This document discusses solar energy and solar physics. It begins by introducing solar radiation and how it powers processes on Earth and in the atmosphere. It then covers the wave and particle nature of light, as well as solar physics concepts like the source of the Sun's energy being nuclear fusion in its core. The document concludes by discussing radiation laws that govern the relationships between the Sun's surface temperature and the energy it emits.

1. 1.15 Solar Energy
Ilhami Yildiz, Dalhousie University, Truro-Bible Hill, NS, Canada
r 2018 Elsevier Inc. All rights reserved.
1.15.1 Introduction 639
1.15.2 Light and Solar Physics 639
1.15.2.1 Light as Waves 639
1.15.2.2 Light as Particles 640
1.15.2.3 Solar Physics 640
1.15.3 Source of the Sun’s Energy 641
1.15.4 The Radiation Laws 641
1.15.5 Characteristics of Solar Radiation 642
1.15.5.1 The Solar Constant 642
1.15.5.2 The Solar Spectrum 643
1.15.5.3 Solar Time 646
1.15.5.4 Solar Geometry 647
1.15.5.5 Solar Radiation 648
1.15.5.6 Solar Angle 649
1.15.5.7 Atmospheric Effects 651
1.15.5.7.1 Direct normal solar radiation 652
1.15.5.7.2 Diffuse solar radiation 653
1.15.6 Insolation Levels at the Earth’s Surface 654
1.15.7 Concluding Remarks 664
References 664
Relevant Websites 664
Nomenclature
a Constant (2897 mm K); or (0.1996 d (Gm)3/2
)
A Albedo; apparent incoming solar radiation at
air mass ¼ 0 (W m2
)
AST Apparent solar time (minutes)
B Dimensionless ratio
c Speed of light (3 108
m s1
); constant;
dimensionless ratio
C Diffuse radiation factor (dimensionless), degree
celsius
d Day; Julian day (number); number of days per
year (365)
E Amount of energy (J s1
, J m2
s1
, MJ m2
s1
or W m2
mm1
); east
ET Equation of time (minutes)
F Angle factor (dimensionless)
FPC Flat plate collector
Gm Gigameter
h Planck constant (6.626 1034
J s)
H Hour angle (degree of arc)
Hz Hertz (cycle s1
)
I Amount of solar radiation (W m2
)
J Joule
K Absolute temperature
L Local latitude (degree of arc)
LON Local longitude (degree of arc)
LSMT Longitude of the standard time meridian
(o
of arc)
LST Local solar time (degree of arc)
m Mass (kg); meter
M Mega
N North
NE Northeast
NW Northwest
Q Amount of heat energy (J, kJ or MJ)
QOP Incident angle for the vertical surface (o
of arc)
QOV Angle of incidence (degree of arc)
R Radius (m or km)
S South
SE Southeast
ST Standard time (degree of arc)
SW Southwest
T Temperature (o
C or K)
W Watt; west
Y Time period (days)
Greek letters
b Solar altitude (degree of arc)
δ Solar declination (degree of arc)
D Difference
e Emissivity
f Solar azimuth angle (degree of arc)
F Tilt angle of the Earth (degree of arc)
g Surface solar azimuth (degree of arc)
Comprehensive Energy Systems, Volume 1 doi:10.1016/B978-0-12-809597-3.00117-6
638

2. l Wavelength (mm)
m Micro
v Frequency (cycles s1
¼Hz)
y Angle of incidence (degree of arc)
s Stefan–Boltzmann constant (5.679 108
J m2
K4
s1
)
S Tilt angle of the surface (degree of arc)
ς Reflectance (dimensionless),
C Surface azimuth angle (degree of arc)
Subscripts
d Diffuse
D Direct
DH Direct component of insolation on a horizontal
surface
DN Direct normal
dg Ground-reflected diffuse
ds Diffuse solar
E Earth
g Ground
H Horizontal
max Maximum
r Ground reflected; summer solstice
S Sun
sg Between the surface and the ground
ss Between the surface and the sky
SE Earth to the Sun
t Direct solar radiation
V Vertical
l Monochromatic
1 Number
2 Number
Superscripts * Blackbody
1.15.1 Introduction
Solar energy powers virtually everything in the Earth and atmosphere system. This energy warms the air and the Earth’s surfaces,
and drives the winds, currents, evaporation, clouds, rain, etc. Essentially, the process starts when the Sun’s energy in the form of
electromagnetic radiation (radiation, in short) enters the atmosphere. The seasonal distribution of this energy obviously depends
on the orbital characteristics of the Earth revolving around the Sun. Solar radiation reaching the Earth is significantly impacted by
the inclination of the Earth’s axis. This axis (the line joining the two poles through the center of the Earth) is tilted 23.5 degrees
from the perpendicular. The axis maintains the same orientation with respect to the galaxy; therefore, the amount of incoming
solar radiation at the top of the atmosphere, hence at the surface of the Earth, varies considerably, creating seasons (by impacting
the duration of daylight and elevation of the Sun in the sky with respect to time).
The solar spectrum covers the range of radiation from very short wavelengths to very long wavelengths. The spectrum belonging
to a blackbody at 6000K is pretty close to the incident radiation from the Sun at the top of the Earth’s atmosphere. When the Sun’s
radiation passes through the Earth’s atmosphere, it is reflected, scattered, and absorbed by dust particles, gas molecules, ozone, and
water vapor. The magnitude of the solar radiation’s attenuation at a given time and location is determined by atmospheric
composition and length of atmospheric pathway the solar radiation travels. Compared to scattering, atmospheric absorption of
solar radiation is relatively small. Ozone’s absorption of ultraviolet radiation is a significant component, which is vital for
sustaining life on Earth. In addition to the ultraviolet absorption, at other wavelengths, absorption by nitrous oxide, carbon
dioxide, oxygen, ozone, and water vapor takes place as well.
The solar radiation reaching a surface on the Earth has both direct and diffuse components. Energetically they act in the same
way. Since diffuse radiation comes from the entire sky, it is difficult to predict its intensity as it varies as moisture and pollutant
contents of the atmosphere change throughout any given day at any location.
This radiant energy entering the Earth and atmosphere system is eventually transformed into a variety of other energy forms.
We will begin this chapter with solar physics, and talk about the source of the Sun’s energy. Then we will cover the radiation laws.
And then, after covering the characteristics of solar radiation in depth, the chapter concludes with a brief conclusion statement.
1.15.2 Light and Solar Physics
Newton was among the first to realize that a sunbeam is the composite of beams of different colors that comprise what is termed
as the visible spectrum. We have spent the last three centuries understanding the nature of light, and now we have a fairly complete
model of the nature of light, or more generally speaking, of radiation.
1.15.2.1 Light as Waves
Light is considered to behave as the composite waves of different wavelengths. Wavelength is the distance between a given point
(let us say the peak) on one wave and the same point (the next peak) on the next wave in the same wavelength. The wavelengths
Solar Energy 639

3. of, let us say, visible light are extremely short; therefore, we use a relatively small unit of wavelength: the micrometer. A micrometer
is one-millionth of a meter, and is abbreviated as mm where m stands for one-millionth, and m indicates “meter.” In the visible
spectrum, the red light has the longest wavelengths, whereas the violet has the shortest. As will be discussed later in depth, the
atmosphere scatters light differently based on its wavelength. In the visible spectrum, for instance, shorter wavelength blue and
violet light are more readily scattered compared to longer wavelength lights. Actually, this is the reason that we see the sky in blue
(as the human eye is not so sensitive to violet wavelengths).
1.15.2.2 Light as Particles
Performed experiments also indicated that light energy behaves like a stream of particles. For instance, it is difficult to understand
how sunlight travels through an empty space, as waves require a medium to travel in or propagate their energy. Ocean and sound
waves for instance have water and air media to travel using the water and air molecules to propagate their energy, respectively.
Without the mentioned media, it would not be possible for them to exist as there would be no molecules to vibrate. Light waves,
however, require no medium to propagate. Light is considered as a stream of particles of radiant energy, also known as photons.
And they have no mass, occupy no space, and travel at the speed of light; in this sense, they are quite different from particles of
matter. As will be presented further in the chapter, the amount of energy carried by an individual photon is extremely small and
inversely related to wavelength. The shorter the light’s wavelength is, the higher the energy content of its photons. In the visible
spectrum, for instance, violet light photons have more energy content than those of red light photons.
As presented above, each of the wave and particle models describes certain behavior of light that the other model cannot.
Hence, light is only explained by this wave–particle duality model.
Another important aspect is that the photons are different from particles of matter. Countless photons are created and
destroyed at any time; however, these creations and destructions do not violate the law of conservation of energy, as they simply
change forms through emission and absorption. Energized particles of matter (a molecule or electron), before discharging their
excess energy fully or partially and returning to their lower energy levels, remain at energized or excited stage for a very short time.
This discharging or shedding of excess energy is done by releasing a photon. Obviously, more energy interactions result in higher
energy photons, and thus, emissions at shorter wavelengths. The energy source leading to photon production can be in any form,
such as nuclear, combustion, and electricity. In summary, a photon can be described as a bundle of energy emitted by an excited
molecule, atom, or electron as it returns from a high-energy level to a lower energy level. Molecules, atoms, and electrons (that is,
the basic particles of matter) create and destroy photons, which form the basic particles of radiant energy.
1.15.2.3 Solar Physics
Solar energy comes from the thermonuclear reactions in the core of the Sun, where most of the solar mass is concentrated (Fig. 1).
In the core, the temperature at a pressure of about 10 106
bar is estimated to be approximately 15 106
K. This energy moves
outwards by radiative diffusion in the interior section; from there it is transferred by convection to the photosphere. Then from this
outer surface zone, the energy, mostly shortwave radiation, is emitted into space in all directions by radiation. The outer surface or
photosphere has an average temperature of about 6000K (more accurately 5780K); however, it fluctuates due to the sunspots,
Core
Interior
Convective zone
Photosphere
Fig. 1 Main radial zones of the Sun. Modified after Taylor FW. Elementary climate physics. New York: Oxford University Press; 2005. p. 29–39.
640 Solar Energy

4. which are relatively cooler regions having temperatures closer to 4000K. When it strikes a material, the radiation can be absorbed,
transmitted, or reflected.
The Sun has a radius (696,000 km) approximately 100 times larger than that of the Earth. And its mass is estimated as 2 1030
kg which is 300 million times bigger than that of the Earth. Just like any other planet, it is believed that the Sun is 4.5 billion years
old, mainly composed of hydrogen (91.2%) and helium (8.7%), and most likely to last for 5.5 billion more years.
1.15.3 Source of the Sun’s Energy
As noted earlier, solar energy comes from the thermonuclear reactions in the core of the Sun, where most of the solar mass is
concentrated. Spectroscopic measurements of sunlight reaching the Earth from the photosphere (Fig. 1) dictates that the solar mass
is mainly composed of two elements, hydrogen (H) – which makes up about 70% of solar mass, and helium (He) – about 27%;
the remaining 3% of solar mass is made up of all the other elements [1]. The reaction is
4 1
H
-4He þ energy þ 2 neutrinos
The conversion of H into He through solar fusion serves as the source of solar radiation (electromagnetic radiation) received on
the Earth. Every second, approximately 630 t of H are estimated to be converted to 625 t of He and 5-t mass equivalent energy
(E¼mc2
), which gives an approximate energy release of 4 1020
MJ every second.
1.15.4 The Radiation Laws
Photosphere, the outer layer of the Sun, continuously loses energy by electromagnetic radiation into space in all directions covering
all regions of the electromagnetic spectrum; therefore, a large temperature gradient exists between the core and the outer surface of
the Sun. This electromagnetic energy is radiated as a stream of light particles, photons, moving along a sinusoidal wave trajectory.
Radiation is a form of energy that is emitted by all objects having a temperature above absolute zero, and can travel through the
vacuum of outer space. Consequently, the energy coming from the Sun and leaving the Earth ought to be in the form of radiation.
The radiation laws govern the relationships between the surface of the Sun and the energy emitted into the space in all
directions. First of these laws is called Planck’s law, which basically states that the wavelength of emission from a perfectly black
object, a blackbody, which is a perfect emitter and absorber of radiation (Kirchhoff’s law), depends on the temperature of the
emitting body.
E
l ¼ c1=fl5
½expðc2=lTÞ21g ð1Þ
where E
l is the amount of energy (W m2 m
m1
) emitted at a single wavelength l (mm) (blackbody monochromatic radiation) at
temperature T (K). The constants c1 and c2 have magnitudes of 3.74 108
W mm4
m2
and 1.44 104
mm K, respectively. Solar
radiation, a very good approximation to that of a blackbody, which follows Planck’s curve, is obtained using Eq. (1) for an average
outer surface temperature (6000K) of the Sun (Fig. 2). Actual objects can emit less than the theoretical blackbody value, that is,
El ¼ el E
l where el is emissivity, which is a measure of emission efficiency.
Example 1: Find: blackbody monochromatic radiation at a single wavelength of 0.5 mm emitted by the Sun’s surface, E
l .
Solution: Assuming a surface temperature of 6000K, blackbody monochromatic radiation at 0.5 mm is
E
l ¼ 3:74 108
W mm4
m2
= ð0:5 mmÞ5
exp 1:44 104
mm K =ð0:5 mmÞ 6000K
ð Þ
21
n o
E
l ¼ 99:3 106
W m2
mm1
108
Solar
Terrestrial
6000K
0 ~0.5 2 0 ~10 60 80
Wavelength (μm)
300K
(W
m
–2
μm
–1
)
15
10
5
0
0
Spectral
irradiance
(W
m
–2
μm
–1
)
Fig. 2 Schematic views of the standard blackbody curves for solar and terrestrial radiations assuming the corresponding temperatures.
Quantitative vertical scales approximately show the differences in total energy emitted by the Sun and the Earth. The values given by the
Stefan–Boltzmann equation (E ) are given by the area beneath the curves.
Solar Energy 641

