Gaylon
S.
Campbell
John
M.
Norman
An Introduction to
Environmental
Biophysics
Second Edition
With
8
1
Illustrations
Springer
Gaylon S. Campbell
Decagon Devices, Inc.
950
NE
Nelson Ct.
Pullman, WA 99163
USA
John M. Norman
University of Wisconsin
College of Agricultural and
Life Sciences Soils
Madison,
WI
53705
USA
Library of Congress Cataloging

1998 Springer
-
Verlag New York, Inc.
All rights resewed. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer
-
Verlag New York, Inc., 175 Fifth Avenue, New
York,
NY
10010, USA), except for brief excerpts in connection with reviews or scholarly analy
-
sis. Use in connection with any form of information storage and retrieval, electronic adaptation,
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the former are not especially identified, is not to be taken as
a
sign that such names, as under
-
stood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by any
-
one.
Production coordinated by Black Hole Publishing Services, Berkeley, CA, and managed by
Bill Imbornoni; manufacturing supervised by Johanna Tschebull.
Typset by
Bartlett Press, Marietta, GA.
Printed and bound by Edwards Brothers, Inc., Ann Arbor, MI.
Printed in the United States of America.
9 8 7 6 5 4 3 2 (Corrected second printing, 2000)
ISBN 0

edition. This book is used as a text in courses taught at Washington State
University and University of Wisconsin and the new edition incorporates
knowledge gained through teaching this subject over the past 20 years.
Suggestions of colleagues and students have been incorporated, and all of
the material has been revised to reflect changes and trends in the science.
Those familiar with the first edition will note that the order of pre
-
sentation is changed somewhat. We now start by describing the physical
environment of living organisms (temperature, moisture, wind) and then
consider the physics of heat and mass transport between organisms and
their surroundings. Radiative transport is treated later in this edition, and
is covered in two chapters, rather than one, as in the first edition. Since
remote sensing is playing an increasingly important role in environmen
-
tal biophysics, we have included material on this important topic
as
well.
As with the first edition, the
ha1 chapters are applications of previously
described principles to animal and plant systems.
Many of the students who take our courses come from the biolog
-
ical sciences where mathematical skills are often less developed than
in
physics and engineering.
Our
approach, which starts with more de
-
scriptive topics, and progresses to topics that are more mathematically
demanding, appears to meet the needs of students with this type of back

a lot of additional work was required. A fourth consideration is that use
of a molar unit immediately raises the question
"moles of what?
"
The
dependence of the numerical value of conductance on the quantity that
is diffusing is more obvious than when units of
m/s are used. This helps
students to avoid using a diffusive conductance for water vapor when
estimating a flux of carbon dioxide, which would result in a
60
percent
error in the calculation. We have found that students adapt readily to the
consistent use of molar units because of the simpler equations and explicit
dependencies on environmental factors. The only disadvantage to using
molar units is the temporary effort required by those familiar with other
units to become familiar with
"
typical values
"
in molar units.
A
second convention
in
this book that is somewhat different from the
first edition is the predominant use of conductance rather that resistance.
Whether one uses resistance or conductance is a matter of preference,
but predominant use of one throughout a book is desirable to avoid con
-
fusion. We chose conductance because it is directly proportional to flux,

is generalized to
nonflat objects, such as animal bodies or appendages,
tree trunks or branches, or conifer needles, then this
"
one
-
side
"
area is
subject to various interpretations and serious confusion can result. Errors
of a factor of two frequently occur and the most experienced biophysi
-
cist has encountered difficulty at one time or another with this problem.
We believe that using element surface area and radiation
''view factors
"
Preface
to the Second Edition
vii
are the best way to resolve this problem so that misinterpretations do not
occur. For those interested only in exchanges with flat leaves, the develop-
ment in this book may seem somewhat more complicated. However,
"flat
leaf' versions of the equations are easy to write and when interest extends
to
nonilat objects this analysis will
be
fully appreciated. When extending
energy budgets to canopies we suggest
herni-surface area, which is one-

taught and worked on in some form by Champ during his years of teach-
ing and research at University of Wisconsin. Both of us have been deeply
influenced by his teaching and his example. We dedicate this edition to
him.
G.
S. Campbell
J.
M. Norman
Pullman and Madison,
1997

