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 (p_s) divided by the acceleration of gravity (g).
M = p_s / 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 ΔT_{CO2 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 = ΔT_{CO2 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.

• The report does not need to be in the "report" format. But, compose one paragraph of sentences, rather than just putting numbers or arithmetic formulas.
• Graphs may be included, but not required.
• When writing numerical values, be careful to include correct units of physical quantities. (Some quantities are "non-dimensional" and units are not applicable to them.)
• If you want to use information other than the assignment, mention the source.
  • Books and journal articles should be shown as in the "references" section of journal articles.
  • For internet sources, the URL (like http://www.tmu.ac.jp/ ) and the date you browsed it should be included.
• Approximate values of mathematical constants "pi (π)" and "e" does not require external sources.

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

• By paper
  • Use A4 size paper (American letter size is permitted but not preferred) in "portlait" (rather than "landscape") orientation.
  • One sheet is enough, but if the report consists of multiple sheets, write your name at every sheet.
• By e-mail
  • PDF format is preferrable. Simple text files, HTML, MS Word "docx", "doc" and LibreOffice "odt" are also OK.
  • The file size should be less than 1 MB.
  • Send to the address "masudak at tmu.ac.jp" .
  • I do not send messages that I got e-mail. (Sorry)