5. Or, it is simply 99.3 MJ per square meter solar surface area every second.
The fundamentals of radiation or the photon emission process were discussed in depth in Section 1.15.2. Absorption of
radiation or photons is the exact reverse of the photon emission process. A photon is absorbed as soon as it interacts with a
molecule, an atom, or one of its electrons. And this interaction destroys the photon and brings the molecule or an atom to an
excited state. The excited molecule or atom subsequently starts reemitting one or more photons, and continues the exchange of
energy from radiant energy to atomic excitation and back again.
Two other particularly useful radiation laws, which can be derived from Eq. (1) by differentiation and integration, respectively,
are Wien’s law for the wavelength of a maximum emission for a blackbody at a given temperature, and the Stefan–Boltzmann law
for the total energy emitted by a blackbody.
Wien’s displacement law states that the wavelength at which a blackbody emits its maximum amount of radiation is inversely
proportional to its absolute temperature in Kelvin.
lmax ¼ a=T ð2Þ
where l is in mm, a is 2897 mm K, and T in K.
Example 2: Find: calculate lmax for the Sun’s surface.
Solution: Assuming an average surface temperature of approximately 6000K, we would have its maximum emission at
lmax ¼ 2897 mm K =6000K
lmax ¼ 0:48 mm
A wavelength of approximately 0.5 mm lies within the visible spectrum.
Example 3: Find: calculate lmax for the Earth’s surface.
Solution: Assuming an average surface temperature of 151C (i.e., 288.15K), we would determine its maximum emission at
lmax ¼ 2897 mm K =288:15K
lmax ¼ 10:0 mm
A wavelength of 10.0 mm lies within the infrared spectrum way beyond the visible spectrum. This shows that a hotter object
emits a greater portion of its energy at shorter wavelengths than a cooler object.
For determining how much radiation a given object emits over all wavelengths combined, we need to sum up all the energy
contributions of the photons at all wavelengths. Actually, this total energy is represented by the area between the object’s blackbody curve
and the x-axis as shown in Fig. 2. That area, and therefore the energy, is given by the Stefan–Boltzmann law, which is simply given as
E ¼ s T4
ð3Þ
where E is the energy in Joules emitted by a square meter of the objects surface per second, s is known as Stefan–Boltzmann constant
and has a magnitude of 5.679 108
J m2
K4
s1
, and T is the absolute temperature of the surface in Kelvin.
Example 4: Find: using the Stefan–Boltzmann Law, estimate the Sun’s radiation emission.
Solution: Assuming an average surface temperature of the Sun as 6000K, we can estimate that the Sun emits:
E ¼ 5:679 108
J m2
K4
s1
6000K
ð Þ4
E ¼ 73:6 MJ m2
every second:
Overall, in all directions with a radius of 6.96 1011
m, we can easily calculate the Sun’s emission as approximately 4.5 1020
MJ of energy every second.
1.15.5 Characteristics of Solar Radiation
This section starts with the solar radiation reaching the outer space of the atmosphere, and analyzes the spectral distribution of this
radiation. And then, variations in the amount of this radiation are studied covering the impacts of different variables, such as time,
solar geometry, and atmospheric effects.
1.15.5.1 The Solar Constant
It is pretty useful to know a few energy terms. The first one is the amount of solar radiation reaching onto a horizontal surface,
which is called the insolation – short for “incoming solar radiation.” The second term is the rate of energy flow, which is also
known as power. The unit of power used in SI units is the watt. One watt is an energy flux of one joule per second; therefore, the
unit of time is built into the definition of the watt. The third term refers to the amount of insolation reaching the top of the Earth’s
642 Solar Energy

6. atmosphere, that is, the amount of solar energy passing through unit area every second at the mean distance of the Earth (perpendicular
to the Earth–Sun) line, and is called the solar constant. The term solar constant provides a convenient way of referring to the flux of
energy radiated by the Sun. Measurements over approximately the past 100 years show that the Sun’s energy output is nearly constant.
The measured flux is virtually the same. The quantity of the solar constant, the amount of solar radiation incident per second on a 1 m2
surface oriented perpendicular to the beam and positioned at the top of the atmosphere at Earth’s mean distance from the Sun, varies
only slightly with time, and expressed in watts, has a mean measured value of 1368 W m2
. And these watts are related to the units in
which people buy electric energy for their households, which are typically given in the unit of kilowatt-hour.
Example 5: Find: using the measured solar surface temperature of 5780K, calculate the solar constant.
Solution:
E ¼ ð5:679 108
J m2
K4
s1
Þ ð5780KÞ4
E ¼ 63;384;522 W m2
And using a surface area of the Sun ( ¼ 4pR2
S ¼ 6:09 1012
km2
), we can calculate E in watts,
E ¼ 63;384;522 W m2
6:09 1018
m2
E ¼ 3:86 1026
W
And dividing this by the surface area of a sphere at the mean distance of Earth to the Sun (4pR2
S ¼ 2:83 1017
km2
), we can
calculate the solar constant as
Solar Constant ¼ E W
ð Þ = 4pR2
SE
¼ 3:86 1026
W = 2:83 1023
m2
Solar Constant ¼ 1364 W m2
This calculated solar constant is pretty close to the mean measured value (by satellites) of 1368 W m2
at an average distance
(Earth orbit radius), RSE, of 1.495 108
km. Note that we employ the inverse-square law here (that is, radiation emitted from a
spherical source decreases with the square of the distance from the center of the sphere, E2 ¼E1 (R1/R2)2
, where R is the radius
from the center of the sphere).
If we multiply, let us say, the measured solar constant 1368 W m2
by the projected area of the Earth (pR2
E, where RE is the
mean radius of the Earth, 6371 km), then using the area of a disk rather than the surface area of a sphere, we can find the
intercepted solar radiation by the Earth as a whole at the top of the atmosphere every second approximately 1.74 1011
MJ. In
reality, incoming radiation is the solar constant minus reflected sunlight, times the area of the intercepting surface; that is, (1 A)
(Solar Constant) (pR2
E), where A is the global albedo (0.3), which will be discussed further in depth later. Overall, the top of the
atmosphere receives about 4.5 1010
of the total energy output of the Sun.
Example 6: Find: determine the intercepted solar radiation by the Earth as a whole at the top of the atmosphere every second.
Solution:
Intercepted Solar Radiation ¼ 1 A
ð Þ Solar Constant
ð Þ pR2
E
where albedo A is 0.3, the measured solar constant is 1368 W m2
, and the mean radius of the Earth is 6.371 106
m. Then,
Intercepted Solar Radiation ¼ 1 0:3
ð Þ 1368 W m2
p 6:371 106
m
2
Intercepted Solar Radiation ¼ 1:22 1011
MJ
Ignoring the losses from the solar beam as it goes through the atmosphere; we can find that a one-square-meter area of the
Earth’s surface oriented toward the solar beam at about 45-degree angle receives 1.368 kWh of solar energy every hour. Con-
sidering that a kilowatt-hour is a 1000-W energy flow lasting for an hour, we can now imagine the amount of solar energy reaching
a roof surface exposed to the Sun during a day.
1.15.5.2 The Solar Spectrum
Fig. 3 shows the complete set of possible wavelengths, also known as the electromagnetic spectrum. The solar spectrum covers the
range of radiation from very short wavelengths (high frequency) to very long wavelengths (low frequency), as shown in Fig. 4. The
smooth spectrum (dashed line) in Fig. 4 belongs to a blackbody at 6000K. And this spectral shape is pretty close to the incident
radiation from the Sun at the top of the Earth’s atmosphere. The observed deviations are mostly in the high-energy (ultraviolet)
region (lo0.4 mm), where the molecular bands responsible for ozone production are found.
The wavelength of peak radiation emission at 0.5 mm actually suggests that the Sun has a blue-green color; however, we see the
Sun as yellow-white due to the radiation’s interaction with the Earth’s atmosphere and relative sensitivity of the human eye (has a
Solar Energy 643

7. maximum sensitivity B0.55 mm). And as shown in Fig. 4, the effect of the Earth’s atmosphere is to reduce the total insolation
reaching the top of the atmosphere to the magnitudes reaching sea level. The solar radiation emission mainly falls in the
wavelength region of 0.15–4.0 mm, with about 9% in the form of ultraviolet radiation (l o0.40 mm), 38% in the visible (0.40–0.70
mm), and 53% in the near infrared (0.7–4.0 mm) regions. In Fig. 4, we see that at very short wavelengths, the Sun emits a relatively
small amount of radiation, and as we move to the right toward the visible spectrum, the emission increases sharply reaching a
maximum at about the middle of the visible range. However, the visible spectrum is still just a segment in a much broader range of
solar radiation. Earlier we called this electromagnetic radiation because it has both electric and magnetic properties. The properties of
light presented earlier in Section 2 apply to radiation throughout the electromagnetic spectrum or solar spectrum. Therefore, moving
to the left in Figs. 3 and 4 also means moving toward radiation of shorter wavelengths and hence more energetic photons. Moving to
the right, on the other hand, means that we move toward longer wavelengths and therefore less energetic photons. As will be
discussed further later, the photons of ultraviolet radiation, for instance, are highly energetic and the stratospheric ozone plays an
important role in shielding the Earth’s surface from these photons. The Sun also emits shorter wavelength X-rays and gamma rays,
and longer wavelength infrared (4.0–100 mm), microwave (0.1–10 mm), and radio (41 cm) photons; however, these do not make
Wavelength (μm)
Radiation
intensity
(amount)
0.4 0.7 1.0
37% 11% Less than 1%
0.001 1 10 100
44%
Near
infrared
Microwaves
TV
waves
Short
radio
waves
AM
radio
waves
Ultraviolet
1.5
Wavelength (m)
Visible
light
Far
infrared
7%
Fig. 3 Electromagnetic spectrum: the complete set of possible wavelengths. Courtesy of Donald C. Essentials of meteorology: an invitation to the
atmosphere. 4th ed. Southbank, Vic.: Thomson Learning Inc.; 2004.
2.0
6000K blackbody radiation
Solar spectrum at top of the atmosphere
Solar spectrum at sea level
1.5
1.0
0.5
Spectral
intensity
(kW
m
−2
μm)
0
0 0.2 0.4 0.6 0.8 1.0
Wavelength, λ (μm)
1.2 1.4 1.6 1.8 2.0
High Low
Frequency
High Low
Photon energy content
Fig. 4 Solar spectrum. The smooth dashed line is the spectrum that the Sun would have if it were a blackbody at the “best fit” temperature
of 6000K. Modified after Sen Z. Solar energy fundamentals and modeling techniques. Springer London; 2008. p. 47–98. Sen, 2008.
644 Solar Energy

8. any significant contribution to the total solar energy reaching to the Earth and atmosphere system. As mentioned earlier, the smooth
spectrum (dashed line) in Fig. 4 belongs to a blackbody at 6000K. Blackbody is the term employed to describe a perfectly efficient
radiator (not referring to its actual color). Therefore, the blackbody radiation given in Fig. 4 represents the maximum radiation the
Sun at a given average temperature of 6000K can emit. And we should also remember that most solids, liquids, and dense gases
radiate very close to the blackbody radiation and have what we call continuous spectra of radiation.
Air molecules, as in the atmosphere, however, are quite separated and have much less interaction with each other compared to
those molecules of denser substances. And each air molecule has distinct mass and structure, vibrates, rotates, and goes through
different processes more or less independent of the surrounding molecules. Substances (such as CH4, N2O, O2 and O3, CO2, and
H2O) that interact with only certain discrete energy level photons and wavelengths are defined as selective absorbers and emitters.
These substances are not considered as blackbodies because at certain wavelengths they emit (or absorb) either very little or no
radiation – line spectra of radiation (Fig. 5). It is because of this reason that the Stefan–Boltzmann equation (which gives the total
amount of radiation emitted or absorbed) is not applicable for a selective emitter or absorber like the atmosphere; therefore the
solar spectrum at sea level has a different shape from the other two in Fig. 4.
As Figs. 3 and 4 show, wavelength (l) and frequency (v) are related, and this relationship can formally be expressed through the
speed of light, c, as follows:
c ¼ l v ð4Þ
where c is the speed of light, which has a value of 3 108
m s1
, l is the wavelength (mm), and v is the frequency (cycles s1
, also
known as Hz). If one is known, then the other can easily be determined using the speed of light, which is a constant.
Example 7: Find: determine the frequency for a radiational wavelength of 0.5 mm.
100 Nitrous oxide
Methane
Molecular
oxygen
and ozone
Watervapor
Absorption
(%)
Carbondioxide
N2O
H2O
CO2
CH4
50
0
0.1
0.3
0.5
0.7
O3
O3
O2
1
5
10
15
20
0.1
0.3
0.5
0.7
1
5
Wavelength (μm)
10
15
20
100
50
0
100
50
0
100
50
0
100
50
0
100 UV
Visible Atm
window
Infrared (IR)
Total
atmosphere
50
0
Fig. 5 Absorption of radiation by gases in the atmosphere – line spectra of radiation. Courtesy of Donald C. Essentials of meteorology: an
invitation to the atmosphere. 4th ed. Southbank, Vic.: Thomson Learning Inc.; 2004.
Solar Energy 645

