Climate scientists use models to understand how the Earth is changing. Models of Earth can be experimented upon to assess the impact of changing factors - such as increasing global temperature, decreasing ice sheets, or increasing cloud cover - on the planet. Climate models describe our planet with mathematical equations. Because Earth is complex, it takes hundreds of very complex equations to model the atmosphere, oceans, and land surface. Because of the complexity, climate models are usually run on powerful supercomputers.
The Very Simple Climate Model is, as the name implies, very simple. In this model, average global temperature is determined entirely by the atmospheric carbon dioxide concentration via greenhouse warming of the atmosphere and uptake of carbon dioxide by the ocean and biosphere, which are kept constant through time. The impacts of changes to the biosphere (such as changes in land use), changes in clouds and weather, other greenhouse gases, and other factors are not considered by this very simple model.
George E.P. Box once said, "all models are wrong, but some models are useful." The more a complex system like Earth is simplified in a model, the more wrong the model is. However, in simplifying this model to temperature and carbon dioxide, The Very Simple Climate Model allows students to focus on the cause and effect relationships of greenhouse gases and climate change. A major educational point embodied in this model is that temperatures depend on CO2 concentration, which rises whenever emissions are greater than zero. When you hear world leaders saying that they are working hard to reduce the rate of growth of greenhouse gas emissions, remember that reducing the rate of growth does not lead to reduced temperatures. Instead, the amount of greenhouse gases continues to grow in the atmosphere whenever emissions are greater than zero.
The assumptions behind this model, though rather limited, are valid as far as they go. The starting values for CO2 concentration, carbon emission rate, and temperature are right around actual values for the year 2015 . The ranges for emission rate choices are in line with predictions scientists think we are likely to see in this century. The relationship between atmospheric carbon dioxide concentration and temperature is well-established; basically, temperature rises about 3° C for each doubling of carbon dioxide concentration. So, for example, if the concentration goes from 400 ppmv to 800 ppmv, we expect to see temperature go up by 3° C. As a reference, pre-industrial CO2 concentrations were at about 280 ppmv, compared to about 400 ppmv in 2015.
According to the Intergovernmental Panel on Climate Change (IPCC) and their 2014 Assessment Report, Earth's average temperature rose 0.6° Celsius (1.1°F) during the 20th Century. Based on the results from about a dozen computer models, the IPCC projects that global warming will continue. Model results project that Earth's average global temperature will rise between 1.8° and 4.0° Celsius (3.2° and 7.2° F) during this century, depending largely on whether humans change their actions to reduce carbon emissions, and if so, by how much.
Details of the Math Behind the Model
How does the CO2 emission rate affect the CO2 concentration?
About 55% of the emissions are absorbed by the ocean and biosphere, which means that 45% of the emissions wind up in the atmosphere. Every 2.3 GtC of the emissions that wind up in the atmosphere would raise atmospheric CO2 concentration by about 1 ppm based on estimates of the total quantity of CO2 in the atmosphere (in gigatons, abbreviated GtC) and of the CO2 concentration.
For example, if emissions were 10.5 GtC, 45% of that would end up in the atmosphere, which is 4.725 GtC. We would expect the CO2 concentration to rise by about 2 ppm ( = 4.725 GtC ÷ 2.3 GtC = 2.05) that year. Total global carbon emissions were around 9.2 GtC by 2006 and increased to 10.34 by 2015.
Also note that a very small amount of carbon (about 0.1% per year) finds its way out of the atmosphere naturally, which is also included in this model.
How does CO2 concentration affect temperature?
We know how much Earth's surface temperature will rise as CO2 levels increase based on both theory and observations. In general, doubling the atmospheric concentration of CO2 causes a certain amount of rise in average global surface temperature. The amount of temperature rise with double the CO2 is called the climate sensitivity.
According to the Sixth Assessment Report by the IPCC (Intergovernmental Panel on Climate Change), the climate sensitivity value is "likely to be in the range 2 to 4.5° C with a best estimate of about 3° C, and is very unlikely to be less than 1.5° C. Values substantially higher than 4.5° C cannot be excluded, but agreement of models with observations is not as good for those values." We have used 3° C for climate sensitivity in this simple model.
An example, if the CO2 level was 380 parts per million (ppm) when global average temperature was 14.5° C, and then the CO2 concentration rose to 760 ppm (2 x 380 ppm), we would expect global temperatures to rise roughly 3° C (5.4° F) to 17.5° C.
The formula used in the Very Simple Climate Model
|T = T0 + S log2 (C / C0)|
- T is the new/current temperature
- T0 is the know temperature at some reference time (for example, 14.3° C in the year 2000)
- S is the "climate sensitivity" factor (the temperature rise as a result of CO2 doubling)
- C is the new/current atmospheric CO2 concentration
- C0 is the known atmospheric CO2 concentration at some reference time (must be the same time as T0)
In the Very Simple Climate Model, the values for T0 and C0 are from the previous calculation. Calculations are made at five year increments.
More Sample Model Runs
There a few common types of carbon emission level scenarios your students might try with this simple model:
- What if carbon emissions were held at current levels?
- What if carbon emissions continue to rise?
- What if carbon emissions continue to rise during the first part of the 21st century, then are held stable or even reduced in the latter part of the century?
There are some important features of each of these scenarios, largely independent of the exact values used, that you might want to point out to your students.
- When CO2 emissions rise steadily, atmospheric CO2 concentration rises at an accelerating pace (its curve "bend upwards").
- Temperature rises less sharply than atmospheric CO2 concentration. This is because one must double the CO2 concentration in order to generate a fixed 3° C (or whatever climate sensitivity value you employ) increase in temperature.
- Even if emissions are reduced to zero, in this model the atmospheric CO2 concentration and temperature will not go back down. This simple model has, effectively, an infinite residence time for CO2 in the atmosphere.