## Radiative Forcing And Temperature

### Annual mean

The latitudinal distribution of incoming solar radiation at the top of the atmosphere in the annual mean and at solstice is shown in Fig. 5.2. Its distribution is a consequence of the spherical geometry of the Earth and the tilt of the spin axis, depicted in Fig. 5.3. If the Earth's axis did not tilt with respect to the orbital plane, the average incident flux would maximize at a value of Smax = So/n = 435Wm-2 at the equator, and fall monotonically to zero at the poles. Because of the tilt, however, the poles do receive solar radiation during the summer half-year, and therefore the annual mean equator-to-pole difference is reduced, as Fig. 5.2 makes clear.

FIGURE 5.2. Distribution of annual mean and solstice (see Fig. 5.4) incoming solar radiation. The slight dip in the distribution at, for example, the winter solstice (December 21st) in the southern hemisphere corresponds to the edge of the polar day.
FIGURE 5.3. At the present time in history, the Earth's axis tilts at 23.5° and points towards the North Star. We sketch the incoming solar radiation at summer solstice when the Earth is tilted toward the Sun.

Seasonal

The daily averaged radiation received at any point on Earth varies through the year for two reasons. First, as illustrated in Fig. 5.4, the Earth's orbit around the Sun is not circular; the Earth is closest to the Sun—and the solar flux incident at the top of the atmosphere therefore maximizes—just after northern winter solstice. However, the variation of the Earth-Sun distance is less than ± 2%; although the corresponding variation in solar flux is not negligible, its contribution to the annual variation of the local solar flux per unit area at any given latitude is much less than that arising from

September 22

September 22

FIGURE 5.4. Earth describes an elliptical orbit around the Sun, greatly exaggerated in the figure. The longest (shortest) day occurs at the summer (winter) solstice when the Earth's spin axis points toward (away from) the Sun. The Earth is farthest from (closest to) the Sun at aphelion (perihelion). The seasons are labelled for the northern hemisphere.

FIGURE 5.4. Earth describes an elliptical orbit around the Sun, greatly exaggerated in the figure. The longest (shortest) day occurs at the summer (winter) solstice when the Earth's spin axis points toward (away from) the Sun. The Earth is farthest from (closest to) the Sun at aphelion (perihelion). The seasons are labelled for the northern hemisphere.

the tilt of the rotation axis. At the present time in Earth history, the spin axis tilts from the vertical by 23.5°, the north pole pointing almost toward the North Star. At northern summer solstice, the north pole is tipped in the direction of the Sun, and the northern hemisphere has the longest day of the year. Conversely, at the northern winter solstice the north pole is tipped away from the Sun, and the northern hemisphere has the shortest day. At the equinoxes, daytime and nighttime are of equal length.

At solstice there is no incoming radiation at the winter pole (nor anywhere within ''polar night''), but there is Sunlight 24 hours a day at the summer pole. It is for this reason that the incoming radiation actually maximizes (slightly) at the summer pole, when averaged over 24 hrs, as shown in Fig. 5.2. Nevertheless, the absorbed radiation at the summer pole is low because of the high albedo of snow and ice.

Before going on, we should emphasize that the Earth's tilt and its orbit around the Sun are not constant but change on very long time scales (of order 104-105 yr) in what are known as Milankovitch cycles. These changes are thought to play a role in climate change on very long time scales and, perhaps, in pacing glacial-interglacial cycles, as will be discussed in Section 12.3.5.

### 5.1.2. Outgoing radiation

The net radiative budget of the Earth-atmosphere system, averaged over the year, is shown in Fig. 5.5. The absorbed solar radiation (incoming minus reflected) has a strong maximum in the tropics, where it is

90°S 60"S 30°S 0" 30"N 80°N 90»N

FIGURE 5.5. Annual mean absorbed solar radiation, emitted long-wave radiation, and net radiation, the sum of the two. The slight dip in emitted long-wave radiation at the equator is due to radiation from the (cold) tops of deep convecting clouds, as can be seen in Fig. 4.26.

90°S 60"S 30°S 0" 30"N 80°N 90»N

### Latitude

FIGURE 5.5. Annual mean absorbed solar radiation, emitted long-wave radiation, and net radiation, the sum of the two. The slight dip in emitted long-wave radiation at the equator is due to radiation from the (cold) tops of deep convecting clouds, as can be seen in Fig. 4.26.

about six times larger than at the poles. The latitudinal variation of emitted long-wave radiation, however, is much less, implying that the actual pole-to-equator temperature difference is smaller than it would be if the atmosphere was in thermodynamic balance at each latitude, column by column. Averaged over the year, there is a net surplus of incoming radiation in the tropics and a net deficit at high latitudes. Since local energy balance must be satisfied, Fig. 5.5 implies that there must be a transport of energy from low to high latitudes to maintain equilibrium (see Problem 1 at the end of this chapter).