9. Solution:
c ¼ lv
v ¼ c=l
¼ 3 1014
m s1
=ð0:5 mmÞ
¼ 3 1014
mm s1
=ð0:5 mmÞ
¼ 6 1014
cycles s1
v ¼ 6 1014
Hz
And similarly, a radiational wavelength of 10 mm has a frequency, v, of 3 1013
cycles s1
(or 3 1013
Hz).
Solar radiation consists of photons, which can be considered as packets of energy, which is related to frequency v as
E ¼ hv ð5Þ
where E is the energy content (J) and h is Planck’s constant (6.626 1034
J s). This shows that shorter wavelengths have higher
frequencies and higher energy contents compared to those of longer wavelengths (lower frequencies), as shown in Figs. 3 and 4.
Example 8: Find: determine the energy content, E, of a frequency of 6 1014 Hz (or 0.5 mm wavelength).
Solution:
E ¼ hv
E ¼ ð6:626 1034
J sÞ ð6 1014
cycles s1
Þ
E ¼ 3:98 1019
J
And similarly, a radiation frequency of 3 1013
Hz (or 10 mm wavelength) has an energy content, E, of approximately
1.99 1020
J. This clearly shows the above-mentioned difference between the energy contents of two different wavelengths.
1.15.5.3 Solar Time
Orbital velocity of the Earth varies throughout the year, as does apparent solar time (AST), determined by a sundial, which changes
in small amount from the mean time, which is kept by a clock running at a constant rate. This change is called the equation of time
(ET). The position of the Sun in the sky is dictated by local solar time (LST), which is determined by adding the ET to the local civil
time. Local civil time, on the other hand, is calculated from local standard time (either by adding to or subtracting from) the
longitude correction of 4 min/degree difference between the local longitude and the longitude of the standard time meridian
(LSTM) for the location in hand (e.g., 75 degrees for the Eastern Standard Time in Canada and the USA).
The relationship between AST and local standard time is provided in Eq. (6):
AST ¼ LTS þ ET þ 4 LSTM LON
ð Þ ð6Þ
where ET is the equation of time in minutes of time (Table 1), LSTM is the local standard time meridian in degree of arc (in Canada
and the USA, the LSTs are 60 degrees for Atlantic Standard Time (ST); 75 degrees for Eastern ST; 90 degrees for Central ST; 105
degrees for Mountain ST; 120 degrees for Pacific ST; 135 degrees for Yukon ST; 150 degrees for Alaska–Hawaii ST), LON is the local
longitude in degree of arc, and 4 is the minutes of time required for the Earth’s 1.0-degree rotation.
Table 1 Equation of time (ET), declination angle, apparent insolation (A) at zero air mass, and related data for the 21st day of each month
Month Equation of time (ET) (min) Solar declination (degrees) A (W m2
) B C
(dimensionless ratios)
January 11.2 20.0 1228.5 0.142 0.058
February 13.9 10.8 1212.8 0.144 0.060
March 7.5 0.0 1184.4 0.156 0.071
April 1.1 11.6 1134.0 0.180 0.097
May 3.3 20.0 1102.5 0.196 0.121
June 1.4 23.45 1086.8 0.205 0.134
July 6.2 20.6 1083.6 0.207 0.136
August 2.4 12.3 1105.7 0.201 0.122
September 7.5 0.0 1149.8 0.177 0.092
October 15.4 10.5 1190.7 0.160 0.073
November 13.8 19.8 1219.1 0.149 0.063
December 1.6 23.45 1231.7 0.142 0.057
Source: ASHRAE. Handbook of fundamentals. American society of heating. Atlanta, GA: Refrigeration and Air Conditioning Engineers, Inc.; 1989. p. 27.1–27.38.
646 Solar Energy

10. In the next section, we will see that the equatorial plane of the Earth is tilted at an angle of 23.5 degrees to the orbital plane
(Fig. 6); and therefore, the solar declination δ (the angle between the Earth–Sun line and the equatorial plane) varies throughout
the year (Fig. 6 and Table 1). And this variation, with its nonuniform periods of daylight and darkness, is the reason behind having
different seasons.
1.15.5.4 Solar Geometry
We know that the planets in the solar system make elliptical orbits around the Sun. The main features of the orbital geometry of
the Earth are shown in Fig. 6. The ellipticity in the solar system is relatively small; therefore, the Earth’s motion around the Sun as
well follows a nearly circular elliptical orbit with a period of 365-1/4 days. Kepler found that, for circular orbits, the time period
(Y) of the orbit is related to the distance (R) of the planet from the Sun, that is, Y¼a R3/2
. Parameter a¼0.1996 d (Gm)3/2
, where
d is Earth days and Gm is gigameters (109
m).
Example 9: Find: the Earth’s orbital period, Y.
Solution: Using an average Sun to Earth distance, R¼149.6 g.
Y ¼ a R3=2
Y ¼ 0:1996 d Gm
ð Þ3=2
149:6 Gm
ð Þ3=2
Y ¼ 365:2 days
Using a leap year every 4 years, the shortcoming of 365 days we use per year is corrected accordingly.
Fig. 6 shows that the Earth is closest to the Sun when it is winter (January) in the Northern Hemisphere, and farthest away in July.
As mentioned earlier, solar radiation reaching the Earth is significantly impacted by the inclination of the Earth’s axis. This axis
(the line joining the two poles through the center of the Earth) is tilted 23.5 degrees from the perpendicular. And, the axis
maintains the same orientation with respect to the galaxy; therefore, the amount of incoming solar radiation at the top of the
atmosphere, hence at the surface of the Earth, varies considerably creating seasons (by impacting the duration of daylight and
elevation of the Sun in the sky with respect to time). The incoming solar radiation reaching a unit horizontal area at any specific
location on the Earth’s surface, therefore, even though the Sun’s output energy is nearly constant, varies between 0 and
1050 W m2
, depending on the latitude, the season, the time of the day, the degree of cloudiness and air pollution. And this
section addresses the variations due to the latitude, the season, and the time.
Fig. 7 shows the Sun’s apparent paths across the sky on different dates. This is called the apparent path because it is
not the actual motion of the Sun; rather, it is the Earth’s rotation about its own axis once per day. As Earth rotates, different
regions start receiving the sunlight and end again. On September 21 (and on March 21), anywhere on the Earth, the Sun seems to rise
from the eastern side of the sky, move toward the west across the sky, and set 12 h later in the west. However, the actual apparent
path varies considerably based on the latitude. Solar beam is actually very rarely perpendicular to the Earth’s surface at any given
location. Fig. 7 shows that the smaller the angle between the incoming solar beam and the Earth’s surface is, the larger the area the
solar energy spreads; as a result, less solar energy is received per unit area. In late September, for instance, at the top of the atmosphere
Northern spring
Southern fall
Northern summer
Southern winter
Northern winter
Southern summer
March 21 Periapsis
January 3
Equinox
147 Mkm
Line of solstice
December 21
152 Mkm
September 21
Apoapsis
July 3
Northern fall
Southern spring
Declination
Angle,
June 21
Fig. 6 Earth’s motion around the Sun (time of orbit is one revolution of 365.242 days).
Solar Energy 647

11. over equatorial regions, more solar energy is received per unit area compared to that over other regions; however, a location directly
on the equator will receive the solar beam directly downward for a very short time around noon.
Daily path of the Sun is not constant throughout the year; rather it shifts slightly and steadily every day. And this has a huge
impact on insolation. The latitude and the season are a result of the solar geometry. For instance, the North Pole has a tilt toward
the Sun when it is summer in the Northern Hemisphere, and is away from the Sun when it is winter. Consequently, the Northern
Hemisphere has more daylight hours in the summer, reaching a maximum value on the summer solstice, June 21 (the position on
the left side of Fig. 6), when the North Pole’s tilt toward the Sun is greatest, and hence, the amount of solar radiation reaching a
horizontal surface is at the maximum in the summer. In the Northern Hemisphere, the Sun does not directly shine down on the
equator, but rather, on latitude 23.51N. On the summer solstice, the daily path is highest in the sky, and the length of daylight is
the longest of the year. In the Southern Hemisphere, on the other hand, the situation is the reverse, and the hemisphere is tilted
farthest from the Sun on or about June 21 and receives the least amount of sunlight and onset of winter. In the Northern
Hemisphere’s winter, however, due to the tilt angle (and the North Pole) facing away, that is, farthest from the Sun, the solar
radiation needs to go through a longer path resulting in more absorption and scattering in the atmosphere; therefore, less radiation
reaches to the Earth’s surface when the need for heat is the greatest. At this time of the year, the Sun is directly overhead at latitude
23.51S, which is called the winter solstice; and at this time, the Southern Hemisphere starts enjoying the beginning of summer with
long hours of the Sun high in the sky. Fig. 7 schematically shows the annual and hourly changes in the Sun’s position and relevant
solar angles for latitude, approximately let us say, 401N latitude. At the extreme, the noontime Sun is directly overhead at either the
Tropic of Cancer (summer solstice), or Tropic of Capricorn (winter solstice). At winter solstice, the areas north of the Arctic Circle
have 24-h darkness, whereas the areas south of the Antarctic Circle have 24-h daylight. When the Sun is directly overhead at the
equator (spring and autumnal equinoxes, on March 21 and September 21, respectively) there are 12 h of daylight everywhere on
the Earth; that is, all latitudes have equal amounts of day and night (Fig. 6).
Fig. 7 shows that as summer moves into fall, and then into winter, the sunrise and sunset times of the Sun’s motion across the
sky gradually move southward. As a result, the day lengths get shorter and the solar path gets lower in the sky. In December, the
Sun rises and sets quite a bit south of east and south of west, respectively. Fig. 7 depicts the Sun’s annual and hourly position only
for 401N. Note that the Sun’s summertime daily path never goes below the horizon; therefore, these regions experience continuous
sunlight (24 h of daylight each day) during summer months, which gives them the highest amount of insolation at the top of the
atmosphere, at least, at that time of the year. We must also note that there is a lack of significant variation in insolation values at
the top of the atmosphere throughout the year along the equator, compared to seasonal changes at higher latitudes. We also need
to recognize that January insolation values decrease drastically as we go from the equator toward the North Pole, but remain
constant south of the equator. In June, however, this pattern is reversed, with northern latitudes exposing little change.
1.15.5.5 Solar Radiation
As it will be discussed in depth in the following section, some solar radiation scattered by air molecules and dust reaches the Earth
in the form of diffuse radiation, Id. The intensity of diffuse radiation is a difficult task to complete as it comes from all directions in
S N
W
E
June 21
December 21
September 21/March 21
Fig. 7 Annual and hourly changes in the Sun’s position for 401N (b is the solar altitude – angle above the horizon, and f is the solar azimuth –
angle from the true south). Modified after Hinrichs RA, Kleinbach M. Energy: its use and the environment. 4th ed. Belmont, CA: Thomson Brooks/
Cole; 2006. p. 160–204.
648 Solar Energy

12. the sky, and varies as moisture and dust content of the atmosphere change throughout any given day. For instance, on an overcast
day, the diffuse component is all the solar radiation reaching the Earth.
The total solar radiation reaching a terrestrial surface, It, is composed of the direct solar radiation ID, the diffuse sky radiation Id,
and the solar radiation reflected from the surrounding surfaces Ir [2]. The direct solar radiation ID, is the product of the direct
normal solar radiation IDN and the cosine of the angle of incidence y between the incoming solar rays and a line normal
(perpendicular) to the surface [3]:
It ¼ IDN cos y þ Id þ Ir ð7Þ
1.15.5.6 Solar Angle
The position of the Sun in the sky is expressed in terms of the solar altitude and the solar azimuth. The height of the Sun, the
elevation of the Sun, is usually given in terms of the solar altitude b (Figs. 4 and 5). This is the angular distance between the
Sun’s rays and the horizon, and is given by Eq. (8) [3]. And the solar azimuth f is the angle measured from the true south
(Figs. 4 and 5), given by Eq. (9) [3].
sin b ¼ cos L cos δ cos H þ sin L sin δ ð8Þ
cos f ¼ ðsin b sin L2sin δÞ = ðcos b cos LÞ ð9Þ
where these angles depend on the local latitude L; the solar declination δ (the angle between the Earth–Sun line and the equatorial
plane (Fig. 6 and Table 1), which is a function of the time of year, and therefore varies from þ 23.5 degree on June 21 to 23.5
degrees on December 21; and the AST, expressed as the hour angle H, where H¼0.25 number of minutes from local solar
noon), in degrees. Hour angle is zero at local noon and increases in magnitude by p/12 (15 degrees) for every hour before or after
noon [3].
Further, assuming that the Earth’s orbit is circular, the solar declination angle for any day of the year can be approximated using
δ¼F cos [C (d – dr)/dy], where F is the tilt angle of 23.5 degrees, C is full 360 degrees, d is the Julian Day, dr is the Julian day for
summer solstice on June 21; and it is 172 for non-leap years, dy is the number of days per year, that is, 365 days (use 366 on a leap
year).
Example 10: Given: F¼23.5 degree; C=360 degree; dr ¼ 172 days; dy ¼ 365 days. Find: the solar declination angle on March 21.
Solution: Assume: Not a leap year.
Using δ ¼ F cos C d2dr
ð Þ=dy
:
δ ¼ 23:5 degree cos 360 degree 80 days 2 172 days
ð Þ=365 days
½
δ ¼ 0:3 degree
On the spring equinox (March 21), the declination angle should be zero; so our calculation is a good approximation. It is still
winter before March 21, and the declination angle should be negative; the values in spring and summer are positive.
Example 11: Find: the solar azimuth and altitude at 0830 Atlantic Standard Time (ST) on March 21 at 451N latitude and 631W
longitude.
Solution: Using Eq. (6), local time is 0830 þ 4 (60–63 degrees)¼0818. Table 1 gives the ET as 7 min, so AST¼0818 – 7¼0811
or 229 min from local solar noon; therefore, the hour angle, H¼0.25 229 min¼57.3 degrees. As calculated in Example 10 and
also provided in Table 1, the solar declination on March 21 is 0 degree. Therefore, using Eq. (8), the solar altitude, b can be
calculated as follows:
sin b ¼ cos 45o
cos 0o
cos 57:3o
þ sin 45o
sin 0o
sin b ¼ 0:382; therefore; b ¼ 22:5o
And, the solar azimuth, f, can be calculated using Eq. (7) as
cos f ¼ ðsin 22:5o
sin 45o
2 sin 0o
Þ = ðcos 22:5o
cos 45o
Þ
cos f ¼ 0:414; therefore; f ¼ 65:5o
Fig. 8 shows the solar angles and incident angles for horizontal and vertical surfaces. Line OV is perpendicular to the horizontal
plane in which the solar azimuth, angle HOS and the surface azimuth, angle POS (C) are located. Angle HOP is the surface solar
azimuth (g) and is given by
g ¼ f C ð10Þ
The solar azimuth angle f is negative for morning hours and positive for afternoon hours. The absolute value of the surface
solar azimuth g is used in Eq. (11). The surface is considered in the shade if g is greater than 90 degrees or less than 270 degrees.
Solar Energy 649

