## S

ice-free terrain, surface albedo is assigned from representative values for the ocean (0.1), forest (0.2), tundra (0.25), and desert (0.3). Snow and ice cover are assigned albedo values of 0.8 and 0.6, respectively. The transition from open water/bare land to sea ice and snow cover is based on a simple temperature rule, with a linearly increasing snow/ice cover as temperature decreases from a mean annual value of 0°C to -10°C. Surface albedo as. is then calculated as a composite of the ice-free and ice-covered values over this transition. This is simplistic, of course, but this model is purely illustrative.

The second term on the right-hand side describes the net outgoing longwave radiation (Eqs. 3.10 and 3.11), for emissivity e, including a factor taj that represents the atmospheric transmissivity to longwave radiation. This term was linearized in the original energy balance models, but it is simple to use the full nonlinear form of Stefan-Boltzmann's law with an iterative solution. The final term in (8.1) is a crude representation of poleward heat transfer, parameterized as a linear function of the meridional temperature gradient. This roughly describes the role of the Hadley cells, western boundary currents, baroclinic eddies, and so forth, in transporting energy from the tropics to high latitudes.

This one-dimensional energy balance model is no replacement for a global climate model, but it is a rough tool to examine the planetary energy budget and the influence of the cryosphere on Earth's albedo and temperature. Parameters in (8.1) can be tuned to give a mean temperature of 14.0°C for the planet, representative of the current mean state. The planetary albedo, aP , is equal to 0.32 in this case, including the compound effects of both the atmospheric and surface reflectivities. In a scenario where all of the snow and ice is removed from the planet, aP = 0.26, and the global average temperature increases to 18.2°C (figure 8.1). A simulation of the last glacial maximum (LGM) conditions with this model, with ice sheets extending to midlatitudes, shifts the results to aP = 0.35 and a global average temperature of 8.8°C.

Latitude

Figure 8.1. Steady-state zonally averaged (a) albedo and (b) temperature in the simple energy balance model of Eq. (8.1), for the present world (heavy solid lines), ice-free world (dashed lines), and LGM world, with continental ice extending to 45° N (dotted lines). The albedo plots in (a) include both atmospheric and surface albedo. The thin solid line plots the surface albedo for the present-day reference model.

### Latitude

Figure 8.1. Steady-state zonally averaged (a) albedo and (b) temperature in the simple energy balance model of Eq. (8.1), for the present world (heavy solid lines), ice-free world (dashed lines), and LGM world, with continental ice extending to 45° N (dotted lines). The albedo plots in (a) include both atmospheric and surface albedo. The thin solid line plots the surface albedo for the present-day reference model.

These scenarios lack many important climatic feedbacks that would attend such major shifts in climate, such as changes in cloud cover and atmospheric circulation, but the calculations provide a rough estimate of the importance of the cryosphere to planetary albedo.

cryosphere-climate processes

Similar hypothetical experiments have been carried out with global climate models. In one such study, simulations with LGM boundary conditions give a global cooling of 3°C accompanied by an increase in planetary albedo from 0.31 to 0.33. Application of the same model to an ice-free world gives the expected reduction in surface albedo, but this is offset by an increase in evaporation and cloudiness in this model, giving a warming of 1.3°C but no net change in planetary albedo.

This result demonstrates the sensitivity of the climate system to feedbacks from both the cryosphere and the hydrological cycle. These also have direct connections at high latitudes, where loss of sea ice exposes more open water, increasing local and regional cloud cover. The inferred changes in planetary albedo are massive in terms of the planetary energy balance. At present, average incoming radiation at the top of the atmosphere is QS0 = 341 W m2, of which 102 W m2 is reflected back to space (a P = 0.30), and the remaining energy, QS' = 239 W m-2, is available to Earth's surface and atmosphere. This gives 9QS'/9a P = -3.4 W m 2 %-1. As an example, a loss of snow and ice causing a decrease in planetary albedo from 0.30 to 0.28 would represent an energy surplus of 6.8 W m-2, which compares with an estimated (ca. 2006) radiative forcing of 2.6 W m-2 associated with the anthropogenic greenhouse-gas buildup in the atmosphere. In other words, albedo feedbacks can be of a similar or greater magnitude to the greenhouse-gas forcing that is driving current climate change.

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