Table Of ContentAN INTRODUCTION
TO SOLAR RADIATION
Muhammad Iqbal
Department of Mechanical Engineering
The University of British Columbia
Vancouver, British Columbia, Canada
1983
ACADEMIC PRESS
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Library of Congress Cataloging in Publication Data Canadian Cataloguing in Publication Data
Iqbal, Muhammad Iqbal, Muhammad
An introduction to solar radiation. An introduction to solar radiation
Includes index. Bibliography: p.
1. Solar radiation. I. Title. Includes index.
QC911.I63 1983 551.5*271 82-7416 ISBN 0-12-373750-8
ISBN 0-12-373750-8
ISBN 0-12-373752-4 (pbk.) ISBN 0-12-373752-4 (pbk.)
1. Solar radiation. I. Title.
C83-098054-7
QC911.I72 551.5*271
83 84 85 86 9 8 7 6 5 4 3 2 1
To my daughter, Isabeau Anisa
PREFACE
This book is written for those who must determine quantitatively the
amount of solar radiation incident on a surface on the earth. The material
has been derived from meteorological and engineering literature. The
emphasis is on an understanding of the subject as well as on the methods of
calculation.
The audience of this book can be divided into six groups: (1) energy
analysts who are responsible for developing national programs on solar
energy utilization and who are required to assess the potential of solar
energy in their region; (2) designers of thermal devices, such as flat-plate
collectors or concentrating devices, who need to calculate hourly and daily
values of the incident radiation; (3) photovoltaic engineers who require an
estimation of the spectral values of the direct plus diffuse solar radiation
under cloudless skies; (4) architects and engineers who need to calculate
thermal loads and natural illumination of buildings; (5) agronomists who
need to estimate the radiative environment of plants; and (6) hydrologists
who need to compute the amount of snowmelt and evaporation from
reservoirs.
The required background for this book is some college-level elementary
physics, chemistry, and calculus, and the book can form part of a course on
solar energy utilization at senior-graduate levels or be used in an introduc
tory course on solar radiation meteorology.
Chapter 1 introduces the trigonometric relationships between the sun-
earth line and the position of an inclined surface. Because this material does
xiii
XIV Preface
not require a priori knowledge of any aspect of solar radiation, it was con
sidered appropriate at the beginning. Chapter 2, on the characteristics of
blackbody radiation, is written as a prelude to Chapter 3, which focuses on
the solar constant and its spectral distribution. Chapter 4 deals with extra
terrestrial radiation. Detailed formulations treating instantaneous, hourly,
and daily quantities of radiation incident on inclined planes are presented.
A cloudless-sky atmosphere and its optics are treated in Chapter 5. The
first part of this chapter describes earth's cloudless-sky atmosphere (U.S.S.A.
1976), concentration of the various molecules, vertical distribution of ozone
and its seasonal variation, vertical distribution of water vapor, evaluation
of the precipitable water through its partial pressure or dew-point tempera
ture, and description of the aerosols. The second part deals with the calcula
tion of optical masses for air, ozone, and water vapor.
Solar spectral radiation under cloudless skies is studied in Chapter 6.
This chapter essentially has four parts. In the first part, the basic Bouguer
equation is laid down; Rayleigh and aerosol scattering are also described,
and aerosol attenuation is described through Angstrom's turbidity formula.
In the second part, molecular absorption is described, and tables of the mono
chromatic attenuation coefficients are given for ozone, uniformly mixed
gases, and water vapor. In the third part, the formulation to compute direct
spectral irradiance is presented. In the fourth part, a simple empirical
approach to calculate the diffuse spectral irradiance is demonstrated; how
ever, in this approach multiple scattering is ignored. The diffuse irradiance
is considered to have three components: (1) Rayleigh-scattered diffuse
radiation, (2) aerosol-scattered diffuse radiation, and (3) multiply reflected
diffuse radiation.
Total (broadband) radiation under cloudless skies is the subject of Chapter
7, in which three parameterization models of calculating direct and diffuse
irradiance are described and compared with each other. Finally, a com
parison is made between one of the three models and the ASHRAE algorithm
for clear-sky irradiance. A revised ASHRAE algorithm is recommended.
