The ‘Mathemagic’ of Climate Change

By now, most people have seen the chart shown below that many believe shows how increased atmospheric CO2 leads to an increase in global temperature. This presumed relationship has been used to justify numerous policies and actions by governments around the world with the aim of reducing, or even eliminating CO2 in the atmosphere. Whole national economies and numerous individual lives and livelihoods have been destroyed by these actions. Indeed, our own government is contemplating declaration of a National Emergency to address what they claim is a Climate Crisis.

Where is the truth? Is there really a crisis that demands a draconian response, or is the crisis a manufactured excuse to justify more control over our lives? The first chart below appears to answer that question.

This familiar chart shows two curves. The upper curve in red is a plot of CO2 measurements mostly by government observers atop Mauna Loa in Hawaii. The lower curve is the government's National Oceanographic and Atmospheric Administration (NOAA) estimates of the global temperature anomaly over time. The anomaly is just the difference between the estimated value and a reference value. Using the anomaly rather than the full temperature serves to emphasize trends, especially the rise in temperature.

The temperature anomaly in degrees C is shown in the scale on the left, while the CO2 concentration is shown on the right in parts per million (ppm).

Clearly, since the CO2 curve lies to the left of the temperature curve, one can see that rising CO2 causes a rise in temperature. This proves that increases in CO2 levels lead to increased temperature. The relationship is obvious and demonstrates that we need to curtail CO2 in order to prevent a catastrophic rise in temperature.

Or does it?

Look at the chart below, where the same data from the same sources is plotted.

Now the CO2 curve lies below and to the right of the temperature curve. What does that mean? We can clearly see that temperature was rising long before the reported rise in CO2. It would appear that the rising temperature is causing a rise in CO2 since the temperature rise happens first and then CO2 rises. Clearly this chart proves that a temperature rise causes a rise in CO2 levels.

How can it be that the same data supports two completely different conclusions? The answer is that neither chart "proves" anything.

The astute reader will notice that I changed the scales between the charts, increasing the amount of time shown, and changing the range of the CO2 value scale. These changes had the effect of causing the CO2 curve to be plotted below the temperature curve without actually changing any of the data values.

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Climate change activists are likely to cry "foul", claiming that I have simply changed how the data is presented in order to support a particular conclusion. In other words, I did the same thing they have done with the first chart, except that I am honest about it. Call it a bit of ‘mathemagic’ in presentation.

We can dig a bit deeper into the meaning of the two curves and why they can support two different conclusions. The first point to notice is that the CO2 data is much more limited than the temperature data. The instrumental record (record of actual measurements) of CO2 on Mauna Loa only goes back to 1979 when collections began. On the other hand, we have good temperature data back to 1850, at least for the US. For several reasons, though, both datasets are insufficient to determine a causal relationship.

One way of identifying cause in a time series of data is to look for inflection points—places where a curve changes direction. If there is a causal relationship, a related curve should also change direction. Lack of a corresponding change strongly indicates the two data sets are not causally related.

While there is a small inflection in the temperature data about 1910, there are no corresponding CO2 measurements and no corresponding inflection point. It is worth noting that coal was not generally used as an energy source until about 1850, and gasoline did not become prominent until after about 1910 when automobiles came into wide use.

As it turns out, there is good data available for both temperature and CO2 concentration that goes back for 800,000 years and more. Some time ago, a Russian team drilled deep into Antarctic ice and drew up a long core of frozen history.

Annual snowfalls trap bubbles of atmosphere as the snow compacts into ice, and certain isotope ratios give information of the average temperature at the time the snow fell. All of that is captured in the annual layers of ice, much like the annual rings record the history of a tree.

That initial core contained the history of over 400,000 years of snowfalls, atmospheric composition and temperature. Since then, many other teams have collected ice cores from locations in both hemispheres, some reaching back as far as 800,000 years. When analyzed, these cores give a fascinating detailed view of Earth's history.

