Outer Earth processes and systems - Physical Processes in Earth and Environmental Sciences - page 248

away on 5-6 July (note that these dates are not the same as
the times of solstice, see below). As a consequence the
solar radiation received varies by about

of the spin axis about a circle, causing the northern and
southern hemispheres to change their times of closest and
furthest approach, at aphelion and perihelion respectively,
approximately every 2.2

3.5 percent from
the mean value. Although these figures are not appreciable
compared to the other effects noted below, exact calcula-
tions of the gravitational effects of the other planets in the
Solar System on Earth's elliptical orbit led to the later
theory (due to Leverrier in 1843) of time-variable eccen-
tricity, whereby the yearly orbit becomes more and less
eccentric on the rather long timescale of around 10 5 yr. At
the present time and for the foreseeable future (Fig. 6.12)
we are in a period of average to low eccentricity; at times
of highest eccentricity it is calculated (originally by Croll)
that the change of radiation may be greater than 5 percent.
A second orbital mechanism is based on the regular
“wobble” of Earth's inclined spin axis relative to the plane
of rotation around the Sun or to some point fixed in space.
This wobble is due to the gravitational attraction of
the Sun and Moon upon Earth's own equatorial bulge.
The practical effect of this leads to the “precession of the
equinoxes,” a phenomenon discovered in about 120 BC by
Hipparchos of Alexandria (see Section 1.4), whose own
observations of star clusters taken at fixed yearly times and
positions compared to those observed by earlier Egyptian
and Babylonian astronomers (going back to about 4,000 BC )
led him to note the gradual shift of familiar star clusters
around the Earth's ecliptic, the plane of the solar orbit,
at times of solstice. One complete wobble involves a circuit

10 4 yr. This is the explanation for
the fact noted above that the solstices (times of maximum
tilt of the Earth away from and toward the Sun) do not
have to coincide with aphelion and perihelion. In terms of
solar radiation received at Earth's surface the Lambert-
Bouguer law (Section 4.19) makes it clear that the effects
of precession are greatest at the equator, decreasing
toward the poles. Minimum levels of radiation for either
hemisphere away from the polar circles occur when peri-
helion corresponds to winter. Today we are close to the sit-
uation of southern hemisphere summer at perihelion:
about 11 ka any Palaeolithic astronomers would have
experienced northern hemisphere summers at perihelion.
A final orbital mechanism depends upon the angle of the
inclined spin axis changing relative to the ecliptic.
Calculations and observations indicate that this is cur-
rently changing by about 1

10 4 deg yr 1 . Over a

4 10 4 yr period the axis varies about extreme values of

21.8 . In

terms of solar radiation received, again according to the
Lambert-Bouguer law, minimum levels are to be expected
in winter when tilt is maximum, but the effect makes no
difference to high polar latitudes since these are in dark-
ness anyway. The effect has greatest influence in moderate
to high latitudes.

and 24.4 . The current value is around 23.44

6.2 Atmosphere-ocean interface

6.2.1 Atmospheric boundary layer: Momentum
exchange over the ocean

lent shear flows (Fig. 6.14). Here we can relate the rate of
increase of m ean velocity with height above the water or land
interface, , to a shear or friction velocity, u * , which
defines the degree of turbulent momentum exchange or
momentum flux associated with any wind. This causes a sur-
face shear stress,

d u /d z

Having considered general atmospheric circulation we now
consider the behavior of the atmospheric boundary layer
(ABL), part of the frictional wind driven over the ocean.
Momentum exchange occurs in the lower parts of the ABL
close to the ocean-atmosphere interface; offshore platforms
are used to determine this (Fig. 6.13). We know from
Chapter 3 that fluid in any boundary layer transmits a stress
to its bounding medium through the transfer of momen-
tum, the rate of transfer being proportional to the overall
rate of fluid flow as measured by some local time-mean
velocity. In the very high Reynolds number situations that
exist in air flows we may completely ignore viscous stresses
and ascribe the fluid momentum transfer and mixing
processes in the interface region to the turbulence. We have
seen previously (Section 4.5) that this region defines what is
known as the “wall-layer” or “logarithmic zone” of turbu-

( u * ) 2 , where C d is a drag (friction)

zx C d

coefficient and is the density of air. The practical problems

of measuring C d are numerous and beyond the scope of this
text; however, they provide the key to many practical ocean
forecast models. The great importance of estimates of sur-
face wind shear lies in its key role in determining coupled
ocean-atmosphere interactions, especially their role in deter-
mining surface flow direction in climate models. For this
purpose longer-term time-mean values, such as monthly
means, must be taken from areas of the ocean correspond-
ing to required model grid spacing. However, computa-
tions of shear must al so take into account shorter-term
fluctuations, , about over periods of days or even hours.

A key application is in the field of tropical cyclone modeling