Page 149 - Geosystems An Introduction to Physical Geography 4th Canadian Edition

aQuantitativeSOlUTiOn Zero-Dimensional Global Energy Balance Model
Using a global energy balance model, we can explain the tem-
perature of Earth’s surface. An energy balance model accounts for
incoming and outgoing energy. For simplicity, we will investigate
a zero-dimensional model in which energy received is spread
uniformly around Earth and there is uniform emission of energy Solving for T from all parts of its surface. E
Extending the model to one dimension, one step closer to reality, would include energy exchange between latitudinal zones. Adding more dimensions further increases model complexity to simulate real-world conditions even better.
“Balance” suggests that the system is at equilibrium—energy gained is balanced by energy lost. The final objective is to solve for Ts, the surface temperature of Earth as seen from space.
We start with incoming solar radiation from the Sun, the solar constant, S (1372 W·m−2). Averaged over time, for Earth’s
radius r, the total energy received is pr2S. This amount is distributed over the whole Earth, which has an area of 4pr2. Because of Earth’s albedo (a), only the amount (1 − a) × S is absorbed. This can all be simplified to:
Energy absorbed by Earth = (1 - a) # S 4
On the outgoing side of the energy balance model, we have:
Energy emitted from Earth = sTE4
where s is the Stefan-Boltzmann constant (5.6705 × 10−8
W · m−2 · K−4) and TE is the global mean effective temperature.
yields:
TE
4
= 4 H
E
# (1 - a) S
4
s
Now that we have both sides, incoming and outgoing, our energy balance model is:
(1 - a)#S = sT4
For a = 0.31, TE = 254 K. These units are Kelvins (see Chapter 5). 1 K = 1°C, and since 273 K = 0°C, our result for TE is −19°C.
Our calculations are correct but the answer for TE is not the cor- rect value for Earth’s actual surface temperature as seen from space. The cause of this discrepancy is the greenhouse effect described in this chapter. The result −19°C is the temperature that Earth would have if there were no atmosphere with greenhouse effective gases.
To reach the final solution for Ts, we must add the amount of the greenhouse effect, 34 K (= 34 C°), called the greenhouse increment (∆T), to TE:
Ts = TE + ∆T
= 254 + 34 = 288 k = +15°C
The surface temperature of Earth as seen from space, Ts, is +15°C.
adapted from: k. McGuffie and a. Henderson-Sellers, A Climate Modelling Primer, 2nd ed., John Wiley & Sons, Chichester, Uk.
concepts review
kEy lEaRninG
■ Define energy and heat, and explain four types
of heat transfer: radiation, conduction, convection, and advection.
Radiant energy from the Sun that cascades to the surface powers Earth’s biosphere. Transmission is the uninter- rupted passage of shortwave and longwave energy through either the atmosphere or water. Our budget of atmospheric energy comprises shortwave radiation inputs (ultraviolet light, visible light, and near-infrared wavelengths) and shortwave and longwave (thermal infrared) radiation outputs. Energy is the capacity to do work, or move matter. The energy of motion is kinetic energy, produced by mo- lecular vibrations and measured as temperature. Potential energy is stored energy that has the capacity to do work under the right conditions, such as when an object moves or falls with gravity. The flow of kinetic energy from one body to another resulting from a temperature difference between them is heat. Two types are sensible heat, energy
that we can feel and measure, and latent heat, “hidden” heat that is gained or lost in phase changes, such as from solid to liquid to gas and back, while the substance’s tem- perature remains unchanged.
One mechanism of heat transfer is radiation, which flows in electromagnetic waves and does not require a medium such as air or water. Conduction is the molecule- to-molecule transfer of heat as it diffuses through a sub- stance. Heat also is transferred in gases and liquids by convection (physical mixing that has a strong vertical motion) or advection (mixing in which the dominant mo- tion is horizontal). In the atmosphere or bodies of water, warmer portions tend to rise (they are less dense) and cooler portions tend to sink (they are more dense), estab- lishing patterns of convection.
transmission (p. 92) heat (p. 93)
sensible heat (p. 93) conduction (p. 93) convection (p. 93) advection (p. 93)
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