13. For any surface, the angle between the incoming solar rays and a line normal to the surface is called the angle of incidence, y.
For the horizontal surface given in Fig. 8, the angle of incidence yH is QOV; the incident angle for the vertical surface yV is QOP.
The incident angle y for any surface is related to the solar altitude b, the surface solar azimuth g, and the tilt angle of the surface
from the horizontal S as shown below [3]:
cos y ¼ cos b cos g sin S þ sin b cos S ð11Þ
where S is the tilt angle of the surface from the horizontal plane. When the surface is horizontal S is equal to zero degrees, and cos
y H ¼sin b. When the surface is vertical, however, S is equal to 90 degrees, and cos y V ¼cos b cos g [3].
Example 12: Find: for the conditions of Example 11 given above, find the incident angle at a vertical surface facing southeast.
Solution: As we have determined that the surface azimuth angle is to the east (AST o1200), and the surface azimuth is also to the
east (Table 2), they both must be negative, that is, f¼ 65.5 degrees and C¼ 45 degrees. Therefore, the surface solar azimuth,
g, can be calculated using Eq. (10) as
g ¼ 65:5 degrees ð45 degreesÞ ¼ 20:5 degrees
The negative surface solar azimuth angle that we calculated above indicates that the Sun at the given time is east of the line
normal to the surface.
As mentioned above, when the surface is vertical, S is equal to 90 degrees, and the incident angle, yv, can then be determined
using the relationship mentioned earlier, cos yv ¼cos b cos g. Therefore,
cos yv ¼ cos 22:5o
cos 20:5o
¼ 0:865
Then, the incident angle, yv, the angle between the incoming solar rays and a line normal to the surface:
yv ¼ 30:1 degrees
N
W
S
E
V
Z
P
Ψ
Σ = Tilt angle
O
Normal to
vertical surface
Solar azimuth
Solar altitude
Earth-sun line
Tilted surface
H
Q
Fig. 8 Solar angles (b is the solar altitude – angle above the horizon, and f is the solar azimuth – angle from the true south). Modified after
ASHRAE. Handbook of fundamentals. American society of heating. Atlanta, GA: Refrigeration and Air Conditioning Engineers, Inc.; 1989. p.
27.1–27.38.
650 Solar Energy

14. 1.15.5.7 Atmospheric Effects
In the previous section, we mainly focused the distribution of insolation at the top of the atmosphere at different times and locations.
In this section, we will trace a beam of solar energy and explore its interactions with the atmosphere. It will be assumed that the beam
has 100 units of energy as it enters the atmosphere. The fate of these 100 units of energy can be tracked by referring to Fig. 9 as we
read. From our daily observations, it would be clear that, if the air is free of clouds and pollution, the solar beam would reach the
ground with little interference from the atmosphere. The solar disk, on the other hand, becomes completely obscured under cloudy
or dirty sky conditions. Clear air is quite transparent to sunlight. Normally, when the Sun’s radiation passes through the Earth’s
atmosphere, it is reflected, scattered, and absorbed by dust particles, gas molecules, ozone, and water vapor. The magnitude of the
solar radiation’s attenuation at a given time and location is determined by atmospheric composition and length of atmospheric
pathway that the solar radiation travels. The length of atmospheric path is given in terms of the air mass m, which is the ratio of the
atmospheric air mass in the actual Earth–Sun path to the mass that would exist if the Sun were overhead at sea level (m¼1.0).
Obviously, above the atmosphere, m is equal to zero. Almost for all purposes, the air mass m at any given time and location equals
the cosecant of the solar altitude b (Fig. 8), multiplied by the ratio of the existing barometric pressure to standard pressure.
Interactions of solar radiation within the atmosphere takes place almost simultaneously; however, these interactions are
separate processes with different consequences, therefore, they must be treated separately.
Whenever a photon hits a particle or an object without being absorbed, scattering of radiation takes place. As soon as radiation
gets into the atmosphere, it starts interacting with small particles; this process is called scattering. When, however, radiation hits a
larger object, then there is a complete change in the photon’s travel direction, and this special condition is called reflection. This
change in travel direction can be in any or multiple directions.
Air molecules have sizes of somewhere between 0.0001 and 0.001 mm, which indeed are much smaller than the wavelength of
the visible band (0.4–0.7 mm). Small particles compared to the wavelength of solar radiation, such as atmospheric gas molecules,
generate something called Rayleigh scattering. How much scattering generated is directly proportional to the fourth power of the
wavelength; therefore, the scattering of blue light (lB0.4 mm) within a cloudless atmosphere without pollution is about 10 times
greater than that for red light (lB0.7 mm). As a result of this Rayleigh scattering process, we see the daytime sky in blue. In the
evening time, however, we observe a much redder Sun and reddish sky. This is because of the very long pathway the radiation
Table 2 Surface orientations and azimuth angles, measured from the south
Orientation N NE E SE S SW W NW
Surface azimuth angle, C 180 degree 135 degree 90 degree 45 degree 0 degree 45 degree 90 degree 135 degree
Source: ASHRAE. Handbook of fundamentals. American society of heating. Atlanta, GA: Refrigeration and Air Conditioning Engineers, Inc.; 1989. p. 27.1–27.38.
Top of the
atmosphere
Earth’s surface
Radiation from
the sun
100%
50% absorbed by
surface
Reflected from
surface, clouds,
and atmosphere
4% 20% 6%
20% absorbed by
clouds and atmosphere
Fig. 9 Schematic distribution of what happens to solar radiation after it falls on the Earth. Modified after Modified after Taylor FW. Elementary
climate physics. New York: Oxford University Press; 2005. p. 29–39.
Solar Energy 651

15. travels through the atmosphere, which causes most of the visible wavelengths to be scattered many more times leaving only the red
wavelength, some of which is also scattered to form a reddish sky.
When larger particles, such as water droplets and pollution particles, exist in the atmosphere – that is, the scattering particles
and the wavelength of the radiation have similar sizes – then a different type of scattering process takes place, which is called and
simplified as Mie scattering. In this case, all wavelengths are scattered almost uniformly, and the scattering is a function of both the
particle size and the wavelength of the radiation. When the atmosphere is polluted or overcast, then no wavelength is preferentially
scattered; as a consequence, it creates a light blue/greyish sky.
Air molecules and other small particles deflect some of the incoming solar beam in all directions. And under clear sky
conditions, 6% of the original 100 units are scattered back to space.
Compared to scattering, atmospheric absorption of solar radiation is relatively small. Ozone’s absorption of ultraviolet radiation is a
significant component that is vital for sustaining life on Earth. In addition to the ultraviolet absorption, at other wavelengths, absorption
by nitrous oxide, carbon dioxide, oxygen, ozone, and water vapor takes place as well. Overall, as shown in Fig. 9, approximately 20% of
the energy reaching the top of the atmosphere is absorbed by the clouds (2%, i.e., 2 units of our sample of 100 units) and the
atmosphere (18%, i.e., 18 units of our sample of 100 units). As mentioned above, some of the atmospheric absorption takes place due
to the molecules of ozone and monatomic oxygen in the upper atmosphere. Actually, it is this absorbed energy that is the cause of the
high temperatures observed in the stratosphere and thermosphere. As a result of the scattering, and the absorption by the clouds and the
atmosphere, only 74 units of the sample 100 units of energy are able to reach the Earth’s surface as direct beam or diffuse solar radiation
(which will be discussed further in the following section). Fig. 9 shows that the clouds alone significantly reduce the amount of solar
energy reaching the Earth’s surface. As mentioned above, clouds absorb 2%, and reflect 20% back to space (Fig. 9). All these
atmospheric processes (absorption, reflection, and scattering) leave only 54% of the original energy, which eventually reaches the Earth’s
surface (Fig. 9). It is obvious that the areas of maximum radiation receipt are the desert regions of the Earth, while minimum radiation is
received in the polar regions. It also needs to be remembered that Fig. 9 represents the long-term, global averages; therefore, the local
values would differ drastically. In high latitudes, for instance, where the solar angle is low, the solar beam has to pass through a much
longer atmospheric path than that at low latitudes; therefore, the solar beam is more likely to be scattered or absorbed further.
As briefly mentioned above, the solar radiation reaching a surface on the Earth has both direct (the radiation that casts a
shadow) and diffuse (radiation scattered from clouds, particles, and air molecules, coming from the entire sky) components.
Energetically though, they act in the same way. Since diffuse radiation comes from the entire sky, it is difficult to predict its
intensity as it varies as moisture and pollutant contents of the atmosphere change throughout any given day at any location. Since
cloud cover and atmospheric pollution vary considerably and are hard to predict, the best one can do is average the solar radiation
received at a location over a number of recent years and assume that, on average, the same amount will be received in the future. At
the Earth’s surface on clear days, solar radiation is approximately 85% direct and 15% diffuse. On a completely overcast day, all
solar radiation reaching the Earth’s surface is diffuse radiation.
1.15.5.7.1 Direct normal solar radiation
As mentioned earlier, the main portion of the solar radiation reaching the Earth’s surface on clear days is direct normal radiation or
solar intensity IDN, which is determined by Eq. (12) [3]:
IDN ¼ A=½exp ðB=sin bÞ ð12Þ
where A is the apparent incoming solar radiation (insolation) at air mass ¼ 0 (Table 2), and B is the atmospheric extinction
coefficient, a dimensionless ratio (Table 2). Both values vary during the year due to the seasonal changes in atmospheric pollution
and water vapor contents and the Earth–Sun distance.
Using Eq. (12) and Table 2, values for direct normal radiation or solar intensity IDN, at the Earth’s surface on a clear day for any
given latitude, can be calculated and tabulated for the daylight hours for the 21st day of each month.
Example 13: Find: for a clear day, find the direct component of insolation, IDH, on a horizontal surface for the conditions given in
our original example.
Solution: We have already determined that the solar altitude, b¼22.5 degrees, and that sin b¼0.382. Using Eq. (12), and the A,
B, and C values provided in Table 2, we can easily determine the direct normal irradiation or solar intensity, IDN, as
IDN ¼ A= ½exp ðB=sin bÞ ¼ ð1184:4 W m2
Þ = ½exp 0:156=0:382
ð Þ
IDN ¼ 787:3 W m2
And therefore, the direct component of insolation, IDH, on a horizontal surface is
IDH ¼ IDN sin b ¼ ð787:3 W m2
Þ sin 22:5 degree
IDH ¼ 301:3 W m2
Example 14: Find: for a clear day, determine the direct component of insolation, ID, on an inclined surface that has a tilt angle of
45 degrees and faces southeast for the conditions used in the examples above. That is, the solar azimuth and altitude at 0830
Atlantic Standard Time (ST) on March 21 at 451N latitude and 631W longitude.
652 Solar Energy

16. Solution: Earlier, the local time was determined to be 0818. And Table 1 provided the ET as 7 min, so AST was determined as
0811 or 229 min from local solar noon; therefore, the hour angle was then calculated as 57.3 degrees. As also determined
previously and provided in Table 1, the solar declination on March 21 is 0 degree. Then, using the solar altitude, b and solar
azimuth were calculated as b¼22.5 degrees and f¼65.5 degrees, respectively. We also determined that the surface azimuth is also
to the east (Table 2), so it must be negative, C¼ 45 degrees. Therefore, the surface solar azimuth, g, was calculated using Eq. (10)
as 20.5 degrees. The negative surface solar azimuth angle obviously indicates that the Sun at the given time is east of the normal
to the surface. Finally, the incident angle, yv, the angle between the incoming solar rays and a line normal to the surface was
calculated as yv¼30.1 degrees.
In Example 13, the direct normal irradiation or solar intensity, IDN, was calculated as 787.3 W m2
. As it was expressed earlier,
the total solar radiation reaching a terrestrial surface, It, is composed of the direct solar radiation ID, the diffuse sky radiation Id,
and the solar radiation reflected from the surrounding surfaces Ir.
The direct solar radiation, ID, is the product of the direct normal solar radiation, IDN, the cosine of the angle of incidence y
between the incoming solar rays and a line normal (perpendicular) to the surface, and also the surface solar azimuth g (as the Sun
is east of the inclined surface):
ID ¼ IDN cos y cos g ¼ 787:3 W m2
cos 30:1o
cos 20:5o
ID ¼ 638 W m2
Example 15: Find: assuming that the solar oven is 20% efficient and the useful rate of heat energy needed for cooking is 200 W,
and that the collector surface is horizontal, and ignoring the diffuse sky radiation and the ground-reflected diffuse radiation falling
on the collector, then find the reflector area of the oven that is needed to receive the required amount of radiation at 0830 Atlantic
time on March 21, 451N latitude.
Solution: The direct component of insolation reaching on a horizontal surface is calculated in Example 13 and already deter-
mined as 301.3 W m2
. The energy needed for the cooker is equal to the direct component of insolation times the oven efficiency
times the reflector are:
301:3 W m2
0:20
ð Þ Area; m2
¼ 200 W
Area ¼ 3:3 m2
We should remember that we have determined the required area for the cooking at 0830 in the morning when the direct
component of insolation reaching a horizontal surface is quite low. In reality, we would use the noontime insolation rate for
determining the required design area. We would also consider the diffuse sky radiation and the ground-reflected diffuse radiation
falling on the collector.
1.15.5.7.2 Diffuse solar radiation
The diffuse solar radiation reaching a surface on Earth may come from the sky and reflected solar radiation from adjacent surfaces.
On a clear sky, a simplified relation for the diffuse solar radiation reaching any surface from the sky is given by Eq. (13) [3]:
Ids ¼ C IDN Fss ð13Þ
where C is the diffuse radiation factor (dimensionless), Fss is 0.5 and 1.0 for vertical and horizontal surfaces, respectively, IDN is the
sky radiation falling on a horizontal surface, and Fss is the angle factor between the surface and the sky (dimensionless) deter-
mined by Eq. (14) for other surfaces [3]:
Fss ¼ ð1:0 þ cos SÞ=2 ð14Þ
where S is the tilt angle measured upward from the horizontal plane (Fig. 8).
Solar radiation reflected by ground has the components of diffuse sky and direct solar radiation falling on a horizontal surface.
The amount of total solar radiation reaching the ground is determined by Eq. (15) [3]:
ItH ¼ IDNðC þ sin bÞ ð15Þ
where IDN times sin b gives the direct radiation falling on a horizontal surface. Then, the ground-reflected diffuse solar radiation on
any surface can be estimated by Eq. (16) [3]:
Idg ¼ ItH ςg Fsg ð16Þ
where ςg is the reflectance of the foreground (dimensionless), and Fsg is the angle factor between the surface and the ground
(dimensionless). Obviously, the sum of the angle factors equals 1.0, and the angle factor for surface to ground is determined by
Eq. (17) [3]:
Fsg ¼ ð1:0 cos SÞ=2 ð17Þ
And if the surface is exposed to only the ground and the sky, then Fss¼(1.0 Fsg). The reflectance values for different ground
surfaces and foreground surfaces are provided by Threlkeld [4].
Solar Energy 653

