In the previous topic, we learned that
the Earth's seasons are controlled by changes in the **duration** and **intensity** of **solar
radiation** or **insolation**.
Both of these factors are in turn governed by the annual
change in the position of the Earth's axis relative to
the Sun (see **Figure 6h-4**).

Yearly changes in the position
of the Earth's axis cause the location of the Sun to
wander 47° across
our skies. Changes in the location of the Sun have a
direct effect on the intensity of solar radiation. The
intensity of solar radiation is largely a function of
the **angle
of incidence**, the angle at which the Sun's rays
strike the Earth's surface. If the Sun is positioned
directly overhead or 90° from the horizon, the incoming
insolation strikes the surface of the Earth at right
angles and is most intense. If the Sun is 45° above
the horizon, the incoming insolation strikes the Earth's
surface at an angle. This causes the rays to be spread
out over a larger surface area reducing the intensity
of the radiation. **Figure 6i-1** models the effect
of changing the angle of incidence from 90 to 45°.
As illustrated, the lower Sun angle (45°) causes
the radiation to be received over a much larger surface
area. This surface area is approximately 40% greater
than the area covered by an angle of 90°. The lower
angle also reduces the intensity of the incoming rays
by 30%.

**Figure 6i-1:** Effect
of angle on the area that intercepts an incoming beam
of radiation.

We can also model the effect the angle of incidence has on insolation intensity with the following simple equation:

## Intensity = SIN (A)

where, **A **is
the angle of incidence and **SIN** is
the sine function found on most
calculators. Using this
equation we can determine that an angle of 90° gives
us a value of 1.00 or 100% (1.00 x 100). Let us compare
this maximum value with values determined for other angles
of incidence. **Note** the
answers are expressed as a percentage of the potential
maximum value.

**SIN 80 **= **0.98
or 98%**

**SIN 70 **= **0.94
or 94%**

**SIN 60 **= **0.87
or 87%**

**SIN 50 **= **0.77
or 77%**

**SIN 40 **= **0.64
or 64%**

**SIN 30 **= **0.50
or 50%**

**SIN 20 **= **0.34
or 34%**

**SIN 10 **= **0.17
or 17%**

**SIN 0 **= **0.00
or 0%**

The yearly changes in the position of the
Earth's axis relative to the **plane
of the ecliptic** also causes seasonal variations
in day length to all locations outside of the equator.
Longest days occur during the **June
solstice** for locations north of the equator
and on the **December
solstice** for locations in the Southern Hemisphere.
The equator experiences equal day and night on every
day of the year. Day and night is also of equal length
for all Earth locations on the **September** and ** March
equinoxes**.

**Figure 6i-2**describes the change in the length of day for locations at the equator, 10, 30, 50, 60, and 70 degrees North over a one-year period. The illustration suggests that days are longer than nights in the Northern Hemisphere from the March equinox to the September equinox. Between the September to March equinox days are shorter than nights in the Northern Hemisphere. The opposite is true in the Southern Hemisphere. The graph also shows that the seasonal (winter to summer) variation in day length increases with increasing latitude.

Figure 6i-2: Annual
variations in day length for locations at the equator,
30, 50, 60, and 70° North latitude. |

**Figure 6i-3** below describes the
potential insolation available for the equator and several
locations in the Northern Hemisphere over a one-year
period. The values plotted on this **graph** take
into account the combined effects of angle of incidence
and day length duration (see **Table
6h-2**). Locations at the equator show the least
amount of variation in insolation over a one-year period.
These slight changes in insolation result only from the
annual changes in the altitude of the Sun above the horizon,
as the duration of daylight at the equator is always
12 hours. The peaks in insolation intensity correspond
to the two **equinoxes** when
the Sun is directly overhead. The two annual minimums
of insolation occur on the **solstices** when
the maximum height of the Sun above the horizon reaches
an angle of 66.5°.

The most extreme variations in insolation
received in the Northern Hemisphere occur at 90 degrees
North. During the **June
solstice** this location receives more potential
incoming solar radiation than any other location graphed.
At this time the Sun never sets. In fact, it remains
at an altitude of 23.5 degrees above the horizon for
the whole day. From September 22 (**September
equinox**) to March 21, (**March
equinox**) no insolation is received at 90
degrees North. During this period the Sun slips below
the horizon as the northern axis of the Earth has an
orientation that is tilted away from the Sun.

The annual insolation curve
for locations at 60 degrees North best approximates
the seasonal changes in solar radiation intensity perceived
at our latitude. Maximum values of insolation are received
at the June solstice when day length and angle of incidence
are at their maximum (see **Table
6h-2** and **section** **6h**).
During the June solstice day length is 18 hours and 27
minutes and the angle of the Sun reaches a maximum value
of 53.5 degrees above the horizon. Minimum values of
insolation
are received during the **December
solstice **when day length and angle of incidence are at their
minimum (see **Table
6h-2** and **section** **6h**).
During the December solstice day length is only 5 hours
and 33 minutes and the angle of the Sun reaches a lowest
value of 6.5 degrees above the horizon.

**Figure 6i-3:** Monthly
values of available insolation in Wm^{-2} for the
equator, 30, 60, and 90° North.