UCAR's Simple Climate Model

UCAR's The Very, Very Simple Climate Model (a flash based application) displays a graph of expected future temperatures based on projected CO2 emissions. It is highly interactive and allows you, the user, to define scenarios combining past, historical data with future emissions of your choice to see how the temperature will change (according to their model). Before reading the rest of this page, I suggest that you access their model and familiarize yourself with it.

In an effort to understand how the model works, I used an swf (flash) decompiler to recover the internal model and the seed (historical) data. Then I implemented an identical model in this OpenOffice spreedsheet. The purpose of this page is to present what I learned.

Spoiler: This analysis demonstrates that the supplied data disproves the association between CO2 and temperature, assuming the default sensitivity of 3.0°C/doubling. However, additional analysis using my GHCN Temperature Plotter tool indicates a pretty good correlation if the sensitivity is reduced to 1.8°C/doubling.

UCAR's Model

UCAR's flash model can be found via UCAR interactives and clicking THE VERY, VERY SIMPLE CLIMATE MODEL. I think it is pretty cool.

You can use it to define future scenarios with various CO2 levels
Under Settings, you can change the Climate Sensitivity from 2.0°C to 5.0°C in 0.5°C steps

However

Flash won't run on many Apple devices
While the provided historical data starts in 1800, the model's starting year is 1960 - as a result, you can't see how bad the fit-to-theory is
There is no way to plot actual (historical) temperature against values predicted using the supplied CO2 concentrations

The purpose of my analysis was to address the last 2 points.

By the way, the NSTA (National Science Teachers Association) recomends this tools to help teach students in grades 6 thru 8 about "climate science".

The Equation

The main equation used to associate a change in temperature to a change in CO2 concentration is the same as the one used by the IPCC and most scientists supporting the CO2 causes Global Warming position.

ΔT = A * log([CO2]/[CO2₀])

where

"A" is known as the "climate sensitivity".
[CO2] is the current CO2 concentration
[CO2₀] is the CO2 concentration at some reference point - my model uses 280 ppm in 1800 AD, theirs uses 369.41 ppm and 14.4°C from about 2000 AD

In this equation, the base of the log is not important - if a different base is selected the value of "A" is changed and the results will still be the same. For this UCAR model, log-base-2 is used.

For log-base-2, the value of "A" is the number of degrees-C the temperature changes for a doubling of CO2. Their default value is 3°C

A table of climate sensitivities (°C) predicted by various models - IPCC AR4
The values range from 2.1 to 4.4

In addition, the reference temperature and CO2 concentration are of little importance because they don't change the shape of the curves and only produce an offset in the vertical direction.

UCAR provides additional details on the associated activity page - select the Background and Extensions tab, scroll down to the Details of the Math Behind the Model section.

Reference issue

At this time, I am not able to find an IPCC equation relating a change in temperature to a change in CO2. However, I did find the following equation (from IPCC FAR (1990), Chapter 2, Radiative Forcing of Climate page 52, Table 2.2) that computes the forcing (in W/m2).

ΔF = 6.3 ln(C/C₀) coefficient derived from Hansen et al (1988)

Values derived from Hansen et al have been multiplied by 3.35 (Lacis, personal communication) to convert forcing as a temperature change to forcing as a change in net flux at the tropopause after allowing for stratospheric temperature change

Then the change in temperature must be computed from the change in forcing. Based on the IPCC comment, a simple division will suffice. Perhaps - but this type of conversion normally depends on the base temperature to the fourth power, some rearranging of terms, and a fourth root.

6.3/3.35 * log₂(e) = 2.713°C/doubling

which is close to 3 - the default UCAR model climate sensitivity when using a log of base 2

When using my tool, the best fit is actually about 1.8°C/doubling - significantly below Hansen's (presumed) value of 2.713°C/doubling.

Plots

These are the charts from the spreadsheet.

Blue	This is the temperature provided in the UCAR seed data
Orange	This is the temperature computed using A=3°C - the model's default value
Yellow	This is the temperature computed using A=1°C

To be clear, the orange and yellow series are the expected temperatures based on their CO2 data and their model. Since their flash application does not provide a way to show the fit between their model and historical data, I produced these plots for that purpose. Since this is a spreadsheet, and because I am providing you a copy, you can change the climate sensitivity (A) to any value you want.