17. Example 16: Find: the diffuse solar radiation incident on a solar collector first, and then determine the overall total solar radiation
reaching a collector surface with a 45-degree slope that faces southeast, at 0830 Atlantic time on March 21, 451N latitude.
Solution: Eq. (8) for the local latitude of L¼45 degrees, the declination angle of δ¼0 degree (Table 1), and the hour angle of
H¼57.3 degrees gave the solar altitude of b as 22.5 degrees. And then, we calculated IDN as 787.3 W m2
for 451N latitude at 0830
Atlantic time (i.e., at AST of 0811). And Table 1 gives C¼0.071 for March 21. Using Eq. (17) we can calculate the angle factor, Fsg,
from the collector to the ground as
Fsg ¼ ð1:0 cos 45o
Þ=2 ¼ 0:146
Remember that if the surface is exposed to only the ground and the sky, then Fss ¼(1.0 Fsg). Therefore, the angle factor from
the collector to the sky, Fss, is calculated as:
Fss ¼ 1:020:146
ð Þ ¼ 0:854
As mentioned earlier, solar radiation reflected by the ground has the components of diffuse sky and direct solar radiation falling
on a horizontal surface. Then, the diffuse solar radiation reaching the collector from the sky can be determined using Eq. (13) as
Ids ¼ 0:071 ð787:3 W m2
Þ 0:854
Ids ¼ 47:7 W m2
The amount of total solar radiation reaching the ground is calculated using Eq. (15):
ItH ¼ ð787:3 W m2
Þ ð0:071 þ sin 22:5o
Þ
ItH ¼ 357:2 W m2
If the ground is crushed rock having a solar reflectance of 20% (Table 3), the ground-reflected diffuse radiation, Idg, falling on
the collector can then be easily determined using Eq. (16) as
Idg ¼ 357:2 W m2
0:20
ð Þ 0:146
ð Þ
Idg ¼ 10:4 W m2
The total diffuse solar radiation falling on the collector is, then, determined as the sum of diffuse sky radiation and the ground-
reflected diffuse radiation, that is, 47.7 þ 10.4¼58.1 W m2
.
And then, the overall total solar radiation reaching a collector surface with a 45-degree slope that faces southeast, at 0830
Atlantic time on March 21, 451N latitude can be determined by Eq. (7) as
It ¼ ID þ Id þ Ir
It ¼ 638 W m2
þ 47:7 W m2
þ 10:4 W m2
It ¼ 696:1 W m2
1.15.6 Insolation Levels at the Earth’s Surface
As explored in the previous section, on a long-term, global average, only 54% of the solar energy passing through the top of the
atmosphere reaches the Earth’s surface (Fig. 9). Just a portion of this energy is absorbed at the Earth’s surface, while the remainder
is reflected. The reflected portion compared to the incoming radiation is defined as the albedo.
Albedo; A ¼ Reflected solar radiation=Incoming solar radiation ð18Þ
Table 3 Solar reflectance values of various surfaces
Foreground surface Incident angle (degrees)
20 30 40 50 60 70
New concrete 0.31 0.31 0.32 0.32 0.33 0.34
Old concrete 0.22 0.22 0.22 0.23 0.23 0.25
Bright green grass 0.21 0.22 0.23 0.25 0.28 0.31
Crushed rock 0.20 0.20 0.20 0.20 0.20 0.20
Bitumen and gravel roof 0.14 0.14 0.14 0.14 0.14 0.14
Bituminous parking lot 0.09 0.09 0.10 0.10 0.11 0.12
Source: Adopted from Threlkeld JL. Thermal environmental engineering. New York, NY: Prentice-Hall; 1962. p. 321.
654 Solar Energy

18. Albedo is normally expressed as a percentage, and satellite measurements indicate that the Earth’s surface has an average
albedo value of 8%; that is, on average, 8% of the insolation reaching the Earth’s surface is reflected back. Albedos for typical
surfaces are presented in Table 4. When both sides of Eq. (18) are multiplied by the incoming solar radiation, then the expression
becomes
Reflected solar radiation ¼ A Incoming solar radiation ð19Þ
Example 17: Find: using Eq. (19) and an average surface albedo of 8% (i.e., 0.08), determine the reflected solar radiation.
Solution:
Reflected solar radiation ¼ A Incoming solar radiation ¼ 0:08 54 units
Reflected solar radiation ¼ 4:32 B4
ð Þ units reflected (see Fig. 9)
If the albedo concept is applied to the whole Earth and atmosphere system, then we obtain the so-called planetary albedo,
which has a long-term average value of 30%; that is, 30 units (20 from clouds, 6 from atmosphere, and 4 from the Earth’s surface)
of the sample 100 units of solar energy are reflected back to space (Fig. 9). The remaining 70% of the solar energy reaching the
Earth and atmosphere system is absorbed and transformed into heat.
In Section 5, we defined insolation as the amount of solar radiation reaching onto a horizontal surface – short for “incoming
solar radiation.” Basically, that means how much sunlight is shining down on us. By knowing the insolation levels of a particular
region, we can actually determine the size of solar collector that is required, and how much energy it can produce. Obviously, an
area with poor insolation levels will need a larger collector area than an area with high levels.
For application purposes, insolation level is generally expressed in kWh m2
day1
, and is the amount of solar energy that
strikes a square meter of the Earth’s surface in a single day. Btu or MJ may also be used, in which case the conversion is: 1 kWh m2
day1
¼317.1 or Btu ft2
day1
¼3.6 MJ m2
day1
. The raw energy conversions are: 1 kWh¼3412 Btu¼3.6 MJ.
As discussed earlier in depth, insolation levels change throughout the year, with the lowest in winter and the highest in
summer. And, close to the equator, the difference throughout the year is minimal whereas at high latitudes winter can be just a
fraction of summer levels. A very high summer value, as we would see in a hot desert area is 7 kWh m2
day1
. For comparison
purposes, the readers are referred to the average annual insolation values for Oslo, Norway¼2.27 kWh m2
day1
(considered as
very low) and Miami, Florida¼5.26 kWh m2
day1
(considered as very high).
Tables 5–10 list the average insolation values for major cities in each region of the world, which can be used in solar
energy project designs [5]. The NASA Surface Meteorology and Solar Energy (SSE) data set consists of resource parameters that
were developed and formulated for assessing and designing renewable energy systems. The monthly average amount of the
total solar radiation incident on a horizontal surface at the surface of the Earth for a given month, is averaged for that month
over a 10-year period. Each monthly averaged value was evaluated as the numerical average of 3-hourly values for the
given month.
Renewable energy technologies range in complexity from the introduction of solar ovens and simple photovoltaics panels into
rural communities to the construction of commercial buildings with integrated photovoltaics and large thermal and wind gen-
erating power plants. The availability of accurate global solar radiation and meteorology data is extremely important for successful
renewable energy projects. NASA’s Earth Science Enterprise (ESE) makes the SSE data set available free of charge over the Internet
(http://eosweb.larc.nasa.gov/sse/).
Historically, climatological profiles of insolation and meteorology parameters calculated from ground measurements have
been used for determining the viability of renewable energy projects. Although ground measurement data have been
used successfully, ground measurement stations are situated mainly in populated regions. In remote areas, where many renewable
energy projects are being implemented, measurement stations are quite limited. Also, at some stations, available data can be
Table 4 Albedos of typical surfaces
Surface A Surface A Surface A Surface A
Fresh snow 75–95 Sandy soil 20–25 Asphalt road 5–15 Tobacco 19
Old snow 35–70 Pet soil 5–15 Dirt road 18–35 Potatoes 19
Gray ice 60 Lime 45 Concrete 15–37 Alfalfa 23–32
Deep water 5–20 Gypsum 55 Buildings 9 Cotton 20–22
Dark wet soil 6–8 Lava 10 Mean urban 15 Sorghum 20
Light dry soil 16–18 Granite 12–18 Fallow field 5–12 Coniferous forest 5–15
Red soil 17 Stones 20–30 Wheat 10–23 Deciduous forest 10–25
Wet clay 16 Tundra 15–20 Rice paddy 12 Green grass 26
Dry clay 23 Sand dune 20–45 Sugar cane 15 Green meadow 10–20
Wet loam 16 Thick cloud 70–95 Winter rye 18–23 Savanna 15
Dry loam 23 Thin cloud 20–65 Corn 18 Steppe 20
Source: Adopted from Stull RB. Meteorology for scientists and engineers. 2nd ed. Pacific Grove, CA: Thomson Brooks/Cole; 2000. p. 23–38.
Solar Energy 655

19. sporadic and incomplete, and data inconsistencies may occur as well. In contrast to ground measurements, the SSE data set is
continuous, consistent, and long-term global insolation data. Although the SSE data within a particular grid cell are not necessarily
representative of a particular microclimate, or point, within the cell, the data are considered to be the average over the entire area of
the cell. The SSE data set is however not intended to replace ground measurement data. NASA reports that it is prepared to fill the
gap where ground measurements do not exist, and to augment areas where ground measurements are available. In utilizing the
SSE data set, the renewable energy resource potential can be determined for any location on the globe and is considered to be
accurate for preliminary feasibility studies for renewable energy projects. Detailed insolation information (including direct solar
normal and diffuse components, and more) for any particular location or time can be directly obtained from NASA [6].
Table 11, on the other hand, lists the estimates of annual solar resource availabilities and ranks around the world, and may
prove to be useful [6].
Example 18: Find: assuming that the flat plate collector (FPC) efficiency is 50% and ignoring the ground-reflected radiation falling
on the collector, determine the collector size to be tilted from the horizontal surface facing south (for both Los Angeles (341N
latitude), California, USA, and Halifax (451N latitude), Nova Scotia, Canada) needed to heat a total of 150 L of hot water per day
(required for four people living in a household) from 10 to 501C in March.
Solution: We know that the amount of heat required for the given temperature difference can be calculated using the equation
Q¼m Cp DT, where m is the mass of water, Cp is the specific heat of water, and Q is the heat needed.
Q ¼ 150 kg 4186 J kg1 o
C1
50210
ð Þo
C
Q ¼ 25; 116; 000 J day1
B25:1 MJ day1
The heat available from the FPC is Q¼Insolation FPC Area Efficiency. Table 10 provides the average intensity of the
insolation falling on the ground for March in Los Angeles as 5.09 kWh m2
day1
. Then, the heat available from the FPC is
25:1 MJ day1
¼ ð5:09 kWh m2
day1
Þ 3:6 MJ kWh1
FPC Area ðm2
Þ 0:5
Collector Area ¼ 2:7 m2
As a useful rule of thumb, the collector should be tilted 44–45 degrees from the horizontal surface facing south for Los Angeles
(341N local latitude plus 10 degrees), California, USA.
Table 5 Monthly and annual average of daily insolation values (kWh m2
day1
) for Africa
AFRICA
Country City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
Avg
B. Faso Ouagadougou 121 240
N 11 300
E 5.48 6.43 6.56 6.62 6.53 6.16 6.76 5.48 5.87 6.18 5.83 5.35 6.02
C. A. Rep. Bangui 181 320
N 1201 360
E 4.13 4.97 5.99 6.61 6.17 5.53 5.73 4.87 5.07 4.55 4.07 3.81 5.12
Cameroon Yaoundé 31 480
N 111 300
W 4.94 5.38 5.16 4.68 4.46 4.42 5.17 5.07 5.03 5.40 5.29 4.83 4.98
Djibouti Djibouti 111 330
N 431 090
E 5.60 5.77 6.59 6.81 6.85 6.87 6.46 6.47 6.56 6.77 6.22 5.56 6.37
Algeria Alger 361 500
N 31 000
E 2.22 2.94 3.87 5.00 5.88 6.69 7.23 6.48 5.15 3.53 2.43 2.02 4.45
Egypt Cairo 291 350
N 311 090
E 3.39 4.17 5.24 6.49 7.11 8.00 7.88 7.40 6.42 5.07 3.86 3.19 5.68
Ethiopia Addis Ababa 91 20
N 381 420
E 5.96 5.80 6.23 6.31 6.11 5.79 5.03 5.00 5.64 6.31 6.15 5.75 5.84
Ghana Accra 51 360
N 01 120
W 5.65 6.01 5.65 5.33 5.00 4.49 4.50 4.59 4.67 5.25 5.70 5.55 5.20
Gambia Gambia 131 280
N 161 390
W 5.01 5.93 6.67 6.92 6.72 6.06 5.48 5.09 5.30 5.67 5.36 4.95 5.76
Guinea Conakry 91 360
N 131 360
E 5.81 6.41 6.51 6.22 5.69 5.69 5.09 5.05 5.46 5.87 5.98 5.60 5.78
Kenya Nairobi 11 160
S 361 480
E 6.05 6.24 6.07 5.70 5.42 5.14 4.88 5.09 5.78 6.03 5.48 5.60 5.62
Liberia Liberia 61 3000
N 91 300
W 5.43 5.72 5.59 5.31 5.11 4.61 4.25 4.19 4.67 5.13 5.24 5.20 5.03
Libya Tarabulus 321 540
N 131 110
W 3.10 4.03 5.19 6.48 6.89 7.77 8.11 7.45 6.12 4.58 3.35 2.76 5.48
Morocco Rabat 321 320
N 91 170
W 3.13 3.86 5.09 6.08 6.89 7.31 7.34 6.80 5.69 4.37 3.25 2.82 5.21
Mali Bamako 121 300
N 71 540
E 5.61 6.35 6.64 6.78 6.42 6.47 5.87 5.65 6.04 6.13 5.85 5.36 6.09
Mauritania Nouakchott 171 450
N 151 450
E 5.31 6.21 6.80 7.54 7.57 7.63 7.20 6.90 6.78 6.34 5.49 4.88 6.55
Niger Niamey 131 300
N 21 120
W 5.42 6.39 6.72 6.79 6.75 6.31 6.07 5.78 6.07 6.16 5.79 5.29 6.12
Nigeria Abuja 91 120
N 71 110
E 5.57 6.33 6.22 6.10 5.89 5.47 4.92 4.65 5.12 5.82 5.81 5.42 5.61
Sudan Al Khurtum 151 330
N 331 320
E 5.46 6.19 6.75 7.25 6.85 6.96 6.52 6.35 6.42 6.17 5.66 5.22 6.31
Sierra Leone Freetown 81 290
N 131 140
W 5.19 5.91 6.08 5.47 4.76 4.09 3.60 3.58 4.25 4.84 4.93 4.94 4.80
Senegal Dakar 141 380
N 171 270
W 4.84 5.77 6.56 6.81 6.70 5.70 5.15 5.01 5.13 5.46 5.03 4.63 5.56
Somalia Muqdisho 21 020
N 451 200
E 6.38 6.81 6.71 6.28 5.85 5.45 5.21 5.61 6.15 6.16 6.00 5.91 6.04
Tunisia Tunis 361 480
N 101 680
E 2.29 3.06 4.09 5.47 6.38 7.16 7.57 6.80 5.33 3.65 2.54 2.08 4.70
656 Solar Energy

