core records further in the past (the ice contains tiny bubbles that trap samples of the atmosphere from the time the snow fell). The aerosol record is based entirely on historical observations and is 0 earlier in times before we began to burn wood and coal on a large scale.
In this experiment, we will add the history of these forcings over the last 1000 years and see how our climate system responds, comparing the model temperature with the best estimates for what the temperature actually was over that time period. Solar variability, volcanic eruptions, and aerosols all change the Ein or Insolation part of the model, while the greenhouse gas forcing change the Eout part of the model. We can turn the forcings on and off by flicking some switches, and thus get a clear sense of what each of them does and which of them is the most important at various points in time.
We can compare the model temperature history with the reconstructed (also referred to in the model as “observed”) temperature history for this time period, which comes from a combination of thermometer measurements in recent times and temperature proxy data for the earlier part of the history (these are data from tree rings, corals, stalactites, and ice cores, all of which provide an indirect measure of temperature). This observed temperature record, shown in graph #1 on the model, is often referred to as the “hockey stick” because it resembles (to some) a hockey stick with the upward-pointing blade on the right side of the graph.
First, open the model [9]with the forcings built-in, and study the Model Diagram to get a sense of how the forcings are applied to the model. If you run the model with all of the switches in the off position, you will see our familiar steady state model temperature of 15°C over the whole length of time. The model time goes from the year 1000 to 1998 because the forcings are from a paper published in 2000.
Graph #1 plots the model temperature and the observed temperature in °C, graph #2 plots the 4 forcings in terms of W/m2, graph #5 plots the cumulative temperature difference between the model and the observed temperature (it takes the absolute value of the temperature difference at each time step and then adds them up — the lower this number at the end of time, the closer the match between the model and the observed temperatures), and graph #6 shows the same thing, but it begins keeping track of these differences in 1850, so it focuses on the more recent part of the history. Graph #1 gives you a visual comparison of the model and the observed temperatures, while graphs #5 and 6 give you a more quantitative sense of how the model compares with reality.
Before running the model set the ocean depth to 50 m. Run the model 4 times with each of the forcing switches turned on separately (i.e., only one forcing switch turned on for each model run) and evaluate which of the forcings does the best job of matching the shape of the observed temperature curve from 1800 to 1998. Which one provides the best match?
A. GHG
B. Aerosols
C. Volcanoes
D. Solar
Before running the model, set the ocean depth to 150 m. Run the model 3 times — once with only the natural forcing switches turned, once with only the anthropogenic forcings turned on, and once with all of them turned on. Which combination does the best job of matching the shape of the observed temperature curve from 1800 to 1998?
A. natural forcings
B. anthropogenic forcings
C. all forcings
D. natural and anthropogenic forcings are about the same.
Links
[1] https://creativecommons.org/licenses/by-nc-sa/4.0/
[2] https://exchange.iseesystems.com/public/davidbice/earth103-m3q1-4/index.html#page1
[3] https://www.youtube.com/channel/UCU1QB1a5XJa_nTHD2lzr7Ew
[4] https://www.e-education.psu.edu/earth103/sites/www.e-education.psu.edu.earth103/files/module03/Earth103%20Lab%203-RevSept2020.docx
[5] https://exchange.iseesystems.com/public/davidbice/earth103-m3q1-4
[6] https://exchange.iseesystems.com/public/davidbice/earth103-m5q5
[7] https://exchange.iseesystems.com/public/davidbice/earth103-m5q5/index.html#page1
[8] https://exchange.iseesystems.com/public/davidbice/earth103-m3-q6-7
[9] https://exchange.iseesystems.com/public/davidbice/earth103-m3-q6-7/index.html