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IIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII L

[H.533 93 00995 9622

LIBRARY
Michigan State
University

 

 

 

 

This is to certify that the

dissertation entitled

MODELING SPATIAL AND TEMPORAL RESPONSES OF PHASEOLUS
VULGARIS ,L. ROOTS AND SHOOTS TO SOIL MECHANICAL
IMPEDANCE AND AERATION

presented by

GHOLAM HOSSEIN ASADY

has been accepted towards fulfillment
of the requirements for

Ph.D. Crop and Soil Sciences

degree in

CI

M rofessor

 

 

Date W/d’g 571/?ng

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

MSU

LIBRARIES
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Place in book drop to
remove this checkout from
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{3.530 6 1995
9.3-:-
‘G:

S???

 

 

MODELING SPATIAL AND TEMPORAL RESPONSES OF PHASEOLUS VULGARIS, L.
ROOTS AND SHOOTS TO SOIL MECHANICAL IMPEDANCE AND AERATION

 

BY

Gholam Hosaein Asady

A DISSERTATION ‘

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Crop and Soil Sciences

1986

ABSTRACT

MODELING SPATIAL AND TEMPORAL RESPONSES OF PHASEOLUS VULGARIS, L.
ROOTS AND SHOOTS TO SOIL MECHANICAL IMPEDANCE AND AERATION

BY

Gholam Hossein Asady

Understanding the spatial and temporal responses of plant cultivars
to the dynamically changing soil environments is important for the
development of a comprehensive plant and soil production system. The
purpose of this study was to obtain experimental information regarding
plant root responses to a mechanically impeding clay soil and put those
results into a model.

A soil core seedling test was developed which could be used as a
fast and inexpensive method of studying root responses to multiple
levels of mechanical impedance and aeration under a constant soil water
potential. Root peneration ratios.(RPR) were measured 14 days after
planting (DAP) without destroying seedling viability. RPR and root
lengths declined linearly with decreasing air filled porosity. The
maxinunn dry matter accumulations and yields occurred at RPR values of
approximately 0.65. The xylem flow rates of plants grown in high bulk
density soils were also reduced to values as low as 5 n1. 3'1.
Transpiration and photosynthetic rates were inversely and diffusive
resistance was directly correlated to mechanical impedance,

respectively.

Gholam Hossein Asady

Severe mechanical impedance reduced total root length by
approximately 80 and 7&5 after 20 and 30 days of growth, respectively.
The average root length density was reduced to less than 1 cm cm'3 in
high density soils. Extension of the roots into deeper layers was
greatly reduced by severe mechanical impedance. Approximately 901 of
the roots grown in severely compacted treatment remained in the surface
2.5 cm compared to 15$ in the control, at 20 DAP.

Greater pathway resistances of the soil pores appeared to influence
the reduced oxygen and increased carbon dioxide concentrations of the
soil more than the reduced aeration treatments of this study. In
addition, nearly 121 of the air filled pores in the surface layers of
the compacted soil were plugged by the roots, at 30 DAP, further
contributing to greater pathway resistances.

A model of shoot growth is proposed which includes the dynamic
relative growth rate and biological growth capacity of the environment.
A model of root growth and water uptake was modified which includes
soil mechanical impedance. This modified, PHASOL model dynamically
calculates the mechanical resistance, aeration porosity, and root
growth responses in different soil layers. Penetration of the roots
completely ceased as the mechanical resistance approached a critical
value of 5.5 MPa. Predicted root and shoot growth, leaf water
potential, and cumulative water use responses of dry edible beans were

parallel to experimental data, for a 20 day period of simulated growth.

To

My new-born daughter Beeta

whose arrival gave my life

a new dimension

ii

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my major professor,
Dr. AuLM. Smucker for his guidance, help, and constructive criticisms.
I am specially indebted to him for his continuous concern,
encouragement, and stimulus during the critical periods of my education
at M.S.U.

Special appreciation is extended to the other members of my
graduate program committee, Drs. Robert 0. Barr from Electrical
Engineering and System Sciences, Charles Cress, Bernard Knezek, and
Raymond J. Kunze from Crop and Soil Sciences. Their contributions to
the successful completion of this study is greatly acknowledged.

I would like to thank Dr. MdL.Huck for sending me a copy of his
model and many correspondences and conversations without which the
modeling task would have been more difficult.

I would also like to thank Dr. S.G. Wellso, and Mr. Robert P. Roxie
of USDA for allowing me to use their microcomputer. Genereous
assistance given to me by Bob enabled me to effeciently use the
wordprocessor which has been greatly appreciated.

Special acknowledgement is given to the following individuals who
have provided me with either advice or equipment during the course of
this study. Dr. A.E. Erickson's advice and supply of platinum for
making microelectrodes is much appreciated. Thanks are due to Dr. J.M.
Tiedje for the use of his gas chromatographic equipment. I would like

to thank Dr. SAL Gupta from the University of Minnesota for measuring

iii

iv

the penetrometer resistance in some of my soil samples. Dr. Tom Hodges
from the University of Missouri provided me with a weather simulator.
His intertest and advice is fully appreciated. Advice given to me by
Dr. J.T. Ritchie on some of the problems encountered when testing the
model is appreciated. Thanks are due to Mr. Dallas Hyde manager of the
soil research farm who has been very helpful to me over the years.

Financial support of the Michigan Dry Edible Bean Research Advisory
Board and Isfahan University of Technology<mf Iran, during this study
is greatly appreciated.

The last but not the least, undertaking a Ph.D. dissertation
requires a great deal of sacrifice and suffering on the part of one's

family, and my caring faithful wife, Fariba, is no exception.

TABLE OF CONTENTS

PAGE
LIST OF TABLES. O O O O O O O O O O O O O O O O O O O O O O O O Vii
LIST OF FIGURES O O O O O O O O O O O O O O O O O O O O O O O 0 ix

INTRODUCTION. 0 O O O O O O O O O O O O O O O O O O O O O O O O 1

CHAPTER 1 : LITERATURE REVIEW
Plant Responses to Root Environments .. .. .. .. .. . A

Root Responses to Soil Environments.... .. .. .. . .. 9
Pore Size. 0 O O O O O O O O O O O O O 11

Mechanical Resistance. . . . . . . . . . . . . . . . . 12
Aeration Stress. . . . . . . . . . . . . . . . . . . . 18
water uptake 0 O O O O O O O O O O O O O O O O O O O O 20

Literature Cited 0 O O O O O O O O O O O O O O O O O O O O 25

CHAPTER 2 : SEEDLING TEST FOR THE QUANTITATIVE MEASUREMENT
OF ROOT TOLERANCES TO COMPACTED SOIL

Abstract .. . .. . .. . .. . .. . .. . . .. . . .. 30
Introduction .. . .. . .. . .. . .. . .. . .. . .. 31
Materials and Methods.. . .. . .. . .. . .. . . .. . 32
Results and Discussion .. . .. . .. . .. .. . .. .. 35
Literature Cited.. . .. . .. . .. . .. . .. . .. . "9

CHAPTER 3 : EFFECTS OF MECHANICAL IMPEDANCE AND AERATION ON
DRY BEAN ROOT GROWTH

Abstract 0 O O O O O O O O O O O O O O O O O O O O O 0 O C 51
IntrOdUCtion O O O O O O O O O O O O O O O O O O O O O O O 53
Materials and Methods.. . .. . .. . .. . .. .. . .. 58

V

Results and Discussion .. . .. .. . .. . . .. . .

Literature Cited

CHAPTER A : A MATHEMATICAL MODEL OF GROWTH IN ANNUAL PLANTS

Abstract . .

vi

IntrOduction I O I O O O O O O O O O O O O I O O O

Exponential Growth . .. . .. . .. . .. . .. . ..

Literature Cited

CHAPTER 5 : PHASOL: A MODEL OF ROOT GROWTH AND WATER UPTAKE

IN A LAYERED-HOMOGENEOUS SOIL PROFILE

Introduction .

Description of the model . . . . . . . . . . . . .
Model Program.
Water Balance.. . .. . .. . .. . .. . .. .
Carbon Balance .. . .. . .. . .. . .. . .
Root Growth and Distribution .

Testing the Model. .. . .. . .. .

Literature Cited

CHAPTER 6 : SUMMARY AND CONCLUSIONS ..

APPENDIX I : PHASOL MODEL

Computer Program . .. . .. . .. .

Input Data 0 O O O O O O O O O O O O 0

Computer Output. .. . .. . .. . .. . .

Glossary of Variables.. . .. . .. . .

APPENDIX II :

Other Data .

PAGE
63
89

91
92
9A

110

112
119
119
120
132
137
11111

157

160

16L:
175
177

201

206

LIST OF TABLES

CHAPTER 2 PAGE

1. Influence of soil compression on the soil bulk
density, water retension, penetrometer resistance, and
aeration status of an expanding clay soil at several
soil water contents. Each value is the average of five
to eight replications. .. . .. . .. . .. . .. . .. . 37

2. Root length density in the top, middle, and bottom
cores when the middle core was subjected to three
levels of soil compaction ” . .. . .. . .. . .. . 38

3. Total and relative root lengths in the top, middle,
and bottom cores when therniddle core was subjected
to three levels of soil compaction. .. . .. . .. .. . 39

ll. Influence of air filled porosity on shoot weight, leaf
area and stomatal diffusive resistance of four dry
edible bean cultivars at 14 days in the soil core
seedling test.. .... . . .. . .. . .. . .. . .. . . N2

5. Influence of air filled porosity on the accumulation
of toxic anaerobic metabolites by black and white dry
edible beans grown for 1H days in the soil core
seedling test.. . . .... . .. . .. . .. . .. . .. . “5

CHAPTER 3

1.Root length distribution responses of Phaseolus
vulgaris to soil compaction, time, and aeration
treatments 0 O O O O O O O O O O O O O O O O O O O O O O 0 6n

2; Oxygen diffusion rate responses of Charity clay soil
measured at three soil depths and at three different
times. 0 O O O O O O 0 O O O O O O O O O O O O O O O O O O 75

3. Specific carbon exchange rate responses of Phaseolus
vulgaris to soil compaction and aeration treatmens .. .. 86

A. Total carbon exchange rate responses of Phaseolus
vulgaris to soil compaction and aeration treatments.. . . 8?

vii

viii

CHAPTER 5 PAGE

1. Simulated shoot and root growth responses of Phaseolus

vulgaris after 5, 10, and 20 days of simulation, at two
3011 bulk densities 1.1 and 1.7 Mg m’3 . . . . . . . . . . 1u5

Simulated cumulative water uptake, transpiration, plant

water potential, and plant and soil hydraulic resistan-

ces of Phaseolus vulgaris after 5, 10 and 20 days

of simulation, for two bulk densities 1.1 and 137 Mg m"3 . 15A

 

LIST OF FIGURES

CHAPTER 2

A

5.

Root penetration ratio responses of four dry edible bean
cultivars to air filled porosities of a clay soil at -8:
2 kPa water potential. Each data point represents the
mean of eight replications. .. . .. . .. . .. . . ..

Xylem accumulation rates of dry edible beans grown in
compacted clay soils. Each data value is the mean of
eight replications. O O O O O O O O O O O O O O O O O O 0

Shoot growth responses of dry edible beans to three
levels of compacted clay soil cores during two weeks of
growth. The square, circle, and triangle symbols repres-
ent air filled porosities of 0.31, 0.18, and 0.06, resp-
ectively. Each data point is the mean of four cultivars
replicated eight times. . . . . . . . . . . . . . . . . .

Multiple correlation of a quadratic function of root
penetration ratios of four dry edible bean cultivars
grown in three levels of a compacted clay soil core to
the dry matter accumulation of the same cultivars grown
on similarly compacted clay soils in the field.Each data
point is the mean of four replications for each cultivar.

Multiple correlation of a quadratic function of root
penetration ratios of four dry edible bean cultivars
grown in three levels of a compacted clay soil core to
the yield of the same cultivars grown on similarly com-
pacted clay soils in the field. Each data point is the
mean of four replications for each cultivar . . . . . . .

CHAPTER 3

1.

 

——-—:

Schematic view of the root chamber and tension table
apparatus. A is the surface aeration chamber, B is the
experimental unit, C is the access port for gas sampling
, D is the tension table, E is the porous plate over the
tension table, F is the burette, G is the air entry poi-
nt, H is the applied matric potential head,and I is

the burette support.. . . .. . .. . .. . .. . .. . .

ix

PAGE

36

111

"3

N7

48

60

 

7.

10.

11.

12.

13.

14.

PAGE
Influence of soil compaction, aeration, and time on root
length density of dry edible beans grown in 25 cm
cores. 1, 2, and _; represent bulk densities of 1.1, 1.11
, and 1. 7 Mg m , respectively.. . .. . .. . .. . .. . 67

Influence of soil compaction on root length density
distribution of dry edible beans after 10 days of growth. . 68

Influence of soil compaction on root length density
distribution of dry edible beans after 20 days of growth.. 69

Influence of nsoil compaction on root length density
distribution of dry edible beans after 30 days of growth.. 71

Influence of soil compaction, aeration and time on

relative root length of dry edible beans. The bulk dens-

ity treatments 1-3 are: 1.1, 1.”, and 1.7 Mg m‘ ,

and A, B, C, and D represent surface, top, middle, and

bottom cores, respectively. . . . . . . . . . . . . . . . . 72

Air filled porosity contained in the pores larger than
the mean pore radius" . .. . .. . .. . .. . . .. . . 73

Influence of soil compaction and aeration on oxygen con-
centration distributions 20 days after planting . . . . . . 76

Influence of soil compaction and aeration on oxygen con-
centration distributions 30 days after planting . . . . . . 77

Influence of soil compaction and aeration on carbon
dioxide concentration distributions 20 days after plant-

ing 0 O O O O O O O O O O O O O O O O O O O O O O O O O O O 78

Influence of soil compaction and aeration on carbon
dioxide concentration distributions 30 days after plant-

ing 0 O O O O O O O O O O O O O C O O O O O O O O O O O O I 79

Relationship between ODR, D/Do and bulk density of Char-
ity clay soil at -6 kPa soil matric potential .. .. .. . 80

Root filled porosity distribution of dry edible beans

after 10 days of growth. 1, 2, and 3 represent bulk den-

sities of 1.1,‘LA, and 1.7 Mg m , respectively.

The bar over each core depth represents LSD at 0.05

level of probability . .. . .. . .. . .. . .. . .. . 83

Root filled porosity distribution of dry edible beans

after 20 days of growth. 1, 2, and 3 represent bulk den-

sities of 1.1, 1.“, and 1.7 Mg m'3, respectively.

The bar over each core depth represents LSD at 0.05

level of probability . .. . .. . .. . .. . .. . .. . 8A

 

xi

15. Root filled porosity distribution of dry edible beans
after 30 days of growth. 1, 2, and 3 represent bulk den-
sities of 1.1, 1.L1, and 1.7 Mg m'3, respectively.

The bar over each core depth represents LSD at 0.05
level of probability .. .. .. . .. . .. . .. . ..

CHAPTER u

1. Measured shoot dry mass accumulations of dry edible
beans grown on Charity clay 3011.. . .. . .. . .. . .

2. Natural log transformations of measured shoot dry mass
accumulations of dry edible beans grown on Charity clay

8011-. O O O O I O O I O O O O O O O O O O O O O O O O O O

3. Absolute growth rate of dry edible bean shoots grown on
Charity clay soil as a function of days after emergence

(DAB) 0 O O O O O O O O O O O O O O O O O O O O O O O O O

u. Absolute growth rate of dry edible bean shoots grown on
Charity clay soil as a function of shoot dry mass. . . .

5. Simulated shoot dry mass accumulations of dry edible
beans grown on Charity clay soil.. . .. . .. . .. . .

6. Simulated and measured shoot dry mass accumulations of
dry edible beans grown on Charity clay soil. The solid
symbols represent measured observations . . . . . . . . .

7. Correlation between the simulated and measured shoot dry

mass of dry edible beans grown on Charity clay soil . .

CHAPTER 5

1. Flowchart representing the water flow processes within
the soil-plant-atmosphere system... . .. . .. . .. .

2. Soil water characteristic modifications of Charity clay
soil with bulk density.. . .. . .. . .. . .. . .. .

3. Hydraulic conductivity modifications of Charity clay
soil at different bulk densities. T is the soil matric
tension and Ln is the natural logarithm . .. .. .. ..

11. Influence of leaf water potential on the leaf abaxial
diffusive resistance of dry edible beans.. .. .. .. .

5. Specific transpiration rate as a function of leaf abaxi-
al diffusive resistance of dry edible beans .. ... ..

PAGE
. 85
O 99
. 100
. 102
. 103
. 105
. 106
. 107
. 121
. 123
. 125
. 128
. 129

xii

PAGE

6. Influence of leaf abaxial diffusive resistance on ralat-

ive transpiration rate of dry edible beans. This is gra-

ph of the water stress factor (WATRST) in the PHASOL
model 0 O O I O O O O O O O O O O O O O O O O O O O O O O O 131

7. Flowchart representing carbon flow processes within the
soil-plant-atmosphere system. .. . .. . .. . .. .. .. 133

8. Influenceof specifictranspirationrateonleaf temper-
ature of dry edible beans .. . .. . .. . .. . .. .. . 136

9. Relationship between soil matric potential and air

filled porosity of Charity clay soil for three bulk
denSIties O O O O O O O O I 0 I O O O O O 0 O O O O O O O 0 1n0

10. Spatial distribution of root water uptake by dry edible
beans after 5 days of simulation.. . .. . .. . .. . .. 1”?

11. Spatial distribution of root water uptake by dry edible
beans after 10 days of simulation . .. .. .. .. . .. . 1A8

12. Water flux distribution in a 25 cm deep Charity clay
soil after 5 days of simulation .. . .. . .. . .. . .. 1A9

13. Water flux distribution in a 25 cm deep Charity clay
soil after 10 days of simulation.. .. . .. . .. . .. . 150

1“. Spatial distribution of soil water potential in Charity
clay soil after 5 days of simulation.. .. .. .. . .. . 151

15. Spatial distribution of soil water potential in Charity
clay soil after 10 days of simulation.. .. .. .. .. . 152

APPENDIX II

1. Changes in partial pressure of 0 inside a diffusion
chamber in which diffusion pathway 8 either free air or
soil porosity. The chamber is filled with N2 at time
zero. P and P0 are 02 partial pressures when diffusion
pathway is the soil or free air, reapectively. Soil is
Charity clay at three different bulk densities (BD), and
at three different matric potentials (MP) . . . . . . . . . 207

2. Diffusion impedance of Charity clay soil as a function
of soil air filled porosity. D is diffusion coefficient
of 02 in the soil, Do is diffusion coefficient of 02 in
the air, and ED is the soil bulk density. . . . . . . . . . 208

3. Spatial variations of oxygen diffusion rate in a Charity
clay soil in the presence of growing roots, at 10 days
after planting. O I O O I O O O O O O O O O O O O O O O O O 209

A.

xiii

PAGE
Spatial variations of oxygen diffusion rate in a Charity
clay soil in the presence of growing roots, at 20 days
after planting. I O O O O O O O O O I O O O O O O O O O I O 210

Spatial variations of oxygen diffusion rate in a Charity
clay soil in the presence of growing roots, at 30 days
after planting. O O I O O O O O O O O O O O O O O O O I O O 211

Relationship between oxygen diffusion rate, D/D , and
soil bulk density in a Charity clay soil. 1.1 to I.7 are
soil bulk densities in Mg m' . The soil was at -6 kPa
matric potential at equilibrium . . . . . . . . . . . . . . 212

INTRODUCTION

Limited natural resources and growing world populations have placed
an unprecedented demand on contemporary agricultural research programs.
The agriculture industry is now faced with developing available
technologies in order to cope with the ever increasing problems
associated with food and fiber production.‘Therefore, it is imperative
that our research be directed toward the problems needing attention.
Unfavorable soil physical conditions are known to be one of the major
limiting factors in agricultural production systems. Mechanization of
agriculture, including utilization of heavy machinery and associated
equipment, coupled with poor management practices have resulted in
compacted soils.

The compaction of soils affects those physical properties which
influence the storage and conduction of water, diffusion of gases,
uptake of nutrients, and the soil mechanical resistance to root
penetration. These adverse physical consequences of soil compaction
cause soil particles to be in closer contact with each other,
consequently increasing the angle of soil internal friction and
cohesive forces, creating smaller mean pore diameters and reducing
total soil porosity which imposes a mechanical barrier to root
development.

The growth and distribution of plant roots determines their

efficiency in water and nutrient uptake and ultimately controls plant

1

2

production. Although root development is genetically controlled, soil
environmental conditions modify the root development of different
genotypes. Soil compaction appears to directly and indirectly influence
the ontogenetic development of plant root systems through certain soil
physical conditions (eg. temperature, aeration, mechanical impedance,
and water potential). The direct influence of soil compaction appears
to be an increasing mechanical resistance to root penetrations. Soil
compaction indirectly affects plant growth by creating an oxygen
stressed environment which promotes anaerobic root respiration and the
formation of toxic anaerobic compounds. The shallow rooting generally
associated with soil compaction results in reduced anchorage of plants.

Expansion of the computer industry and the wide scale availability
of digital processors has provided scientists from different
disciplines a new avenue to organize their thoughts and implement their
ideas through the development of simulation models. Models have become
established as a means for understanding concepts which elude the
brain's unaided ability (Radford, 1968). Models developed for
simulating a system (M‘ organism are designed to represent the
mechanisms which control the activities of that system or organism. A
model is usually amenable to manipulation which would be otherwise
impossible, too expensive, or impractical to perform on the entity it
portrays (Naylor gt_§l,, 1966). A fundamental rationale for developing
simulation models is our increasing quest for knowledge concerning the
future. Computer simulation models for predicting crop production
systems appear to provide researchers with an additional analytical
tool. Application of plant growth simulation models has great potential

in forecasting yields of large areas which could provide valuable

3

information at the local, state, and federal levels of decision making.

The primary objective of this study was to evaluate the effects of
mechanical impedance and associated stresses on the growth and
development of the dry edible beans (Phaseolus vulgaris,lu ) root
systenn Other objectives include development of a quick and inexpensive
method of studying plant-root system grown under multiple levels of
soil physical environments. The experimental data which quantitatively
describes the underlying relationships is put into a feasible model to
predict the drybean root growth and distribution under a given set of
conditions. This, both summarizes what we already know about the
drybean and also projects what is not yet known. The model needs more
testing against field data and parameter estimations before it could be

used for management decisions.

