Table Of ContentTo my wife Vivien
Solar and Terrestrial
Radiation
METHODS AND MEASUREMENTS
Kinsell L. Coulson
Department of Meteorology
University of California
Davis, California
ACADEMIC PRESS New York San Francisco London 1975
A Subsidiary of Harcourt Brace Jovanovich, Publishers
COPYRIGHT © 1975, BY ACADEMIC PRESS, INC.
ALL RIGHTS RESERVED.
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ACADEMIC PRESS, INC.
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United Kingdom Edition published by
ACADEMIC PRESS, INC. (LONDON) LTD.
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Library of Congress Cataloging in Publication Data
Coulson, Kinsell L
Solar and terrestrial radiation.
Includes bibliographies and index.
1. Solar radiation-Measurement. 2. Terrestrial
radiation-Measurement. I. Title.
QC912.C68 551.5'271 74-17986
ISBN 0-12-192950-7
PRINTED IN THE UNITED STATES OF AMERICA
Preface
Dr. Andrew J. Drummond was to have coauthored this book with me.
His tragic illness and subsequent death prevented his participation beyond
the extent of his reading and commenting on the sections of Chapters 3
and 4 dealing with pyrheliometers and pyranometers. Because of his daily
contact with these instruments, I am fortunate to have had his expert
advice on these sections. But I also feel certain that the entire book could
similarly have profited from his counsel, and I know that I have missed the
anticipated personal contacts with a good friend and colleague.
In the general design of the book, I was guided by the thought that
this is an appropriate time for a summary dealing primarily with radiation
instrumentation for the meteorologist or atmospheric physicist. The
developments over the last decade or two have brought instruments for
routine measurements of solar and terrestrial radiation at the earth's
surface to a stage that is probably adequate for most meteorological and
climatological purposes. The instruments, when properly used, are certainly
adequate to erase many of the present deficiencies in climatological data
and routine monitoring of the radiative regime of the surface and lower
atmosphere. They do not, however, provide the precision required for
studies of climatic change, spectral distribution of atmospheric radiation,
and certain other meteorological or technological requirements. An entirely
new generation of radiation instruments has been developed in the space
program for use on meteorological and other types of satellites. Unfortu
nately these very sophisticated types of devices are beyond the scope of this
book, but they probably indicate the direction that future routine monitor
ing devices will take.
The major emphasis in the book is on radiation instrumentation.
I have tried to include enough underlying theory to make the book useful in
understanding the basic radiative processes in the atmosphere and a
sufficient number of historical notes to indicate the rich traditions in
science to which the radiation meteorologist is beneficiary. The level of the
discussions is designed for the upper division or beginning graduate college
student and the professional meteorologist. The format of each chapter is
IX
X Preface
to include the theory and background information in the first part and
discussions of individual instruments in the last part. This did not seem
feasible, however, for terrestrial radiation, so the theory and background
information is included in Chapter 10 and instrumentation in Chapter 11.
I want to express my appreciation to my colleagues for furnishing
information I requested, and especially to the firms and institutions for
supplying, mostly without compensation, many of the instrument photo
graphs which appear in the various chapters.
Kinsell L. Coulson
CHAPTER ONE
Principles of Radiation Instruments
1.1 DEFINITIONS, TERMINOLOGY, AND UNITS
There is a great diversity in notations and terminology used in dis
cussions of radiation so it is important at the outset to define the main
quantities and terms with which we will be concerned in this book. The
notation introduced by Chandrasekhar (1950), which has been widely ac
cepted in the field, will be followed as closely as feasible in mathematical
expressions, and the individual symbols are defined in Appendix A. The
terminology for the various radiation fluxes and the classification of the
associated instruments are those recommended by the World Meteor
ological Organization (1969). The units have been chosen on the basis of
standard use (principally in the field of meteorology) and ease of physical
interpretation. They do not necessarily conform to any one of the many
sets of units which have been recommended by various organizations.
1.1.1 Solid Angle
The concept of a solid angle can be illustrated as follows. We assume
a line through point 0 moving in space and intersecting an arbitrary sur
face located at some distance s from point 0. If the locus of the point of
intersection forms a closed path on the surface but does not intersect itself,
then a unique area is defined on the surface. We assume the area is an
elemental area, da, the surface normal of which makes an angle y with the
direction to point 0. Then, the projected area as seen from point 0 is
1
1. Principles of Radiation Instruments
r sin θ αφ
Fig. 1.1 Illustration of solid angle and its representation in spherical coordinates.
dA = da cos 7, and the elemental solid angle, subtended at 0 by da is de
fined by άω = dA/s2. Obviously for a finite area the total solid angle ω =
/ dvi, where dco* is the solid angle subtended by the ith areal element dA
it
For purposes of illustration, we assume the surface is the surface of a
sphere of radius r, as shown in Fig. 1.1. For this case, y = 0 everywhere,
and the solid angle subtended at the center of the sphere by area dA on its
surface is άω = dA/r2. For the special case of a unit sphere (r = 1), άω
and dA have the same numerical value if άω is expressed in steradians
(sr), and dA and r are expressed in the same system of units. Since the
area of the surface of a sphere is 4πΓ2, the total solid angle subtended at a
point by the entire surrounding sphere is 4nr2/r2 = 4T sr.