5.1.3. The energy balance of the atmosphere

The required transport is quantified and plotted in Fig. 5.6 based on satellite

90°S 60°S 30°S 0" 30°N 60°N 90°N Latitude

FIGURE 5.6. The northward energy transport deduced by top of the atmosphere measurements of incoming and outgoing solar and terrestrial radiation from the ERBE satellite. The units are in PW = 1015W (see Trenberth and Caron, 2001). This curve is deduced by integrating the ''net radiation'' plotted in Fig. 5.5 meridionally. See Chapter 11 for a more detailed discussion.

90°S 60°S 30°S 0" 30°N 60°N 90°N Latitude

FIGURE 5.6. The northward energy transport deduced by top of the atmosphere measurements of incoming and outgoing solar and terrestrial radiation from the ERBE satellite. The units are in PW = 1015W (see Trenberth and Caron, 2001). This curve is deduced by integrating the ''net radiation'' plotted in Fig. 5.5 meridionally. See Chapter 11 for a more detailed discussion.

measurements of incoming and outgoing solar and terrestrial radiation at the top of the atmosphere (see Section 11.5). In each hemisphere, the implied flux of energy is around 6 x 1015 W = 6 PW.2 As will be discussed in the following chapters (particularly Chapters 8 and 11), the transport is achieved by fluid motions, especially in the atmosphere, but with the ocean also making a significant contribution.

5.1.4. Meridional structure of temperature

### Troposphere

The observed structure of annual-mean temperature T (where the overbar implies zonal average3) and potential temperature 9 in the troposphere and lower stratosphere are shown in Figs. 5.7 and 5.8 respectively. Temperature decreases upward and (generally) poleward in the troposphere. The annual average surface temperature is below 0°C poleward of about 60° latitude, and reaches a maximum of 27°C just north of the equator. The annual-mean pole-to-equator temperature difference over the troposphere is typically 40°C.

As can be seen in Fig. 5.8, surfaces of constant potential temperature, often referred to as isentropic (constant 9 implies constant entropy; see Problem 5 of Chapter 4) surfaces, slope upward toward the pole in the troposphere. Moreover 9 (unlike T) always increases with height, reflecting the stability of the atmosphere to dry processes discussed in Section 4.3.2. The closely spaced contours aloft mark the stratosphere, the widely spaced contours below mark the troposphere. The transition between the two, the tropopause, is higher in the tropics than over the pole.

3The zonal average of a quantity X is conventionally written X (with an overbar) where:

Zonal-Average Temperature (°C)

Zonal-Average Temperature (°C)

Utitude

FIGURE 5.7. The zonally averaged annual-mean temperature in °C.

Utitude

FIGURE 5.7. The zonally averaged annual-mean temperature in °C.

Figure 5.9 shows the annual mean equivalent potential temperature, 0e, defined by Eq. 4-30, and vividly displays the effects of vigorous convection in the tropics which remove vertical gradients of 0e. This should be contrasted with the large vertical gradients of dry potential temperature, 0, seen in Fig. 5.8.

### Stratosphere

The zonally averaged temperature is again shown in Fig. 5.10 (plotted here against height rather than pressure to emphasize upper altitudes) for solstice conditions. The features of the vertical temperature structure discussed in Chapter 3 are even clearer in Fig. 5.10: the temperature minima at the tropopause (at height 10-16 km) and mesopause (near 80 km), and the maximum at the stratopause (near 50 km). Note the latitudinal variation of these features, especially the variation of the tropopause, which is high and cold in the tropics, and much lower and warmer in high latitudes. In fact, there is something like a discontinuity of the tropopause in the subtropics (the ''tropopause gap''), which, as we will see in Chapter 8, is associated with the presence of strong winds in the jet stream. Air moving between the troposphere and stratosphere in a vertical direction (upward in the tropics, downward in the extratropics) does so very slowly, so that it has time to adjust its potential temperature to ambient values in response to weak diabatic processes. However, air can be exchanged more rapidly across the tropopause gap, since it can do so adiabatically by moving almost horizontally along isentropic surfaces between the tropical upper troposphere and the extratropical lower stratosphere.

The latitudinal temperature variation of the stratosphere is consistent with the incoming radiation budget; its temperature is greatest at the summer pole, where the averaged incoming radiation is most intense. However, in the troposphere the pole remains far colder than the tropics, even in summer. The polar regions, after a long cold winter, remain covered in highly reflective ice and snow (which do not have time to melt over the summer) and so have a high albedo (typically around 60%,

Zonal-Average Potential Temperature (K)

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