CHAPTER 1

LITERATURE REVIEW

Plant Responses to Root Environments

Crop production is often limited by prevailing environmental
conditions, iJL by the existing complex of physical, chemical and
biological factors (Feddes gt__a_l_., 1978). Plants, as a whole, live in
two realms, the atmosphere, and the soil, each of which has its own
charateristics and complexity, of these two, the soil seems to be much
more complex. Terresterial portions of plant root systems are confined
to the soil and exposed to multiple chemical, physical and biological
environments. The paucity of information concerning the root-soil
interface and the many environmental conditions which influence this
interface are of prime importance to the tolerance of plants to soil
related stresses .

Plant growth is an integration of two principle factors with time.
Those which genetically control development of the different plant
characteristics, and the environmental conditions which appear to
modify this genetic bahavior. Most of the changes in plant
characteristics may be an expression of ontogenetic drift (Hunt, 1978).
This is due to developments which occur within the plant with the
passing of timec‘These developments occur against the background of
changing environments. In order to obtain a greater understanding of

4

5
the relative importance of these two effects, plants should be grown in
constant or controlled environments.

Basically shoot and root functions remain the same, even though
their relative contributions to the whole growth process may be altered
by the environment. Shoots are specialized to convert the chemical
energy into metabolites through the complex biochemical process of
photosynthesis on which the whole plant growth depends. It is not
exagerated to say that the biological capacity of the earth is
ultimately dependent upon the energy received from the sun through many
natural light detectors and sensors (Hunt 1978). In contrast, the major
functions of root systems include absorption of water and
nutrients,anchorage, and synthesis of some of the plant growth
regulators(Russell, 1977), all of which are coordinated with the
components of the shoot. One of the main functions of the root system
is uptake and fixation of nitrogen. The daily nitrogen requirements for
growth of a plant or plant part with dry matter W, and its associated

respiration cost are defined as

Fn dW/dt (1)

and

a Fn dW/dt (2)

respectively, where Fn is the fractional nitrogen content of plant dry
weight (eg. Kg N/Kg dry wt.), a is the respiration cost per unit
nitrogen taken up (eg. Kg C02/Kg N), and dH/dt is the time rate of dry
matter production LJohnson, 1983).Another metabolic activity'of the

root system is the utilization of carbohydrate. An efficient root

6

system appears to be one which can support the minimum metabolic
demands during periods oflnaximum stress without putting excessive
demands on the limited quantities of photoassymilates. The metabolic
investments for developing and maintaining a functional root system
subjected to adverse environments are much greater than in nonstressed
environments (Smucker, 198”). Complete analysis of the growth and
functions of either roots or shoots is impossible without considering
the interrelationship between both organs (Russell, 1977).

Interactions between root and shoot activities has been the subject
of considerable research by those scientists (Fischer and Turner, 1978;
Huber, 1983; Moony, 1972; Novoa and Loomis, 1981; Russell, 1977;
Thornley, 1977; Hareing and Patrick, 1975) who tried to quantitatively
describe the processes of growth in a whole plant system. Charles
Edwards (1976) model of shoot-root activities during steady state
exponential growth, describes and relates the growth constants to the
specific activities of both shoot and roots. Reynolds and Thornley
(1982), expressed this functional relationship between the size and
activity of the roots and the size and activity of the shoots as

0 "8h ‘3‘- C W (3)

C N r
where 0C is the specific shoot activity (i.e. the net rate of carbon
uptake per unit of shoot structural dry matter), wsh is shoot
structural dry matter, UN is specific root activity with respect to
nitrogen (i.e. the rate of nitrogen uptake per unit of root structural
dry matter), and "r is root structural dry matterz'The value of the

specific shoot activity ( 0C) is dependent on environmental variables

7
SUCH 83 light flux d8081tY. C02 concentration, and temperature.
Specific root activity (GIN might be determined by factors such as
soil temperature, and soil nitrogen concentration. Based up on these
principles, Reynolds and Thornley (1981) developed a two compartment
(shoot and root). two substrate (carbon and nitrogen) semi-mechanistic,
semi-impirical shootzroot partitioning model.

Understanding the conseqences of metabolic activities of roots on
the whole plant is necessary in order to assess the integrated growth
behavior at the whole plant level. This is a central problem, however,
as little is known concerning the carbohydrate requirements of root
growth into a new soil volume. Although the absorption of nutrients
increases, additional photosynthates, which could have been used in the
shoot growth are required by the root. Novoa and Loomis (1981) reported
that the leaves have first priority in the use of carbon supply,
largely because of their proximity to the photosynthate source. Roots
on the other hand, are considered to have a similar priority in
nutrient and water uptake. The balance operates to restrict root or
shoot growth depending upon whether shoot- or root-supplied factors are
more limiting at the moment.

Huck and Hillel (1983) considered carbohydrate partitioning between
the root and shoot to be a function of plant water potential. When
abundant water is available, shoot growth will be stimulated with
little change in the formation of new roots. According to Huber (1983).
dry matter distribution between the shoot and root may be related to
photosynthate partitioning into soluble carbohydrates and starch.
Increased partitioning of the daily photosynthates into starch is

inversely related to the relative dry weight of roots in several plant

8

species. Carbon partitioned into leaf starch was preferentially
utilized for growth of shoots at night. This relationship didn't appear
to change with the nutritional status of the plant. As growth proceeds,
development of the different parts of the plant and their consistant
relative sizes are evidence of the close coordination which exists in
plant growth processes. Brouwer (1963) showed that if half the leaves
or roots of bean plants are removed, the original root/shoot ratio
will soon recover, provided that the meristemic tissues remain on both
parts of the plant. Some of the root produced hormones (i.eu
cytokinins)may be involved in this coordination (Russell, 1977).
Dependence of the shoot function on the roots in a number of prennial
plants has been indicated by the straight line relationship between the
incremental dry weight and incremental mineral uptake rates under many
different environmental conditions (Richards, 1980).

Plant organs are continuously competing for the available
carbohydrate produced in the leaves. A simple analysis would suggest
that to have the highest rate of shoot growth, there is a minimum
diversion of carbohydrate to the roots which are currently providing
adequate water and nutrients. In this situation, greater root growth
would seem to dissipate those metabolites which otherwise could be
invested in the photosynthetic apparatus. This analysis may seem
reasonable for plants growing under favorable environments, but seldom
occurs under natural conditions. Therefone it is believed that
successful plant growth strategies are those that provide for the
instantaneous needs of the entire plant system. In this situation then,
plant productivity may be determined by the development of a root

system that is adequate to support plant growth during the time of

maximum stress.

Adverse physical and chemical root environments are a major cause
of plant physiological stresses. Soil properties such as temperature,
water, aeration and mechanical impedance are manifestations of the
resultant dynamic physical forces acting on the soil body. It is these
forces which determine to a large extent the physical characteristics
of the soil-root interface and the degree of contact between the root

and the soil.

Root Responses to Soil Environments

The soil and root interface could be classified into three major
categories, chemical, physical, and biological. Although it is
recognized that there is a dynamic interaction among these three
categories, this report will emphsize the physical factors which
primarily influence root growth. In spite of the many chemical stresses
which may be eliminated by soil fertility and leaching, physical
inadequacies are difficult to eliminate and at best may be temporarily
alleviated. Therefore, it is important to continuously maintain the
physical condition of the soil.

Adverse physical conditions which roots experience may be
categorized into four major classes: mechanical impedance, shortage of
oxygen (excessive water), water stress(inadequate water) and
unfavorable soil temperature regimes. All of these may cause an adverse
environment which stresses the growing roots depending on the degree of
their severityu Boyer (1982) describes stress as, plants growing in
natural environments which are often pevented from expressing their

full genetic potential for reproduction.]kiorder to understand the

10
mechanisms of physical restraints, we must comprehend the soil
structure and its corresponding constituents.

Soil is a three phasic dynamic body consisting of solids ( eg.
mineral matter derived from parent rock), liquid (eg. water) and gases
( eg. oxygen, carbon dioxide, nitrogen and other trace gases). Between
“0 to 60 percent of the total soil volume commonly consists of its
solid phase including the organic matter (Russell, 1977L.The solid
phase is penetrated by a network of irregularly shaped pores, filled
with air and/or water. The distribution of pores is an important
factor in describing the physical state of the soil. For a steady state
condition an ideal soil porosity for good root penetration is when 501
of the soil volume is occupied by the solid phase ,251 by water, and
251 by air (Vomocil and Flocker, 1961L.From the mechanical point of
view, a soil satisfactory for root growth might be visualized as a
deformable storage tank which contains liquids and gases and at the
same time acts as a conductor of these fluids .

Attempts to describe the physical state of the soil by'a single
index has led to definitions like, bulk density, void ratio, soil
strength, soil compaction, etc. The definition of soil compaction could
be described as the increasing of soil bulk density. Although this
definition might be satisfactory for agronomic use, it should be
realized that soil bulk density only reflects the total volume of pores
and does not consider the more important criteria of pore size
distributions. Bulk density is generally a confusing term when
comparing the porosity of contrasting soil textures, as coarse textured
sandy soils normally have higher bulk densities. Too much compaction

strengthens the soil, impeding root growth and reducing crop yields

11
(Dunlap and Weber, 1971). Soil compaction must be characterized in
terms of both soil and plant related conditions. Symptoms of soil
compaction in plant systems include the presence of horizontal root
systems above the compacted zone (Steinhardt, 1982), thicker roots
(Goss, 1977), a reduction in dry weight (Asady 33 31,, 1985), and

reduced mycorrhizal infections (Mulligan gt a_l., 1985).

Pore Size

The size and continuity of soil pores determines the water
potential of the soil and the energy required to extract that water.
In a simulated wheel-track experiment, where the average pore size was
smaller, the hydraulic potential values were more negative in the
wheel-track area than those in the nonwheel-track area (Reicosky fl
£93, 1981L.Pore size distribution not only depends upon the state of
compaction, but also on the soil texture. Compacted clayey soils
generally have smaller pores, consequently the water is more tightly
held. The saturated hydraulic conductivity of a compacted soil is
usually reduced due to a reduction in total pore volume, with
ancillary changes in the size, shape, and continuity of pores.
Sinclair _e_t_ 2}, (19711) estimated nonsteady state permeability from soil
water desaturation data which is the direct consequence of soil
porosity.

Russell (1977) classifies the soil pores into three broad
categories. Pores which drain freely under forces of gravity so that
they are air filled when the soil is at or close to field capacity. The
minimum size of the pores in this class is 30-60 uM. Because the

diffusion coefficient of oxygen in water is 10000 times less than in

12
air, soil aeration at field capacity largely depends upon these small
water filled pores. The second class of pores are the ones which hold
water against gravitational forces but in which the water potential is
sufficiently high for absorbing roots to withdraw from it. That is to
say, the water potential is above -15 bar(less negative). The minimum
size of such pores is 0.2 uM. The quantity of pores between 0.2 and 60
uM is a major factor which determines the reserves of available water.
The third class are fine pores which hold water at potentials less than
-15 bars (more negative)sothat it is essentially inaccessible to

roots.

Mechanical Resistance

Root penetration into the soil may be considered from at least two
perspectives. First, root penetration is primarily a function of the
difference between mean pore diameter and mean root diameter. The
second model ignores the direct influence of pore diameter and
considers the soil strength as a determinant factor. If a growing root
encounters a pore which has a smaller mean diameter than the root tip,
it would either have to apply ample pressure to expand the pore or
decrease its diameter to be able to penetrate. The later alternative
seems unreal, because the diameter of mechanically impeded roots
usually increases. 6033 (1977) and Hiersum (1957) indicated that plant
roots are unable to reduce their diameters when they encounter pores
with small mean diameters and mechanical impedance caused their
diameter to increase. However, mechanically impeded roots start
proliferating and generating fine laterals which penetrate the smaller

pores.‘The increased growth of laterals may then result.in the total

13

root dry weight being unaffected by the mechanical resistant. This
compensatory growth of roots is analogeous to those observed when part
of a root system is subjected to other restraints. For example, when
barley roots were grown in rigid ballotini sand having pores with
diameters midway between that of the axis and lateral roots, so that
the laterals were unimpeded, the total weight of the root was
unaffected (Goss, 1977). These smaller branches might be the source of
confusion by some workers occasionally reporting a reduction in
diameter of mechanically impeded roots (Russell, 19?“).

Expansion of the soil pores is a function of root tip pressure and
soil resistance to external pressure. Soil is a heterogenous medium and
the enlargment of pores by roots can vary due to either the
displacement of the particles or to their deformation. Results of
studies on effects of mechanical impedance on root growth using rigid
mediums.(Gill and Miller, 1956; Goss, 1977; Hiersum, 1957; G033 and
Russell, 1980) has demonstrated that rigidity of pore structure is also
a factor governing mechanical resistance to root penetration. As long
as the roots can displace or deform soil particles they can force
through pores originally smaller than themselves. Results of
interactions between pore diameter, rigidity of pore structure and root
penetration indicated that when the pore size was sufficient to allow
penetration by the narrower roots, the depth of penetration increased
as the rigidity of the pore structure diminished (Wiersum, 1957). It is
generally believed that soil compaction adversely affects plant root
growth by (1) increasing the mechanical impedance and (2) altering the
extent and configuration of the pore space. A major difficulty in

studying the effects of mechanical impedance on root penetration in the

1A

soil is that compacting the soil not only increases mechanical
resistant to penetration, but also changes the balance of water and
aeration. Aside from the direct influence of mechanical impedance on
the supply of oxygen to the soil it is implicated that mechanical
impedance induces physiological changes in the root system which
predisposes them to greater oxygen deficiencies (Schumacher and
Smucker, 1981). The observed responses of root morphology may,
therefore, be the consequence of complex interactions of these
variables.

Barley (1962), indicated that corn roots can exert longitudinal
pressure as high as 12 atmospheres per unit area when subjected to
pressures within a flexible diaphrann The maximum pressure, however, is
not as important as thetninimum soil mechanical pressure which can
appreciably reduce root growth. Other investigations whose
experimental systems provided an opportunity to measure the direct
affects of the pressures which roots experience have reported that the
elongation of root axes is reduced when they are subject to root
pressures of 0.5 bar or less (Barley, 1972 ; Gill and Miller, 1956;
Abdalla gt 9;" 1969). Greacen and Oh (1972) attribute the sensitivity
of root growth to mechanical impedance and relative insensitivity of
root growth to changes in soil water potential, to partial
osmoregulation of roots against the variable external pressure and
complete osmoregulation against the soil water potential.

There are evidences suggesting that the resistance to root
extension can not be due solely to the physical effects of external
pressure on the elongation of cells. Goss and Russell (1980) conducted

an experiment in which the tip of barley root seedlings were subjected

15
to a small external pressure. There was an appreciable time lag, three
or more days, from the time of relief of the external pressure until
the rate of root elongation increased to that of unimpeded roots. They
suggested that physical restraints imposed on the enlargement of the
vacuolating cells was not the only factor responsible for root
responses to small external pressures. This information suggests that
root responses to mechanical stresses depehd upon a complex of many
interacting physiological processes.

Morphological effects of mechanical resistance on root growth can
include reducing the length of the axes and thickening of laterals.
Goss and Russell (1980) reported that when mechanical resistance caused
barley roots to curve laterals were initiated on the convex or tension
side of the curve and root hairs were more abundant on the concave
side» Less impeded roots are much thinner than the roots grown at a
high mechanical resistant (Boone and Veen, 1982). Goss(1977) indicated
that the rate of root elongation in a number of agronomically important
crop plants, including barley, was reduced considerably by small
mechanical resistances, when other characteristics of the rooting
medium and environmental conditions where favorable to growing roots.
Schumacher and Smucker (1981) reported that drybean root systems grown
on 1 mm rigid matrix had larger root tissue densities than 3 mm matrix.
They also reported that the finer soil matrix reduced porosity of the
roots. Wilson gt_§g, (1977) indicated that the diameter of the steele,
near the apex of the barley roots, grown under mechanical stress,
exceeded that of unimpeded roots by as much as 221. The increased
diameter was not fully accounted for by the shorter roots indicating a

reduction in volume by about “0%.‘There was also a significant increase

16
in the total number of cells in the steele of apical barley root tips.

Attempts to characterize soil properties such as soil strength and
its effect on plant root growth has led to the wide use of soil
penetrometers (Bradford, 1980; Voorhees gt 3%,, 1975; Blanchar gt_§g,,
1978). Koolen and Kuipers(1983) believes that penetrometers can be used
for quick determination of soil mechanical or physical properties such
as cohesion, angle of soil internal friction, pore space, moisture
content, cu“ soil water suction. There are three principle
characteristics of the root, however which are quite different from
penetrometers and cannot be simulated. These are : (1) the root apex is
quite capable of deformation and (2) can curve round the obstacles
which they may encounter, and (3) the lubricating effects of the
mucigel sheath at the surface of the root cap. It is these
considerations, which has caused scientists to use many different
static and dynamic penetrometers varying from cone shape and angle to
metal and plastic.

Correlation of root elongation rates and penetrometer resistances,
has indicated that primary root elongation of pea seedlings were more
closely corelated to a 10 degree probe than a 60 degree probe (
Voorhees st 31,, 1975). Close correlation between root elongation rates
and soil resistance normal to the probe, which does not include soil-
metal friction, may therefore suggest that the root-soil friction is
negligible. The complexity of the soil system appears to be the main
factor responsible for lack of mechanistic approaches to the problem of
soil strength and root growth. Gerard §t_§g, (1982) derived regression
equations describing penetrometer resistance and root growth. The

critical soil strength at which root elongation stopped was found to

17

be 60-70 bars in coarse textured soils to 25 bars in clay soils.

Changes in environmental factors such as soil aeration, soil water
potential and soil temperature, may modify the response of roots to
mechanical resistance. Gill and Miller (1956) indicated that the
reduction in root elongation can be enhanced if the concentration of
oxygen in the gaseous phase around the roots is reduced to less than
101. They managed to demonstrate that the ability of roots to overcome
mechanical resistant is related to the amount of oxygen available.
Rickman gt_gl. (1966) indicated that limiting oxygen concentrations in
the root zone of tomato plants reduced the rate of water uptake by the
roots almost equally in mechanically compacted and noncompacted soils,
even though root growth was quite different. This indicates that in
oxygen deficient environments,the rate limiting factor is primarily
oxygen partial pressure rather than mechanical impedance. Many
investigators (Gill and Miller, 1956; Barley, 1962; Eavis, 1972;
Schumacher and Smucker, 1981) have attempted to differentiate the
effects of mechanical resistance from aeration in mechanically impeded

soils. Eavis (1972) introduced an aeration deficiency index as

ADI = (1- E1/E2)'100 (A)

where E1 is the effects obtained when mechanical impedance and aeration
effects are both operating. E2 is the effects obtained when only

mechanical impedance operating.

18

Aeration Stress

The effects of oxygen stresses on root growth might be due to
diffusion resistance in either soil or plant pathways. A third
possibility might be the presence of toxic anerobic materials
accumulated in the root zone by the high diffusion resistances in the
escape pathways (Eavis, 1972). Plant roots growing in the soil may
receive their oxygen requirements through two pathways: soil pathway
includes diffusion of oxygen through the soil pores and eventally the
cell walls. The plant pathway is the diffusion of oxygen in
intracellular gas spaces of plants. This pathway appears to be less
important for field crops than it is for bog plants (Luxmoore and
Stolzy, 1972). Consequently it is generally believed that the soil
aeration is the primary factor responsible for diffusion of oxygen
into, and carbon dioxide out of the root zone of upland crops.

The rate at which oxygen can diffuse into a porous media may be

described by the partial differential equation (Lemon, 1962)

ac__ 2 (5)
3t DVC

in which(3is the concentration or partial pressure of oxygen, t is
time and D is the coefficient of gas diffusion in the diffusing medium.
The gas diffusion coefficient appears to be the predominate factor
controlling the rate of oxygen supply to the soil and describes the
resistance of soil pathways to diffusion processes. Therefore, the pore
size distribution is an important soil characteristic defining the
diffusion pathway. Reducing the size of the pores beyond the mean free

path of diffusing oxygen molecules increases the chance of collisions

19
between the gas molecules and the pore walls resulting in a reduction
in the number of molecules transferred. Many investigators (Lemon,
1962; Luxmoore 33 gg,, 1970; Luxmoore and Stolzy, 1972; Woolley, 1965;
Jensen gt 32,, 1967 ) have tried to integrate the oxygen demand
characteristics of the plant and oxygen supplying power of the soil in
a unified model. Lemon (1962) solved the general equation of gas

diffusion and derived the following equations

C1=CR-(Q/HD1)(R2-l’12) (6)
where

CR:CP+(QR2/ZDeMJKR/re) (7)

Ci is the oxygen concentration (3 cm'3) inside the root at the radial
distance r1 (cm) from the root axis, q is the rate of oxygen
consumption per unit volume of the root tissues (3 cm'3 5'“), CR is the
concentration (g cm'3) of oxygen at the root surface at the distance of
R (cm) from the root center, CD is the oxygen concentrations (3 cm'3)
in the liquid at the gas-liquid interface, some radial distance, re
from the root axis. Di and De are coefficients of gas diffusion (cm2
3") inside the root and at the liquid-solid interface, respectively.

Lemon's model does not take into account the longitudinal
diffusion of oxygen within the roots. Luxmoore gt_§g, (1970) described
a model which accounts for longitudinal as well as radial oxygen
diffusion, and considers root respiration to be a function of oxygen
concentration and position along the root. Lemon (1962) defined the

critical oxygen concentration as the oxygen concentration at the root

surface below which the oxygen consumption rate by the root is

20
reduced. It appears that the soil diffusion is the rate limiting
factor below the critical oxygen level. The critical oxygen

concentration can be estimated by the equation
CR=qR2/AD1 (8)

where 06 is the critical oxygen concentration at the root surface at
radial distance (R) from the root center, q is the oxygen consmption
rate, and D is the coefficient of gas diffusion inside the root.
Schumacher and Smucker (1981) used Lemon's equation to calculate the
different critical oxygen concentration for the drybean roots under
various mechanical stresses. The calculated Cfi was 0.011, 0.05, and 0,09
atm. when roots were in the solution culture, 3mm and a 1mm matrix of
glass beads respectively, at 25C temperature.

Eavis (1972) reported that root elongation of pea seedlings were
reduced progressively when the 02 partial pressure fell below 0.16 atm.
He attributes this decline in root elongation rates to the shorter
individual cells,since the total number of cells remained the same at

this range. The rate of cell division declined when the partial

pressure of 02 reached 0.03 atm.