A hemispheric solid angle is 2π sr. As can be seen from Fig. 1.1, an
elemental solid angle is conveniently expressed in a spherical (0, φ) co
ordinate system as
(r dd) (r sin0d0)
1.1.2 Intensity and Flux
Let us consider a pencil of radiation crossing the elemental area da of
Fig. 1.2 and confined to the elemental angle άω, which is oriented at some
angle Θ to the normal of da. The energy dE contained in the frequency
v
interval dv which crosses da in time increment dt is given by
dE = /„ dv dt άω da cos Θ (1.2)
v
1.1 Definitions, Terminology, and Units 3
This relation defines the monochromatic specific intensity in the most
general way as
dE
v
h = (1.3)
dv dt do) da cos Θ
Thus the definition of specific intensity, or simply intensity, implies a
directionality in the radiation stream—an intensity in a given direction.
The term flux, however, is simply a flow of energy, and it may or may
not have an implied direction. For instance, the monochromatic flux of
energy across da is given by the integration of the normal component of
I over the entire spherical solid angle Ω. Thus
v
F = dv dt da I Ι(ω) cos θ άω (1.4)
v ν
or, in terms of spherical coordinates Θ and φ,
/·2π /.7Γ
F = dvdtda / 7,(0, φ) sin Θ cos θ άθ άφ (1.5)
P
On the other hand, for radiation instrumentation purposes we are mainly
interested in the radiant energy which is incident on a surface from less
than the entire possible solid angle. The monochromatic flux on a plane
(one-sided) surface, for instance the sensing surface of a pyranometer, is
received from one hemisphere only, and is given by
*2ΤΓ -T/2
F = dv dtda / J„(0, φ) sin Θ cos θ άθ άφ (1.6)
v
•'ο •'ο
Then the entire flux of energy at all frequencies on a plane (one-sided)
da
Fig. 1.2 Diagram of a pencil of radiation through elemental area da and confined to
elemental solid angle άω.
4 1. Principles of Radiation Instruments
surface, per unit area and unit time, is
/.oo /·2π /.π/2
F = / I(v;6 φ) sine cose άθ άφάν (1.7)
f
•'ο •'ο •'ο
Two singularities in the above relations have important implications
in instrumentation. First, it is seen from the definition of intensity in Eq.
(1.3) that for a finite amount of energy dE the intensity /„ —> oo if άω —> 0.
v
Thus the concept of intensity breaks down for parallel radiation. In that
case we speak only of flux of energy from the specified direction. The
second singularity occurs for the case in which the intensity is isotropic
(the same in all directions). For an isotropic intensity distribution l can
v
be taken outside the integral of Eq. (1.6), which simplifies to
F = wldv dtda (1.8)
v v
and Eq. (1.7) becomes
F = 7Γ f Idv (1.9)
v
1.1.3 Transmission, Absorption, Emission, and Scattering
The transfer of radiation through a medium such as the Earth's
atmosphere has been discussed at length by many authors (e.g., Chan-
drasekhar, 1950; Goody, 1964; Kondratyev, 1969; Ambartsumian, 1958),
although much still remains to be learned about the interaction of radiation
with matter. In general, the medium may exhibit both absorption and scat
tering of incident radiation, each of which affects the characteristics of the
transmitted radiation, and any real medium also emits radiation. It is well
at the outset to put these concepts on a firm physical basis through the
equation of radiative transfer.
The equation of transfer for a medium which absorbs, emits, and
scatters radiation may be derived as follows (Chandrasekhar, 1950). We
consider a pencil of radiation of intensity I incident on an elemental sur
v
face da in unit time, as shown in Fig. 1.3. For simplicity we consider the
elemental surfaces to be normal to the incident beam. During its traverse
of the pathlength ds through the medium, the incident energy is attenuated
by scattering and absorption, the intensity of radiation finally emerging
from the cylinder being I + dl. The mass of material dm of density p,
v v
contained in a cylinder of unit cross section and elemental solid angle, is
dm = p ds
1.1 Definitions, Terminology, and Units 5
so we can define a mass attenuation coefficient κ such that
dl = - Kl ds (1.10)
v vP
In general, the attenuation coefficient is the sum of a scattering co
efficient K S and an absorption coefficient κα. The energy lost by absorption
V ν
goes to heating the medium, to producing photochemical reactions, or to
some other form of energy, and is thus lost to the radiation field. However,
that lost by pure scattering emerges as radiation, still of the same wave
length, only the direction of propagation having been changed in the process
of attenuation. This scattered component is responsible for the skylight
in the case of the sunlit sky.
On integration of Eq. (1.10) over the pathlength from one arbitrary
point pi to another p in the medium, we obtain the intensity of the emer
2
gent radiation as
7„ = 7,o expi - I κρ ds) = 7,o exp[—2\(pi, p )] (l.H)
ν 2
where the exponent defines the optical thickness T between pi and p .
2
This is one form of the Bouguer-Lambert law for the transmission of
radiation.
Since the scattered energy is not lost to the radiation field we can
consider κ * to be also a (virtual) emission coefficient. The intensity of
ν
Fig. 1.3 Diagram of the change of radiant intensity over a pathlength ds in a medium
which exhibits scattering, absorption, and emission.