Preface to the
First Edition
The study of environmental biophysics probably began earlier in man's
history than that of any other science. The study of
organism-
environment interaction provided a key to survival and progress.
Systematic study of the science and recording of experimental results goes
back many hundreds of years. Benjamin Franklin, the early American
statesmen, inventor, printer, and scientist studied conduction, evaporation,
and radiation. One of his observation is as follows:
My desk on which
I
now write, and the lock of my desk, are both
exposed to the same temperature of the
air,
and have therefore the
same degree of heat or cold; yet if
I
lay my hand successively on

to environmental biology, since the intent to teach the student to calcu
-
late actual transfer rates, rather than just study the principles involved.
-
-
-
'~rom
a
letter to John Lining, written April
14,
1757.
The entire letter, along with other
scientific writings
by
Franklin, can
be
found in Reference
[1.2].
Preface
to
the
First Edition
Numerical examples are presented to illustrate many of the principles,
and are given at the end of each chapter to help the student develop
skills
using the equations. Working of problems should be considered as es
-
sential to gaining an understanding of modern environmental biophysics
as it is to any course in physics or engineering. The last four chapters of
the book attempt to apply physical principles to exchange processes of

more understandable. Several authors and publishers gave permission to
use figures, Karen Ricketts typed all versions of the manuscript, and my
wife, Judy, edited the entire manuscript and offered the help and encour
-
agement necessary to bring this project to completion. To all of these
people,
I
am most grateful.
Pullman,
1977
G. S.
C.
Contents
Preface to the Second Edition
Preface to the First Edition
List of Symbols
Chapter
1
Introduction
1.1 Microenvironments
1.2 Energy Exchange
1.3 Mass and Momentum Transport
1.4 Conservation of Energy and Mass
1.5 Continuity in the Biosphere
1.6 Models, Heterogeneity, and Scale
1.7 Applications
1.8 Units
References
Problems
Chapter

3.4 Spatial and Temporal Variation of Atmospheric Water
Vapor 47
3.5 Estimating the Vapor Concentration in Air
49
References 50
Problems 50
Chapter
4
Liquid Water in Organisms and their Environment
53
4.1 Water Potential and Water Content
4.2 Water Potentials in Organisms and their Surroundings
4.3 Relation of Liquid
-
to Gas
-
Phase Water
References
Problems
Chapter
5
Wind
5.1 Characteristics of Atmospheric Twbulence
5.2 Wind as a Vector
5.3 Modeling the Variation in Wind Speed
5.4 Finding the Zero Plane Displacement and the
Roughness Length
5.5 Wind Within Crop Canopies
References
Problems

7.10 Combined Forced and Free Convection
7.1 1 Conductance Ratios
7.12 Determining the Characteristic Dimension of an Object
7.13 Free Stream Turbulence
Summary of Formulae for Conductance
References
Problems
Chapter
8
Heat Flow in the
Soil
8.1 Heat Flow and Storage in Soil
8.2 Thermal Properties of Soils: Volumetric Heat Capacity
8.3 Thermal Properties of Soils: Thermal Conductivity
8.4 Thermal
Diffusivity and Admittance of Soils
8.5 Heat Transfer from Animals to a Substrate
References
Problems
Chapter
9
Water Flow in Soil
9.1 The Hydraulic Conductivity
9.2 Infiltration of Water into Soil
9.3 Redistribution of Water in Soil
9.4 Evaporation from the Soil Surface
9.5 Transpiration and Plant Water Uptake
9.6 The Water Balance
References
Problems

12.5 Qualitative Analysis of Animal Thermal response
12.6 Operative Temperature
12.7 Applications of the Energy Budget Equation
12.8 The Transient State
12.9 Complexities of Animal Energetics
12.10 Animals and Water
References
Problems
Chapter 13 Humans and their Environment
13.1 Area, Metabolic Rate, and Evaporation
13.2 Survival
in
Cold Environments
13.3 Wind Chill and Standard Operative Temperature
13.4 Survival in Hot Environments
13.5 The Humid Operative Temperature
13.6 Comfort
References
Problems
Chapter 14 Plants and Plant Communities
14.1
Leaf
Temperature
14.2 Aerodynamic Temperature of Plant Canopies
14.3 Radiometric Temperature of Plant Canopies
14.4 Transpiration and the
Leaf
Energy Budget
14.5 Canopy Transpiration
14.6 Photosynthesis

15.1 1 Remote Sensing and Canopy Temperature
15.12 Canopy Reflectivity
(Ernissivity) versus Leaf
Reflectivity
(Emissivity)
15.13 Heterogeneous Canopies
15.14 Indirect Sensing of Canopy Architecture
References
Problems
Appendix
Index