Water Uptake

Plants growing in the soil may maintain their water uptake, as
water is extracted, by either exploring a large volume of the soil or
exploiting the particular volume tola greater extent. This could be
achieved by roots growing deeper or proliferating within the particular

volume and increasing the root density. In both situations it is

21
necessary to have a soil zone loose enough to allow such root
activities. From a physical point of view, this simple analysis seems
reasonable. However, larger root systems do not always translate into
higher water uptake rates. The hydraulic resistances across the soil-
plant pathways must be low enough to permit the water to flow freely
within the plant system.

The integrated view of the water transport processes within the
soil-plant system has led to considerable research in the area of soil-
plant water movement ( Arya _e_t_§_l_., 1975; Biscoe £12.22." 1976; Elston
_tga_1., 1976; Feddes e_t_.a_l., 1978; Fiscus and Markhart, 1979; Gardner,
1960; Gardner, 196A; Hillel, 1977; Hillel and Talpaz, 1976; Isdo, 1982;
Taylor and Klepper, 1978). Many mathematical models have been proposed
to quantitatively describe these processes (Huck and Hillel, 1983;
Hillel gt fl" 1976; Lomen and Warrick, 1978; Neuman gt fl" 1975;
Rowse _e_t_ _a_l., 1983; Warrick and Lomen, 1983; Warrick _e_t_ 2}." 1980). All
of these models have one thing in common ie., the driving force is the
water potential gradient and movement is in the direction of decreasing
energy resulting from resistances present along the water flow
pathways. Passioura (1981) classifies the flow of water from the soil
to the plant as consisting of five major sections: (1) Pararhizal,
which starts from a distant soil to the soil close to the roots; (2)
perirhizal, from soil close to the roots to the soil-root interface;
(3) flow across soil-root interface ; (11) radial flow through cortex
and steele to the xylem and (5) axial flow along the xylem.

The flow of an incompressible fluid in a rigid, homogenous,
isotropic, and isothermal porous medium can be described by a

combination of two equations. The first is Darcy's law, namely

22

q:_Kve (9)

which describes the flux of water (q) to be proportional to and in the
direction of the driving force, and hydraulic conductivity (K) of the

porous medium.‘The second is the conservation of mass principle

39 (10)

5—‘=‘V. q
which states that the time rate of change of water content ( e ) in a
controlled volume must be equal to the divergence (v,) of the flux (q)
(Hillel. 1977). When describing the flow of water across a soil-root
interface and into the plant, modifications of the basic flow equations
are necessary to account for the hydraulics of the root system. Hillel
gt_§l, (1976) used such an equation to simulate the pattern of soil
water depletion and the spatial distribution of soil-water potentials
in the presence»of a nonuniform growing root system.‘This transient

state one-dimensional flow equation may be described as

30

fi=§E{ Ms) S (1‘)

W

 

3(hm-Z)}_
82

where K( e ) is the hydraulic conductivity of the soil as a function of
the soil volumetric water content ( 6 ), hm 13 matric potential head,
3w is the sink term for roots, and z and t are the space and time
dimensions respectively. Many equations have been proposed to simulate
the sink term. Nearly all are driven by the water potential gradient.

Gardner (196“) defined the water extraction rate from a unit soil

23

volume to be

SH=(HS-Hp)/(RS+RP) (12)

where subscript.s and p represent the soil and plant, H is the total
water potential and R is the resistance to flow. The impedance of soil
to water movement (Rs) may be a function of unsaturated soil hydraulic

conductivity (K) and root length density (L) such that

38:1/9 K L (13)

where B is a constant representing the efficiency of the roots to water
uptake. Rowse gt_§l, (1983) derived the impedance to water movement in

the soil to be

R3=(-Ln(L 1r r2))/(ll 1. n K) (111)

where L is the root length density, r is the root radius, K is the
hydraulic conductivity. Tinker (1976) described the root water uptake
assuming a cylinderical shape root growing into a cylinderical shape
hollow of soil whose inner radius (a) is that of the root and whose
outer radius is b. Water flows into the root radially at a constant

rate per unit length of the root as follows

 

 

— I

217Dw 2.1 a

where 6 is the average water content of the soil, 9a is water content

24
at the root surface, Iw is the water uptake rate per unit length of the
root, and Dw is the water diffusivity.

Feddes _e_t_ a}, (1978) considerations of the root system as a sink
for soil water differs from the others in that the water uptake rate is
not a constant function of water potential gradients over the whole
range of soil water potentials observed. They defined three soil-water
potential intervals, each having different water uptake rates. The
first is from saturation ( Ibo) to an anaerobic point (all ) where the
water uptake rate is either zero or reaches zero very quickly. The
second is from uq_ to a limiting point (02 ) where the water uptake
rate is maximum. The third is from If? to a wilting point (W3) where
the water uptake decreases linearly to zero. It is within the first and
third regions where plants generally suffer the most from water stress.
Boyer gt_gg, (1980) also indicated that water deficits of soybeans may
develop during the mid-day period especially where roots are shallow
regardless of soil water status. This period represent a period of high
solar radiation and rapid photosynthesis. Their observations reiterate
the inhibitory role of pathway resistances in meeting the
evapotranspiration demands of the atmosphere. When the leaf water
potential dropped below a threshold value of -11 bars, the
photosynthesis rate droped sharply.

Soil temperature is known to be one of the major components of the
soil physical conditions affecting plant growth. Although the thermal
conductivity and diffusivity of soils appears to be adversely affected

by soil compaction, this variable will not be considered in this study.

LITERATURE CITED

Abdalla, A.M., D.R.P. Hettiartchi and A.R. Reece. 1969. The mechanics
of root growth in granular media. J. Agric. Eng. Res. 111:236-2'48.

Arya, L.M., G.R. Blake and D.A. Farrell. 1975. A field study of soil
water depletion patterns in presence of growing soybean roots.
III. Rooting characteristics and root extraction of soil water.
Soil Sci. Soc. Am. Proc. 39:187-999.

Asady, G.R., A.J.M. Smucker and M.W. Adams.1985. Seedling test for the
quantitative measurement of root tolerances to compacted soil. Crop
Science 25:802-806.

Barley, K.P. 1962. The effect of mechanical stress on the growth of

Biscoe, P.V., Y. Cohen and J.S. Wallace. 1976. Community water
relations. Daily and seasonal changes of water potential in
cereals. Philo. Trans. Roy. Soc. London. Ser. B. 273:565-581.

Blanchar, R.W., C.R. Edmonds and J.M. Bradford. 1978. Root growth in
cores formed from fragipan and 82 horizones of Hobson soil. Soil

Boone, F.R. and B.W. Veen. 1982. The influence of mechanical resistant
and phosphate supply on morphology and function of maize roots.

Boyer,J.S. 1982. Plant productivity and environment. Science, 218:9113-
A188.

Boyer, J.S., R.R. Johnson and 8.6. Saupe. 1980. Afternoon water
deficits and grain yields in old and new soybean cultivars. Agron.
J. 72:981-985.

Bradford, J.M. 1980. The penetration resistance in a soil with well-
defined structural units. Soil Sci. Soc. Am. J. ill-1:601-606.

Brouwer, R. 1962. Distribution of dry matter in the plant. Neth. J.
Agr. Sci. 10:361-376.

Charles-Edwards, D.A. 1976. Shoot and root activities during steady-
state plant growth. Ann. Bot. l10:767—772.

Dainty, J. 1981. The movement of water across the plant root. Plant and
Soil. 63:11-19.

25

26

Dunlap,W.H. and J.A. Weber. 1971. Compaction of an unsaturated soil
under a general state of stress. Trans. of The ASAE. 601-607.

Eavis, B.W. 1972. Soil physical conditions afffecting seedling root
growth. I. Mechanical impedance, aeration and moisture availability
as influenced by bulk density and moisture levels in a sandy loam
soil. Plant and Soil. 36:613-622.

Eavis, B.W. 1972. Soil physical conditions affecting seedling root
growth. III. Comparisons between root growth in poorly aerated soil
and at different oxygen partial pressures. Plant and Soil. 37:151-
158.

Elston, J., A.J. Karamanos, A.H. Kassam and R.M. Wadsworth. 1976. The
water relation of the field bean crops. Philo. Trans. Roy. Soc.
London. Ser. B. 273:581-591.

Feddes, R.A., P.J. Kowalik and H.2aradny. 1978. Simulation of field
water use and crap yield. John Wiley and Sons. New York. pp:1-10.

Fischer, R.A. and N.C. Turner. 1978. Plant productivity in the arid and
semi-arid zones. A. Rev. Plant Physiol. 29:277-317.

Fiscus, E.L. and A.H. Markhart III. 1979. Relationship between root
system water transport properties and plant size in Phaseolus.
Plant Phys. 69:770-773.

Gardner, W.R. 1961i. Relation of root distribution to water uptake and
availability. Agron. J. 56:111-115.

Gardner, W.R. 1960. Dynamic aspects of water availability to plants.
Soil Sci. 89:63-73.

Gerard, C.J., P. Sexton and G. Shaw. 1982. Physical factors influencing
soil strength and root growth. Agron. J. 711:875-879.

Gill, W.R. and R.D. Miller. 1956. A method for study of the influence
of mechanical impedance and aeration on the growth of seedling
roots. Soil Sci. Soc. Am. Proc. 20:159-157.

Goss, M.J. 1977. Effects of mechanical impedance on root growth in
barley (Hordeum Vulgare L.). I. Effects on the elongation and
branching of seminal root axes. J. Exp. Bot. 28:96-111.

Goss, M.J. and R.S. Russell. 1980. Effects of mechanical impedance on
root growth in barley (Hordeum Vulgare L.). III. Observations on
the mechanism of response. J. Exp. Bot. 31:577-588.

Greacen, E.L. and J.S. Oh. 1972. Physics of root growth. Nature New
Biol. 235:29-25.

Gupta,S.C. and W.E. Larson. 1979. A model for predicting packing
density of soil using particle-size distribution. Soil Sci. Soc.

27

Hillel, D. 1977. Computer simulation of soil water dynamics. A
compendium of recent work. Box. 8500, Ottawa, Canada K1G 3H9.

Hillel, D. and H. Talpaz. 1976. Simulation of root growth and its
effect on the pattern of soil water uptake by a non-uniform root
system. Soil Sci. 307-312.

Hillel, D., H. Talpaz and H. Van Kuelen. 1976. A microscopic-scale
model of water uptake by a non-uniform root system and of water and
salt movement in the soil profile. Soil Sci. 121:2'42-255.

Huber, 8.0. 1983. Relation between photosynthetic starch formation and
dry -weight partitioning between the shoot and the root. Can. J.
Bot. 61:2709-2716.

Huck, M.G. and D. Hillel. 1983. A model of root growth and water uptake
accouunting for photosynthesis, respiration, transpiration, and
soil hydraulics. In Advanced In Irrigation. ed. D. Hillel . 2:273-

333.

Hunt, R. 1978. Plant growth analysis. Edward Arnold (Publisher)
Limited. 111 Bedford Square. London. WC1B3DP.

Isdo, 8.8. 1982. Non-water stressed baselines: A key to measuring and
interpreting plant water stress. Agric. Meteo. 27:59-70.

Jensen, G.R., L.H. Stolzy and J. Letey. 1967. Tracer studies of oxygen
diffusion through roots of barley, corn and rice. Soil Sci. 103:23-
29.

Johnson, I.R. 1983. Nitrogen uptake and respiration in roots and shoots
: a model. Physiol. Plant. 58:145-1117.

Koolen, A.J. and H. Kuipers. 1983. Agricultural Soil Mechanics. Spring-
Verlag, Berlin, Heidelberg, New York, Tokyo. pp.139-170.

Lemon, E.R. 1962. Soil aeration and plant root relations. I. Theory.
Agron. J. 59:167-170.

Lemon, E.R. and C.L. Wiegand. 1962. Soil aeration and plant root
relations. II. Root respiration. Agron. J. 511:171-175.

Lomen, D.O. and A.W. Warrick. 1978. Linearized moisture flow with loss
at the soil surface. soil Sci. Soc. Am. J. 112:396-1100.

Luxmoore, R.J. and L.H. Stolzy. 1972. Oxygen diffusion in the soil-
plant system. VI. A synopsis with commentary. Agron. J. 611:725-729.

Luxmoore, R.J., L.H. Stolzy and J. Letey. 1970. Oxygen diffusion in the
soil-plant system. I. A model. Agron. J. 62:317-322.

Mooney, H.A. 1972. The carbon balance of plants. A. Rev. Ecology and
Systematics. 3:315-3A6.

28

Mulligan, M.F., A.J.M. Smucker and G.F. Safir. 1985. Tillage
modifications of dry edible bean root colonization by VAM fungi.

Naylor, T.H., J.L. Balintfy, D.S. Burdick and K. Chu. 1966. Computer
simulation techniques. John Wiley and Sons. New York.

Neuman, S.P., R.A. Feddes and E. Bresler. 1975. Finite element analysis
of two-dimensional flow in soils considering water uptake by roots.
I. Theory. Soil Sci. Soc. Am. Proc. 39:229-230.

Novoa, R. and R.S. Loomis. 1981. Nitrogen and plant production. Plant
And Soil. 58:177-204.

Passioura, J.B. 1981. Water collection by roots. In : Physiology and
Biochemistry of Drought Resistance in Plants. L.G. Paleg and D.
Aspinall.(eds.) pp.39-55. Academic Press.

Radford, P.J. 1968. Systems, models and simulation. In : Annal Report
of the Grassland Research Institute. pp.77-85. GRI. Hurley,
Berkshire.

Reicosky, D.C., W.B. Voorhees and J.K. Radke. 1981. Unsaturated water
flow through a simulated wheel track. Soil Sci. Soc. Am. J. l15:1-8.

Reynolds, J.F. and J.H.M. Thornley. 1982. A shootzroot partitioning
model. Ann. Bot. l19:585-597.

Richards, D. 1980. Root-shoot interactions: effects of cytokinin
applied to the root and/or shoot of apple seedlings. Scientia
Hort.12:1u3-152.

Rickman, B.W., J. Letey and L.H. Stolzy. 1966. Plant responses to
oxygen supply and physical resistance in the root environment. Soil
Sci. Soc. Am. Proc. 30:304-307.

Rowse, E.R., W.K. Mason and H.M. Taylor. 1983. A microcomputer
simulation model of soil water extraction by soybeans. Soil Sci.
136:218-225.

Russell, R.S. 1977. Plant root systems : their function and interaction
with the soil. Mc Graw-Hill Book Co.(UK) Ltd. pp:9-27.

Russell, R.S. and M.G. Goss. 19711. Physical aspects of soil fertility:
The response of roots to mechanical impedance. Neth. J. Agric. Sci.
22:305-318.

Schumacher, T.E. and A.J.M. Smucker. 1981. Mechanical impedance effects
on oxygen uptake and porosity of drybean roots. Agron. J. 73:51-55.

Sinclair, L.R., D.W.Fitzsimmons and G.L.Bloomsburg. 197A. Permeability
of unsaturated field soils calculated from laboratory desaturation
data. Trans. of The ASAE. 399-1105.

29

Smucker, A.J.M. 1989. Carbon utilization and losses by plant root
systems. In: Roots, Nutrient and Water Influx and Plant
Growth.(eds.) Barber and Bouldwin. ASA. Special Pub. Madison
Wisconsin. pp27-ll5.

Steinhardt, 6.0. 1983. Soil compaction : a hidden problem. Better Crops
With Plant Food.

Taylor, H.M. and B. Klepper. 1978. The role of rooting characteristics
in the supply of water to plants. Adv. In Agr. 30:99-128.

Tinker, P.B. 1976. Roots and water. Transport of water to plant roots
in soil. Philos. Trans. Roy. Soc. London. Ser. B. 273:9115-1161.

Thornley, J.H.M. 1977. Root:shoot interactions . Symp. Soc. Exp. Biol.
31:367-389.

Vomocil, J.A.,and W.J. Flocker. 1961. Effect of soil compaction on
storage and movement of soil air and water. Trans. of The ASAE.

Voorhees, W.B., D.A. Farrell and W.E. Larson. 1975. Soil strength and
aeration effects on root elongation. Soil Sci. Soc. Am. Proc.

39:938-953.

Wareing, P.F. and J. Patrick. 1975. Source-sink relations and the
partition of assimilates in the plant.In: Photosynthesis and
Productivity in Different Environments. (ed.) J.P. Cooper. ppll81-ll99.

Warrick, A.W. and D.O. Lomen. 1983. Linearized moisture flow with root
extraction over two-dimensional zones. Soil Sci. Soc. Am. J.

Warrick, A.W., 0.0. Lomen and A. Amoozegarfard. 1980. Linearized
moisture flow with root extraction for three-dimensional steady
conditions. Soil Sci. Soc. Am. J. llll:911-91ll.

Hiersum, L.K. 1957. The relationship of the size and structural
rigidity of pores to their penetration by roots . Plant and Soil.

Wilson, A.J., A.W. Robards and M.J. Goss. 1977. Effects of mechanical
impedance on root growth in barley (Hordeum Vulgare L.). II.
Effects on cell development in seminal roots. J. Exp. Bot. 28:1216-
1225.

Woolley, J.T. 1965. Drainage requirements of plants. Drainage for
effecient crop production. Conf. Proc. ASAE.St. Joseph, Mich. PP:2-
5.

CHAPTER 2

SEEDLING TEST FOR THE QUANTITATIVE MEASUREMENT OF

ROOT TOLERANCES TO COMPACTED SOIL

ABSTRACT

Root responses of plant genotypes to compacted soils have not
been well defined. This experiment was conducted under controlled
environments using a soil core seedling test consisting of an
experimentally compacted soil having air filled porosities of 31, 18,
and 6%. Root penetration ratios were measured 14 days after planting
without destroying seedling viability. Root penetration ratios and
root lengths declined linearly with decreasing air filled porosity.
Xylem accumulations of toxic anaerobic metabolites were directly
correlated with soil bulk density and inversely related to oxygen
diffusion rates in the soil. High correlations (R=0.9l) were observed
between root penetration ratios of this rapid test and the growth and

yield of field grown dry edible beans.

30

INTRODUCTION

Root penetration and exploration of the soil horizons are
essential if maximum crop yields are to be achieved. Plant root
growth is generally reduced by the soil matrix, especially if the soil
particles are compacted by traffic or tillage. Excessive tillage and
traffic generally reduce both the size and abundance of soil pores
through which plant root systems develop (Cassel, 1982). Root systems
stunted. by compacted soils generally reduce ‘plant ‘vigor and crop
yield. The selection. of crop cultivars ‘having, some tolerance to
certain compacted soils is expensive using conventional plant breeding
field programs (Ghaderi ££_gl., 1984). It is also very difficult to
quantify root morphological responses of plant pOpulations grown in
the field. Furthermore, we believe that more quantitative information
relating specific root responses to compacted soils must be available
before improved selection programs can be established.

Bohm (1979) reported that several container experiments have been
designed to measure the influence of soil bulk densities on the growth
of roots. Those approaches demonstrate the adverse effects of greater
soil bulk densities on the growth of roots, but are not designed to
provide rapid and quantitative root responses to multiple levels of
soil compaction. The objective of this study was to examine some of
the primary morphological and physiological root responses of several
cultivars to soil compaction using a rapid and nondestructive soil

core seedling test.

31

MATERIALS AND METHOD S

Polyvinyl chloride cylinders, having inside diameters of 7.6, and
a wall thickness of 0.64 cm were used to establish the layered soil
containers consisting of a stack of three cores. Each three layered
container consisted of top and middle cores which were 2.5 cm in
height and a bottom core which was 7.6 x 7.6 cm. The cores of this
study were filled with Charity clay, an illitic, calcareous, mesic,
Aerie Haplaquept soil containing 532 clay and having a consistency
ranging from very elastic when wet, to very hard when dry. Soil
aggregates sieved to a range of 0.25-2.0 mm, were equilibrated to a
constant gravimetric soil moisture content of 18% and uniformly
compacted to the desired bulk densities. The soil was compressed into
2.5 cm. high cores by a piston (7.6 cm. diameter) attached to a
hydraulic press (Carver Type, Model 20505-11). Initial bulk density
levels of 1.1, 1.4, and 1.7 Mg m.-3 were established by pressing a
specific quantity of soil into the middle 2.5 cm core. Compacted
cores were sandwiched between the top and the bottom cores which had
approximate bulk densities of 1.1 Mg m-3. The three cores were sealed
together into one air and water-tight soil container by wrapping them
with 5 cm wide plastic impregnated duct tape. Each soil container was
saturated for 48 h, drained, and seedlings were transplanted into the
surface 8011. Each experimental unit of soil consisted of one core

assembly containing two plants. Soil moisture contents were

32

33

determined by weighing the experimental units daily and adjusting the
moisture content as directed by the water retention curve (Richards,
1965). Oxygen diffusion of the soil at an equilibrium matric
potential of -8 kPa was measured by the D/DO method of Taylor (1949).
Oxygen diffusion rates were measured at the same water potential by
the platinum. microelectrode method of Lemon and Erickson (1955).
Aeration status, water content and bulk density of the soil in each
treatment are reported in Table 1.

Seeds of Phaseolus vulgaris L. cultivars 'Black Turtle Soup',

 

'NEP-Z', 'Swan Valley', and 'Domino' were surface sterilized with 0.1%
sodium hypochlorite and germinated on wet paper surfaces
@ 25° C. 'Swan Valley' (a small white seeded cultivar) and 'Domino'
(a small black seeded cultivar) are progeny of the cross between
'NEP-Z' (a small white seeded cultivar) and 'Bladk Turtle Soup' (a
small black seeded cultivar). Two uniform seedlings were transplanted
to each core and grown for 14 days in the growth chamber at a constant
humidity of 65 1 5%, day/night temperatures of 24/18°C and a 16 h
photoperiod with a light intensity of 640 mol m.-2 s-l. Water was
applied twice daily to maintain an average soil water potential of
-8:2 kPa. Nutrient solution, 10 ml of a 50% Hoaglands, was applied
daily during the second week of growth. The experimental design was a
randomized complete block. which ‘was replicated four times. Each
experiment was repeated once and the data combined for the analysis of
variance.

Two weeks after transplanting, leaf abaxial diffusive resistance

was measured by a LICOR Model 3000 diffusion porometer. Then

seedlings were harvested by cutting the stems at the first

34

cotyledonary node, stems were blotted and fitted with a latex rubber
tube which accumulated the xylem exudate for one hour. Acetaldehyde
and ethanol contents in the xylem exudate were determined by
gas-liquid-chromatography (Smucker and Erickson, 1976). Morphological
plant parameters measured were shoot and root fresh and dry weights,
leaf area, root length and root penetration ratios. The root
penetration ratio (RPR) is defined as a ratio of the number of roots
which exit the compacted middle core divided by the number of roots
which penetrate the same core. Values of the RPR were determined for
the central 20.3 cm2 area of the middle core to eliminate any
influence the soil and container interface could have on root growth.
Roots in each layer of the soil container assembly were determined by
cutting the system into its three primary components and washing the
roots from the soil of each layer by the hydropneumatic elutriation
method of Smucker gt _a_l_. (1982). Root length for each layer was
approximated by the line intercept method of Newman (1966).

