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Thursday, May 21, 2015

CO2 Emissions, Levels, and a Simple Moldel of AGW

Some 150 years ago, atmospheric CO2 level was about 280 PPM.  Now it is 400PPM, the global temperature is measured around 1 degree C higher.  This is not mere observation; it follows from (a version of) the Arrhenius law (http://www.ams.org/notices/201010/rtx101001278p.pdf)

delta T = ~3 * ln(C(current)/C(initial))

where delta T is the temperature rise, ln is the natural logarithm (base e), C(current) and C(initial) the 400 and 280 PPM CO2 levels just mention, and ~3 the constant needed to convert the ratio to delta T.  Plugging the 400 and 280 PPM measurement into this equation does indeed a yield of 1 degree C.

If one looks at the data for CO2 emissions, levels, and the first derivative of those levels:













Figure 1 -- CO2 emissions 1900 - 2010 (http://www.epa.gov/climatechange/ghgemissions/global.html)














Figure 2 -- CO2 detailed level increments 1959 - 2014 (http://www.epa.gov/climatechange/ghgemissions/global.html)














Figure 3 -- First derivative of CO2 detailed level increments 1960 - 2014 (http://www.epa.gov/climatechange/ghgemissions/global.html),

we see that, from the second chart, that from around 1960 - 2014, the average CO2 rise is about 1.5 PPM per years, somewhat greater from the first ~100 years), and that the first derivative is almost exactly 0.  This means CO2 has been rising in a perfectly straight line for over the last 60+ years.

If we project this increase out to 2100, CO2 levels will be about 529 PPM, and the resulting rise in temperature will be = 3 * ln(529/400) = 0.84 C.  However, most likely CO2 emissions will scale back dramatically during this century; if the levels are only 0.5 * 129 + 400 = 465 PPM, the resulting T will equal 0.45 C.  On the other hand, should yearly increment levels increase to 2 PPM (highly unlikely), the temperature should be about 1.5 C.

Given that a significant increase is highly unlikely, we are probably looking at a temperature increase somewhere between 0.5 and 1.0 degrees C.  Incidentally, I am assuming the same degree of methane and albedo changes as part of the temperature record (i.e., no "tipping points"), so those don't affect the results.  Frankly, for such small changes in Earth's temperature (even a total of 2.5K out of 288K is < 1%, the assumption of no dramatic changes is reasonable.

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