20. Table 7 Monthly and annual average of daily insolation values (kWh m2
day1
) for Canada
CANADA
Province City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Avg
AB Edmonton 531 340
N 1131 310
W 1.45 2.36 3.41 4.25 4.91 5.42 5.55 4.76 3.52 2.18 1.43 1.21 3.37
BC Victoria 481 250
N 1231 190
W 1.00 1.82 2.93 4.01 5.13 5.54 5.85 5.28 3.88 2.17 1.11 0.86 3.29
MB Winnipeg 491 540
N 971 140
W 1.21 2.08 3.27 4.55 5.54 5.80 5.85 4.84 3.32 2.21 1.33 1.02 3.41
NL St. Johns 451 190
N 651 530
W 1.56 2.27 3.48 4.19 4.76 5.05 5.05 4.54 3.53 2.29 1.43 1.27 3.28
NS Halifax 441 390
N 631 340
W 1.56 2.31 3.46 4.09 4.82 5.27 5.41 4.86 3.92 2.54 1.53 1.30 3.42
ON Toronto 431 410
N 791 380
W 1.44 2.27 3.19 4.13 5.15 5.83 5.67 4.82 3.66 2.47 1.48 1.20 3.44
QC Montreal 451 280
N 731 450
W 1.45 2.36 3.41 4.25 4.91 5.42 5.55 4.76 3.52 2.18 1.43 1.21 3.37
SK Regina 451 190
N 651 530
W 1.14 1.96 3.02 4.69 5.48 5.79 6.14 4.96 3.42 2.29 1.30 0.95 3.42
Table 6 Monthly and annual average of daily insolation values (kWh m2
day1
) for Asia-Pacific
ASIA-PACIFIC
Country City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Avg
UAE Abu Dhabi 241 280
N 541 220
E 3.92 4.50 5.22 5.87 7.06 7.33 6.90 6.64 6.39 5.53 4.54 3.79 5.64
Australia Adelaide 341 550
S 1381 360
E 7.20 6.58 5.18 3.85 2.65 2.23 2.48 3.20 4.46 5.69 6.59 6.74 4.74
Australia Brisbane 271 990
S 1531 080
E 6.93 6.09 5.44 4.34 3.50 3.29 3.52 4.43 5.62 6.18 6.74 6.93 5.25
Australia Hobart 421 520
S 1471 190
E 5.97 5.33 4.05 2.73 1.79 1.44 1.68 2.41 3.60 4.78 5.92 6.18 3.82
Australia Melbourne 371 470
S 1441 580
E 6.78 6.22 4.76 3.40 2.29 1.84 2.04 2.79 3.94 5.27 6.28 6.46 4.34
Australia Perth 311 570
S 1151 520
E 7.70 6.75 5.41 4.16 3.06 2.67 2.89 3.66 4.76 6.09 7.04 7.76 5.16
Australia Sydney 341 000
S 1511 000
E 6.34 5.68 4.87 3.60 2.74 2.50 2.67 3.54 4.67 5.61 6.32 6.60 4.59
Bangladesh Dhaka 231 420
N 901 220
E 4.44 5.08 5.87 6.06 5.50 4.41 4.09 4.37 4.17 4.50 4.37 4.13 4.75
China Beijing 391 550
N 1161 250
E 2.37 2.92 3.58 5.61 4.83 5.68 5.42 4.49 4.25 3.20 2.66 2.04 3.92
China Nanjing 321 030
N 1181 530
E 2.04 2.22 2.65 4.50 3.84 4.47 4.93 4.50 3.67 3.02 2.88 2.08 3.40
China Shanghai 311 100
N 1211 280
E 2.29 2.63 3.07 4.54 4.38 4.59 5.52 5.23 4.03 3.39 2.97 2.38 4.01
China Hong Kong 221 180
N 1141 100
E 2.59 2.56 3.06 3.93 4.13 4.74 5.81 4.95 4.68 4.05 3.56 2.93 4.18
Indonesia Jakarta 61 110
S 1061 500
E 4.15 4.59 5.00 4.94 4.88 4.71 5.09 5.46 5.66 5.36 4.76 4.47 5.03
Israel Tel Aviv 321 050
N 341 460
E 2.78 3.50 4.73 6.03 6.86 7.87 7.81 7.22 6.19 4.63 3.32 2.62 5.73
Iran Tabriz 381 480
N 461 180
E 1.79 2.40 3.37 4.58 5.54 6.71 6.97 6.06 5.20 3.26 2.14 1.56 4.13
Iran Tehran 351 400
N 511 260
E 2.23 2.84 3.72 5.12 5.99 7.32 7.20 6.41 5.59 3.90 2.61 2.02 4.58
Iran Mashhad 361 160
N 591 340
E 2.22 2.97 3.88 5.21 6.29 7.49 7.41 6.78 5.70 4.13 2.78 2.06 4.74
Iran Bandar Abbas 271 150
N 561 150
E 3.63 4.43 5.14 6.29 7.43 7.96 7.41 6.97 6.58 5.51 4.29 3.37 5.75
India New Delhi 281 000
N 771 000
E 3.68 4.47 5.50 6.60 7.08 6.55 5.01 4.62 5.11 4.99 4.15 3.42 5.10
India Bombay 181 330
N 721 320
E 5.22 6.03 6.66 7.05 6.77 4.59 3.54 3.40 4.72 5.39 5.15 4.80 5.28
India Bangalore 121 570
N 771 370
E 5.00 5.90 6.44 6.42 6.13 4.76 4.48 4.59 4.98 4.68 4.34 4.40 5.18
Iraq Baghdad 331 200
N 441 240
E 2.79 3.64 4.59 5.76 6.83 8.10 7.97 7.29 6.25 4.44 3.04 2.52 5.27
Jordan Amman 311 570
N 351 570
E 2.93 3.67 4.83 6.04 6.88 7.91 7.86 7.27 6.25 4.71 3.47 2.76 5.80
Japan Tokyo 351 350
N 1391 380
E 2.31 2.99 3.70 4.90 5.07 4.47 4.88 5.42 3.82 2.98 2.50 2.23 4.00
Cambodia Phnom Penh 111 330
N 1041 510
E 5.27 5.78 6.02 5.76 5.09 4.30 4.55 4.07 4.34 4.41 4.88 5.03 4.85
North Korea Pyongyang 391 000
N 1251 180
E 2.50 3.35 4.50 5.17 5.60 5.35 4.51 4.63 4.22 3.51 2.46 2.09 4.20
Korea Seoul 371 310
N 1271 000
E 2.62 3.40 4.29 5.24 5.63 5.15 4.26 4.55 3.99 3.64 2.60 2.24 4.16
Laos Vientiane 181 070
N 1021 350
E 4.30 4.94 5.52 5.74 5.11 4.24 4.22 4.19 4.61 4.26 4.21 4.24 4.63
Lebanon Beirut 331 540
N 351 280
E 2.64 3.40 4.63 6.03 6.96 7.90 7.84 7.19 6.13 4.50 3.14 2.44 5.68
Myanmar Yangon 161 470
N 961 090
E 5.40 6.06 6.65 6.69 5.14 3.24 3.30 2.99 4.12 4.51 4.82 5.05 4.65
Mongolia Ulaanbaatar 471 550
N 1061 540
E 1.79 2.77 4.24 5.53 6.26 6.15 5.55 4.88 4.17 3.00 1.82 1.40 4.30
Malaysia Kuala Lumpur 31 070
N 1011 420
E 4.54 5.27 5.14 5.05 4.80 4.98 4.91 4.78 4.54 4.51 4.23 4.07 4.70
New Zealand Auckland 361 520
S 1741 450
E 6.37 5.90 4.71 3.43 2.44 2.00 2.25 2.95 4.13 5.23 6.05 6.56 4.34
New Zealand Christchurch 431 320
S 1721 370
E 5.90 4.95 3.86 2.75 1.72 1.21 1.47 2.15 3.30 4.34 5.43 5.64 3.57
New Zealand Wellington 411 170
S 1741 470
E 6.27 5.31 4.17 3.00 1.95 1.54 1.74 2.46 3.66 4.70 5.73 6.01 3.88
Oman Muscat 231 370
N 581 370
E 4.34 5.00 5.85 6.69 7.54 7.56 6.91 6.71 6.55 5.93 4.95 4.23 6.29
Philippines Cebu 101 190
N 1231 540
E 4.53 5.15 5.83 6.25 5.90 4.83 4.76 4.93 4.96 4.75 4.49 4.44 5.07
Philippines Manila 141 370
N 1201 580
E 4.82 5.62 6.42 6.75 6.19 4.96 4.94 4.41 4.86 4.63 4.59 4.50 5.22
S. Arabia Riyadh 241 390
N 461 420
E 4.03 4.92 5.56 6.24 7.27 7.99 7.86 7.46 6.83 5.80 4.58 3.82 6.03
Singapore Singapore C. 11 000
N 1031 000
E 4.43 5.52 5.05 5.05 4.62 4.66 4.51 4.61 4.49 4.50 3.98 3.93 4.61
Thailand Bangkok 131 450
N 1001 300
E 4.42 4.65 4.84 5.03 4.75 3.77 4.22 3.46 3.63 3.89 4.16 4.40 4.27
Thailand Chiang Mai 181 000
N 991 000
E 4.79 5.51 6.11 6.29 5.53 4.44 4.16 4.18 4.50 4.34 4.28 4.48 4.88
Vietnam Hanoi 211 000
N 1051 540
E 2.52 2.94 3.81 4.34 4.66 4.51 4.62 4.62 4.57 3.64 3.29 3.17 3.89
Yemen Aden 121 500
N 451 020
E 5.45 5.78 6.52 6.48 6.71 6.72 6.33 6.33 6.41 6.54 5.99 5.39 6.22
Solar Energy 657

21. Table 7 provides the average intensity of the insolation falling on the ground for March in Halifax as 3.46 kWh m2
day1
.
Then, the heat available from the FPC is
25:1 MJ day1
¼ ð3:46 kWh m2
day1
Þ 3:6 MJ kWh1
FPC Area ðm2
Þ 0:5
Collector Area ¼ 4:0 m2
Again, the collector should be tilted 55 degrees from the horizontal surface facing south for Halifax (451N local latitude plus 10
degrees), Nova Scotia, Canada. As more insolation is available in Los Angeles compared to that in Halifax, much less (B32%)
collector area is required to heat the same amount of water.
This example gives us rough approximations for the required collector areas. For a detailed analysis, we would use the average
monthly direct and diffuse components of solar radiation per square meter per day, or daily or hourly direct and diffuse
components of solar radiation per square meter when available, and perform detailed calculations for the average direct, diffuse,
and ground-reflected solar radiation reaching the collector surface for a given collector orientation and tilt angle. Then we would
decide what the design collector area is for this application.
Example 19: Find: assuming that the flat plate collector (FPC) efficiency is 50%, determine the collector size needed to heat a
household for one day when the heating load is 5.86 kW. Use a mean daily insolation falling on the ground as 2.25 kWh m2
day1
(or 8.1 MJ m2
day1
) and the local latitude as 401N.
Solution: Remember that Q¼Insolation FPC Area Efficiency. The thermal energy that is needed for a day will be 5.86 kW
(24 h day1
) (3600 s h1
)¼506,304 kJ day1
¼506.3 MJ day1
.
The solar energy collected in one day will be (8.1 MJ m2
d1
) FPC Area Efficiency. Therefore,
Collector Area ¼ 506:3 MJ day1
= ½ð8:1 MJ m2
day1
Þ 0:5
Collector Area ¼ 125 m2
Table 8 Monthly and annual average of daily insolation values (kWh m2
day1
) for Europe
EUROPE
Country City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Avg
Austria Vienna 481 130
N 161 220
E 1.10 1.81 2.80 3.76 4.76 5.12 5.72 4.98 3.68 2.15 1.28 0.93 3.52
Belgium Bruxelles 501 450
N 41 300
E 0.74 1.31 2.29 3.68 4.67 4.48 4.82 4.20 2.86 1.73 0.92 0.56 3.02
Bulgaria Sofija 421 400
N 231 180
E 1.50 2.04 2.97 4.05 5.00 5.80 6.29 5.68 4.46 2.75 1.62 1.27 3.99
Cyprus Limassol 341 400
N 331 030
E 2.52 3.26 4.54 6.00 6.85 7.81 7.80 7.18 6.11 4.43 3.02 2.31 5.61
Croatia Zagreb 451 290
N 151 350
E 1.30 2.00 2.94 3.91 5.03 5.37 5.93 5.19 3.94 2.39 1.39 1.09 3.72
Germany Hamburg 531 330
N 91 590
E 0.54 1.11 2.09 3.68 4.86 4.47 4.47 3.89 2.59 1.48 0.69 0.40 2.52
Germany Munich 481 050
N 111 230
E 1.05 1.80 2.82 3.95 4.84 4.65 5.14 4.46 3.20 2.00 1.02 0.79 2.98
Spain Madrid 401 250
N 31 410
W 1.93 2.75 4.09 4.83 5.85 6.52 7.11 6.30 4.91 3.07 1.97 1.59 4.62
Spain Malaga 361 430
N 41 420
W 2.52 3.24 4.51 5.40 6.35 7.09 7.64 6.81 5.39 3.70 2.58 2.14 5.16
Spain Barcelona 411 240
N 21 90
E 1.89 2.71 3.97 4.99 5.82 6.56 7.01 6.07 4.72 3.11 2.04 1.70 4.60
Spain Alicante 381 400
N 01 300
W 2.23 3.02 4.26 5.39 6.13 6.89 7.34 6.53 5.11 3.45 2.34 1.94 4.94
France Lyon 451 460
N 41 500
E 1.26 1.97 3.02 4.08 4.97 5.40 6.03 5.23 3.93 2.27 1.43 1.08 3.74
France Paris 481 520
N 21 200
E 0.89 1.62 2.62 3.95 4.90 4.83 5.35 4.61 3.33 2.00 1.12 0.72 3.34
France Toulouse 431 370
N 11 260
E 1.39 2.14 3.19 4.03 4.82 5.16 5.86 5.07 4.09 2.48 1.58 1.25 3.75
Greece Athens 381 000
N 231 430
E 2.00 2.52 3.67 5.21 6.38 7.52 7.61 6.91 5.57 3.50 2.16 1.63 4.56
Hungary Budapest 471 300
N 191 300
E 1.00 1.71 2.76 3.90 5.03 5.30 5.62 4.84 3.57 2.24 1.17 0.88 3.17
Ireland Dublin 531 200
N 61 150
W 0.56 1.07 1.97 3.32 4.40 4.30 4.30 3.40 2.69 1.43 0.77 0.43 2.39
Italy Milan 451 280
N 91 120
E 1.27 1.89 2.91 3.65 4.84 5.36 5.97 5.21 3.91 2.40 1.42 1.08 3.33
Italy Rome 411 530
N 121 300
E 1.78 2.52 3.71 4.87 5.98 6.84 7.08 6.34 4.83 3.08 1.98 1.56 4.21
Netherlands Amsterdam 521 210
N 41 540
E 0.61 1.21 2.27 3.76 4.88 4.73 4.78 4.13 2.80 1.60 0.78 0.45 2.67
Norway Oslo 591 560
N 101 440
E 0.30 0.87 1.68 3.12 4.65 4.84 4.59 3.36 2.22 1.02 0.42 0.19 2.27
Romania Bucharest 441 260
N 261 060
E 1.36 1.94 2.91 3.94 5.03 5.60 6.15 5.53 4.15 2.59 1.37 1.10 3.47
Portugal Lisboa 381 400
N 91 110
W 2.27 2.99 4.30 5.15 6.13 6.46 6.89 6.33 5.11 3.44 2.27 1.84 4.43
Portugal Oviedo 431 210
N 51 500
W 1.67 2.29 3.44 4.59 5.56 6.32 6.86 5.95 4.51 2.71 1.77 1.46 3.93
Turkey Ankara 391 570
N 321 530
E 1.77 2.38 3.69 4.54 5.53 6.63 6.99 6.55 5.22 3.24 1.99 1.51 4.17
Ukraine Odessa 461 300
N 301 460
E 1.08 1.78 2.68 3.87 5.40 5.70 6.39 5.63 3.96 2.45 1.06 0.87 3.41
U. Kingdom Edinburgh 551 560
N 31 100
W 0.44 0.94 1.86 3.18 4.33 4.34 4.13 3.41 2.43 1.20 0.59 0.32 2.26
U. Kingdom London 511 320
N 01 50
W 0.67 1.26 2.22 3.48 4.54 4.51 4.74 4.01 2.86 1.65 0.89 0.52 2.61
Switzerland Bern 461 570
N 71 260
E 1.10 1.77 2.74 3.60 4.70 5.07 5.68 4.95 3.66 2.18 1.26 0.92 3.14
Switzerland Lausanne 461 320
N 61 390
E 1.10 1.81 2.80 3.76 4.76 5.12 5.72 4.98 3.68 2.15 1.28 0.93 3.17
Yugoslavia Beograd 441 500
N 201 300
E 1.29 1.89 2.92 3.86 4.88 5.45 6.00 5.30 4.05 2.50 1.40 1.11 3.39
658 Solar Energy