Chapter 8 treats the estimation of solar radiation arriving at horizontal
surfaces on the earth through cloudy skies. Here, it is assumed that mean
daily global (direct plus diffuse) radiation either is known from meteoro
logical data or can be easily estimated through simple procedures such as
the use of empirical correlations between global radiation and the number
of bright sunshine hours or cloud cover. A number of such correlations are
described, site dependent as well as site independent. The rest of the chapter
discusses methods of predicting diffuse radiation when the global value is
known. A critical examination of the predictive correlations for global as
well as diffuse radiation is presented.
Preface XV
In Chapter 9 the ground albedo and its spectral and angular variation are
described, and tables of the albedo values for natural ground covers and
man-made surfaces are presented.
Chapter 10 deals with calculation of angle factors. The angle factors
between the ground and inclined surfaces and between the sky and inclined
surfaces are developed.
The calculation of insolation on inclined surfaces is treated in Chapter 11.
Direct, ground-reflected, and sky diffuse irradiance are taken up separately.
Angular distribution of sky diffuse intensity is studied, and models of the
anisotropic sky diffuse irradiance are presented.
Solar radiation measuring instruments are described and illustrated in
Chapter 12. Development of the pyrheliometers beginning from Abbot
water-flow and Angstrom electrical compensation to the modern cavity-
type radiometers is presented. The different types of pyranometers and sun
shine recorders are discussed. Sources of errors and methods of calibration
are presented.
The subject matter in this book is liberally illustrated by diagrams and
worked examples. Wherever necessary, tables containing useful data are
provided. At the end of each chapter, suggestions for further reading are
given to encourage the enthusiast. With a few exceptions, SI units are used
throughout. In Appendix A all basic constants are given in the SI as well as
the conventional units. The nomenclature familiar to the community in this
field is retained. A table of conversion factors is given in Appendix B.
ACKNOWLEDGMENTS
I have derived material from many research journals and am indebted
to the authors of those publications and to these journals for granting per
mission to reproduce many useful diagrams and tables. A significant portion
of this book is based on the research of several graduate students and assist
ants in this department who were supported by the Natural Sciences and
Engineering Research Council of Canada. I am indebted to the Research
Council for its indirect help. The Atmospheric Environment Service of
Canada, which maintains an extensive radiation network and runs an excel
lent data collection and distribution system, was invaluable for development
of this subject.
Several individuals have generously supplied me with unpublished reports,
specific climatological data, and other useful information that has enriched
this volume. I am particularly indebted to C. Fröhlich for supplying the
table of extraterrestrial solar spectral irradiance and many other helpful
reports from the World Radiation Center, to John Hay for allowing me early
access to some of his research publications, to Marie Mermier and P.
Fournier for some of the French data, and to Schieldrup Paulsen for the
Norwegian data. The comments of Eldon C. Boes, who reviewed the manu
script, helped me improve this text.
Among my close collaborators, Cecilia Cameron carried out the initial
computations, prepared diagrams and tables, and worked examples. Clement
Ma reworked and extended the numerical procedures. I am indebted to
Clement also for excellent proofreading of the final manuscript. Toby
xvii
XVlll A cknowledgments
Brine and Meinrad Mächler, through their theses and discussions, improved
the contents of Chapters 6 and 7. David Morton prepared the albedo tables
for Chapter 9.
Donna Schmid patiently typed and retyped several versions of the manu
script during a period of two years. Not only was her typing work excellent,
but luckily she could also read my handwriting. My thanks are also due to
Jean Horner for overseeing the typing of the manuscript. Richard Brun and
Monica Gutirezz prepared the diagrams, and Irvine Devries edited my writ
ing. Finally, I am indebted to my institution, which maintains and promotes
a climate conducive for creative pursuits.
This book is based on my classroom notes, and I have kept, deliberately
in spots, some informality in presentation.
Chapter 1
SUN-EARTH
ASTRONOMICAL
RELATIONSHIPS
1.1 Introduction
This book begins by considering the motion of the earth around the sun,
the motion of the earth around its polar axis, and the angle between the
earth's equator and the plane containing the sun-earth orbital system.
Trigonometric equations relating the position of the sun to a horizontal or an
inclined surface are presented. The main objective, however, is to write down
the relevant astronomical relationships that do not require a priori knowledge
of solar radiation.
1.2 Sun-Earth Distance r
The earth revolves around the sun in an elliptical orbit with the sun at one
of the foci (Fig. 1.2.1). The amount of solar radiation reaching the earth is
inversely proportional to the square of its distance from the sun; an accurate
value of the sun-earth distance is, therefore, important. The mean sun-earth
distance r is called one astronomical unit:
0
1 AU = 1.496 x 108 km
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