1) Solar radiation intensity governs seasonal climate changes and local climates due to variations in the sun's apparent height. 2) Incoming solar radiation is not evenly distributed across latitudes, creating heating imbalances between the equator and poles. 3) Calculations of solar radiation incident on Earth's curved surface must account for variables including latitude, time of day, day of year, and Earth's tilted orbit which causes seasons.

1. Riccardo Rigon
IlSole,F.Lelong,2008,ValdiSella
Solar Radiation
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2. R. Rigon
Radiation intensity
Solar intensity governs seasonal climatic changes and the local climatic niches
which are linked to the apparent height of the Sun.
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3. R. Rigon
Insolation and latitude
Incoming solar radiation is not evenly distributed across all lines of latitude,
creating a heating imbalance.
Figure3.7
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4. R. Rigon
Radiative imbalance
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5. R. Rigon
decreases towards the poles and it is reduced in areas where clouds
form frequently
For example, the complete energy balance is greater at the equator but the
greatest amount of insolation is in the subtropical deserts
Average annual radiation is
< 80 W/m2 in the cloudy parts of the arctic and the antarctic
>280 W/m2 in the subtropical deserts
Radiation received from the Sun
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6. R. Rigon
From a subjective point of view, the Sun varies its height in the sky seasonally.
This is the subject of interest in the study of the geometry of radiation.
The geometry of radiation
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7. R. Rigon
Calculations of the incident radiation onto the surface of the Earth need to
take account of the geometry of the interaction between the Sun’s rays and
the surface of the Earth, which is curved and therefore variably
exposed with respect to the direction of the Sun in function of latitude,
time of day (longitude) and, naturally, day of the year. Moreover the
Earth rotation is inclined with respect to its orbit around the Sun , and
this causes seasons to happen.
To sum up
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8. R. Rigon
The geometry of radiation
To calculate the aforementioned
quantities it is usual to use a
topocentric coordinate system,
that is, with the origin in the
geographic position of the
observer, which is right-handed
and positioned on the plane
tangent to the Earth’s surface in
the considered point.
N.B. - A coordinate system located at the
centre of the Earth id called geocentric.
NauticAlmanacOffice,1974
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9. R. Rigon
The geometry of radiation
The X-axis is, therefore, tangent
to the earth and positive in a
West-East direction. The Y-axis
is tangent in the North-South
direction and is directed towards
the South. The Z-axis lies on the
segment joining the centre of the
Earth with the point being
considered on the surface.
It is assumed that the Sun lies in
the ZY plane at the solar noon.
NauticAlmanacOffice,1974
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10. R. Rigon
Solar Vector
The solar vector can be expressed as a
function of the angles that have been
defined. The resulting trigonometric
expression is:
Therefore, to determine the position of
the Sun one needs to know the latitude,
t h e h o u r a n g l e , a n d t h e s o l a r
declination.
⌥s = ⇤
sin ⇥ cos
sin ⇤ cos ⇥ cos cos ⇤ cos
cos⇤ cos ⇥ cos + sin ⇤ sin
⇥
⌅
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X
Y
Z

11. R. Rigon
Hour angle
The hour angle can be easily
calculated as:
⇥ =
t
12
1
⇥
if t is the solar hour
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12. R. Rigon
Solar declination
The solar declination is a function of the day of the year (and the era). It
requires complex calculations that take account of the precession movements
of the Earth. There are, however, various approximations. The one that is
presented here is due to Bourges, 1985:
where is the day of the year
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Is the angular height of Sun from the horizon at equator at noon*
*http://en.wikipedia.org/wiki/Declination

13. R. Rigon
X
Y
Z
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Projection on a plane at a certain
latitude
is the solar vector
⌥s = ⇤
sin ⇥ cos
sin ⇤ cos ⇥ cos cos ⇤ cos
cos⇤ cos ⇥ cos + sin ⇤ sin
⇥
⌅
If is the vertical unit row-vector
corresponding to the Z axis:
and
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14. R. Rigon
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Projection on a plane at a certain
latitude
with the symbols explained above
Then the projection of the solar
irradiation on the plane YX is reduced by
the factor where:
or:
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X
Y
Z

15. R. Rigon
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To sum up:
Was:
Is now:
The solar constant can be modified as follows.
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