22. Table 9 Monthly and annual average of daily insolation values (kWh m2
day1
) for South America
SOUTH AMERICA
Country City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
Avg
Argentina Buenos Aires 341 490
S 581 320
W 6.44 5.67 4.53 3.53 2.74 2.04 2.31 3.27 4.23 5.12 6.36 6.44 4.39
Argentina Cordoba 311 240
S 641 120
W 7.07 6.30 4.90 3.87 3.01 2.65 2.79 3.63 4.76 5.93 6.63 6.96 4.88
Argentina Rio Gallegos 511 370
S 691 130
W 5.47 4.63 3.32 2.02 1.07 0.71 0.81 1.61 2.87 4.26 5.53 5.79 3.17
Belize Belize City 171 300
N 881 110
W 3.73 4.59 5.45 5.97 5.75 5.19 5.03 5.16 4.82 4.50 3.99 3.54 4.81
Brazil Belem 011 270
S 481 290
W 4.54 4.34 4.26 4.46 4.75 4.99 5.27 5.50 5.85 5.79 5.52 4.96 5.02
Brazil B. Horizonte 191 550
S 431 560
W 5.45 5.63 5.34 4.78 4.30 4.09 4.32 4.82 5.05 5.26 5.25 4.98 4.94
Brazil Brasilia 151 520
S 471 560
W 5.21 5.15 5.09 4.99 4.80 4.59 4.86 5.46 5.28 5.23 4.97 4.82 5.03
Brazil Curitiba 251 260
S 491 150
W 5.48 4.88 4.32 3.57 2.95 2.83 2.96 3.47 3.87 4.65 5.44 5.41 4.15
Brazil Fortaleza 031 430
S 381 310
W 5.85 5.44 4.82 4.80 5.11 5.34 5.74 6.34 6.60 6.62 6.50 6.16 5.78
Brazil Manaus 031 080
S 601 010
W 4.15 4.12 4.22 4.34 4.08 4.24 4.55 4.98 5.23 4.93 4.72 4.23 4.48
Brazil Porto Alegre 301 020
S 511 130
W 6.08 5.56 4.54 3.48 2.81 2.27 2.50 3.06 3.89 5.01 5.93 6.50 4.30
Brazil Recife 081 050
S 341 540
W 6.59 6.22 5.95 5.05 4.84 4.61 4.38 5.07 5.78 6.23 6.40 6.48 5.63
Brazil Rio de Janeiro 221 540
S 421 100
W 5.40 5.34 4.87 4.11 3.43 3.35 3.39 3.83 3.77 4.41 4.97 4.98 4.32
Brazil Salvador 121 590
S 381 300
W 5.89 5.79 5.28 4.59 4.09 3.75 3.83 4.26 4.79 5.32 5.38 5.61 4.88
Brazil Sao Paulo 231 330
S 461 390
W 5.44 5.05 4.75 4.21 3.47 3.36 3.54 4.19 4.25 5.09 5.73 5.38 4.54
Bolivia La Paz 161 290
S 681 080
W 5.30 5.57 5.16 5.01 4.78 4.37 4.51 4.96 5.66 5.98 6.15 5.92 5.28
Bolivia Santa Cruz 171 470
S 631 100
W 4.57 4.90 4.57 3.92 3.44 3.25 3.44 4.01 4.45 5.00 5.21 5.01 4.31
Bolivia Sucre 191 020
S 651 150
W 1.67 2.29 3.47 4.58 5.59 6.37 6.86 5.97 4.51 2.73 1.77 1.46 3.93
Chile Iquique 201 130
S 701 100
W 7.42 7.34 6.19 4.70 3.45 2.78 3.04 3.39 4.53 5.37 6.36 7.40 5.16
Chile Osorno 401 350
S 731 140
W 6.78 6.02 4.34 2.93 1.91 1.43 1.69 2.48 3.50 4.95 6.47 6.98 4.12
Chile Santiago 331 270
S 701 420
W 7.55 6.56 5.13 3.83 2.59 2.22 2.38 3.09 4.08 5.64 6.84 7.82 4.81
Chile Valparaiso 331 010
S 711 380
W 7.55 6.56 5.13 3.83 2.59 2.22 2.38 3.09 4.08 5.64 6.84 7.82 4.81
Columbia Bogota 041 360
N 741 050
W 4.50 4.48 4.67 4.46 4.45 4.63 4.71 4.70 4.80 4.28 4.24 4.32 4.52
Columbia Cali 031 270
N 761 300
W 3.63 3.90 4.09 3.89 3.76 3.71 4.05 3.93 3.89 3.52 3.49 3.44 3.78
Columbia Cartagena 101 250
N 751 320
W 5.74 6.18 6.54 6.30 5.62 5.56 5.66 5.72 5.35 4.72 4.90 5.30 5.63
Columbia Medellin 061 140
N 751 340
W 3.95 4.22 4.38 3.95 4.01 4.36 4.67 4.51 4.37 3.82 3.78 3.86 4.16
Costa Rica San Jose 091 590
N 841 040
W 6.09 6.74 7.23 6.64 5.26 5.00 4.94 4.84 4.76 4.63 4.63 5.30 5.51
Cuba Havana 231 090
N 821 210
W 4.09 4.97 5.92 7.06 7.15 7.10 6.90 6.86 6.10 5.12 4.26 3.74 5.77
Ecuador Guayaquil 021 130
S 791 540
W 6.07 6.01 6.31 6.31 5.83 4.88 4.50 4.50 4.95 4.69 5.29 5.93 5.44
Ecuador Quito 001 140
S 781 300
W 3.57 3.56 3.71 3.71 3.73 3.81 3.85 3.88 3.89 3.79 3.85 3.68 3.75
El Salvador San Salvador 131 400
N 891 100
W 5.58 6.23 6.68 6.52 5.95 5.74 6.22 6.18 5.49 5.61 5.42 5.30 5.91
Guatemala City 141 370
N 901 310
W 4.93 5.48 5.90 5.81 5.35 4.91 5.27 5.12 4.59 4.68 4.65 4.62 5.11
Guiana Cayenne 041 560
N 521 270
W 3.91 4.34 4.55 4.66 4.04 4.25 4.96 5.40 5.81 5.51 4.91 4.29 4.72
Guyana Georgetown 061 500
N 581 120
W 4.12 4.57 4.98 5.09 4.49 4.32 4.65 4.90 5.15 4.88 4.42 4.01 4.63
Honduras Tegucigalpa 141 050
N 871 140
W 4.26 5.08 5.84 5.99 5.54 5.35 5.34 5.47 5.04 4.43 4.15 3.91 5.03
Jamaica Kingston 171 580
N 761 480
W 4.92 5.67 6.45 6.80 6.50 6.82 6.84 6.61 6.23 5.45 4.76 4.58 5.97
Martinique Fort de France 141 370
N 611 050
W 5.35 5.98 6.59 6.94 6.70 6.42 6.49 6.45 6.03 5.87 5.15 5.15 6.09
Mexico Acapulco 161 500
N 991 540
W 5.46 6.30 7.17 7.41 7.06 6.16 6.29 6.20 5.45 5.94 5.56 5.19 6.18
Mexico Cancun 211 100
N 861 500
W 4.16 5.14 6.04 6.86 6.79 6.47 6.63 6.65 5.86 5.19 4.51 3.90 5.68
Mexico Chihuahua 281 390
N 1061 050
W 3.41 4.34 5.63 6.43 6.88 6.53 5.69 5.30 5.14 4.65 3.89 3.26 5.10
Mexico Guadalajara 201 400
N 1031 400
W 4.24 5.18 6.21 6.71 6.89 6.00 5.23 5.41 5.14 5.11 4.79 4.13 5.42
Mexico La Paz 241 090
N 1101 180
W 3.73 4.67 5.75 6.63 7.16 7.07 6.40 6.06 5.52 4.93 4.11 3.51 5.46
Mexico Mexico City 191 260
N 991 080
W 4.34 5.07 5.89 5.95 5.90 5.03 4.76 4.86 4.57 4.73 4.57 4.29 5.00
Mexico Monterrey 251 400
N 1001 230
W 3.33 4.20 5.40 5.71 6.06 5.89 5.59 5.44 4.76 4.49 3.90 3.23 4.83
Mexico Oaxaca 171 040
N 961 430
W 4.36 4.99 5.74 6.08 5.86 5.01 4.92 4.95 4.43 4.63 4.38 4.08 4.95
Mexico Puerto Vallarta 201 390
N 1051 140
W 4.20 5.29 6.39 7.12 7.51 6.96 6.17 5.99 5.32 5.30 4.82 4.00 5.76
Mexico Tijuana 321 320
N 1171 010
W 3.32 4.15 5.23 6.37 6.61 6.43 6.46 6.31 5.40 4.26 3.65 3.08 5.11
Mexico Veracruz 191 100
N 961 070
W 3.55 4.13 4.86 5.35 5.40 5.12 5.15 5.17 4.66 4.45 3.92 3.43 4.60
Nicaragua Managua 121 100
N 861 150
W 5.34 5.89 6.59 6.54 5.83 5.67 5.70 5.69 5.43 5.39 5.15 5.05 5.69
Panama Panama City 081 580
N 791 330
W 5.27 5.92 6.23 5.75 4.78 4.11 4.16 4.15 4.24 3.99 4.23 4.66 4.79
Paraguay Asuncion 251 200
S 571 310
W 6.10 5.77 4.98 3.84 3.48 2.76 3.09 3.97 4.49 5.26 6.22 6.26 4.68
Peru Arequipa 161 250
S 711 320
W 4.95 5.26 4.88 4.90 4.80 4.53 4.78 5.16 5.70 5.84 5.96 5.54 5.19
Peru Cusco 131 300
S 711 580
W 4.19 4.43 4.23 3.99 3.74 3.56 4.01 4.29 4.55 4.72 4.67 4.50 4.24
Peru Lima 401 420
N 841 020
W 1.57 2.48 3.21 4.46 5.37 5.97 5.58 5.18 4.58 3.09 1.81 1.33 3.71
Puerto Rico San Juan 181 150
N 661 300
W 4.26 4.90 5.70 6.09 5.89 6.09 6.08 5.78 5.26 4.80 4.36 4.15 5.28
Suriname Paramaribo 051 490
N 551 090
W 4.13 4.63 5.07 5.08 4.78 4.78 5.12 5.42 5.87 5.61 4.97 4.47 4.99
Venezuela Caracas 101 300
N 661 540
W 5.14 5.82 6.11 5.94 5.76 5.63 5.77 5.77 5.72 5.56 5.01 4.84 5.59
Venezuela Maracaibo 101 390
N 711 360
W 4.71 5.09 5.42 5.22 5.12 5.28 5.49 5.31 5.20 4.68 4.55 4.51 5.05
Venezuela Valencia 101 090
N 681 000
W 5.75 6.68 7.17 7.28 6.48 5.11 5.92 6.26 6.26 6.13 5.76 5.41 6.18
Solar Energy 659