List
of
Symbols
fds
{mol m-2 s-I
)
{mol m-2 s-'
)
{mol m-2
s-'
}
carbon assimilation rate
amplitude of the diurnal soil surface
temperature
plant available water
Jlwc
density of blackbody radiation
speed of light

view factor for
dzfuse solar radiation
view factor for ground thermal radiation
view factor for solar beam
xviii
List of Symbols
{mol m-2 s-'
}
Ws2
I
{mol m-2 s-'
}
{mol m-2 s-I
)
{mol mF2 s-I
}
{mol m-2 s-I
}
{mol m-2 s-I
}
{mol m-2 s-'
)
{mol m-2 s-'
)
{mol mF2 s-I
}
{mol mP2 s-I
}
{mol m-2 s-I
}

}
(W/m
2
)
jlux
density ofj at location z
gravitational constant
conductance for heat
boundary layer conductance for heat
whole body conductance (coat and tissue)
for an animal
coat conductance for heat
sum of boundary layer and radiative
conductances
tissue conductance for heat
radiative conductance
conductance for vapor
boundary layer conductance for vapor
surface or
stomata1 conductance for vapor
soil
heatJEwc density
canopy height
Planck's constant
relative humidity
sensible
heatJEwc density
water+ density
thermal conductivity
Boltzmann constant

speciJic humidity (mass of water vapor
divided by mass of moist air)
PAR
photonjux density
List
of
Symbols
xix
{m
2
s
mol-'
}
{m
2
s mol-'
}
{J mol-'
C-'
}
{w/m2
)
{pmol m-2 s-'
}
{m
4
s-I kg
-
'
}

Jlwc
density of solar radiation
perpendicular to the solar beam
Jlwc
density of reflected solar radiation
the solar constant
Jlux
density of total solar radiation
time
time of solar noon
temperature at height z
temperature at time t
dew point temperature
operative temperature
standard operative temperature
humid operative temperature
apparent aerodynamic surface
temperature
average soil temperature
base temperature for biological
development
maximum temperature on day i
minimum temperature on day i
kelvin temperature
friction velocity of wind
maximum Rubisco capacity per unit leaf
area
mixing ratio (mass of water vapor divided
by mass of dry air)
mass wetness of soil

IWm3
1
height in atmosphere or depth in soil
roughness length for heat
roughness length for momentum
absorptivity for radiation
absorptivity for solar radiation
absorptivity for
longwave radiation
solar elevation angle
solar declination
slope of the saturation vapor pressure
function
emissivity
emissivity of clear sky
emissivity of sky with cloudiness c
emissivity of surface
thermodynamic psychrometer constant
(cp/h)
apparent psychrometer constant
light compensation point
dimensionless diurnal function for estimating
hourly air temperature
osmotic
coeficient
latitude
diabatic influence factor for momentum
diabatic influence factor for heat
diabatic influence factor for vapor
JEwc

in air
List of Symbols
xxi
angle between incident radiation and a
normal to a surface
volume wetness of soil
thermal time
period ofperiodic temperature variations
sky transmittance
thermal time constant of an animal
fraction of beam radiation transmitted by a
canopy
fraction of beam radiation that passes through
a canopy without being intercepted by
any objects
Jtaction of incident beam radiation trans
-
mitted by a canopy including scattered and
unintercepted beam radiation
fraction of
dzfuse radiation transmitted by a
canopy
atmospheric stability parameter
angular frequency ofperiodic temperature
variations

Introduction
1
The discipline of environmental biophysics relates to the study of energy
and mass exchange between living organisms and their environment. The

inusing the equations.
Working the problems should be considered as essential to gaining an un
-
derstanding of modern environmental biophysics as it is to any course in
physics or engineering.
A
list of symbols with definitions is provided at the beginning of this
book, and tables of data and conversions are
in
appendices at the end of
the book. It would be a good idea to look at those now, and use them
frequently as you go through the book. References are given at the end of
Introduction
each chapter to indicate sources of the materials presented and to provide
additional information on subjects that can be treated only briefly in the
text. Citations certainly are not intended to be exhaustive, but should lead
serious students into the literature.
The effects
ofthe physical environment on behavior and life are such an
intimate
part of our everyday experience that one may wonder at the need
to study them. Heat, cold, wind, and humidity have long been common
terms in our language, and we may feel quite comfortable with them.
However, we often misinterpret our interaction with our environment
and misunderstand the environmental variables themselves. Benjamin
Franklin, the early American statesman, inventor, printer, and scientist
alludes to the potential for misunderstanding these interactions.
In
a letter
to John Lining, written April 14,

