Carbon dioxide and (steady state) climate change (2)

"Discovery of global warming"

• Not "Rising temperature is observed" → "What is the cause?"
  • In 1960-1975, records of Northern Hemisphere average temperature showed decrease (cooling). By simple extrapolation, some "predicted" global cooling.
  • Also, increase of aerosols (partly because of conbustion, partly because of land-use change) is observed. Which also suggested cooling, with large uncertainty.
  • In addition, theoretical thinking about glacial cycles had progress, and cooling in the time scale of thousands of years are "predicted".
• Rising carbon dioxide concentration was already evident around 1963.
• Then, theoretical thinking about "greenhouse effect" lead to an outlook of global warming.
• The order-of-magnitude of warming seem robust around 1975, when results of 3-dimensional models basically agreed with those of vertical 1-dimensional models.

Physics-based mathematical & numerical models

• The behavior of the atmosphere and the ocean can be described by basic physical laws.
• Physical laws
  • Conservation of energy (1st law of thermodynamics)
  • Conservation of mass (of air, of water)
  • Equation of motion
  • Equation of state (this is "diagnostic" rather than prognostic)
  • (2nd law of thermodynamics, or increase of entropy)
• Physical laws (applied to continuous media) can be written in partial differential equations where the independent variables are spatial coordinates (x, y, z) and time (t). And the important ones are "prognostic", by which future values of variables can be calculated from the present values.
• The equations cannot be solved or "integrated" by pure mathematics, though (except for the case of extremely simple models).
• The equations can be approximated, typically replacing differentials (dX/dt) with finite differences (ΔX/Δt), and approximate solutions can be calcluated by digital computers.
• To get solutions, initial conditions and boundary conditions are needed. (Note: some external parameters, which are not necessariliy boundary conditions of partial differential equations, are included in "boundary conditions".)
• Thus, the numerical simulation of the atmosphere is possible, and used for weather prediction.
• Numerical models of the atmosphere, coupled with similar numerical models of the ocean, is used for climate studies.
• First, (quasi-)steady states with constant boundary conditions were simulated.
• Then, time-dependent behaviour of the climate system with changing boundary conditions were simulated.
• Climate models have various degrees of complexity. The simplest one is 0-dimensional energy balance models. The typical one for realistic simulation is 3-dimensional coupled ocean-atmosphere general circulation models.
• Usually climate models have carbon dioxide concentration as an external parameter.
• Some models have carbon dioxide as variables, and have equation of the conservation of mass of carbon. Currently, researchers often call these models "earth system models" rather than climate models.

Steady-state response with vertical 1-dimensional models

See [Materials of the previous week]

Steady-state response with 3-dimensional models

• Manabe & Wetherald (1975)
  • Steady-state response of global mean surface air temperature to CO₂ doubling was 2.9 K.
  • Difference of this and 2.3 K of vertical 1-dimensional model of Manabe & Weatherald (1967) may be incidental, but it may be due to ice-albedo feedback. (The 3-dimensional model did include variable snow and sea ice, and the 1-dimensional model did not.)
• Hansen's group at NASA Goddard Institute of Space Studies got somewhat larger response (ca. 4 K). The likely cause of difference is assumption about formation of clouds.
• A review published in 1979 concluded that the steady-state response is likely to be between 1.5 K and 4.5 K. Science has advanced since then, but the range of likely response has not changed so much.

Major feedbacks in the climate system

Assume that the global average surface air temperature (T) is the key variable.

• Blackbody radiation feedback (-) ... T → infra-red emission to space →(-) T [not mentioned in lecture yet]
• Water vapor feedback (+) ... T → water vapor content → greenhouse effect → T [not mentioned in lecture yet]
• Ice albedo feedback (+) ... T →(-) extent of snow and sea ice → reflectivity of solar radiation → (-) absorption of solar radiation → T
• Cloud feedback
  • Interaction with solar radiation and terrestrial radiation ... probably solar radiation is more important.
  • Cloud amount: fraction of surface area covered by clouds. It is uncertain which is the case:
    • (-) ... T → cloud water mass → cloud amount → reflectivity of solar radiation →(-) absorption of solar radiation → T
    • (+) ... T → vertically developing clouds →(-) cloud amount → reflectivity of solar radiation →(-) absorption of solar radiation → T