## Q

7.27 x 10-5s-1

Surface gravity

g

9.81 ms-2

a

6.37 x 106m

Surface area of Earth

4na2

5.09 x 1014m2

Area of Earth's disc

na2

1.27 x 1014m2

with altitude and does not have a definite top. As we shall see in Chapter 3, its density decreases approximately exponentially away from the surface, falling by a factor of e about every 7 km. About 80% of the mass of the atmosphere is contained below 10 km altitude. Fig. 1.1 shows, to scale, a shell of thickness 10 km on a sphere of radius 6370 km.

The thinness of the atmosphere allows us to make some simplifications. For one thing, we can take g to be constant (the fractional decrease in gravity from the Earth's surface to 10 km altitude is about 10-4 and so is negligible in most applications). We will see that we can often neglect the Earth's

FIGURE 1.1. The thinness (to scale) of a shell of 10 km thickness on the Earth of radius 6370 km.

curvature and assume planar geometry. But there are of course (as we will also see) some aspects of spherical geometry that cannot be neglected.

Land covers about 30% of the surface of the Earth and, at the present time in Earth's history, about 70% of Earth's land is in the northern hemisphere (see Fig. 9.1). As Fig. 1.2 illustrates, the height of mountains rarely exceeds 2 km and so is a relatively small fraction of the vertical decay scale of the atmosphere. Thus, unlike the ocean, the atmosphere is not confined to basins. As it flows around the globe, air is deflected by topography but never completely blocked.