Plant dry weight and yield values from the field are the average
of a three year study at the Michigan State University Research Farm
near Saginaw, Michigan. The Charity clay soil on this farm was
compacted to a depth of 7-10 cm by multiple passes of wheel traffic
and secondary tillage (Smucker, 1985) which resulted in
bulk. densities similar' to those reported. above for the soil core

seedling test.

RESULTS AND DISCUSSION

Reduced air filled porosity, resulting from greater compression
of soil in the middle core, caused a reduction in the root penetration
ratios of the four dry edible bean cultivars evaluated in this study
(Figure 1). Root growth at 14 days ‘was directly related to the
aeration. status of the soil (eg., air filled porosity' and oxygen
diffusion rate) and inversely related to the mechanical resistance of
the soil. Mechanical impedance of the soil, approximated 'by the
penetrometer (Table 1), reduced root penetration and root length
densities in both the middle and bottom soils of the core assembly,
Table 2. Although more roots accumulated in the top soil, as
compaction of soil in the middle cores increased (Table 2), the total
length of roots which accumulated in the entire core assembly was
significantly reduced by soil compaction, Table 3. Root growth in the
middle and bottom cores of the most compacted soil, was greatly
inhibited by mechanical impedance and oxygen exclusion (Tables 1 and
3). Greater soil bulk densities not only created an oxygen stressed
environment for the roots, but also reduced the mean diameter of air
filled pores. Assuming macroscopic pore continuity and applying
capillary theory, one can approximate the air filled pore diameters to
be 2 0.03 mm at a soil matric potential of -8 kPa. As the soils
became more compacted, the air filled porosities for the same water

potential were reduced to 18 and 6% for the intermediate and most

35

36

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37

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n\a moo vmafiau ufi< uuuoEouuocom nouns Hfiom mufimsov Mann Hfiom

 

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umuoaouumcmm .nowucuuou nouns .huflmcov Jana Hfiom can so scammuunaou Hwom mo ouaoaamaH .H manna

38

Table 2. Root length density in the top, middle, and bottom cores
when the middle core was subjected to three levels of soil

 

 

 

compaction.
Air filled Root length density
porosity Cultivars Weighted Top Middle Bottom
average

Z ------- km In.3 -------
Black Turtle 45 gi 43 ab 57 de 42 d

31 NEP-2 43 fg 41 a 62 e 36 c
Swan Valley 41 def 46 ab 44 b 37 cd
Domino 42 efg 45 ab 57 de 35 c
Black Turtle 41 def 70 de 52 cd 28 b

18 NEP-Z 34 c 54 bc 48 be 23 b
Swan Valley 38 cde 62 cd 44 b 28 b
Domino 37 cd 68 d 45 bc 24 b
Black Turtle 19 b 89 f 7.3 a 0 a

6 NEP-Z 11 a 50 abc 5.2 a 0 a
Swan Valley 17 b 80 ef 7.0 a 0 a
Domino 13 a 59 cd 4.1 a 0 a

 

+ Values in each column followed by the same letter are not signifi—
cantly different at the 0.05 level of probability according to the
Least Significant Difference.

39

 

 

 

Table 3. Total and relative root lengths in the top, middle, and
bottom cores when the middle core was subjected to three
levels of soil compaction.

Air filled Total Relative root length

porosity Cultivars root Top Middle Bottom

length

2 m ------ z --------
Black Turtle 26.34 3+ 19.1 a 25.4 bcd 55.5 d

31 NEP-2 24.71 fg 19.4 a 29.5 e 51.1 d
Swan Valley 23.50 def 22.9 a 21.8 b 55.3 d

Domino 24.09 efg 21.6 a 27.6 cde 50.8 d

Black Turtle 23.83 def 34.4 bc 25.3 bcd 40.3 be

18 NEP-Z 19.86 c 31.4 b 28.3 de 40.3 be
Swan Valley 22.16 cde 32.1 b 23.0 b 44.9 c

Domino 21.50 cd 36.7 c 24.1 bc 39.2 b

Black Turtle 11.15 b 92.4 d 7 6 a 0.0 a

6 NEP-2 6.41 a 90.4 d 9 6 a 0.0 a
Swan Valley 10.05 b 91.7 d 8.3 a 0.0 a

Domino 7.32 a 93.4 d 6 6 a 0.0 a

 

+ Values in each column followed by the same letter are not signifi-
cantly different at the 0.05 level of probability according to the
Least Significant Difference.

40

compacted soils, respectively. These changes may be attributed to the
reduction in the number of pores with diameters; 0.03 mm in the
compacted soil. Since the weighted mean diameters of dry edible bean
roots are reported to range from 0.3 to 0.8 mm (Schumacher, 1979 and
Fiscus, 1981), the proportion of air filled pores having diameters
smaller than roots is greatly increased. Consequently, the roots of
plants growing in highly compacted soils are more likely to be impeded
by the smaller pores. This, along with anaerobic conditions created
by soil compaction, suggests that most of the roots in this experiment
were unable to penetrate due to their large diameters and low
metabolic energy (Russell, 1977). The greater percentage of roots in
the surface soil of this study (Table 3), is very similar to field
observations and a previous report of soybean root distribution in
compacted clay soils (Smucker, 1985). These phenomena, combined with
reductions in total plant root length, reduce plant tolerances to
short-term dry surface soils.

Smaller root systems of the physically stressed 14 day-old
seedlings appear to cause lower rates of xylem accumulation and
greater leaf diffusive resistances (Figure 2 and Table 4) even though
soil. matric potentials were similar. These root-related stresses
caused a general reduction in the dry weight and leaf area of seedling
shoots when the soil was compacted (Table 4). Shoot growth rates of
dry edible beans grown on the most compacted soil began to decline 6—8
days after transplanting (Figure 3). Shoot growth during the first 14
days of this soil core seedling test was similar to the power function
described by Fiscus (1981). Our data indicate that coefficients of

those equations must be different for each level of soil compaction.

41

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comm .meom Smao vmuomaaou a“ c3ouw mammn macawm map mo mmumu coaumasesuum Emflmx .N upswwm

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42

Table 4. Influence of air filled porosity on shoot weight, leaf
area and stomatal diffusive resistance of four dry edible
bean cultivars at 14 days in the soil core seedling test.

 

 

Air filled Shoot Diffusive
porosity Cultivars dry mass Leaf area resistance
Z 3 cm2 s m-1

Black Turtle 1.08 d1 198.0 c 910 a
31 NEP-Z 0.96 bcd 174.2 be 870 a
Swan Valley 0.79 ab 166.7 be 1150 ab
Domino 1.01 cd 186.0 c 1140 ab
Black Turtle 1.02 cd 179.8 be 1210 ab
18 NEP-2 0.88 abcd 151.4 ab 1320 ab
Swan Valley 0.84 abc 176.2 be 980 a
Domino 1.02 cd 185.7 c 1050 a
Black Turtle 0.84 abc 128.4 a 1710 ab
6 NEP-Z 0.82 abc 132.7 a 2330 b
Swan Valley 0.70 a 123.5 a 2370 b
Domino 0.94 bcd 127.2 a 4040 c

 

1 Values for each column followed by the same letter are not
significantly different at the 0.05 level of probability according

to the Least Significant Difference.

43

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Internal aeration of the soils in this study' was inversely
related to the extent of compaction (Table 1). As the air filled
porosity decreased to 67'. the diffusion of oxygen was too low to
support optimum aerobic root growth (Erickson, 1982). Declining
oxygen availability decreases oxidative phosphorylation causing more
of the photoassimilate carbon of roots to be converted to ethanol via
acetaldehyde (Russell, 1977). Acetaldehyde and ethanol accumulations
in the xylem exudates of Phaseolus cultivars appeared to be inversely
related to the aeration status of the soil treatments (Table 5).
Although there were no significant differences for the cultivar 'Black
Turtle Soup', acetaldehyde and ethanol accumulations of the cultivar
'NEP-Z' were significantly greater when grown (Hi the most compacted
soils.

Total length of accumulated root growth appeared to be the most
significantly different growth variable among the four cultivars grown
in the phytotron conditions of this study. 'Black Turtle'
had a significantly greater root length than 'Swan Valley' at the
lowest level of soil compaction. This difference was reduced with
increasing bulk density. The root length of 'Black Turtle' was
significantly greater than 'NEP-Z' at the intermediate level of
compaction and significantly greater than both 'NEP-Z‘ and 'Domino' at
the greatest level of soil compaction (Table 3). The cultivar 'Black
Turtle' appeared to have the greatest values for root length, root
length density, shoot weight and leaf area for nearly all levels of
soil compaction. Root penetration ratios were significantly different
between 'Domino' and 'Swan. Valley' at the lowest level of soil

compaction (Figure 1). This difference" was negated, however, by

45

Table 5. Influence of air filled porosity on the accumulation of
toxic anaerobic metabolites by black and white dry edible
beans grown for 14 days in the soil core seedling test.

 

 

Air filled
porosity Cultivars Acetaldehyde Ethanol
Z ug Lbls'.1 pg Lula-1
31 Black Turtle 2.14 ai 1.50 a
18 Black Turtle 1.89 a 1.53 a
NEP-Z 3.22 ab 1.36 a
6 ' Black Turtle 2.86 ab 7.33 a
NEP-Z 5.75 b 15.03 b

 

+ Values for each column followed by the same letter are not
significantly different at the 0.05 level of probability according
to the Least Significant Difference.

46
increasing levels of soil compaction.

Although the soil core seedling test provides the experimental
conditions for morphological and metabolic measurements, the real test
of this method is how well these results from the growth chamber may
be correlated with those of field studies. A quadratic function of
RPR was highly correlated (R=0.92) with plant dry weights of field
samples (Figure 4). Figure 5 reports an excellent multiple
correlation (R=0.91) between a quadratic function of RPR values from
the soil core seedling test and the yields of dry edible bean
cultivars grown on the same soil type having similar bulk densities.
The close correlation between these two plant variables and the RPR
values suggest that the soil core seedling test could be used to
determine specific genotype responses to soil compaction. In
addition, these data suggest that RPR values from multiple field
samples could be used to develop a RPR index for evaluating dry edible
bean and other cultivar responses to specific soil and tillage
conditions. It further indicates that when RPR values approach 0.65
the growth and yield of dry edible beans appear to be no longer
affected by soil physical conditions which control root penetration
(Figures 4 and 5). Since RPR. measurements can be made without
destroying the entire root system, soil core seedling tests in the
laboratory and field should be useful to breeding programs for
determining the inheritance of root tolerance to compacted and other

specific soil conditions.

47

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mnu ou muou Hfiom Smau vmuumaaou m we mHm>mH mmwnu :H asoum mum>fiuanu ammo macfinm

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LITERATURE CITED

Bohm, W. 1979. Container methods. In: Methods of Studying Root
Systems. Springer-Verlag. Berlin.

Cassell, D.K. 1982. Tillage effects on soil bulk density and
mechanical impedance. _13: Predicting Tillage Effects on Soil
Physical Properties and Processes. ASA Spec. Pub. No. 44 In»
45—67.

Erickson, A.E. 1982. Tillage effects on soil aeration. In;
Predicting Tillage Effects on Soil Physical Properties and
Processes. ASA Special Pub. No. 44. pp. 91-104.

Fiscus, E.L. 1981. Analysis of the components of area growth of
bean root systems. Crop Sci. 21:909-913.

Ghaderi, A., A. J. M. Smucker, M. W. Adams and A. W. Saettler.
1984. Breeding implications of stress induced by soil
compaction. Euphytica 33:377-385.

Lemon, E. R. and A. E. Erickson. 1955. Principle of the platinum
microelectrode as a method of characterizing soil aeration. Soil
Sci. 79:383-391.

Newman, E.I. 1966. A method of estimating the total length of
root in a sample. J. Appl. Ecol. 3:139—145.

Richards, L. A. 1965. Physical condition of water in soil. 12:
Methods of Soil Analysis, Physical and Minerological Properties.
Part I. Agronomy 9:128-152. C. A. Black (ed.).

Russell, R. S. 1977. Effects of anaerobic soil conditions. In:
Plant Root Systems Their Function and Interaction with the
Soil. McGraw-Hill, London.

Schumacher, T. E. 1979. The influence of mechanical impedance and
short term anoxia on respiration, growth and structure of
Phaseolus vulgaris L. roots. M.S. Thesis. Michigan State Univ.
p. 52.

 

Smucker, A.J.M. 1985. Soybean crop responses to soil environmental
stresses. (R. Shibles, ed.) Proceedings World Soybean Research
Conference III. Ames, Iowa 15 pp.

Smucker, A. J. M. and A. E. Erickson. 1976. An aseptic mist
chamber: A method for measuring root processes of peas.
Agron. J. 68:59-63.

49

50

Smucker, A. J. M., S. L. McBurney and A. E. Srivastava. 1982.
Quantitative separation of roots from compacted soil profiles
by the hydropneumatic elutriation system. Agron. J. 74:500-503.

Taylor, S. A. 1949. Oxygen diffusion in porous media as a measure
of soil aeration. Soil Sci. Soc. Am. Proc. 14:55-61.

CHAPTER 3

EFFECTS OF MECHANICAL IMPEDANCE AND AERATION

ON DRY BEAN ROOT GROWTH

ABSTRACT

Spatial and temporal responses of dry edible beans (Phaseolus
vulgaris L.; cv. Seafarer) grown under different compaction and
aeration treatments were studied in a greenhouse environment.
Extreme soil compaction resulted in mechanical resistances as high as
5500 kPa. This mechanical impedance reduced total root length by 80 and
71% in the aerated treatments, and 81 and 77% in the nitrogen treated
treatments for 20 and 30 days after planting (DAP) respectively. Root
extension into deeper layers was practically halted at a depth of 10
cm, with approximately 90% of the roots being at the surface 2.5 cm, 20
DAP.

Oxygen diffusion into and carbon dioxide out of the soil was
significantly curtailed by high mechanical impedance. Oxygen
concentration depressions and carbon dioxide elevations within the
soil reached as much as 5 and 101 respectively. Oxygen diffusion rate
(ODR) and D/Do characterization of the soil aeration status, both
indicated that anaerobic soil conditions resulted from the high bulk
densities. Approximately 121 of the air filled pores of the surface

51

52
layers were plugged by the compensatory root growth in this layer due
to high mechanical resistance of the compacted soil. These deleterious
effects of soil compaction on plant growth necessitate cultural

practices which avoid traffic of heavy machinery on the field.

INTRODUCTION

Studies of the physical factors which influence root growth often
include the characterization of those physical and biological soil
processes which are associated with bulk density'(Gupta and Larson,
1982). One of the major reasons for manipulating agricultural soil is
to create a physical condition of the soil which favors root growth.
The development of this condition includes minimization of the
mechanical barriers to root growth, and optimization of soil aeration,
soil water content, and soil temperature.

Soil compaction may be described as the manifestation of excessive
physical forces acting on a soil body resulting in a relatively static
condition which influences the dynamic responses of plants to soils.
The degree of soil compaction depends very much on the biophysical
state of the soil. For instance, when a tillage tool is pulled across a
field, conditions of the moving soil are changed. Soil properties such
as size and distribution of particles, water content, soil structure
and organic matter content respond to the applied forces. Soil
compaction usually changes.the existing balance between the liquid,
gas, and solid phases in a given unit of soil volume» The net result
usually is a reduction of liquid and gas in the pores, an increase in
the proportion of the solid phase, an increase in the pore water and
air pressures, and a rearrangement of the particles. All of these
changes contribute to the increasing mechanical resistance of a

53

54
compacted soil.

Mechanical resistance may be characterized by several methods which
assess the different mechanical properties of a soil. These include,
penetrometers, modulus of rupture, shear planes, and triaxial tests,
all of which give empirical results. These values should be calibrated
against specific plant growth variables before they can be used for
prediction equations (Bowen, 1981). Since plant growth is dependent
upon mechanical as well as physio-chemical soil properties,
penetrometer results should be calibrated against plant growth
variables only when all other soil properties are optimunIand plant
growth response is largely due to mechanical soil properties. Some
physical soil properties such as water content strongly affects the
mechanical behavior of a given soil.

Mechanical resistance of the soil is a constraint to both root
growth and plant production. Root responses to mechanical impedance can
vary from the bending of root tips to abrupt changes in root diameters
and direction. Voorhees gt al.(1975) reported that the root length
density of peas, grown on mechanically compacted soils, increased due
to an increase in the root length of first order laterals of primary
roots. This mechanical impedance usually resulted in the reduction of
plant growth and yield. Carmi and Heuer (1981) characterized plants
with restricted roots as being smaller and having leaves with smaller
surface areas and shorter internodal distances. They attributed these
differences to be hormonally regulated and suggested that mechanically
impeded roots may control the balance of hormones.

Mechanical impedance appears to be inversely related to the root

elongation rates and directly related to the root diameters in many

55

annual plants. Penetrometer resistance of 580 to 1150 kPa appeared to
severely reduce the elongation rates of cotton roots (Taylor and
Ratliff, 1969a,b). Mechanical impedance as low as 25 kPa reduced the
root elongation rates of maize and peas by 69%, and barley by 43%.
Russell and Goss (1979) reported that the extension rate of barley
roots was reduced 50% by 20 kPa, and 801 by 50 kPa external pressures.
Voorhees it: _a_l. (1975) reported an inverse relationship between root
elongation rates and penetrometer resistances. They obtained a better
correlation when the penetrometer tip had an angle of 10 degrees than
60 degrees. This suggests that normal point resistance is a better
indicator of soil resistance to root penetration than total point
resistance. Mechanical impedance appears to increase root diameter.
Taylor gt El: (1972) reported that when the root tips encountered
resistance, their elongation regions increased in diameter .

Root growth pressure is known to be the main driving force behind
penetrating,roots.lt.is therefore logical to assume that the higher
the root growth pressure, the higher the elongation rates for a given
soil condition. Maximum root growth pressure for cotton has been
reported to be less than 1300 kPa (Taylor and Ratliff, 1969a). Even
though there are cultivar differences in these root responses to
external pressures, there is a general agreement that maximum
longitudinal root growth pressures seldom exceed 1500 KPa for most
common crops (Taylor and Ratliff, 1969a; Russell and Goss, 1974;
Kibreab and Danielson, 1977).

An adequate supply of oxygen to the roots is essential if maximum
growth of plants is desired. Lack of sufficient oxygen in the soil is

perhaps one of the greatest limiting factors in the development of an

56
extensive root system. Since active surfaces of the roots are covered
with a film of water and the diffusion of oxygen in water is 10'“ that
in air, the composition of air in the rhizosphere is not as important
as oxygen fluxes toward the roots. Consequently, the oxygen supplying
power of a soil is complicated by the distributions of capillary and
noncapillary pores and the degree of saturation.

A low internal aeration capacity is usually accompanied by those
soil conditions which mechanically impede root growth.‘Vomocil and
Flocker(1961) reported that when the soil moisture content was at
field capacity root growth was inhibited when the soil aeration
porosity fell below 101. Crop yields are often reduced when the non-
capillary pore space drops below 101 (Erickson, 1982L.Hence, it is
generally believed that the lower limit of aeration porosity of most
soils is around 101 for common crops (Stolzy, 1974; Erickson, 1982).

Aeration intensity, or composition of air in the rhizosphere is
another factor which might influence the development of a root system.
Taylor 9.2.3.}.- (1972) and Armstrong (1979) however, indicated that the
rate of oxygen supplied to the root surface is more accurately
estimated by measuring oxygen flux to an oxygen sink, than by oxygen
concentration. Furthermore, oxygen flux depends not only on oxygen
concentration gradients, but also on the resistance of a soil matrix to
diffusion (Blackwell and Wells, 1983).

Gas diffusion pathway resistances can be divided into three
distinguishable regions. One, the region in which diffusion is taking
place in a gas-gas system (ien, diffusion of oxygen through air filled
porosity). Two, the aqueous pathway where diffusion occurs in a gas-

liquid system (egp, where oxygen diffuses—into water films surrounding

57

the roots). Three, diffusion through cell walls and into the plant.
Interactions of the heterogenous and porous soil further complicates
the study of these three phases. Tackett and Pearson (1964a,b)
indicated that the penetration of cotton roots through low bulk density
soil cores was not affected until oxygen partial pressures dropped
below 101 or carbon dioxide concentrations reached 24%. They also
reported that root penetrations were unaffected by oxygen or carbon
dioxide partial pressures of high bulk density soils.

Diffusion is defined as the net transport of a substance from one
region to another within the same medium in the absence of mixing (Reid
and Sherwood, 1966). This transport may be due to thermal diffusion,
pressure diffusion, molecular diffusion or to convective mixing.‘Taylor
(1949) introduced a technique for measuring the oxygen diffusion
coefficient in the porous medium (D), and in the stirred air (Do). The
ratio of D/Do is then used to evaluate the diffusion characteristics of
the porous medium. It indicates the degree of resistance which the
medium offers to incoming oxygen from the atmosphere. Diffusion of
oxygen to the root surfaces appears to be limited most by the liquid
phase surrounding the roots. The ODR method of Lemon and Erickson
(1955) thus, appears to be more realistic index of soil aeration
capacity. Erickson(1982) concludes that, plant roots will not grow at
ODR's below 0.20 ug cm'2 min", and their growth could be retarded at

MATERIALS AND METHODS

Seeds of dry edible beans (Phaseolus vulgaris, L. cv; Seafarer)
were surface sterilized with a 0.51 sodium hypochlorite solution for
ten minutes, rinsed with distilled water 5 times and germinated at 25
°C on trays containing wet cheesecloth covered with wet paper towels.
After four days, uniform seedlings were tranplanted into experimental
units containing a Charity clay soil ( illitic, calcareous, mesic,
Aeric Haplaquept ) prepared and compacted by the soil core seedling
test method of Asady g .a_l. (1985). Several modifications were made in
preparing the experimental units for this experiment. Each experimental
unit was made up of four primary cores. The cores were cut from
schedule 80 PVC drainage pipes. The top core was 2.5 cm and succeeding
lower cores were each 7.5 cm high. A 5 mm diameter access port was
drilled in the center of each 7.5 cm core and sealed by a rubber serum
which provided a means for sampling soil gases. The three 7.5 cm cores
were sealed together into one gas- and water-tight cylinder by wrapping
them with 5 cm wide plastic impregnated duct tape.