If the model was correct, then the computed temperature (the orange diamonds) should overlap the historical temperatures (the blue squares) in both plots. The fact that they aren't even close demonstrates, without a doubt, that CO2 does not affect the temperature in the way the model claims.

The fact that I used a different calibration point than the UCAR model (see next section) really has no effect. The shape of the computed temperature curve should still be the same - but with an offset in the vertical direction.

The Temperature vs CO2 plot could be interpreted to show that above 370 ppm, increased CO2 either has no effect, or might actually cause the temperature to decrease. However, I want another 20 years of data before claiming something that radical ... but it is what their data shows.

And this is the real problem - since the UCAR model starts in 1960, it shows a close correlation between the theory and the actual data. The complete lack of agreement is only visible when all the data is used! In my opinion, this would be cherry picking of the worst kind ... except that they did not bother to even show that much data on their plots. To be clear - their model tacks projected data on to historical data without showing any overlap between the historical and projected temperatures. (By overlap I mean showing both the historical and modeled data for the same time period on the same plot.) The graphs above show the overlap .. and lack of agreement.

(To be fair, if I had not found such a blatant discrepancy I probably would not have produced this page. I was analyzing the model so that I could use the base formula in another program. The plots were made just to test the accuracy of the model. I expected poor agreement - but nothing this dramatic.)

Notes

These are just a few notes about the model. This is the key model statement

 this._temperature = this._baselineTemperature + this._climateSensitivity * Math.LOG2E * Math.log(this._co2Concentration / this._baselineCO2Concentration);

located in

  public class World extends Object

Other useful statements.

 this._climateSensitivity = 3; // 3°C per doubling CO2

  public function set climateSensitivity(param1:Number) : void
  {
     this._climateSensitivity = param1;
  }

 private var _baselineTemperature:Number = 14.4008;
 private var _baselineCO2Concentration:Number = 369.41;

_climateSensitivity can be changed via the Settings dialog - 2.0°C to 5.0°C in 0.5°C steps
The default temperature and CO2 concentration appear to be near 2000 AD, but don't match any values in the table
_baselineCO2Concentration and _baselineTemperature can be reset depending on the baseline year, but the current application does not allow the user to change those values.

GHCN Temperature Plotter

I was not very happy with the spreadsheet plots

Too difficult to modify the parameters - sensitivity and base year
Not able to compare data with other sources (such as GHCN)
Users need to download the data and open it in a spreadsheet to modify the parameters

As a result, I modified my GHCN Temperature Plotter tool to simplify parameter modification and provided full instructions on how to use the new CO2 tab.

I found that the best fit uses a base year of 1975 (the UCAR model uses 2000, the spreadsheet uses 1800) and the doubling is actually about 1.8°C - significantly below Hansen's (presumed) value of 2.713°C/doubling and the UCAR model's default of 3°C/doubling.

In the UCAR model, the base year is not important since they do not show both the model results and the historical data for each year - they just tack the model results on to the end of the historical data. As a result, there is no way for anyone to make a judgment on the validity of their model. In my opinion, .. well, I don't think much of their model.

Seed Data

This is the data used to seed the UCAR model. It is the same data used in the spreadsheet to produce the graphs and in my GHCN Temperature Plotter tool. I have not attempted to verify this data but have simply accepted it as presented.

co2Emissions	Gt - "10" probably means "unknown"
co2Concentration	ppm (parts per million)
temperature	°C

According to NASA, the average temperature of the Earth is 15°C
The U.S. Standard Atmosphere, 1976 document says (on page 20) that The International Standard Atmosphere sea-level temperature of 15�C was adopted in 1924 by Resolution 192 of the International Commission for Air Navigation.

Yet, none of the values in the provided table are that high. In fact, the UCAR data sets the temperature in the 1920's to be about 13.7°C!

Conclusions

It should be obvious from the plots that increasing CO2 has no effect on the temperature.

The other interpretation is that the supplied historical data is wrong - very wrong.

Either way, after a failure of this magnitude, all UCAR interactive models must be considered suspect. Use caution.

Author: Robert Clemenzi