1. Chapter 12 Long-Term Climate Regulation Snowball Earth

2. Introduction to Climate Modeling: 1-dimensional radiative-convective model 1-D Rad-Conv Model surface S/4(S/4)*A Radiation in each wavelength band Convection, latent fluxes Surface: latent, sensible

3. Introduction to Climate Modeling: 2-dimensional climate model Surface North Pole South Pole

4. Modeling Snowball Earth with a relatively simple Energy Balance Climate Model (EBM) - recall ‘energy balance’ comes from accounting for ‘energy in’ and ‘energy out’ an area/region and computing the heating (over some time) that the balance allows. Assumptions:  Take the Earth to be symmetric about the Equator, and divide the surface in 18 latitude bands, each of 10 degree wide - recall SP is at -90 degrees, the NP is at +90 degrees, hence distance SP-NP spans 180 degrees  Heat transport between bands is accomplished by diffusion – unrealistic but coefficients cleverly adjusted to represent known values of meridional heat transfer on Earth Model can estimate size of ice caps, hence can be used to look at glaciations Results of calculations are in Box Figure 12-1

5. present day solar flux stable climate solutions for modern Earth: 1. snow covered, 2. ‘small ice cap’ (that’s what we have now), 3. ice- free sin(ice-line) ≈ 0.95  boundary of ice cap about 72deg of latitude All unstable solutions correspond to ice caps that fall equatorward from 30deg of latitude (this also marks the line for half the surface area of Earth in this model) – ‘run away’ albedo feedback would lead to ice- covered surface. X

6. Box Figure 12-1 1. The horizontal axis (usually the independent variable) is the effective solar flux (S eff, proportional to solar luminosity) = solar flux through geological time/present day flux – a value of 1 corresponds to solar constant today 2. The vertical axis (usually the dependent variable, what we want to learn about as a function of the values on the horizontal axis) displays the values of the sine (ice-line latitude) - recall the ‘ice-line latitude’ is the latitude (in degrees) of the position of the ice-snow line, can think of it as a measure of the latitudinal location of the extent of the ice cap sin 0deg = 0 (Equator)sin 30deg = 0.5 sin 45deg = 0.7071sin 90deg = 1 (Pole) 3. Lines and curves represent ice-line extent: a value of sin (ice-line) if 0 implies the ice-snow covered areas have reached the Equator, a value of sin(ice-line) of 1 implies that the ice-snow extent is really a point - the Poles; these are the horizontal lines denoted by ‘Ice-covered’ and ‘Ice –free’, respectively

7. Box Figure 12-1 4. Each curve represents the variation of the position of the ice-snow line on earth with changing solar luminosity AND for different atmospheric CO 2 concentrations (measured by partial pressure values) CO 2 concentration closest to today’s value ≈ 300 ppm, which is the curve pCO 2 = 3 x 10 -4 bar 5. Solid curves correspond to stable solutions and dashed curves to unstable solutions stable: after a reasonably small perturbations, the ice-snow covered earth will return to the original state (as described by any point of the stable branch of the curve) unstable: these solutions are possible but any small perturbation to such an Earth covered by an ice cap extending beyond a certain latitude will provide for a situation in which the Earth runs away from the original state, leading to an ice-covered Earth – Snowball Earth 6. The points where the curve(s) intersect a vertical line at S eff = 1 correspond to climate solutions for the modern Earth; three of these are stable, one is unstable.

8. Box Figure 12-1 7. An unstable solution is possible but it can lead to an ice-covered Earth, which is then a stable state. Under these conditions, the carbonate-silicate cycle (a sink for atmospheric CO 2 ) would stop allowing for CO2 to accumulate (from volcanism) in the atmosphere to a level that would make the greenhouse effect due to CO 2 (working along the warming due to the water vapor feedback) effective enough to take the Earth out of the Snowball state. Note that if volcanic activity lead to a concentration of pCO 2 of 0.12 (12,000 ppm), the corresponding curve in the figure has the unstable (dashed line) intersect the Equator for S eff = 1 (see (X) in fig.) which means that the ice-covered solution is no longer stable: as the greenhouse effect due to CO 2 warms the climate a little, the Ca-Si cycle leads to a decrease in CO 2 concentration (jump to next curve with less CO 2 ), ice-line positions moves toward poleward, albedo decreases which combined with greenhouse warms climate further, jumping to next climate solution and so to (rapidly) reach the ice-free solution! 8. Then again, as the climate warms the carbonate-silicate weathering cycle begins to extract CO2 from the atmosphere and cooling the Earth.

9. Use the ‘clean’ Box Figure 12-1 provided below to answer the questions below

10. For a value of S eff = 0.95 1. give the approximate geological time for this value of S eff. 2. how many possible solutions are there according to this EBM? Explain what is meant by ‘climate solution’. 3. What do the solutions depend on, besides S eff ? 4. Describe these solutions: How many are stable?, how many unstable?, position of ice cap in each case (include the latitude values!) 5. Explain what ‘stable’ and ‘unstable’ solution means physically. 6. How would get Earth out of ice-free or ice-covered stable solutions?