Three levels of bulk density were established by a hydraulic press
equipped with a plunger 7.5 cm diameter as described by Asady £1; El.
(1985). A 2.5 cm high core was then placed on the top and sealed as
described above. Therefore, each experimental unit consisted of a
cylinder, 25 cm in height, with three access ports 7.5 cm apart. Filter
paper and cheesecloth prevented the soil from being lost at the base of

58

59
the container. After compaction each experimental unit was saturated by
distilled water for 48 hours and the free water drained for 24 hours at
a matric potential of -6 kPa. Seedlings were transplanted to the top
core, covered with loose soil, and irrigated.

Four porous plate tension tables (Hillel, 1980) were established on
the greenhouse bench. Each consisted of a fine mesh screen and
regular desk top blotting paper. Experimental units were placed on the
blotting paper equilibrated at -6 KPa of water potential which was
applied to the base of the experimental units. A modified tension table
(Figure 1) which included a burette and manometer, also provided a
method for measuring water use. The graduated burett served as a water
supply reservoir for the tension tables. Each tension table was covered
with black plastic film having water tight ports for the cores to
prevent direct evaporative losses. Four days after transplanting
(DAP) the experimental units were sealed in the top using plastic
impregnated cardboard container caps and cutting a small hole at the
middle for the plant stems. The caps were sealed using parawax to
minimize the air exchange with the atmosphere.

Two aeration treatments were applied by continuously flushing the
space above the soil surface with saturated compressed air or nitrogen
gas at the rate of 40 ml/min per experimental unit. Gas sampling from
the top of the cores indicated that this reduced the oxygen
concentrations to 14:11 at the 3011 surface.

The experimental design was a 3 factor factorial, randomized
complete block, replicated four times. The three factors were : (1)
three levels of bulk density (1.1, 1.4, and 157 Mg m‘3) at 18%

gravimetric water content, (2) two levels of aeration (air and nitrogen

60

y
S . .. F 3‘
\fl Ai N2

 

 

 

 

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m

N"""' I'"""Iv1 ' 7'"! 8' ' 7
rI-l

 

 

 

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1

 

 

 

To
Tension Table

Figure 1. Schematic view of the root chamber and tension table
apparatus. A is the surface aeration chamber, B is the
experimental unit, C is the access port for gas sampling,
D is the tension table, E is the porous plate over the
tension table, F is the burette, G is the air entry point,

H is the applied matric potential head, and I is the burette
support.

61
gas), (3) and three harvest times (10, 20, and 30 DAP) giving the study
a total of 72 experimental units. A modified 25% Hoagland's nutrient
solution was supplied to plants each week beginning witmlthe second
week of growth. The greenhouse conditions were set to humidity of 65;
51, day/night temperature of 24/18 oC, and a 16 h photoperiod with
light intensity of 640 umol In'2 3".

Several plant and soil measurements were taken during the
experiment and at each harvest. Plant physiological measurements
included abaxial diffusive resistance of the leaf , transpiration rate,
and leaf temperature using a steady state leaf porometer, model Licor
LI-1600. Leaf water potentials were measured with a Scholander model
3005 pressure bomb (1965 ) and plant water contents by the gravimetic
method. Morphological measurements included fresh and dry shoot
weights, leaf area by the optical method using a Licor model LI-3000 ,
stem dry weights and water contents. Root measurements were root length
and dry weight distributions in the soil containers.

The carbon exchange rate was measured by placing a 4.5 liter,
cylinderical shaped, plexiglass chamber over the plant for one minute.
Hypodermic syringes were used to extract 7.5 ml gas samples from the
chamber, 10 and 60 seconds after a pump started stirring the gas inside
the chamber; The carbon dioxide concentrations in the samples were
measured by an infrared gas analyzer(IGA). The carbon exchange rate was
determined to be the 002 depression for 50 seconds.

During the course of this experiment several gas measurements were
taken for a period of 6-7 hours. Point source sampling of gases was
achieved by extracting one ml of air samples from the rhizosphere

through the access ports. Concentrations of oxygen, carbon dioxide and

62
nitrogen at three different depths in the rhizosphere were then
measured. Hypodermic syringes (1cc tuberculin type B-D) equipped with
3L8 cm, 18 gauge needles, provided a means for the point source gas
sampling.‘The gas samples were injected into a gas chromatograph
(Carle Instruments, model 8500) equipped with a conductivity detector
and a 200 cm by 3.2 mm internal diameter column filled with Porpak 0
(P0) in parallel with a molecular sieveI(MS) column having the same
dimensions. Columns were maintained at 40 C. The He carrier gas was at
the flow rate of 30 ml/min. The detector temperature was maintained at
the low setting. Detector polarity switching allowed alternate sides of
the parallel column arrangement to act as the reference . For instance,
the PQ column could either bypass or be put in a series with the MS
column. This provided a method for separating the three gases from the
same sample. The component peaks were electronically integrated by a
computer integrator (Autolab, system I)and compared with standards
prepared using an exponential dilution flask held at 25 C and
atmospheric pressure. Normal atmospheric levels of C02, 02 and N2 were
300 ppm v/v, 20.8x105 ppm v/v and 78x105 ppm v/v respectively. The
P0 column separated C02 from 02 and N2 and MS separated 02 from N2
gases. The oxygen diffusion rates were also measured using the modified
method of Lemon and Erickson (1955) where microelectrodes were radially
inserted 3.8 cm into the soil through the three access ports. Soil
temperatures were also measured through the access ports using a

portable digital thermocouple (STI type K model A2501).

RESULTS AND DISCUSSION

Mechanical impedance was simulated under greenhouse environments by
exposing the growing dry edible bean root tips to a compacted soil
layer similar to that of a plow pan in the field. The average
penetrometer resistances in the compacted soil layers were
approximately 430, 2140, and 5500 KPa for the bulk density levels of
1.1, 1.4, and 1.7 Mg m'3, respectively. These values are within the
bulk range of critical soil strengths reported for different crops.
Gerard g 91. (1982) reported that cotton root elongations stopped when
the mechanical resistance reached 2500 kPa in clay soils and 6000-7000
KPa in sandy soils.

Root growth was inversely related to soil bulk density. Less root
growth in the compacted layers resulted in the accumulation of roots in
the overlying layers. Total accumulations of root length were
significantly greater after 20 days for plants growing in the least
compacted soil (Table 1). After 10 days, there were 48 and 46S
reductions in the root growth of Phaseolus beans grown on the aerated
Charity clay soils compressed to bulk densities of 1.4 and 1.7 Mg m’3.
Total root growth was reduced 80 and 71%, and 81 and 771 in the two
most compacted soils after 20, and 30 days of growth, respectively; The
accumulations of roots in the overlying layers of compacted soils were
significantly higher than the control.

The cumulative total root length distributions in the soil

63

64

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O O.AOA O m.OeA u m.OmO OU O.OAO O O.HHmN Om
s 0.0e e m.ee~ e O.OOH sO O.Ome s m.OOmH ON s.H HH<
s 0.0 s m.H s m.Oe OU 0.0mm s m.~Om OH
H O.OOOm e m.mmmH O O.HOO e O.OO w 0.0Hsm Om
O O.~OOH O O.OOOH O m.OOO O m.mOH H m.OOAm ON H.H HHO
s 0.0~ O O.OOm e m.OO~ es m.OHH es O.Hms OH
1 1 I 1 1 1 1 1 1 1 I I I I 1 1 HIHHO so 1 I I I 1 1 1 1 m<o mus w:
m~-m.AH n.5HIOH OH-O.N m.N-O seHH HOHmseO eHsO OOO
EU 3”“an HHOm Hmu OH. mufiwfiuwwHH
. muflmfiumwuu

 

coaumumm new .mEHu .GOOHUmQEoo Hfiom Cu mfiumwas> msaommmcm we mmmaoammw coauacfiwumfiv suwcma uoom .H macmfi

65

containers indicate a significant reduction in total root length with
increasing mechanical impedance CTable 1L. The direct relationship
observed between soil compaction at the lower soil layers and root
growth at the surface soils (Table 1) are similar to those obtained for
maize (Shierlaw and Alston, 1984). These data illustrate the inhibitory
effects of soil compaction on root penetration. The direct relationship
between harvest times and root growth in all treatments and depths, is
a natural consequence of the dynamics of root growth. Root length
present at the surface 2.5 cm of 1.1 Mg m'3 soil treatment , at 20 DAP,
was 11% lower than 10 DAP; AT 30 DAP, root growth was 14% lower than 20
DAP. These results though not significantly different may be due to
root turn over in the soil. Five to seven percent reduction in oxygen
concentration at the surface soil in the nitrogen treated samples
appeared to have no significant effects on the root growth for most
treatments. These results are similar to those of Gill and Miller
(19560 who reported that root growth was significantly reduced only
when oxygen partial pressures fell below 10%.

Root growth at the 2.5-10 cm depth, was significantly lower when
the soil was compacted to a bulk density of 1.7 Mg m'3, than when the
bulk density was 1.4 Mg m‘3 for nearly all treatments. Similar results
were observed at lower soil depths. Comparisons between root growth in
soils compacted to a bulk density of 1.1 and 1.4 Mg m'3 indicate that
the mechanically impeded root growth of this study became significantly
different at approximately 20 DAP. At the extreme bulk density,
practically no roots penetrated beyond the depth of 10 cm. This bulk
density corresponds to a penetrometer resistance of 5500 KPa, and is

much greater than the 1000 KPa reported to be the limiting resistance

66
for pea roots (Voorheesgt El" 1975), and the 2500 KPa which is
reported to limit cotton (Gerardgt 31., 1982). The reduction of root
growth in the intermediate bulk densities indicates that the limiting
pressure for Phaseolus vulgaris root growth appears to be somewhat
less than 2140 KPa.

Root length density (RLD), defined as root length per unit soil
volume may be one of the most important factors effecting water and
nutrient uptake. RLD appeared to be inversely related to soil
compaction with no significant aeration effects (Figure 2). This
inverse relationship , however, didn't become significant until 20 DAP.
Compression of soil to a bulk density of 1.4 Mg 111'3 reduced root length
density more severely than 1.7 Mg m'3 for both aeration treatments.
This is additional evidence that the limiting mechanical resistance

for Phaseolus vulgaris is below 2140 KPa . The average rate of RLD

 

increases during the second 10 days of growth ranged from 37.6 S/day,
24.7 S/day, and 9.7 S/day for the none, intermediate, and most
compacted treatments respectively. These values were reduced to 6.2
S/day, 11.2 i/day, and 4.1 S/day for the same treatments, during the
third 10 day period of growth.

Spatial distributions of RLD within the soil containers after 10
days of growth indicate that the maximum RLD was 0.8 cm cm’3 at a depth
of 5-10 cm for the noncompacted treatments (Figure 3). At the same
region of soil containers, the maximum RLD was 0.3 and 0.1 cm cm'3 for
the intermediate and most compacted treatments, respectively. After 20
days, the maximum RLD increased to 3.6, 1.6, and 0.4 cm cm'3, for the
none , intermediate, and most compacted treatments respectively (Figure

4). The region of maximum root growth occurred at a depth of 15-20 cm

67

.zam>wuomammu .mIE w:
~.H can .O.H .H.H mo mmHuHmamp xasn ucommuamu m van .N .H .mmuou Eu mm cw :3ouw mammn
panama sun we uufimcmv zuwama uoou do mEfiu mam .cOOHmumm .COHuumano Haom mo mocmsamcH .N muswflm

can can
am am on On am a_

m
[178 BDBBBAH

[U23 UUZJ

 

68

.nu3ouu mo mzmv OH umuum mammn
pagans Sun «0 cofiusnfiuumwv SuHmcmu nuwcufi uoou co coauumanu Haom mo mocmaamcH .m muawwm

Eu I IHQUD JHom

 

 

 

 

 

8m mm 8m mH 8H m 8
4 .. II 4 1 8.8 a
O
0
II.
. . m8 1
3
N
5
Il-
r . v.8 H
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3
N
. .99 B
u

Te Oz ....Huam e

. _
Hale Oz THIOO - 3mm O
m
One Oz H.Huum 4 O
F F p P P as“ w

 

69

.nu3ouw mo mxwv ON uwuwm mcwwn

manavm xuv mo cowuanfiuumfiv mufimcmw numcma uoou co cowuumasou Hfiom mo mucwsaucH .q muswfim

Sm

ccnu

mm mm

IHQUQ JHom

mfi

B"

m

 

 

c.
1 mn.

NIT.

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a C d

m: n.~nam
m: v.~uom

m: H.~unm

d

4

l

 

 

ALISNBU HlDNBW i008

UJCJ UJCJ

70

for the control and didn“t change for the other treatments. At 30 DAP,
the maximum RLD increased to 8.0 cm cm"3 and 2.1 cm cm'3, at the depth
of 20 cm for the none and intermediate compaction treatments,
respectively (Figure 5). Sevene mechanical resistance resulted in RLD
values which were less than 1 cm cm'3

Relative root length (RRL) is defined as the ratio of root length
present in each soil compartment to total root length. It represents
the relative distribution of roots within each depth of soil and
appears to be an appropriate index for normalizing root growth data
which may be used in models. RRL distributions after 20 days of growth,
indicate that 90% of the bean roots were within the surface 2.5 cm
soil, when the underlying layers were severely compacted (Figure 6).
Soil compaction apparently reduced the number of macro-pores which were
similar in size to plant roots. This is shown in Figure 7 where the air
filled porosity was severely reduced for a given pore diameter, at high
soil bulk densities. This mechanical barrier slowed down or completely
stopped the movement of roots downward. At the same time, only 15% of
the roots were within the surface and 85% were below 2.5 cm depth, in
the noncompacted treatments. These data demonstrate that drybean roots
grown under noncompacted soil conditions have grown downward with
little external mechanical forces limiting their development. As a
result, plant roots grown in the noncompacted soil penetrated deeper
into the profile. RRL within the surface 2J5 cm soil generally
decreased with time. The rate of decline was most significant for the
none and intermediate compaction treatments. RRL increased with time in
the bottom soil compartment because root extension was limited to

proliferation within this section of the soil.

71

.cusoux mo mxmv cm umuum memos

manawm sup mo cofiunnfipumfiv zuwmcmc sumcma uoou so ceauumasoo Hfiom mo mucosaucH .m musufiu

Em mm

ccnu

am

I Ihamo JHom
ma Ofi

m

 

d

 

‘1-

d

 

mus m: 578
TE m: vguom
mus m: #4qu

p k

‘

 

 

mfi

ALISNBU HiDNEW i008

UJCJ [U23

72

 

 

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ucmmmuamu a mum .o .m .< cam .MIE w: m.H tam .¢.H .H.H "mum mIH muamEummuu uuwmcmv xaan one
.mammn manfivm zap mo nuwcma uoou m>HumHmu :0 mafia vam :ofiumumm .GOHuomanu HHom mo mucosamcH .o muswfim

 

mm: am: man man
on cu m. on o~ o.
w on 3 a. on a... a. 5.9 w
1 ~ 1
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on o~ a. on o~ o. . on o~ a. on n~ o.

(”3 BI-S'Z) 3803 601 16 158

 

(”3 S'Z-B) 3803 BDBJEHS 18 188

73

.mawvmu upon some msu cmnu wwwuma mmuoa mnu :H wwcflmucoo %uHmouoa vaHHw ufi< .m muswflm

E: I mDHDEm umoa ZEN: JHom

 

Essa 88“ 8“ fl
88m QGN Om 8N m m
. . . J . T Q
A“. o u ccccccc’ %
4 c c c c
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...: m: finom 4 44
> F L k L 5 fl?

 

 

 

AiISOBOd [IE-1713 BIB _IIOS

y.—

74

Soil aeration stresses in this study may have resulted from either
oxygen shortages due to high diffusion resistances in soil, or carbon
dioxide accumulations due to high resistances in the escape pathways.
Oxygen diffusion rate (ODR) was significantly reduced wdth increasing
levels of soil compaction for most treatments (Table 2). Aeration
treatment appeared to have no significant effects on the ODR, when the
soil was extremely compacted. These along with the low oxygen and high
carbon dioxide concentrations present in the lower layers of highly
compacted soils (Figures 8-11) may therefore suggest that the high
pathway resistance to gases is the main obstacle to diffusion of oxygen

into the soil. Lower oxygen concentrations in the N2 treated samples

had significant effects on the ODR for some treatments (Table 2).
Intermediate soil compaction decreased ODR due to a reduction of the
mean pore diameter (Figure 7) and an increase in the thickness of water
films. The pathway resistance probably was not high enough to prevent
diffusion of oxygen into the soil, because the oxygen concentrations
were similar (Figures 8 and 9).

The Relationship between soil compaction, pathway resistances, and
the thickness of water films can be described in Figure 12. At the
regions of high bulk density the rate of increase in ODR per unit
increase in D/Do (eg., slope of the curve) is small, because the air
filled porosity is predominately comprised of micro-pores, the
thickness of the water film is high, and the soil has a high resistance
to diffusion of oxygen. This region of the curve has a gentle slope and
ODR is mainly controlled by the porosity. As decompression proceeds,
the pore diameters increase, the resistance to diffusion decreases, and

the ODR is no longer entirely controlled by porosity. This region of

75

Table 2. Oxygen diffusion rate responses of Charity clay soil
measured at three soil depths and at three different times.

 

Time of measurements

 

 

Treatments
Gas Bulk Density Depth 10 DAP 20 DAP 30 DAP
Mg m"3 cm ----- ug m‘2 3‘1 -------
6.25 88.7 3* 79.” ghi 78.7 f
Air 1.1 13.75 81.9 fg 89.6 hi 57.8 de
21.25 79.1 ef 88.0 i 59.1 de
6.25 81.7 fg 56." de 86.3 f
Air 1.” 13.75 51.6 cd 60.3 def 67.7 ef
21.25 71.0 e 73.6 fghi 69.u ef
6.25 20.9 a 32.6 abc 29.5 ab
Air 1.7 13.75 21.8 a 26.u ab 28.3 a
21.25 32.5 b 46.8 cd 38.3 abc
6.25 82.2 fg 73.2 efghi 57.8 de
N2 1.1 13.75 70.5 e 60.9 def “0.6 abcd
21.25 76.3 ef 69.9 efgh ”8.0 bcd
6.25 78.8 cd 65.9 efg 57.8 de
N2 1.” 13.75 99.6 c 69.6 efg 36.8 abc
21.25 60.7 d 67.7 efg 55.u cde
6.25 21.9 a 21.8 a 39.5 ab
N2 1.7 13.75 17.2 a 32.3 abc 32.0 ab
21.25 2H.6 ab 39.1 bc 36.9 abc
LSD0.05 9.3 16.6 11.2

 

+Values in each column followed by the same letter are not
siginificantly different at 0.05 level of probability according to
the Least Significant Difference.

76

.acfiucmaa uwumm mzmv om

mcofiunnwuumwv cowumpucoucou commxo co coaumumm mam cowuumanu Hfiom mo mucosamcH .w muswwm

 

 

 

 

EU I I._.n_wD JHom

Em Ev Em EN 8“

”a. 1 . . . 1 . . .
3.3.. H
T mu... 9.. WT Nz -
mu... m: TT m2 4
. mu... m: a T Nz c
. mus m: n.7mHm a
75 m: TTmE 4
f 72 m: 775.0 0

 

 

 

mfl

vfi

mfi

mm

- SNOIlaaiNaoNoa 20

7.

77

.wcwuamaa umumm mzmw om
mcowusnwuumfiw coaumuucmucoo cmwxxo co coaumumm cam coauumasou Hfiom mo mucosamaH .o muswfih

So I Ihlmm JHom

 

 

 

 

mm av Sm mm 82 8
ch} 1 n J u u q u q '1 Q
Jt 31
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Do
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I
Ni»: me; v .~.l qu‘ AV AU
, e m: _.T Nz c N
m: S
. 72 m: WTmE n. ma _
mu... m: v.7.mE 4 /.
. m1... m2 TTmE o

 

 

 

mm

78

.wcaucmaa Hmumm mhmv om maoauanfiuumaw

coaumuucwocoo mvHxOfic conumo co coaumuwm cam cowuomanu HHom mo mucosamaH

mm

 

 

So I IHQUD JHom
av mm mm as a
. . J 4 a I. ... ‘14 “1,1
. < (5\\\\ .
m®.snm4
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mu... m: 77.5.”. 4
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.OH muawam

(n
- SNOIlHalNaaNoa 203

7.

79

.wcwucmaa umuwm mxmv om mcowusnwuumfiv
cofiumuucwucou mvfixoac :onumo co cowumucm cam coauomchu Hwom mo mucosamcH .HH muswwm

Eu I Ihmwn JHom

 

 

om Ev mm SN 9“ m
. a J a 4 a a . I...\I..I . a

. c|c“\m4\ .
. 3
mm a 0
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3
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N
. m1... m2 nél NZ I . v «w.
m N
. mIE m: vQI z 4 .. . m“
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. mu... a: TT Nz c . . w l
I
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. Te m: «415$ 4 . m _
, mu... m: 2.7%.... o J 7.

 

 

 

b . . p r . b p b a“

80

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um Hfiom >mHo zuwumsu mo zuamcmc xaan cam .oa\n .mp0 cmmauon nfismcofiumamx .NH muswfim

08\D
mm.8 8m.8 mm.8 8N.8 m~.8 88.8 m8.8 88.8
a a a a a a a

 

 

 

 

 

81

the curve has a sharp slope and the ODR appears to be controlled by the
thickness of the water films.

It appears that the ODR of the soils in this experiment is
controlled by the thickness of the water film fOr soil bulk densities
as high as 1.“ Mg m'3. This is supported by the fact that oxygen
concentrations were not significantly affected by soil compaction up to
bulk densities of 1.11 Mg m'3 (Figures 8 and 9). The 0DR , however, was
significantly reduced for most treatments (Table 2). The oxygen
partial pressure and ODR values significantly dropped with depth due
to high diffusion resistances in the soil resulting from high bulk
densities. The practical implications of these phenomena might be that
ODR would provide little information about the thickness of water film
in highly compacted soils, if such information is desired, and D/Do
would likewise be a poor index of oxygen availability to roots. These
data also indicate that the 6-81 reductions in oxygen partial pressures
due to aeration treatments did not significantly effect the root growth
of dry edible beans. Results of experiments on pea seedlings (Eavis,
1972) indicated that root elongation rates of pea seedlings did not
change until the oxygen concentration fell below 161. Carbon dioxide
accumulations in the soil containers were parallel to the reduction of
oxygen partial pressures (Figures 10 and 11), suggesting that high
resistances in the escape pathway were probably responsible for CO2
concentrations which approached 10$.

