Question

I apologize but this is one question that has multible parts .

There are currently (as of July 2018) 411 parts per million of CO2 in our atmosphere. In July 2000 the concentration of CO2 was 365 ppm. a) calculate the average exponential growth rate in this period b) at this growth rate what will the concentration of CO2 in the year 2100. A reasonable approximation of the amount of surface temperature (in degrees C) increase as related to CO2concentration is given by: ΔT = 0.8 * ΔF where for CO2 ΔF = 5.35 * LN(Cnow/Cbefore); Cbefore = 280 ppm Note that LN stands for the natural logarithm; for instance ln(10) = 2.32 (just type ln 10 in to Google) ΔF (what we call climate forcing) represents the change in flux due to changing CO2 levels and that determines ΔT c) Using the result obtained in Part b, what is the predicted temperature change in the year 2100 and is this prediction above or still below the Paris accord agreement of no more than 2C before 2100 above the pre-industrialized temperature? Over the last few years, CO2 growth is occurring at a larger rate than long term average. The following list gives you the necessary values to compute the relevant growth rates for the question below. Jan 1970 325 ppm Jan 1990 353 ppm Jan 2005 378 ppm Jan 2019 411 ppm d) Using the same calibration as above, calculate the exponential growth rate and predicted 2100 temperature from that growth rate for the periods 1970-1990 1990-2005 2005-2019 please explain step by step how you came to this answer. I would like to beable to do this myself in the future. thank you

Answer 1

a) If CO2 concentration follows exponential growth then, at any time

where, is the concentration at time , is the initial concentration (here July 2000). is the average exponential growth rate.

Putting in the numbers we get,

.

Therefore,

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b) Using the same formula with the given rate and , we get

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c)

Here, and given,

Therefore,

which is clearly greater than the Paris accord agreement of .

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d) We are given

Therefore, and similarly, . Dividing these two equations gives us

. Therefore,

Now, . Again . Dividing both, we get

Here, in these cases to find the temperature difference we simply need to put the given concentration as and the concentration for given year as . Thus, for

1970

1990

2005

2019

2100