23. NOTE: A useful rule of thumb is that the collector for space heating should be south facing and inclined at an angle (collector
tilt angle from the horizontal) equal to the local latitude plus 10 degrees. Therefore, we would have the collector in the example
facing south at 40 degrees plus 10 degrees¼50 degrees. This example gives us a rough approximation for the required collector
Table 10 Monthly and annual average of daily insolation values (kWh m2
day1
) for the USA
UNITED STATES OF AMERICA
State City Lat Long Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
Avg
AL Birmingham 330
3400
N 860
4500
W 2.29 3.31 4.04 5.14 5.92 5.98 5.81 5.70 4.80 3.93 2.96 2.25 4.34
AK Anchorage 610
1000
N 1500
0100
W 0.21 0.76 1.68 3.12 3.98 4.58 4.25 3.16 1.98 0.98 0.37 0.12 2.09
AR Little Rock 320
2500
N 940
4400
W 2.36 3.39 4.01 5.32 5.71 6.19 6.15 5.85 5.25 4.17 2.95 2.25 4.46
AZ Phoenix 330
2600
N 1120
0100
W 3.25 4.41 5.17 6.76 7.42 7.70 6.99 6.11 6.02 4.44 3.52 2.75 5.38
CA Los Angeles 340
0000
N 1180
0000
W 3.09 4.25 5.09 6.58 7.29 7.62 7.45 6.72 6.11 4.42 3.43 2.72 5.40
CA San Francisco 380
3100
N 1210
3000
W 2.35 3.33 4.42 5.95 6.84 7.39 7.55 6.51 5.75 3.92 2.65 2.06 4.89
CO Denver 390
4500
N 1040
5200
W 2.25 3.20 4.32 5.61 6.11 6.71 6.50 5.86 5.47 4.01 2.59 1.98 4.55
CT Hartford 410
4400
N 720
3900
W 1.70 2.43 3.48 4.07 5.14 5.58 5.38 5.04 4.13 2.91 1.81 1.42 3.59
DE Dover 390
0800
N 750
2800
W 1.85 2.62 3.60 4.33 5.44 5.91 5.64 5.30 4.38 3.23 2.21 1.66 3.84
FL Miami 250
4800
N 800
1600
W 3.72 4.61 5.42 6.40 6.61 6.29 6.26 6.08 5.47 4.84 3.96 3.46 5.26
GA Atlanta 330
3900
N 840
2600
W 2.31 3.37 4.08 5.20 6.02 6.01 5.81 5.59 4.76 3.95 2.98 2.33 4.37
HI Honolulu 210
2000
N 1570
5500
W 4.38 5.15 5.99 6.69 7.05 7.48 7.37 7.07 6.51 5.46 4.41 4.01 5.96
IA Dubuque 420
2400
N 900
4200
W 1.64 2.58 3.34 4.57 5.54 6.06 5.81 5.26 4.33 3.03 1.72 1.35 3.77
ID Boise 430
3400
N 1160
1300
W 1.73 2.72 3.77 5.22 5.90 6.57 7.17 6.12 5.28 3.29 1.74 1.46 4.24
IN Indianapolis 390
4400
N 860
1700
W 1.67 2.59 3.28 4.67 5.46 6.11 5.79 5.37 4.76 3.33 1.97 1.46 3.87
IL Chicago 410
5300
N 870
3800
W 1.50 2.45 3.20 4.48 5.56 6.07 5.68 5.27 4.51 3.07 1.69 1.26 3.72
KS Kansas City 390
1200
N 940
3600
W 2.06 2.89 3.62 4.92 5.58 6.17 6.21 5.59 4.90 3.49 2.20 1.75 4.11
KY Louisville 380
1100
N 850
4400
W 1.71 2.65 3.32 4.73 5.38 6.08 5.79 5.35 4.80 3.42 2.10 1.56 3.90
LA New Orleans 290
3700
N 900
0500
W 2.64 3.73 4.67 5.80 6.60 6.15 6.09 5.70 5.13 4.48 3.49 2.68 4.76
MA Boston 420
2200
N 710
0200
W 1.66 2.50 3.51 4.13 5.11 5.47 5.44 5.05 4.12 2.84 1.74 1.40 3.58
MD Annapolis 380
3500
N 760
2100
W 1.96 2.80 3.71 4.55 5.54 6.03 5.77 5.34 4.48 3.40 2.37 1.81 3.98
ME Portland 450
3600
N 1220
3600
W 1.38 2.33 3.49 4.57 5.46 6.09 6.64 5.78 4.80 2.79 1.41 1.10 3.82
MI Detroit 420
2500
N 830
0100
W 1.43 2.33 3.19 4.34 5.44 5.98 5.64 4.99 4.25 2.73 1.52 1.14 3.58
MO St. Louis 380
4500
N 900
2300
W 2.02 2.82 3.52 4.97 5.56 6.21 6.05 5.63 4.91 3.55 2.21 1.73 4.09
MN Minneapolis 440
5300
N 930
1300
W 1.60 2.61 3.30 4.55 5.44 5.86 5.77 5.12 4.12 2.90 1.62 1.34 3.68
MS Jackson 420
1600
N 840
2800
W 1.47 2.41 3.22 4.33 5.46 5.93 5.57 4.99 4.30 2.78 1.55 1.17 3.59
MT Billings 450
4800
N 1080
3200
W 1.55 2.57 3.52 4.82 5.63 6.45 6.39 5.75 4.67 3.19 1.77 1.30 3.96
MT Great Falls 430
3300
N 960
4200
W 1.30 2.36 3.41 4.84 5.56 6.18 6.44 5.53 4.40 2.90 1.53 1.11 3.79
NC Charlotte 350
1300
N 800
5600
W 2.22 3.17 3.95 4.98 5.80 6.01 5.76 5.27 4.58 3.75 2.76 2.21 4.20
ND Fargo 460
5400
N 960
4800
W 1.44 2.39 3.36 4.79 5.62 5.82 5.94 5.14 4.01 2.83 1.59 1.31 3.68
NE Omaha 410
1800
N 950
5400
W 1.92 2.76 3.45 4.74 5.60 6.14 6.11 5.46 4.74 3.34 2.00 1.57 3.98
NH Manchester 420
5600
N 710
2600
W 1.66 2.50 3.51 4.13 5.11 5.47 5.44 5.05 4.12 2.84 1.74 1.40 3.58
NJ Trenton 400
1300
N 740
4600
W 1.71 2.39 3.43 4.04 5.26 5.67 5.39 5.14 4.18 3.00 1.98 1.48 3.63
NM Albuquerque 350
0300
N 1060
3700
W 2.92 3.97 4.92 6.30 6.68 6.94 6.66 5.80 5.68 4.18 3.16 2.50 4.97
NV Las Vegas 360
1800
N 1150
1600
W 3.02 4.13 5.05 6.57 7.25 7.69 7.37 6.42 6.08 4.26 3.18 2.60 5.30
NY New York 410
0000
N 740
0000
W 1.67 2.37 3.41 3.93 5.11 5.48 5.26 5.01 4.05 2.85 1.82 1.40 3.53
OH Columbus 390
1600
N 850
5400
W 1.64 2.57 3.26 4.63 5.40 6.08 5.73 5.29 4.74 3.29 1.96 1.45 3.83
OK Tulsa 360
1200
N 950
5400
W 2.33 3.22 3.90 5.25 5.58 6.32 6.40 5.80 5.08 3.80 2.62 2.06 4.36
OR Portland 450
3200
N 1220
4000
W 1.38 2.33 3.49 4.57 5.46 6.09 6.64 5.78 4.80 2.79 1.41 1.10 3.82
PA Philadelphia 390
5300
N 750
1500
W 1.85 2.62 3.60 4.33 5.44 5.91 5.64 5.30 4.38 3.23 2.21 1.66 3.84
PA Pittsburgh 400
2700
N 790
5700
W 1.59 2.40 3.26 4.07 5.05 5.53 5.27 4.94 4.05 2.88 1.86 1.41 3.53
RI Providence 410
4400
N 710
2600
W 1.70 2.46 3.53 4.20 5.17 5.67 5.48 5.08 4.21 2.97 1.80 1.43 3.64
SC Columbia 380
5800
N 920
2200
W 2.14 2.91 3.62 5.03 5.56 6.22 6.13 5.64 4.95 3.57 2.25 1.82 4.15
SD Sioux Falls 450
2700
N 980
2500
W 1.72 2.71 3.31 4.65 5.61 6.10 6.04 5.42 4.47 3.20 1.78 1.43 3.87
TN Nashville 360
0700
N 860
4100
W 1.94 2.90 3.54 4.76 5.57 5.90 5.86 5.62 4.63 3.53 2.45 1.82 4.04
TX San Antonio 290
3200
N 980
2800
W 2.57 3.70 4.43 5.54 5.94 6.62 6.49 6.28 5.70 4.67 3.43 2.62 4.83
TX Houston 290
5900
N 950
2200
W 2.47 3.50 4.40 5.59 6.03 6.45 6.36 6.07 5.46 4.61 3.30 2.44 4.72
UT Salt Lake City 400
4600
N 11100
5200
W 2.23 3.15 4.09 5.57 6.26 6.98 6.86 5.98 5.39 3.68 2.29 1.97 4.53
VA Washington 380
5100
N 770
0200
W 1.95 2.80 3.66 4.46 5.42 5.88 5.63 5.22 4.38 3.36 2.34 1.79 3.90
VT Montpelier 440
1600
N 720
3500
W 1.58 2.54 3.50 4.05 5.00 5.24 5.37 4.92 3.79 2.46 1.52 1.28 3.43
WA Seattle 470
3200
N 1220
1800
W 1.14 2.04 3.23 4.26 5.19 5.75 6.27 5.46 4.43 2.50 1.21 0.90 3.53
WI Milwaukee 420
5700
N 870
5400
W 1.43 2.41 3.29 4.48 5.60 6.09 5.74 5.21 4.34 2.90 1.60 1.20 3.69
WV Charleston 380
2200
N 810
3600
W 1.75 2.64 3.34 4.26 5.20 5.67 5.49 5.19 4.26 3.19 2.15 1.62 3.73
WY Casper 420
5500
N 1060
2800
W 1.93 2.80 3.79 5.13 5.90 6.68 6.50 5.90 5.13 3.59 2.06 1.65 4.25
660 Solar Energy

24. Table 11 Global estimates of annual solar resource availabilities and ranks
Country Total solar resource Rank Country Total solar resource Rank
(MWh year1
) (MWh year1
)
Russia 30,586,340,907 1 Western Sahara 941,144,534 62
Antarctica 29,799,042,216 2 Cote d’Ivoire 896,134,633 63
China 27,373,606,560 3 Burkina Faso 891,425,628 64
Australia 25,097,791,333 4 Malaysia 874,948,870 65
Brazil 24,993,114,081 5 Vietnam 842,394,206 66
USA 24,557,081,452 6 Japan 809,152,634 67
Canada 21,214,183,621 7 Philippines 792,147,409 68
India 9,877,095,200 8 Italy 752,180,333 69
Sudan 8,702,766,347 9 Uganda 743,105,754 70
Algeria 8,162,220,322 10 Guinea 730,013,129 71
Argentina 7,853,433,856 11 Sweden 720,428,393 72
Congo 7,245,440,119 12 Ghana 706,055,035 73
Saudi Arabia 6,966,439,615 13 Laos 669,083,990 74
Kazakhstan 6,684,341,327 14 Gabon 636,664,662 75
Mexico 6,469,155,958 15 Senegal 625,811,191 76
Libya 5,976,855,697 16 Germany 618,698,988 77
Iran 5,183,911,292 17 Ecuador 606,283,904 78
Indonesia 4,967,990,842 18 New Zealand 592,697,733 79
Mongolia 4,774,191,855 19 Guyana 575,822,087 80
Chad 4,522,957,089 20 Romania 546,457,548 81
Mali 4,312,187,336 21 Poland 546,278,796 82
Niger 4,254,446,931 22 Cambodia 545,084,676 83
South Africa 4,204,499,012 23 Kyrgyzstan 537,285,421 84
Greenland 4,094,804,148 24 Finland 525,698,867 85
Angola 3,874,754,634 25 Syria 525,529,130 86
Ethiopia 3,799,653,474 26 Uruguay 480,236,704 87
Egypt 3,688,671,549 27 Tunisia 467,022,409 88
Mauritania 3,598,925,249 28 Nepal 466,643,167 89
Peru 3,576,841,559 29 Norway 461,031,108 90
Bolivia 3,220,149,178 30 Eritrea 421,357,819 91
Namibia 3,033,492,156 31 Tajikistan 410,128,118 92
Pakistan 3,010,691,250 32 Azerbaijan 406,543,854 93
Colombia 2,888,939,688 33 Suriname 402,456,417 94
Tanzania 2,877,063,979 34 United Kingdom 391,017,510 95
Nigeria 2,783,723,951 35 Bangladesh 380,054,187 96
Venezuela 2,586,860,121 36 Belarus 379,989,767 97
Mozambique 2,477,570,615 37 Nicaragua 359,009,793 98
Zambia 2,425,883,282 38 Malawi 356,284,837 99
Turkey 2,208,294,782 39 Benin 351,781,829 100
Somalia 2,163,991,070 40 Cuba 341,066,748 101
Botswana 2,087,670,494 41 Guatemala 328,690,841 102
Afghanistan 1,982,757,812 42 Honduras 322,616,232 103
Chile 1,972,640,705 43 Greece 315,471,728 104
Myanmar 1,940,406,489 44 North Korea 308,975,078 105
Madagascar 1,904,631,470 45 Jordan 305,225,384 106
Kenya 1,857,790,043 46 Portugal 254,296,700 107
Central African Republic 1,833,110,584 47 South Korea 250,682,398 108
Yemen 1,655,035,662 48 Bulgaria 246,668,630 109
Thailand 1,557,506,043 49 Liberia 246,447,095 110
Turkmenistan 1,483,722,811 50 French Guiana 230,746,872 111
Spain 1,376,540,386 51 U. Arab Emirates 227,379,935 112
Iraq 1,354,153,408 52 Serbia 204,507,081 113
Morocco 1,315,121,215 53 Sierra Leone 197,129,589 114
Zimbabwe 1,302,865,151 54 Hungary 193,442,667 115
Cameroon 1,288,799,143 55 Sri Lanka 189,451,980 116
Papua New Guinea 1,244,136,982 56 Panama 185,228,630 117
Ukraine 1,202,370,998 57 Austria 171,630,421 118
Uzbekistan 1,194,990,362 58 Togo 164,906,100 119
France 1,182,610,432 59 Georgia 154,072,843 120
(Continued )
Solar Energy 661