Pores plugged by growing roots may significantly decrease the
internal aeration of the highly compacted soils. In order to
demonstrate how the diffusion pathway is affected by root plugging, we

introduced the concept of root filled porosity (RFP). RF? is defined as

82

the ratio of the volume of pores occupied by roots to the volume of
pores occupied by air at a given water potential. After 10 days of
growth, RFP was highest at the surface 2.5 cm soil, and ranged from 2%
in the control to about 51 in the most compacted soil (Figure 13). As
growth proceeded, the percentage of root filled pores in the surface
layers of the compacted soils increased to 9 and 121 after 20 and 30
days of growth, respectively'(Figures 1n and 15%.These data suggest
that the plugging effects of the roots on the aeration status of a soil
may become significant in severely compacted soils where root growth is
confined to the surface layers.

All biomass accumulations by plants ultimately depend upon the net
carbon exchange rate. The effects of soil compaction on photosynthetic
rates were determined by measuring the amount of 002 exchanged by the
total plants. Processes accompanying photosynthesis, such as,
respiration and translocation, however, can be major deterants to plant
productivity. Photosynthetic activity is strongly dependent upon the
incoming solar radiation intensity as well as the openings of the
stomatal aperture. Thus, the carbon exchange rate is a dynamic process
which is determined by the instantaneous conditions of the soil and
atmosphere at the time of measurements.

Mechanical impedance appeared to have no significant effect on the
specific carbon exchange rate of most treatments, at 20 DAP (Table 3).
Increased mechanical impedance, however, increased the specific
photosynthetic activity, at 30 DAP (Table 3). The photosynthetic
activity of the total plant, grown under high mechanical impedance, was
significantly decreased for the air and N treated treatments at 20 and

2
30 DAP, respectively (Table 11). The carbon exchange rate responses of

83

.muwaanmnoua mo Hm>mH mo.o um am; mucwmmucmu cucmv ouou some um>o amp use
.%Hm>fiuuoamou .m1& at h.H vcm .¢.H .H.H mo mmfiufimcwv xfisn ucwmwuamu M van .N .H
.nu3ouw mo mxmv 0H uwumm mammn maawvm App 80 :ofiusnwuumfiv anamouon vaHHu uoom .ma wuswfim

80 I mIanD mmou JHom
mmlmQL m.n~I8_ 8_Im.m m.NI8

N

F1

to
AJ. ISOc‘JOcJ [131—11 .4 lOOEI

 

84

.x m>.>WfiMfinmnwuc mo Hm>oH no.0 um 9mg mucmmmuamu nuawv muoo some uw>o amp one
.Muzwwum New» mus a: N.H vcm .¢.H .H.H mo mofiufimcmv xasn ucommunou m vcm .N .H
u no on umumm mcmwn manavm haw mo coausnwuumfiv xufimouon vaqu uoom .qH muswam

EU I mIanD umou JHom

mNIm.nfi m.n—I8d 8~Im.m m.NI8

- AlISOBOd UE—I'IIJ 1.008

7.

 

8d

85

.xufiafinmnouc mo Hm>mH mo.o um awq mucwmmaawa :ucmc muou some um>o umn use
.mao>«uumcmmu .mIE a: n.H vac .¢.H .H.H mo mmfiufimcmv xasn ucommucmu m vcm .N .H
.cuzoum mo m>mv om uwuum mecca wanficm map 80 :ofiusnfiuumfiv zufimouoa voHHHm uoom .mH maawum

Eu I mIHQMD mmou JHom
mmlm.n_ m.n~I8_ 8_Im.m m.NI8

ALISOBOd 031713 1008

mg

X...

 

m8

86

Table 3. Specific carbon exchange rate responses of Phaseolus vulgaris
to soil compaction and aeration treatments.

 

Days After Planting - DAP

 

 

Treatments
Gas Bulk Density 20 30
Mg m'3 - - - - mg dm'2 h'1 -----

1.1 29.9 ab+ 10.5 a

Air 1.“ 38.2 ab 16.8 ab
1.7 35.“ ab 20.6 b
1.1 26.4 ab 1u.5 ab
1.7 21.2 a 20.7 b

 

*Values in each column followed by the same letter are not
significantly different at 0.05 level of probability according
to the Least Significant Difference.

87

Table u Total carbon exchange rate responses of Phaseolus vulgaris
to soil compaction and aeration treatments.

 

 

Days After Planting

 

 

Treatments
Gas Bulk Density 20 30
Mg m'3 - - - - mg h"1 plt'1 - - - -
1.1 39.9 c+ 2n.1 bc
Air 1." 25.3 bc 26.7 c
1.7 13.8 ab 11.5 ab
1.1 22.9 abc 29.7 c
N2 1.“ 27.7 C 28.3 C
1.7 9.5 a 11.1 a
LSD0.05 13.5 12.7

 

+Values in each column followed by the same letter are not
significantly different at 0.05 level of probability according
to the Least Significant Difference.

88

the intermediate and low bulk densities were similar. The increased
specific carbon exchange rate with high mechanical impedance on the one
hand, and the decreased total plant photosynthetic ratecnathe other
hand, therefore supports the hypothesis that plants grown under
environmental stresses have a leaky root system (Smucker, 1984).

In conclusion, soil compaction reduced root growth and dry matter
accumulation of dry edible beansw Highly compacted soils prevented
roots from penetrating downward and causing high accumulations of roots
in the upper layers of the soil profileu‘The root length density was
significantly reduced by severe soil compaction. The aeration status of
the soil was curtailed by greater resistances to gas movement by the
smaller and plugged pores. Plants growing in severely compacted soils
appear to have a leaky root system as was suggested by Smucker (1984L
In lieu of these detrimental effects of soil compaction on root growth
and plant development, crop production systems should devise management

practices which would require minimum traffic across the field.

LITERATURE CITED

Armstrongm. 1979. Aeration in higher plants. Adv. Bot. Res. 7:225-332.

Asady, G.R., A.J.M. Smucker and W. Adams. 1985. Quantitative
measurements of root tolerances to compacted soil. Crop Science 25

Blackwell, P.S. and H.A. Wells. 1983. Limiting oxygen flux densities
for cat root extension. Plant Soil 73:129-139.

Bowen, R.D. 1981. Alleviating mechanical impedance. In: G.F. Arkin and
R.M. Taylor (eds.). Modifying the Root Environment to Reduce Crop
Stress. ASAE. Monograph No. 11.

Carmi, A. and B. Heuer. 1981. The role of roots in control of bean
shoot growth. Ann. Bot. 118:519-527.

Eavis, B.W. 1972. Soil physical conditions affecting seedling root
growth. III. Comparisons between root growth in poorly aerated soil
and at different oxygen partial pressures. Plant Soil 37:151-158.

Erickson, A.H. 1982. Tillage effects on soil aeration. In: Predicting
Tillage Effects on Soil Physical Properties and Processes. ASA
Special Publication # ”11:91-105.

Gerard, C.J., P. Sexton and G. Shaw. 1982. Physical factors
influencing soil strength and root growth. Agron. J. 74:875-881.

Gill, W.R., and R.D. Miller. 1956. A method for study of the influence
of mechanical impedance and aeration on the growth of seedling
roots. Soil Sci. Soc. Am. Proc. 20:1511-157.

Gupta, 8.0., and W.E. Larson. 1982. Modeling of soil mechanical
behavior during tillage. In: Predicting Tillage Effects on Soil
Physical Properties and Processes. ASA Special Pub. I l01:151-479.

Hillel, D. 1980. Foundamentals of Soil Physics. Academic Press Inc. pp

Kibreab, T. and R.E Danielson. 1977. Measurement of radish root
enlargement under mechanical stress. Agron. J. 69:857-860.

Lemon, E.R. and A.E. Erickson. 1955. Principle of the platinum
microelectrode as a method of characterizing soil aeration. Soil

89

90

Sci.79:383-391.

Reid, C.R. and T.K. Sherwood. 1966. The Properties of Gases and
Liquids. McGraw-Hill Book Co. pp 520-567.

Russell, R.S. and M.G. Goss. 19711. Phyysical aspects of soil fertility
- The response of roots to mechanical impedance. Neth. J. Agric.
Sci. 22:305-318.

Scholander, P.F., H.T. Hammel, E.D. Bradstress, and E.A.Hemingsen.
1965. Sap pressure in vascular plants. Science. ”18:339-346.

Shierlaw, J. and A.M. Altson. 1984. Effect of soil compaction on root
growth and uptake of phosphorus. Plant Soil. 77:15-28.

Smucker, A.J.M. 1984. Carbon utilization and losses by plant root
systems 11: Roots, Nutrient and Water Influx, and Plant Growth.
(eds.) Barber and Bouldwin. pp27-115. ASA Special Pub. Madison
Wisconsin.

Stolzy, L.H. 1974. Soil atmosphere. In: E.R. Carson(ed.). The Plant
Root and Its Environment. Univ. Press of Virginia, Charlottesville.
PP 335-361.

Tackett, J.L. and R.M. Pearson. 196lIa. Oxygen requirements of cotton
seedling roots for penetration of compacted soil cores. Soil Sci.
Soc. Am. Proc. 28:600-605.

Tackett, J.L. and R.M. Pearson. 196llb. Effect of carbon dioxide on
cotton seedling root penetration of compacted soil cores. Soil Sci.
Soc. of Am. Proc. 28:741-743.

Taylor, R.M. and L.F. Ratliff. 1969a. Root growth pressures of cotton,
peas and peanuts. Agron. J. 61:398-402.

Taylor, H.H. and L.F. Ratliff. 1969b. Root elongation rates of cotton
and peanuts as a function of soil strength and soil water content.
Soil Sci. 108:113-119.

Taylor, R.M., M.G. Buck and B. Klepper. 1972. Root development in
relation to soil physical conditions. _I_n: D. Hillel(ed.).
Optimizing the Soil Physical Environment Toward Greater Crop
Yields. Academic Press, N.Y. pp 57-77.

Taylor, S.A. 19119. Oxygen diffusion in porous media as a measure of
soil aeration. Soil Sci. Soc. Am. Proc. 111:55-61.

Vomocil, G.A. and W.J. Flocker. 1961. Effects of soil compaction on
storage and movement of soil, air, and water. Trans. Am. Soc.
Agric. Eng. l1:2112-2116.

Voorhees, W.B., D.A. Farrell and W.E. Larson. 1975. Soil strength and
aeration effects on root elongation. Soil Sci. Soc. Am. Proc.

CHAPTER 4

A MATHEMATICAL MODEL OF GROWTH IN ANNUAL PLANTS

ABSTRACT

A model of plant growth was introduced which simulates the growth
of plants from seedling to physiological maturity. It takes into
account the dynamic relative growth rate with the upper limit being
treated as a constant and equal to that of the exponential growth.
This model has the advantage of both the classical approach, where the
model variables have biological meaning, and the functional approach
where the instantaneous values of variables are calculated. Potential
use of the model includes curve fitting and predicting the plant
responses beyond the range of the data base. The model was used to
evaluate the dry mass accumulations of two dry edible bean cultivars
grown under two soil management practices. It accounts for a
biological growth capacity and competition effects among plant organs

subjected to environmental stresses.

91

INTRODUCTION

Plant growth analysis has received a great deal of attention for
many years. The methodology has evolved from classical approaches,
where the plant variables were evaluated on the basis of mean values of
such variables as relative growth rates, absolute growth rates, unit
leaf area, etc., which.‘were calculated for an interval ‘between two
harvest times. The instantaneous value of these variables can be
calculated if there is an approximate mathematical function to describe
the experimental data. Hunt (1979) describes advantages of the
functional approach which summarizes data in a convenient way and
replaces the original and often scattered data with a smooth, continuous
function.

Considerable research has been devoted to developing the
appropriate methodology for the functional approach (Duchateau E£.§Qr
1972; Elias and Causton, 1976; Hunt and Parsons, 1977; Hunt, 1978, 1979;
Hunt and Evans, 1980; Hurd, 1977; Parsons and Hunt, 1981; Sivakumar and
Shaw, 1978). Duchateau, g£_‘al, (1972) fitted parabolic curves to
segments of growth progression data. Polynomial equations of varying
degrees were used to fit each segment of the experimental data. They
used both sliding parabola and parabolic splines to describe the entire
data range. Similar analysis was devised by Hunt and Parsons (1977).
Sivakumar and Shaw (1978) applied both classical methods and a
functional approach to analyze soybean growth and concluded that the

latter is preferred.

92

93
Other investigators have used polynomial exponentials, where

polyomial equations have been fitted to logrithmic transformations of

the experimental data (Hughes and Freeman, 1967; Hunt and Parsons, 1974;
Parsons and Hunt, 1981). All of these methods have arisen from the fact
that ‘many investigators had an incomplete ‘mathematical function to
describe a complete time series of data. Although, polynomial equations
may adequately describe the experimental data, they nevertheless lack
the biological basis and their constants have no biological meaning
(Hurd, 1977). Hurd (1977) also objected to the use of polynomial
equations on the grounds that they may easily overfit the experimental
data. Based on these arguments Hurd (1979) attempted to use a general
purpose equation which was derived by Richards to describe the complete
range of plant growth progression data. The purpose of this report is
to introduce a model of plant growth which simulates all stages of
growth. The model variables have biological meaning, and offer a new

approach to plant growth analysis.

EXPONENTIAL GROWTH

In 1879 Kreusler and colleagues demonstrated that growth of an
annual plant under natural conditions follows the law of exponential
growth. Blackman (1919) was the first to describe the mathematics of an
annual plant growth by applying the principles of compound interest.
This process has come to be known as typical of many plants. The
process can be described by a linear first order differential equation

such as

dP(t)/dt - K1P(t) (1)

where P(t) is a growth variable at time t, and K is the propor—

1
tionality constant. Separating the variables

dP/P - Kldt
and integrating between times t1 and t2
1n(P2/P1) - K1(t2-t1)
Then
P2/P1 c EXP(K1(t2-t1)) or
P2 - PIEXP(Kl(t2-t1)) (2)

94

95

where P2 and P1 are growth variables at times t2 and t1,

quantity eg. mass (M), and K is the proportionality factor (t-l).

a scalar

1

In plant growth analysis K is called specific growth rate (SGR),

1
relative growth rate (RGR), or what Blackman (1919) called efficiency

index of dry weight production, when applied to biomass accumulations.

In the classical approach K is calculated as a mean value across a

l

harvest time, for instance

ln(P2)-ln(P1) A ln(P)
- - —— (3)
1 (tz-tl) At

7”
l

 

which is a value calculated for the time interval At. The instantaneous

RGR is mathematically defined as

11m A1n(P) _ d1n(P)
K1 At+o At ’ dt (4)

which is the slope of the graph of natural log transformations of the
growth variable P versus time. The growth of many annual plants is
exponential for a given phase of development. Therefore, the plot of
the natural logarithms of P (ln(P)) versus time will be a straight line
relationship where the instantaneous and mean RGR are equal and constant
(Hunt, 1978). As plants grow, the proportion of assimilates invested
into structural material increases. Thus, RGR can not remain constant
and would decline as more and more photoassimilates are diverted from
photoassimilate metabolism to the development of structural compounds.
This is indeed the essence of applying the functional approach to plant

growth analysis.

96

The true RGR is thus a time variant variable with the upper limit
being equal to RGR at the exponential period of growth and lower limit

equal to zero. The true differential equation of growth thus becomes

dP(t) _
'7fi;- - K(t) P(t) (5)

If we assume that RGR deviates from the upper limit proportionately to
the quantity of growth, then the dynamic RGR changes as

K(t) = K - K2P(t) (6)

1

where K2 is the proportionality constant. Substituting this into

equation (5) results in

dP(t)

2
dt = K1 P(t) - K2 P(t) (7)

Gold (1977) used this equation in describing the competition effects in
populations of organisms growing in an environment where the growth

components are limited. He called parameter K , the competition factor.

2
The relative magnitude of parameters K1 and K2 in eq. (6), is such that
at the early stages of development where P is small, KZP is much smaller

than K1. Therefore RGR is controlled primarily by K

continues, P increases and the effects of K

1. As plant growth

2P ‘becomes increasingly

significant, until a steady state condition is reached then

K1 = K2 P(t)

and

97

P(t) = Kl/K2 (8)

At this point the absolute growth rate, eq.(S), and RGR, eq.(6) are
zero. If the value of P at which a steady state condition of growth is
achieved is denoted by p88, then eq.(8) becomes

pSS = xl/x2 (9)

Applying these principles to the growth of microorganisms, Gold (1977)
called p88 the carrying capacity of the environment. Feddes et a1.
(1978) used a similar concept to describe the effects of radiation,
temperature, and CO2 on the rate of plant growth. They stated that

every set of environmental conditions bears a biological growth capacity

 

or potential growth. I integrated equation (7) with the initial
conditions of P(t)=P1 at t=ti, as
klt
Pi e
P(t) = K t K K t K t (10)
1 i 2 1 1 i
e + K— Pi(e -' e )

where P is the initial value of the plant growth variable at initial

 

1
time ti. If P1=Po at ti=0, then eq. (10) reduces to
K t
Po e1
P(t) = K2 Klt (11)
1 + — Po(e - l)
K

98

The mean value of K over a time interval t to t can be estimated by

 

2 1
Klt K11:i
e _ e
P(t) P1
K2 7 K1 K c K t (12)
1 1 1
(e - e )

In order to derive the equation's parameters from experimental
data, and test the model we used the shoot dry matter accumulation of
dry edible bean cultivars which were grown on mechanically compacted
soil as the growth variable (P). A time series of data was generated by
harvesting 10 plants every 3-7 days for each treatment. Two dry edible
bean cultivars, BlaCk Turtle Soup (BTS), and Seafarer (SEA) combined
with two soil compaction treatments, no secondary tillage (NST) and
excessive secondary tillage (EST) produced four growth progression
curves (Figure 1). These curves indicate that soil compaction
significantly reduced the growth potential of both cultivars. Growth
potential of the Seafarer cultivar appeared to be greater than BTS for
both environmental soil conditions of this experiment.

Soil compaction apparently delayed plant growth about equally for
both cultivars. If we plot the natural logarithms of dry matter mass
versus time (Figure 2) we observe that plants either showed no change or
lost mass during the first 10 days of growth. The straight line segment
of the curves is representative of the exponential phase of growth where
RGR was maximum and equal to the slope of the lines. These values were

calculated to be 0.159 and 0.130 day--1 for the SEA, and 0.154 and 0.120

99

.Haom

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MZHH

mum.

mumw

mwmw

mww.

uwmmnu
mm,“

mwm”

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11

u

u

mkmlhmm

mwmlhmw
mkmlhmz

mumlkmz

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8

v S
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m

m l
0
a

mwg .A
N
w.

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.

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¢
OJ

lOO

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manapm zap ho macaamHSEJUOm mmmE zap uoocm pwasmmmE mo mcoaumEaOMmcmau on Hmasamz .N waswam

 

 

 

 

man I mzaa
an mm mm me me mm mm am 3 m
. a a 1 a a a - MT moml
. u
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101

day--1 for the BTS cultivar grown under NST and EST soil treatments,
respectively. The end of this phase of growth corresponds to the
inflection point in Figure 1, and the maximum points in Figures 3 and 4.
The second stage of growth thus ended approximately 42 and 52 days after
emergence (DAE) for NST and EST soil treatments reapectively (Figure 3).
The accumulated dry matter mass at this time was, however, roughly 11
and 9 g/plt for the SEA, and 9 and 6.5 g/plt for BTS cultivars grown
under NST and EST soil treatments, respectively (Figure 4).

The third stage of growth started when the competition for limited
carbohydrates among plant organs and reproduction systems forced RGR to
deviate from linearity in Figure 2 and a descending trend in Figures 3
and 4. The points at which graphs in Figures 3 and 4 crossed the X
axes, represent the steady state conditions where RGR is equal to zero.
The biological capacity or potential growth of these plants were
approximately 21.5 and 18.0 g/plt for SEA and 17.0 and 13.5g/plt for BTS
cultivars grown under NST and EST treatments, respectively (Figure 4).
Plant physiological maturity was delayed similarly for the two
cultivars. Plants grown under the EST soil treatment reached
physiological maturity about 100 DAE. These same cultivars matured
85-90 DAE when grown under NST soil treatment (Figure 3).

The competition factor, K2, may now be calculated using eq.(9) and
knowing the biological growth potential and maximum RGR. These values
are calculated to be 0.0073 and 0.0072 3'1 d"1 for the SEA, and 0.0090
and 0.0089 g-1 d-1 for BTS, cultivars grown under NST and EST treatments

respectively. Substituting these values into eq.(7) and numerically

102

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m mm Haom zmHo zawamcu co caoaw mucosm amen manwpm zap mo mama nusoaw musaomn< .m maswam

 

 

man I 82:.
88_ 8m 8m 8m 8m 8m 8v 8m 8m 8a 8
...d a a . ... ... mom
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m
T . m8 0
l.—
. . 3
. w
. . v 8 M
II.
. . H
. msmuamu ._ . m6 w
_ i
. mwmlhmu c . 3
. mamuamz 4 n m.m L
. mumuamz . . p

 

 

 

r F! r p p F F . - Sc"

103

.mme zap aoczm mo coHaucsw
m mm Hwom zmau zawamzo co cBoaw maoocm amen manwpm zap mo Mama Lazoaw masaomn< .q maswam

m I mmcz >mn sooxm

 

 

mm 8N m— 8g m 8

u’ u g u u q a d a Sea
. . z . s
O grave -r_ MW
1 0 0‘ II ‘ A N.S 0
o 04 I IN. I.
. . e4 .... msmlamu .. A 3
I II III.‘ . w
.. 9 ‘ ll .4. 4 V S M
I.
. . o e cumuamm e .4 A H
‘e.. .U I. Av ‘4 O mw_.mw MG
. m “D
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o o .

. . . L m8
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. p P p a a a p P Q..— I

104

integrating or into eq.(lO) and calculating, produced the simulated
values of plant dry weight (Figure 5).

Soil compaction apparently reduced the efficiency index of dry
matter productions for both cultivars. The competition factors however
remained unchanged for the same cultivars but were different for each
cultivar. Based upon these experimental data one might suggest that the
competition effects may be genetically controlled. The effects of RGR
and competition factor on final. plant growth are analogous to the
effects of interest and taxation rates on the final income. One has a
positive and the other a negative effect. Numerical integration of .
eq.(7) with initial conditions of P(0)=0.0245 g produced shoot dry mass
progression data presented in Figure 5. The measured and calculated dry
masses are overlayed in Figure 6 to indicate how this model simulates
the actual field data. This graph along with Figure 7 indicates a good
agreement between the calculated and actual data.