The period includes records of at least eleven different ice ages, not just the last one that most of us learned about in school. As one might guess, there are many different inflection points included in the record as temperatures rose between ice ages, turned around to become cold, and then turned warm again as the ice age ended. With high consistency, what that record shows is that rather than causing temperatures to change, atmospheric CO2 concentrations followed changes in temperature!

The third piece needed to establish a causal connection, in addition to complete datasets, and turning points, is a mechanism that links the two sets together. As it turns out, just such a mechanism exists and is even well known to most of us, even if we haven't made the connection.

Unlike most other familiar materials like salt and sugar, where the amount that can be dissolved increases with increased water temperature, CO2 behaves differently. Cold water can dissolve the most CO2, with the least when the water is hot. This is why carbonated drinks go flat as they warm up—a fun fact for your next party.

The oceans contain vast amounts of dissolved CO2, many times more than is in the atmosphere. If the ocean warms up just a little bit, it releases huge quantities of its CO2 into the atmosphere, increasing the atmospheric concentration. This is why the second chart above is more likely to represent truth, even though it can't provide proof. If the reverse were true, we would have to say that the high concentration of CO2 in your beverage was what caused it to heat up. Anyone want to argue that?

So why all the fuss about CO2 and all the claims that it is causing climate change? That brings us to climate models. It turns out that nearly all the "evidence" for CO2 caused climate change comes from mathematical systems implemented in climate models. Did I hear someone mention ‘mathemagic’ again?

Don't misunderstand. As someone who has written and used computer models for over fifty years, I can attest to their value when they are properly designed, implemented, and used within their limitations. Unfortunately, in most cases, none of these conditions are met in climate models. A model is only as good as the assumptions used in its construction, and many of the assumptions used in making climate models don't hold up well.

Take for example, the basic assumption of the relationship between CO2 concentration and temperature. Almost all models use a mathematical formula that says increases in CO2 concentration will result in higher temperatures. Models incorporating this formula are then run to "prove" that increases in CO2 concentration will result in higher global temperatures. Does anyone notice a problem here?

This formula was introduced and its use endorsed by the Intergovernmental Panel on Climate Change (IPCC) of the UN. You know, the same people who are saying that we all need to cut back on fossil fuel consumption and CO2 release to save the planet. To be fair, there is good laboratory data to show that in particular conditions, the relationship holds true. But to simply build it into a model is to neglect the complex dynamics of energy exchange, absorption and release of energy that exist in a real atmosphere.

A second and related issue is how most computer models treat the effects of clouds. The IPCC —remember them?—considers that the only effects of clouds are in their reflection of sunlight back to space (albedo effects) which reduce the amount of solar heat that reaches the Earth's surface, and the ability of clouds to reflect heat energy back to the surface. The entire complex dynamics of heat transport coupled with phase changes as water vapor condenses to liquid water and sometimes to ice is completely ignored.

One of my fellow scientists and I have been working on an analysis that shows how clouds can transport great quantities of heat from the surface of the Earth, through the low-lying layer of CO2, upwards to high altitudes where that heat can be radiated out to space. The quantities of heat involved, as well as the mechanisms of transport work to maintain the Earth temperature within a fairly narrow range in much the same way that a furnace and air conditioning act to keep a comfortable temperature in a building. We expect to publish a professional paper on this research later this summer.

It is worth noting that most of the "evidence" supporting the idea of a Climate Crisis comes from projections based on computer models. As we see, these models have several important flaws, only two of which we've described here. The contrary evidence, on the other hand, largely comes from hard data obtained from real-world investigations, such as the ice core data described.

This hard evidence largely contradicts the model supported ideas that human sourced CO2 is causing the global temperatures to rise and climate to change. Instead, it tells a story of natural cycles of change over timescales ranging from decades to centuries to thousands to millions of years, and humans are just along for the ride.

Stage magic is fun and entertaining, but makes no statement about the real world other than to point out how easily humans can be misled about what is happening. The damage happens when we allow magic to infiltrate our science and our politics and mislead us about the world. It is time to reveal the ‘mathemagic’ that is deceiving us in our understanding of climate change. The magic show has gone on too long and is too expensive to be considered entertaining. Reality must trump illusion. Time to draw the curtain and move on.

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