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Simple model for Global Warming

I am doing something a little different for this posting. I am referencing a site by one of the more frequent commenters on this site, Mike Alexander. Dr. Alexander holds a PhD in Chemical Engineering and has written a variety of books on things that interest him (see his financial analysis books here). Luckily for us, his interest also includes the changes to the global climate.

Dr. Alexander put out a rather straight-forward discussion on global warming that is primarily focused on the greenhouse effect. While the goal of this discussion was to keep it “simple” you will definitely need to strap on your thinking cap to follow all of the math. If you are math challenged, the wording around the equations is fairly easy to follow.

It doesn’t make sense to quote a lot of things from this paper, rather I will quote the beginning and the ending.


In this article I will develop a simple* model for understanding the complex phenomenon of global warming. By global warming I mean the rising trend in average surface temperature of the entire Earth that has occurred over the past century. I start by describing the fundamental principles driving global temperature, which are quite straightforward. Basically, the Earth receives energy from the sun, which warms the Earth, and radiates energy out into space, which cools the Earth. Radiation increases with higher temperature and so the temperature of the Earth is that temperature at which energy outgo equals energy income. How the Earth radiates energy depends on properties of its surface and atmosphere. Here is where the complexity comes in because many things affect the ability of the Earth to radiate energy and so affect the temperature. This article deals with the three major factors, greenhouse gases, solar effects and the effect of aerosols.

The model developed here is greatly simplified yet it contains enough elements to allow a non-expert to gain an understanding of how greenhouse gases work to warm the climate and how clouds affect it. The model is used to describe an important recent development in climate science, the cosmic ray climate driver hypothesis. This theoretical mechanism has been cited by many global warming skeptics as an alternate explanation for warming besides greenhouse gases. This article shows that although the theory is useful for explaining early 20th century warming, it does not explain recent warming.


CO2-mediated greenhouse warming is the dominant mechanism responsible for global warming over the past three decades. If present CO2 output trends continue atmospheric CO2 could more than double from its current level by the end of this century. A doubling in CO2 level would produce a forcing of about 3.7 watts m-2 according to equation 27. With ? = 0.76, the value obtained with the simple model considering all feedbacks, the predicted temperature increase would be 2.8

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