The methodology presented here can be used in two ways depending
upon availability of a complete range of experimental data, or having
limited growth information. In the first case derivation of equation
parameters include extraction of maximum RGR from graphs similar to
Figure 2, and the steady state growth potential from the maximum point
of graphs similar to Figure 1. The competition factor, K2 is then
calculated from eq.(9). In this case we are primarily involved in curve
fitting and producing a smooth set of growth progression data from which
plant growth analysis can proceed.

If experimental data are limited but still have some points in the

region of exponential growth, like our data presented here, then we can

lOS

.dHOm

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888

MED

8m 8m 8m. 8m 8m 8v 8m 8m 88

I ”..th

 

 

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cc .. mum Emu
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88

mm

SSHN A80 .LOOHS

B-

106

 

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ssoaw memos mHanm zap mo msoaamH:Esoom mums zap aoonm pmasmmme pcm puamassam .o maswam

MED I Hit.
88_ 8m 8m 8m 8m 8m 8*. 8m 8m 8" 8

 

 

 

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n o
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. ooozamfimmu so mumuamm o . _
. Zea mam-.52 q . mm s
. 222222: mumuamz e .
P, P F P L r a P P mm

 

107

.Haom zmHo zaaamco co csoaw

mammn manapo zap mo mums zap acozw pmasmmme pcm pmamasaam mza :mwaamn soaamamaaou .z maswaa

mm

8m

m

mmmz zmn DumDmmmz

m—

8—

m

 

 

d

mkmlhmu
mumlkmu

mhmlhmz
mwmlhmz

 

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8a

m—

88

mm

SSHH A80 UBIHWDDWHD

108

estimate the maximum RGR, K from Figure 2 as described above. The task

1
is now to find that value of K which would best simulate the existing

2

experimental data by trial and error. Using one of the points as the
initial condition and eq.(12), the approximate ‘value of K2 can. be
obtained. We may then generate a complete range of data like those
presented in Figs. 3-5. In this case our model has prediction
capabilities and we were able to estimate not only the existing data but
also go beyond the data. base and gain new' information. The data
presented in Figure 6 predicts that accumulated shoot dry mass in the
SEA cultivar grown under EST soil treatment would probably exceed that
of BTS grown under NST after 70 DAE. This might be attributed to the
compaction induced delayed maturity of the SEA cultivar.

In conclusion, the concept of carrying capacity or potential growth
may provide a convenient way to integrate the combined performances of
various parts of plants, when used to compare different species or
treatments. New information may be gained from calculating potential
growth of each subcomponent. This not only takes into account the
efficiency index of plant growth, which is a measure of the economical
conversion of its energy to different subcomponents. but also accounts
for the competition which exist between subcomponents. It may also be a
useful tool in screening plant performances grown under controlled
environments. The assumptions made in devising this analysis were (1)
that growth has an exponential course at some stage of its development,

(2) the growth function resembles a sigmoid curve, and (3) the

environmental conditions of the experiment are essentially constant such

109

that the potential growth does not undergo a drastic change resulting in

a relatively constant end point.

LITERATURE CITED

Blackman, C.V. 1919. Ann. Bot. 23:353-

DuChateau, P.C., D.L. Nofziger, L.R. Abuja, and D. Swartzendruber.
1972. Experimental curves and rates of change from piecewise
parabolic fits. Agron. J. 64:538-542.

Elias, 0.0. and D.R. Causton. 1976. Studies on data variability and
the use of polynomials to describe plant growth. New Phytol.
77:421-430.

Feddes, R.A., P.J. Kowalik and H. Zaradny. 1978. Simulation of field
water use and crop yield. John Wiley and Sons. New York. pp.
1-50.

Gold, R.J. 1977. Mathematical Modeling of Biological Systems. An
Introductory Guide Book. pp. 145-186.

Hughes, A.P. an P.R. Freeman. 1967. Growth analysis using frequent
small harvests. J. Appl. Ecol. 4:553—560.

Hunt, R. 1979. Plant growth analysis: The rationale behind the use
of the fitted mathematical functions. Ann. Bot. 43:245-249.

Hunt, R. 1978. Plant growth analysis. Studies in biology no. 96.
Edward Arnold, London. 67pp.

Hunt, R. and G.C. Evans. 1980. Classical data on the growth of
maize: Curve fitting 'with statistical analysis. New Phytol.
86:155-180.

Hunt, R. and I.T. Parsons. 1977. Plant growth analysis: Further
applications of a recent curve-fitting program. J. Appl. Ecol.
14:965-968. Hunt, R. and I.T. Parsons. 1974. A Computer program
for deriving growth-function in plant growth analysis. J. Appl.
Ecol. 11:297-307.

Hurd, R.G. 1977. Vegetative plant growth analysis in controlled
environments. Ann. Bot. 41:779-787.

Parsons, I.T. and R. Hunt. 1981. Plant growth analysis: A program

for the fitting of lengthy series of data by the methods of
B-splines. Ann. Bot. 48:341-352.

110

lll

Sivakumar, M.V.K. and R.H. Shaw. 1978. Methods of growth analysis in
field grown soy beans (Glycine Max L. Merrill). Ann. Bot.
42:213-222.

CHAPTER 5

PHASOL: A MODEL OF ROOT GROWTH AND WATER UPTAKE

IN A LAYERED-HOMOGENEOUS SOIL PROFILE

INTRODUCTION

A model may be described as an abstract description of a real
phenomena in the universal language of mathematics. Plant growth models
are built for many different purposes which vary from summarizing the
data to predicting plant responses and interpreting those responses.
The purpose of a model then, influences its comprehension and degree of
universality. The development of a comprehensive mathematical model is
one of the most powerful means of describing and analyzing the various
ongoing interactions among parameters of a complex system such as the
soil-plant-atmosphere continuum. However many models of plant growth
and development generally ignore the influence of the soil environment
on the physiological processes of growth of the whole plant system.

Modeling soil physical processes is one of the important areas in
building any comprehensive plant growth model. Soil physical
environments influencing plant growth usually include soil water
potential, soil aeration status, soil strength, and soil temperature.
It is therefore imperative for plant growth models to quantitatively

describe the transport processes involving the movement of liquids and

112

113

gases in the soil. A number of models have been constructed which
describe the processes of soil water movement in the absence of plant
root systems (Beese 3211:, 1977: James and Larson, 1976; Rowse and
Stone, 1978) as well as several which include growing plants (Arya g
_a_l" 197Sa,b; Hillel, 1977: Huck and Hillel, 1983; Rowse 3331., 1978;
Warrick 11:131., 1980; Warrick and Lomen, 1983). The complexity of
modeling the physical processes involved in the transport of water in
the soil has arisen from the fact that soil is a nonhomogenous highly
irregular and tortuous medium. The flow of water through this medium
is assumed to be via hypothetical conduits, which are often
discontinuous. Thus, flow of water in the soil is limited by many
constrictions and at best can be described in a macroscopic continuum
approach.

Darcy's law is one of the first equations quantifying the flow of
water through a saturated porous medium. This equation can be written

as

where q is the vector of water flux density, which is directly
proportional to the hydraulic gradient vector, VH (Hillel, 1980). The
proportionality factor is a scalar quantity called the hydraulic
conductivity (K), which depends upon the flowing fluid as well as
porous medium. Development of equations describing the flow of water
through unsaturated porous media involves combining the equation of
continuity with Darcy's law. The assumption is that Darcy's equation is
applicable to all flow conditions. Kirkham and Powers (1972) derived

this equation for 3 dimensional flow as follows

114

39 3 3h 8 3h 8h
——=__ _ +_ — 2
3t 8x<Kx3x) 8y(Ky3y)+ 3—(Kzaz) ()

where O is the volumetric water content of the soil, t is the time, h

is the soil matric potential, and va K and K2 are the hydraulic

y!
conductivity values in the three principle directions. This equation

for an isotropic medium may be reduced to

v.( K Vh ) (3)

where V. and V are the divegence and gradient operators respectively.
In unsaturated conditions the hydraulic conductivity is dependent on
soil matric potential or water content.

A major problem encountered in modeling the transport of water in
the presence of growing roots is the inherent complicated time-space
relationships (Hillel, 1977). Roots are growing in different directions
and spacings. Their absorption capacity changes with age creating
sectional differences in water uptake. Their elongation rate is further
complicated by the soil physical environment. Construction of models
describing the transport of water in the presence of growing roots
often involves modifications of Darcy's equation which includes the
root as a sink. The vertical transient state movement of water in an

isotropic and uniform medium containing roots can be described by

a_e _3____(h+z) _
at —{ 1((0)az } sw (4)

where t is the time, 2 is the depth, K(0) is the hydraulic

115
conductivity as a function of the volumetric water content (9), h is
the matric potential head, and Sw is the root extraction rate
representing the sink term (Hillel, 1977). Therefore, The hydraulic
properties of soil and plant are very important in modeling the water
transport within the soil-plant system.

Hydraulic soil properties are usually assumed to be defineable in
the sense of a macroscopic continuum approach (Klute, 1982). At each
mathematical point of this continuum, macroscopic variables such as
soil porosity, conductivity, water capacity, water content, and
pressure head are assumed to be defineable, and are obtained by
averaging the local microscopic variables of the medium over a small
control volume. The physical state of a soil however, is not static,
rather it is in a dynamic equilibrium with the prevailing environmental
conditions. For example the no tillage approach to crop production
leaves crop residues in the surface creating,a layer of mulch which
reduces evaporation losses. The soil water content is then higher than
conventional tillage influencing such soil hydraulic properties as
soil water potential h(0), hydraulic conductivity K(O), and soil water
capacity dO/dh (Phillips 33 _l,, 1980). Even though these hydraulic
soil properties are important in characterizing the physical state of a
soil, the difficulties and complexities involved in sampling and
measuring these properties has often discouraged scientists from
characterizing the soil directly from these indices. Many
investigators have attempted to improve or modify the existing theories
and procedures for measuring hydraulic soil properties (Arya £11.,

1975; Brakensiek, 1979: Clapp and Hornberger, 1978; Ghosh, 1976; Gupta

and Larson, 1979; Mualem, 1976; Nagpal and deVries, 1976).

116

Two fundamental hydrological soil properties, the soil water
retention curve and the hydraulic conductivity are the major components
of the quantitative analysis of soil water processes. The soil water
characteristic curve is usually determined by desorption of an
initially saturated soil to a prespecified pressure and then
determining its equilibrium water content(Richards, 1965). The field
measurement involves the in situ estimation of soil matrix potential
using tensiometers or psychrometers and concurrent measurements of soil
water content by gravimetric sampling, neutron probe, or gamma ray
attenuation techniques.

Arya 31131. (1975) proposed the in situ measurements of hydraulic
soil properties by a so called zero-flux method, where a moving plane
of zero flux is obtained from the field desaturation data and the soil
water pressures are monitored at several depths by tensiometers. The
soil hydraulic conductivity then may be calculated from the Darcian

flux equation
2
1((h) = [ZN 36 / at )dz] /( aH/az )z (5)
0

where K is the soil hydraulic conductivity at depth 2 as a function of
soil matric potential (h), 20 is the depth of zero-flux plane, 0 is
volumetric water content, t is the time, and H is the total soil
water potential at depth 2. Theoretical calculations of unsaturated
hydraulic conductivity often involves Poiseuille's law . Most
theoretical equations needs the water release curve and the saturated
hydraulic conductivity or water content to estimate the unsaturated

hydraulic conductivity (Kunze 51311., 1968; Jackson, 1972). Jackson

117
(1972) introduced an impirical component in the form of a matching
factor into the theoretical equation

In
Ki =Ks(Oi/Os)° .2. [(23+1-21m321/ E [(2j-1)h32] (6)

3:1 J 1
where K1 is the hydraulic conductivity which corresponds to a
volumetric water content of 01, K8 is hydraulic conductivity measured
at saturation (03), m is the number of intervals in O, h is the
suction head at the midpoint of each 0 interval, 3 and i are summation
indices, and c is an arbitrary constant often taken as unity.

A simpler, more easily determined measurement for assesing soil
physical conditions including;hydraulic properties may be soil bulk
density. The Physioempirical model of Arya and Paris (1981) estimating
soil moisture characteristic curve from particle size distribution and
bulk density is a step toward this approach. The problem with soil bulk
density , however, is that it is a crude measure of physical
conditions of a soil. It only considers the total pore volume of the
soil and ignores the more important criteria of pore size distribution.
Pore size distributions have traditionally been determined by applying

capillary theory to soil water characteristic curve as follows
h : 2 0 cos 0/ r (7)

where h is the capillary pressure or suction head with which the water
is held in the pores, r is the pore radius,0 is the surface tension of
water, and 0 is the angle of contact between water and solids. Nagpal

‘g£.gl.(1972) reported a good agreement between this method and mercury

118
intrusion technique for nonswelling soils.

The purpose of this study was to modify the ROOTSM model of Huck
and Hillel (1983), to account for the effects of mechanical impedance
on root growth and distribution. Empirical equations were derived from
experimental data which describe the processes of water movement and

root growth in a layered-homogeneous soil profile.

DESCRIPTION OF THE MODEL

The PHASOL model of root growth and water uptake presented here is
a modified version of the ROOTSM model reported by Huck and Hillel
(1983L.The model takes into account the balance of carbon and the
movement of water through plants growing in a one-dimensional multi-
compartment soil profile. The present version of the model provides the
inclusion of different bulk densities in a 10 layered soil profile. The
model is driven by solar radiation, estimated by a solar radiation
simulator (SOLSIM) which uses daily maximum and minimum temperatures as
well as precipitation to generate daily solar radiations.(Hodges 33
33,, 1983).'The algorithm is based upon Richardson's (1981) weather
simulator. The location specific variables used in this algorithm are
available for the continental United States in the form of contour
maps. Inputs to the model are soil and plant variables related to the

experimental study of this report.

Model.Program
The PHASOL model of root growth and water uptake in a layered

homogeneous, isotropic soil medium is programmed in FORTRAN V, and run
on a CYBER 750 computer. The model consists of a main program and three
subprograms. The SOLSIM subroutine is called to generate the daily
solar radiation intensities as needed. The other two subprograms are

functions INTGRL and AFGEN for rectangular integration and table

119

120
function generation, respectively. There are other subprograms which
could be used for plotting purposes but are not called by the present
model, and their presence in the program listings (APPENDIX), is for

documentation only.

Hater Balance

The water balance portion of the model takes into account the water
supplying power of the soil and roots and the transpiration potential
of the atmosphere. The approach considers flow of the water in the
transpiration stream to be down a gradient of potential energy from
the soil to the roots and to the atmosphere. The gradient-driven
concept of water flow within the soil-plant-atmosphere system is
originated from the Van den Honert (1948) analogy of the transpiration
stream to an electrical circuit. The flow of water within each segment
of the stream is directly proportional to the potential gradient and
inversely related to the resistance. The water balance flowchart for
the PHASOL model is presented in Figure 1. The description of the
symbols in these flow charts follows Forrester's (1961) conventions.
Rectangular boxes describe the state variables, and the valves
represent the rate variables which are usually constrained by some
other processes. The water could be supplied to the system through
irrigation or rain and may move downward by the Darcian flow and be
taken up by the roots simultaneously.

The flow of water in the PHASOL model is considered to be upward
within a one-dimensional, 10-layered medium which is isotropic,
homogeneous within each layer. This system is hydraulically equivalent

to a homogeneous, anisotrOpic medium. Equation (4) is the flow equation

121

 

HATER
VAPOR

LEAF AREA

1* FWRANSPIRATION RATE gag; __
RAIN-IRRIGATION >q

 

 

 

 

 

l
-- PLANT wATER CONTENT 14-—

EVAPORATION RAE, LWATER UPTAKE-LAYER 11+.

__ _ __ __ wATER CONTENT AT
1" \ SOIL LAYER 1

 

 

  
  

 

 

 

 

 

 

- UPTAKE RATE-LAYER 1}!

_I’

 

 

 

 

 

 

 

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WATER CONTENT AT

SOIL LAYER 2 UPTAKE RATE-LAYER 2 f

 

I]

 

 

 

I... ___L__. .... ..."..-

 

 

 

 

L WATER UPTAKE-LAYER 10

—‘

 

wATER CONTENT AT -
SOIL LAYER 10 UPTAKE RATE-LAYER 10].- —

 

 

 

 

 

CAPILLARY-DRAINAGE ‘ —' — -L MECHANICAL IMPEDANCE? -.

Figure l. Flowchart representing the water flow processes within the
soil-plant-atmosphere system.

 

 

122
which is solved numerically by a finite-difference scheme subject to

the following boundary conditions

(1) at (1:0 and z>=O 0:01
(2) at t>=0 and z=zb h=-0.60
(3) at t>=0 and 2:0 q=O

The flux is considered to be positive downward with 2 equal to zero at
the soil surface and 2 equal to zb at the bottom of the soil profile.
The first boundary condition corresponds to an initial soil moisture
content (01) within the soil profile. The second boundary condition
corresponds to a constant matric potential head of -0.60 meter at the
bottom of the soil profile for all times (t). The third boundary
condition corresponds to zero evaporation from the soil surface. Other
boundary conditions could be used if so desired.

Data on the relationship between soil matric potential head (h),
hydraulic conductivity (K), and volumetric water content(O) in the
PHASOL model is limited to those obtained from destructive core
sampling. An empirical equation was fitted to the water characteristic
curves (Figure 2) which estimates the matric potential head (POTM(I))
from the soil bulk densities (BD(I)) and the volumetric water content

(THETA(I)) for each soil layer (I) as follows

POTM(I)=-93878.06*EXP(-37.‘12'THETA(I)/BD(I)) (8)

where POTM is in m, THETA in m3 m'3, and BD in Mg m'3. This equation

estimates the matric potential head reasonably well for the range of

123

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124
soil bulk densities and water contents encountered under most field
conditions. The relationship between hydraulic conductivity and matric
potential head is more difficult to measure experimentally, especially
under different soil bulk densities. The unsaturated hydraulic
conductivities for 3 bulk densities (Figure 3) were estimated from
eqn.(6). The saturated hydraulic conductivities were measured in the
laboratory by applying a constant head permeameter to core samples. An
empirical equation was fitted to these data which estimates the
hydraulic conductivity (COND(I)) from matric potential head, and soil

bulk densities for each soil layer in this model. This equation is

COND(I)=EXP[6.77-4.21'BD(I)-O.93845'ALOG(-POTM(I))-

O.07445'(ALOG(-POTM(I))21 (9)

where COND is in cm d", POTM in cm Of water, and BD in Mg m‘3.

The rate of root water uptake (5w) from the soil-root interface
and its transport to plant-air interface is estimated on the basis of
Ohm's law analogy with the potential gradient between the tranpiring
leaves and each soil layer acting as the driving force. The rate of
root extraction from each soil layer (RTEX(I)) is thus estimated by

ROOTSM in the following equation
RTEX(I)=AMAX1(0.0, (POTH(I)-POTCR)/(RSSL(I)+RSRT(I))) (10)
where POTH is the hydraulic potential head, POTCR is the leaf water

potential, RSSL is soil resistant to water flow, and RSRT is the root

resistance to water flow for each soil layer. After summing the initial

125

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126

root water uptake rates over all soil layers, the total (SUMR) is
compared to the transpiration rate (TRANSP). The leaf water potential
is then adjusted iteratively so that the two are within 11 of one
another. Thus, if the transpiration rate is greater than the sum of
root removal rate from all soil layers, the leaf water potential would
be decreased in order to stimulate more water uptake. This leaf water
potential is used as the initial estimate for the next time step.

Evapotranspiration is a name given to the combined process of water
loss from the soil (evaporation), and plant (transpiration). The model
estimates potential evapotranspiration (PET) from the measured daily
pan evaporation (MPANEV) and maximum daily solar radiation (MAXRAD).

Thus

PET =AMAX1 (0.01'DTRDEM/86‘IOO" PI'RADN'MPANEV/MAXRAD) (11 )

where PET is considered to be the maximum of either 11 of the daily
transpiration demand (DTRDEM) or a daily measured pan evaporation
scaled to the incoming solar radiations (RADNL. Partition of PET into
soil evaporation (SLEVAP), and transpiration (TRANSP) involves leaf
area index (LAI). In the absence of a canopy, the water loss is limited
to soil evaporation only.

The relative contributions of SLEVAP and TRANSP to PET is
modified by the existance of water stress in the plant. If the plant
has an adequate water supply the transpiration rate is controlled
primarily by the incoming solar radiation. Excess transpiration rate
over water uptake rate, however, produces water deficit which

decreases plant water potential and stomatal aperature. The ROOTSM

127

estimation of the transpiration portion of PET is as follows

TRANSP=PET'HATRST'LAIFAC (12)

The water stress (HATRST) and leaf area (LAIFAC) factors are variables
between 0 and 1 to adjust the transpiration rate for changing plant
water potentials and leaf areas.

Changes in stomatal resistance are the most obvious mechanisms by
which the leaf water potential influences the transpiration rate. When
the turgor pressure of the guard cells fell below a threshold value,
the stomatal aperture decreases and stomatal resistance increases. The
curvilinear relationship between the leaf water potential (POTCR), and
abaxial diffusive resistance (DR) in the PHASOL model (Figure 4) may
suggest that the stomatal aperture had changed little so long as the
leaf water potential was above -10 meter. A least squares equation was

fitted which quantitatively describes this relationship as

DR=EXP(4.271-0.0316'POTCR) (13)

where DR is in s m", and POTCR is in m. Until more Objective
information is available, which sheds light on the true nature of the
transpiration process under a stress environment, it is assumed that
environmental stresses including mechanical impedance may indirectly
affect transpiration by influencing the mechanisms which control the
stomata. In this study, the transpiration rates were the least and
diffusive resistances were the greatest on the treatments having very

high mechanical impedance (Figure 5). The curvilinear relationship

128

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130
between transpiration rates.and1diffusive resistances cfi‘the PASOL
model, approached an asymptotic value for high diffusive resistances.
Therefore, it appears reasonable to suggest that the stomatal aperture
may not have become completely closed (Figure 5). A least squares
equation was fitted to this curve which estimates the specific

transpiration rate (SPTRNS) from diffusive resistance (DR) as follows

SPTRNS=0.011+0.113'EXP(-0.00374’DR) (14)

where SPTRNS is given as g H20 111'”2 of leaf 3‘1 and DR as 3 III"1

Intuitively, the maximum SPTRNS should occur when the stomata are
wide open, the diffusive resistance is minimum, and the potential
evapotranspiration (PET) is maximum. The minimum value of DR is the
intercept of the curve in Figure 4., which is found to be 72 s m"1 in
this study. This nonzero intercept appears to be reasonable because the
leaf conductance (1/DR) never becomes infinite. The water stress

factor (HATRST) of the PHASOL model is calculated as the ratio of the

SPTRNS to the maximum SPTRNS as follows

HATRST=SPTRNS/0.097 (15)

where 0.097 is the maximum SPTRNS, calculated from eqn.(14) for the DR

value of 72 s m“. Substituting eqn.(14) into eqn.(15) results in

HATRST=(0.011+O.113'EXP(-0.00374'DR))/0.097 (16)

which is graphically presented in Figure _6.

