Climate change (Class of 2019): exercise 1

The circumference of the earth is 40 million metres (40 thousand kilometres) as a very good approximation, because of the initial design of the unit "metre".

The atmosphere is approximately in hydrostatic balance (when we consider horizontal scale larger than tens of kilometres). Then, the mass of air above the surface per unit area (M) is (approximately) the pressure at the surface (ps) divided by the acceleration of gravity (g).
M = ps / g .
The global mean surface (not always sea-level) pressure is approximately 980 hPa (hectopascals), and 1 hPa is 100 Pa (pascals). Pa is the SI unit for pressure. The acceleration of gravity at the surface is 9.8 m/s2.

Question 1. Calculate the total mass of the atmosphere [in kg] based on the information given here.

Carbon dioxide concentration in the atmosphere is approximately 400 ppm at present. It was approximately 280 ppm before industrialization, as based on ice core samples from Antarctica.

"ppm" is parts per million, and in this case, "by volume" or "by number of particles" or "by mol", not "by mass" or "by weight".

The molecular weight of CO2 is 44 g/mol, and the average molecular weight of air is approximateyl 29 g/mol . Note that "gram" rather than "kilogram" is involved here.

Question 2. Calculate the total mass of CO2 in the atmosphere [in kg] at present as well as before industrialization.

The steady-state response of global average surface temperature to CO2 doubling is estimated to be between 1.5 and 4.5 K. Tentatively we use ΔTCO2 doubling = 3 K as a typical value.

It is known that steady-state response is (roughly) proportional to logarithm of CO2 concentration. The steady-state temperature is denoted by T and the CO2 concentration is denoted by c. Then
T2 - T1 = ΔTCO2 doubling log(c2/c1) / log(2)
(Either natural (e-base) logarithm or common (10-base) logarithm can be used, as long as one definition is consistently used.)

Question 3. Calculate the steady-state response [in K or in ℃, which are the same thing in this context] of CO2 increase from 280 ppm to 400 ppm. (The calculation does not need the answer of Question 2.)

Report assignments

Answer the three questions above.

Submit answer by 13 June either by paper or by e-mail.

Updated: 2019-May-30
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