cold stress, and each involves the flux of something to or from the organ
-
ism. The steady
-
state exchange of most forms of matter and energy can
be expressed between organisms and their surroundings as:
Flux
=
g
(C,
-
C,)
where
C,
is the concentration at the organism exchange surface,
C,
is
the ambient concentration, and
g
is an exchange conductance. As already
noted, our senses respond to fluxes but we interpret them in terms of
ambient concentrations. Even if the concentration at the organism were
constant (generally not the case) our judgment about ambient concen
-
tration would always be influenced by the magnitude of the exchange
conductance. Franklin's experiment illustrates this nicely. The higher con
-
ductance of the metal made it feel colder, even though the wood and the
metal were at the same temperature.
Energy Exchange

variables. Variables of concern may be temperature, atmospheric mois
-
ture, radiant energy flux density, wind, oxygen and COz concentration,
temperature and thermal conductivity of the substrate (floor, ground, etc.),
and possibly spectral distribution of radiation. Other microenvironmental
variables may be measured for special studies.
We first concern ourselves with a study of the environmental
variables-namely, temperature, humidity, wind, and radiation. We then
discuss energy and mass exchange, the fundamental link between organ
-
isms and their surroundings. Next we apply the principles of energy and
mass exchange to a few selected problems
in
plant, animal, and human
environmental biophysics. Finally, we consider some problems in radia
-
tion, heat, and water vapor exchange for vegetated surfaces such as crops
or forests.
1.2
Energy Exchange
The fundamental interaction of biophysical ecology is energy exchange.
Energy may be exchanged as stored chemical energy, heat energy, radiant
energy, or mechanical energy. Our attention will be focused primarily on
the transport of heat and radiation.
Four modes of energy transfer are generally recognized in our common
language when we talk of the
"
hot
"
sun (radiative exchange) or the

molecular interaction. If you touch a hot stove, your hand is heated by
conduction.
Heat transport by a moving fluid is called convection. The heat is first
transferred to the fluid by conduction; the bulk fluid motion carries away
the heat stored in the fluid. Most home heating systems rely on convection
to heat the air and walls of the house.
Unlike convection and conduction, radiative exchange requires no in-
tervening molecules to transfer energy from one surface to another. A
surface radiates energy at a rate proportional to the fourth power of its
absolute temperature. Both the sun and the earth emit radiation, but be
-
cause the sun is at a higher temperature the emitted radiant flux density
is much higher for the surface of the sun than for the surface of the earth.
Much of the heat you receive from a campfire or a stove may be by radi
-
ation and your comfort in a room is often more dependent on the amount
of radiation you receive from the walls than on the air temperature.
To change from a liquid to a gaseous state at
20"
C,
water must absorb
about 2450 joules per gram (the latent heat of vaporization), almost 600
times the energy required to raise the temperature of one gram of water by
one degree. Evaporation of water from an organism, which involves the
latent heat required to convert the liquid water to vapor and convection of
this vapor away from the organism, can therefore be a very effective mode
of energy transfer. Almost everyone has had the experience of stepping
out of a swimming pool on a hot day and feeling quite cold until the water
dries
from their skin.

ence), hE is the rate of latent heat loss from the surface (E is the rate of
evaporation of water and
h
is the latent heat of evaporation or the heat
absorbed when a gram of water evaporates), and
G
is the rate of heat stor
-
age in the vegetation and soil.
A
similar equation could be written for the
water balance of a vegetated surface. Since conservation laws cannot be
violated, they provide valuable information about the fluxes or storage of
energy or mass.
In
a typical application of Eq. (1.2) we might measure or
estimate
R,,
M,
H, and
G,
and use the equation to compute E. Another
typical application is based on the fact that R,,
H,
E, and
G
all depend on
the temperature of the surface. For some set of environmental conditions
(air temperature, solar radiation, vapor pressure) there exists only one
surface temperature that will balance

what portion of the system is of interest
in
a particular analysis.
Animals may be components of this system from microscopic organ
-
isms in films of water in the soil to larger fauna such as worms, or animals
onleaves such as mites or grasshoppers, or yet larger animals in the canopy
space. The particular microenvironment that the animal is exposed to will
depend on interactions among components of this continuum. Animals,