Death by Global Warming

In this blog post I intend to demonstrate a simple model of global warming derived from the Stephan-Bolzmann law, and use it to build an interactive model of global warming. The end goal of the model is to look at one of the most direct results of an increase in global tempurature: human death due to natural heat.

Why Global Warming? Why death to natural heat?

Global warming is an oft-discussed topic that has become a hot-button issue in many political discussions. The politization of global warming has turned it into a highly controversial issue - but an issue that is only really controversial in the media, and amongst laypeople. In the scientific community, there exists a broad scientific consensus that human inflicted climate change is not only possible, but highly likely if current trends persist. In fact, no scientific body of international standing disagrees with this view (Source). All too often in the media, we discuss various sensor measurements and debate various mechanisms that have affected temperature through history - but interpretation of the various measurements and theories we hear have nothing to do with this consensus. These theories and measurements are set up as a straw man that make global warming appear much more controversial than it actually is - I'm positive you have heard of arguments about global heating and cooling cycles by now (Like this).

The problem with these sorts of arguments is that the scientific foundation of global warming doesn't stem from a belief in any sort of cycle, or any past trend of measurement, incidence of ice age, or anything else. In fact, the broad scientific consensus really has its foundation in a simple law of physics you can find in any college level textbook - the Stephan-Bolzmann Law. Given this law, it is mathematically demonstrable that an increase in CO2 concentrations in the atmosphere will increase global tempurature. I intend to demonstrate that math here (It isn't hard), and show the repercussions of that math given the current trends of CO2 production relative to CO2 absorption. The earth absolutely has natural processes of heating and cooling independant of human driven processes, but when discussing global warming it is really more of an issue of how much mankind can directly 'move the needle' independant of any cycle or historical fluctuation - and change global temperatures from what they would be otherwise. To put it in perspective, the absolute range of mean temperature in the last five million years as measured via delta-O-18 (a ratio of two oxygen isotopes that are produced in different ratios at different temperatures) in geological core samples is about 10 degrees C from max to min - so even a single degree of climate change from baseline in a thousand years due to human processes would still be massively significant. (Source: here for delta-Os, using the relationship that that a delta-O of 0.22‰ is equivalent to a 1 degree C  cooling, ceteris paribus.)

As for why I chose to fixate on death to natural heat, again I want to stick to the things I can demonstrate on paper in a way any typical college educated layperson should be able to understand. Natural heat kills hundreds of people every year in the USA, sometimes even reaching the thousands. It follows that more heat means more death to heat - a trend which I can demonstrate using government death statistics on a state-by-state level. There are any number of theories on the disastrous consequences of changes in global tempurature - but it is hard to prove undeniably that any of these disasters will happen. Death to natural heat, on the other hand, already happens - it is a fact that natural heat is deadly, so it is a much more concrete consequence that I can form my model on top of.

The Law, and our CO2 Production:

The Stefan-Bolzmann law relates the power radiated from a black body to its temperature. By accounting for a body's emissivity, the model can be extended to cover grey bodies, such as Earth. The following is the law:




Now, differentiating the law and solving for dT, we can get a relationship between change in F and change in T as follows:


Plugging in the given numbers, we reach a dT of 0.984K - essentially just under 1 degree C. Treating Earth as a gray body and accounting for emissivity actually doesn't change this number too much - yielding a dT of around 1.6C instead - which is more in line with IPCC estimates built using historical observational data (Source).  Nevertheless, the 1C number is an oft-used bare minimum estimate in climate science, so for the sake of building a conservative model, I will use the 1C number.

In terms of CO2 production, most estimates put us in the range of 30 gigatons of CO2 annually (Source) with 46% of that actually being absorbed by the amosphere (The rest gets absorbed by plants and the ocean - Source). To put those numbers in perspective, the Earth's atmosphere contains roughly 750 gigatons of CO2 in total (Source).

The Data on Death to Natural Heat:

I used a government dataset provided by the NCHS (available on NBER here) that has a complete listing of official state death records. Starting from around 2000, these records broke out the category 'X30' - which is death by natural heat. After 2005 the government stopped breaking down records on a state by state place of occurence level. So I used the years 2000-2005 to determine deaths to natural heat by state. I then got data on the average tempurature in each state as well as population statistics for each state, and came up with a micromort exposure vs average state temp graph. I fit an exponential model to the graph, and use it to extrapolate how average tempurature affects micromort exposure to heat. The real goal here is to see what sorts of death tolls we could expect to see in a developed country like the USA (developing countries fare much worse) at different tempurature levels.

Supplementary data I used for the model such as tempuratures and populations available here and here, assuming a .7% population growth rate.

A Description of the Model:

The two sliders available control the rate of increase of CO2 production year over year, and the rate of CO2 production tapering year over year.

The production slider is done using percentage change, whereas the cutback slider is an absolute fraction of that percentage (i.e. a 2.9% production increase with a .1% cutback assumes a 2.9% production teh first year, 2.8% the second, and so on). So by the default values, the model starts at a 2.9% increase year over year (which has been our historical rate of increase in the past decade), and assumes we taper that rate of increase down to 0% after 52 years, continuing to reduce our absolute rate of production after that. This represents a fairly average case model by IPCC standards.

Other considerations:

The model assumes a 1% decay of the 46% absorption rate of the atmosphere (i.e. the atmosphere absorbs more and more every year as our production outpaces the earths ability to absorb it). This is because although the atmosphere absorbs 46% of our production today, as we produce more the fraction absorbed will not remain the same - if the earth is absorbing 14 gigatons of carbon into plants and the ocean today, it is unlikely it will be able to absorb 46 gigatons yearly if we were to start producing 100 gigatons yearly.

While it is likely that if we absolutely stopped CO2 production altogether the Earth may begin to absorb that CO2 back, the model as it stands does not allow for CO2 levels to decline in an absolute sense year over year - i.e. the model can drop below the baseline 30 gigaton production rate if the cutback slider is high enough, but 'negative CO2 production' is not allowed by the model.

The Model:

Conclusion:

In conclusion, human driven climate change is a near certainty at this point. With some luck, we might catch the earth in a natural cooling trend, but our rate of carbon production is so high that even a record breaking cooling cycle wouldn't be able to stop it. At best it could buy us some time. Short of that, climate change in the next 100 years is inevitable - and as the above model demonstrates - is going to cause disastrous outcomes even when using conservative numbers. Simply put, if we continue to inject politics into global warming when the objective data and the basic laws of the universe imply disastrous outcomes, we are digging ourselves into a hole we might never be able to get out of. Human driven climate change is not an opinion, or a conspiracy, or a political stance, it is a cold hard fact. Public views on global warming need to change fast, or it will be too late.