131

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132

The ROOTSM model estimates soil evaporation as

SLEVAP=PET'(1.0-LAIFAC) (17)

Soil evaporation in the PHASOL model, however, was zero thus

SLEVAP=0.0

Carbon Balance

A schematic flowchart for the carbon balance portion of the PHASOL
model is presented in Figure 7. In this model C02 diffuses into the
leaf through stomatal apertures and is incorporated into a labile pool
which is controlled by photosynthetic carbon fixation processes.
Photosynthetic activity is constrained by leaf area, leaf water
potential, and the incoming solar radiation or portions of it which are
frequently referred to as photosynthetic active radiation. Aside from a
shortage of photosynthetic active radiation, the major environmental
stresses affecting photosynthesis are unfavorable temperature,
inadequate water balance, or nutrient deficiencies (Koller, 1975). All
of these environmental stresses appear to be directly related to
mechanical impedance. Thus, mechanical impedance is assumed to
indirectly influence photosynthesis through impeding water uptake and
reducing the canopy water potential. The rate at which carbon dioxide
diffuses into the leaf and incorporates into the labile pool is defined

by the ROOTSM model of Huck and Hillel(1983) as

PHOTSN=RADN' MAXFOT/HAXRAD 'WATRST'LAIFAC (18)

133

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13“
Where RADN is the instantaneous incoming solar radiation intensity

estimated by

RADN=MAXRAD'(AMAX1(0.0, SIN(2.0'PI'(DAY-0.25)))) (19)

The HAXRAD is the maximum daily solar radiation intensity estimated by
the solar radiation generator (SOLSIM) in the PHASOL model as described
earlier. The instantaneous estimation of the solar radiation intensity
by a sine function assumes proportionality between the incoming solar
radiation and the solar angle, such that the peak radiation is at noon
each day. MAXFOT is the maximum photosynthetic rate measured at maximum
solar radiation intensity. Since diffusion of C02 into, and water
vapor out of the leaf is a concurrent process, it seems reasonable to
assume that photosynthetic activity and transpiration are similarly
affected by plant water stresses and leaf areas. The HATRST and LAIFAC
factors thus are the same as those for transpiration.

Allocation of carbohydrates in the labile pool is such that all
organs have equal access to the pool. However, maintenance respiration
requirements of the plant is assumed to be independent of the pool
size. Therefore, maintenance respiration requirements should be
satisfied before any carbohydrate can be used for growth. Maintenance
respiration is assumed to be a function of the temperature and tissue
mass. The model separately calculates the maintenance respirations of
the roots and shoots. Hence, shoot maintenance respiration (SHMRES) is
assumed to be a function of the shoot mass (SHOOTW) and temperature

(Huck and Hillel, 1983). Thus

135
SHMRES=SHOOTH'TMPFCS‘RSPFAC (20)
where

THPFCS:10.0“((TEMP-REFT)‘0.030103) (21)

The temperature factor of the shoot (TMPFCS) has the effect of doubling
SHMRES for each 10 °C rise in temperature. The instantaneous
temperature values (TEMP) are calculated by a sine function which makes

the peak temperature at 3 PM each day. Hence

TEMP:REFT+SIN(2.0'PI '(DAY-0.375))'RANGE (22)

where REFT is the average daily temperature, and RANGE is the
amplitude of the daily maximum and minimum temperatures. The PHASOL
model caculates daily values of REFT and RANGE from meteorological data

as

REFT: (THAX+THIN)/2.0 (23)
and

RANGE: (TMAX—THIN)/2.0 (24)

where THAX and THIN are the measured daily maximum and minimum
temperatures, respectively.

Stress environments adversely affect the development of a
functional root system by increasing the repiratory requirements of
roots (Smucker, 1984). Our data indicated that increasing mechanical
impedance decreased transpiration rates and increased leaf temperature

(Figure 8) resulting in increased shoot respiration rates. At high bulk

136

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137
densities more than 801 of the observed leaf temperatures were higher
than the ambient by as much as<L5 degrees.‘There appeared to be no

correlation between leaf temperature and transpiration at night.

Root Growth and Distribution

The approach of the PHASOL model to carbohydrate partitioning is
based more upon a variable partitioning strategy than on a fixed
scheme. The fraction of carbohydrate partitioned to root growth is
assumed to be dependent upon plant water stress. In fully turgid plants
the partitioning strategy favors the shoots. Greater shoot growth
however, is accompanied by higher transpiration rates and an increased
demand for greater water uptake by the root system. The greater demand
for water results in an increase in root growth (Huck and Hillel,
1983). Growth of roots into new layers requires energy which is
provided by the carbohydrate partitioning . The model thus calculates

the total root growth rate (TOTRG) as

TOTRG=(1.0—FRAC)'SOLCHO’GROFAC'TMPFCR (25)

where FRAC is the fraction of labile carbohydrates remaining in the
shoot as a function of soil water potential, SOLCHO is the available
carbohydrate reserve as the labile pool, TMPFCR is the temperature
factor of the root which is calculated from eqn.(21) with TEMP being
the soil temperature, and GROFAC is the relative consumption rate of
carbohydrate reserves (Huck and Hillel, 1983). TMPFCH adjusts the root
growth rate for changes in soil temperature and varies between 0 and 1.

TOTRG is the total root growth rate representing the maximum amounts of

138
carbohydrate available for root growth. It has been indicated,
however, that appreciable amount of carbohydrates may be lost from the
roots of plants growing under stressed environments (Smucker, 19814).
The PHASOL model assumes that root exudation losses are proportionate
to the level of mechanical resistance in the soil. The total root

growth rate is then modified as

TOTRG=K1.0-FRAC)'SOLCHO'GROFAC'TMPFCR‘MNMIFC (26)

where MNMIFC is the minimum value of mechanical impedance factor

(MIFAC) among all soil layers, namely

MNHIFC=AMIN1(MIFAC(I), I=1,10) (27)

With this approach, the root exudation losses are simulated by reducing
TOTRG for the highest level of mechanical resistance (lowest MIFAC) in
the soil. Modifications of ROOTSM for the effects of mechanical
impedance is on the basis of experimental results reported before. When
mechanical resistance of a soil layer reached a critical resistance,
root growth into that layer completely stopped. The critical mechanical
impedance (CRMI) for these experiments were estimated to be
approximately 6 MPa. Thus a mechanical impedance factor is introduced

which continuously calculates the level of impedance as follows :

MIFAC(I)=1.0-EXP(-CC*MIDIF*'DD) (28)
and

MIDIF: AMAX1(0.0,(CRMI-MI(I))) , (29)

139

MIDIF calculates the difference between the instantaneous mechanical
impedance (MI) and critical mechanical impedance (CRMI) in each soil
layer. MIFAC is the mechanical impedance factor, ranging from 0 to 1,
which adjusts root growth for dynamically changing mechanical
resistance in each soil layer. The parameters CC and DD are constants
derived from the experimental data such that if mechanical impedance
was zero MIFAC would be close to 1, and if mechanical impedance is at
or greater than CRMI then MIFAC would be close to zero. For CRMI equal
to 6 MP3 (600 m of water), the exponential parameters CC and DD were
estimated to be 0.102 and 0.502 respectively. AMAX1 and AMIN1 are the
maximum and minimum FORTRAN functions, respectively.

Mechanical impedance in this model is evaluated on the basis of
resistance of the soil to a dynamic penetrometer. Replicated core
samples similar to those used for these studies were sent to the
University of Minnesota laboratories in order to evaluate their
penetration resistances. These data indicated that mechanical impedance
was strongly dependent on soil bulk density and air filled porosity. An
empirical equation was derived which estimated mechanical impedance
(MI) from soil bulk density (BD) and air filled porosity (FA) as

follows

MI(I)=521.0—1550.0'BD(I)+912.0'(BD(I)'*2.0)+396.0'FA(I) (30)

where MI is given in m of water, BD in Mg m‘3, and FA in m3 m'3. Air
filled porosities were calculated from soil desaturation data at

different soil matric potentials and bulk densities (Figure 9). A least

140

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squares equation was fitted to these data for calculating air filled
porosities from soil bulk densities and matric potentials (POTM) with

the PHASOL model as follows

FA(I):(ALOG(-POTM)+35.1-21.0‘BD(I))/52.1 (31)

where FA is given in m3 m’3(air/soil), POTM in cm H20, and BB in Mg m'
3. TOTRG is the aggregate root growth which has to be distributed among
all soil layers.

The PHASOL model takes into account the inhibitory effects of
mechanical impedance on root distributions. Experimental data of this
study reported earlier (Asady gt al,, 1985) indicated that root
distribution was strongly influenced by mechanical resistance. These
data demonstrated that root growth into mechanically impeded soil
layers was greatly reduced and increased in the nonimpeded overlying
layers. Root growth in the severely compacted soil layers was from
proliferation of the existing roots rather than to the extension of the
new roots from adjacent layers. Therefore, the root proliferation and

extension rates of the PHASOL model are as follows :

BIRTH(I)=BR*MIFAC(I)'WTRFCB (32)
and

EXTENSKI)=EXTNRT'MIFAC(I)'WTRFCE (33)

The BIRTH and EXTENS are birth and extension rate factors for each soil
layer which are calculated by multiplying the proliferation rate (BR)

and extension rate (EXTHRT) of the roots grown under ideal

142
environmental conditions, with mechanical impedance factor (MIFAC),
soil water potential factors for birth (WTRFCBL. and extension
(WTRFCE). The BR and EXTNRT could be estimated from experimental data
to match the overall root growth. The birth rate factor (eqn. (32)) is
further modified to increase the root growth in the less impeded layer

overlying a more impeded soil as follows :
BIRTH(I-1)=BIRTH(I-1)'(1.0+(MIFAC(I-1)-MIFAC(I))/MIFAC(I-1)) (311)

This equation increases the BIRTH factor proportional to the difference
in mechanical impedance of the two layers. The PHASOL estimation of the
water potential factors is based on the assumption that proliferation
and extension rate of the roots may be stopped if the soil water
potential head has reached threshold minimum values of -10 (BRMIN),and
-100 (EXTMIN) m, respectively. The water potential factors are

defined (Huck and Hillel, 1983) as

WTRFCB:(1.0-EXP(-AA'X"BB) (3S)
and
WTRFCE=(1.0-EXP(-AA'XX"BB) (36)
Where
X=AMAX1(0.0,(POTH(I)—BRMIN)) (37)
and
XX=AMAX1(0.0,(POTH(I)-EXTMIN)) (38)

Where POTH is the hydraulic potential of each soil layer and AA and BB

are constants.

1113
The root growth potential of each soil layer (RTGRO(I)) is
estimated by multiplying the birth rate factor of that layer (BIRTH(I))
by the partial root length of the same layer (PRTL(I)) and added to the
extension rate factor of the same layer (EXTENS(I)) times the partial

root length of the overlying layer (PRTL(I-1)) as follows :

RTGRO(I)=BIRTH(I)‘PRTL(I)+EXTENS(I)‘PRTMI-1) (39)

The root growth potential of the whole root system (SUMRG) is the sum
of RTGRO for all soil layers. The SUMRG, however, can not be greater
than the upper limit for the growth of the entire roots (TOTRG) already
established from the available carbohydrates (eq.(26)). In order to
bring these two into conformity with one another, the potential root
growth in each layer has to be normalized (Huck and Hillel, 1983) to

give

RTG R0 ( I ):RTGRO(I )‘TOTRG/SUMRG'LNGFAC ('40)
where LNGFAC is the root length factor which translates the root mass
into the root length (eg. root length per unit root mass). The average
LNGFAC of dry edible beans in this study was found to be inversely
related to soil bulk density (BD), namely

LNGFAC=83100.0-26666.0*BD (ll 1 )

where LNGFAC is in m kg" and so in Mg m'3.

TESTING THE MODEL

To test the overall performance of the model, a series of
simulation run was carried out for the experimental conditions of the
previous chapters. A dry edible bean plant was assumed to be growing in
a 25 cm deep Charity clay soil. The initial time for all simulation
runs is julian day 120.

The initial equilibrium condition of soil water was equivalent to a
constant soil matric potential of -0.006 MPa at the base of the soil
and -0.0085 MPa at the surface of the soil. The lower boundary
condition was kept constant throughout the simulation runs. No
evaporation losses were allowed from the soil surface. The upward water
flux was identical to the root extraction rates.

The initial plant variables were chosen to represent a 10 day old
dry bean plant which was already growing in a uniform and nonimpeded
soil. The initial shoot (SHOOTW) and root (ROOTW) weights of plants
were 0.021 and 0.0095 kg m'a, respectively (Table 1). The initial
carbohydrate reserve (SOLCHO) was assumed to be 3% of the shoot and
root masses (Huck and Hillel, 1983). The initial distribution of the
roots within the soil were such that 181 of the roots were at the top
2.5 cm, 142% were at 2.5-10 cm, 37% were within 10-17.S cm, and 3% were
below 17.5 cm depth.

Initially, the model was tested to see how plants grow under the
original condition of a uniform soil profile with a bulk density of 1.1

144

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146

Mg m'3. The model was then run with plants growing in a soil profile
with a bulk density of 1.1 Mg m'3 at the surface 2.5 cm, and 1.7 Mg m"3
at a depth of 2.5-25 cm. Comparison of plant growth variables after 5
and‘H)days of simulated growth under two different soil conditions
indicated that both shoot (SHOOTW) and root (ROOTW) masses of dry
edible beans were reduced at high bulk density soils (Table FL The
soluble cabohydrate reserves in the labile pool (SOLCHO) were also
reduced by mechanical impedance» High mechanical impedance reduced
total root length (ROOTL) of dry edible beans (Table 1). The thickening
effect of mechanical impedance on root growth is not included in root
length calculations in these simulation runs because it was assumed all
the roots have the same length per unit mass.

Mechanical impedance greatly reduced the root water uptake.The
spatial and temporal patterns of simulated root water extraction, under
two soil conditions, is characterized by'a gradual increase in root
water uptake, gradual deepening zones of moisture extractions (Figures
10 and 11), gradual increase in upward water flux (Figures 12 and 13),
and gradual steepening of the water potential gradient between the
water source at the bottom and water sinks at the top (Figures 111 and
15).'The zone of maxinnnn water extraction corresponded to the region of
high root density in both soils. Large quantities of water were
extracted from the nonimpeded surface layer overlying high bulk density
soils (Figures 10 A 11). The root water uptake from the nonimpeded soil
layers was about three times greater than from the impeded soil.‘The
upward water flux passing through the bottom of the soil was, however,
6 and 12 times greater after 5 (Figure 12) and 10 (Figure 13) days of

simulated growth, respectively. Because maximum water flux had not

147

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153
occurred at the base of the high bulk density soil (Figures 12 and 13),

demonstrated that highly compacted soils were progressively depleted of
their water without being recharged. The regions of maximum root
density in these soils, were depleted at a faster rate, creating
localized spatial water stresses. This is further demonstrated in
Figures 14 and 15 where the soil water potential shows a nonequilibrium
behavior.

These phenomena are primarily due to very high hydraulic
resistances in the soil (RSSL) and in the roots (RSRT) of plants grown
under high mechanical impedance (Table 2). Hydraulic resistances of the
soil (RSSL(3)) and roots (RSRT(3)) in the third soil layer indicated
that soil hydraulic resistances to water uptake increased with time due
to a decrease in unsaturated hydraulic conductivity of the soil (Table
2). A decrease in root hydraulic resistance with time, is the result of
increase root growth (Table 2). Sum of the soil and root hydraulic
resistances, however, increased with time emphasizing a greater
importance of the soil rather than root hydraulic resistance.

The transpiration demand often exceeds the water supplying power of
mechanically impeded soils.‘Therefore these soils can not meet the
transpiration demands fast enough to prevent water stress. The mid-day
water potential of the leaf (POTCR) thus become very low (Table 2). The
low leaf water potential activated the control mechanisms of the
stomata to reduce their openings, thereby reducing excessive water loss
and plant dehydrations. This is accompanied by reducing photosynthetic
rate and soluble carbohydrates (Table 1).

In the noncompacted soils, on the other hand, the water flux is

maximum at the base and gradually approaches zero at the soil surface

154

 

 

 

 

 

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155

(Figures 12 and 13). The soil hydraulic potential is at
quasiequilibrium, with the highest value'at the base and the lowest
value at the top with a smooth transition (Figures 14 and 15).
Therefore, in nonimpeded soils the water supply usually meets the
demand, such that localized water shortages would not be developed, and
the system may approach equilibrium for most of the time. The
cumulative water removal from all soil layers (CUMREM) was slightly
greater than the cumulative transpirations(CUMTRN) for both soils
(Table 2), indicating a limited potential for storing water in the
plant as reported by Huck and Hillel (1983). CUMREM and CUMTRN were
both decreased at high soil bulk densities (Table 2).

In conclusion, the PHASOL model of root growth and water uptake
presented here simulated the effects of soil mechanical impedance on
dry edible beans root growth. Results of several simulation runs
demonstrated that the model behaves as expected. Validation of the
model against experimental data is necessary, however, before it could
be used for management decisions. Further improvement of this model
requires more parameter estimations. A complex model of this sort, has
many site and plant specific variables which have to be estimated from
experimental data. We have derived as much information, regarding the
plant, as possible from the experimental data of this study. Those
plant parameters which were not available to us, were assumed to be
similar to those which were used by MJL.Huck in testing his ROOTSM
model (1983) for faba beans in Australia. Stability of this sort of
model is dependent upon the manitude of the time step as well as the
thickness of each soil layer. The numerical accuracy of the model

decreases if either the time step or the thickness of the soil layers

156
are increased. The most critical region for error is where there is a
large gradient of water content. Thus, it is wise to use as thin of
soil layers as possible at those regions. Sensitivity analysis may be
necessary to isolate those parameters to which the model is most
sensitive, and determine the acceptable range of errors for their
estimation. Finally, it should be noted that numerical oscillations
were encountered in some simulation runs involving noncompacted soil
conditions. The problem was associated with the size of the calculated

conductivity 0.5 cured the problem for these calculations.

LITERATURE CITED

Arya, L.H., D.A. Farrell and G.R. Blake. 1975. A field study of soil
water depletion patterns in the presence of growing soybean roots.
1. Determination of hydraulic properties of the soil. Soil Sci.
Soc. Am. Proc. 39: 11211-430.

Arya, L.H., G.R. Blake and D.A. Farrell. 1975a. A field study of soil
water depletion patterns in the presence of growing soybean roots.
II. Effect of plant growth on soil water pressure and water loss
patterns. Soil Sci. Soc. Am. Proc. 39: 1130-1136.

Arya, L.M., G.R. Blake and D.A. Farrell. 1975b. A field study of soil
water depletion patterns in the presence of growing soybean roots.
III. Rooting characteristics and root extraction of soil water.
Soil Sci. Soc. Am. Proc. 39:437-444.

Arya, L.H., and J.F. Paris. 1981. A physicoempirical model to predict
the soil moisture characteristic from particle-size distribution
and bulk density data. Soil Sci. Soc. Am. J. 45: 1023-1030.

Asady, G.H., A.J.M. Smucker and M.W. Adams. 1985. Seedling test for the
quantitative measurement of root tolerances to compacted soil. Crop
Science 25:802-806.

Beese, F., R.H. Van Der Ploeg and W. Richter. 1977. Test of a soil
water model under field conditions. Soil Sci. Soc. Am. J. I11:979-
9814.

Brakensiek, D.L. 1979. Comments on "empirical equations for some soil
hydraulic properties" by Clapp & Hornberger. Water, Resource Res.
15: 989-990.

Clapp, R. B. and G. M. Hornberger. 1978. Empirical equations for some
soil hydraulic properties. Water Reso. Res. 111: 601-604.

Forrester, J.W. 1961. Industrial Dynamics. M.I.T. Press, Cambridge,
Massachusetts. (chapters 1-5).

Ghosh, R. K. 1976. Model of the soil moisture characteristic. J. Ind.
Soc. Soil Sci. 2‘4: 353-355.

Gupta, S. C. and W. E. Larson. 1979. Estimating soil water retention
characteristics from particle size distribution, organic matter
percent, and bulk density. Water Reso. Res. 15: 1633-1635.

Hillel, D. 1977. Computer Simulation of Soil Water Dynamics. A
compendium of recent work. International Development Research
Center. Box 8500, Ottawa, Canada. 214p.

157

158

Hillel, D. 1980. Fundamentals of Soil Physics. Academic press, Inc.

Hodges, T, V.French and S.LeDuc. 1983. Estimating solar radiation for
plant simulation models. Presented at the 6th Annual Workshop of
The Biological System Simulation Group . Univ. of Illinoise.

Huck, M.G. and D. Hillel. 1983. A model of root growth and water uptake
accounting for photosynthesis, respiration, transpiration and soil
hydraulics. Adv. In Irrig. (ed.) D. Hillel. 2:273-333.

Jackson, R. D. 1972. On the calculation of hydraulic conductivity. Soil
Sci. Soc. Am. Proc. 36: 380-382.

James, L.G. and C.L. Larson. 1976. Modeling infiltration and
redistribution of soil water during intermittent application. Am.
Soc. Ag. Eng. Trans. 19:482-488.

Kirkham, D. and W.L. Powers. 1972. Advanced Soil Physics. John Wiley &
Sons, Inc. NY. London, Sydney, Toronto. pp46-75, 235-278.

Klute, A. 1982. Tillage effects on the hydraulic properties of soil: a
review. Predicting Tillage Effects on Soil Physical Properties and
Processes.ASA. Special publication No.44. ASA, SSSA, 677 South
Segoe Road, Madison, Wisconsin 53711.

Koller, D. 1975. Effects of environmental stress on photosynthesis.
Conclusions. In: Photosynthesis and Productivity in Different
Environments (ed.) J.C. Cooper. p587-589.

Kunze, R.J., G. Uehara and K. Graham. 1968. Factors important in the
calculation of hydraulic conductivity. Soil Sci. Soc. Am. Proc.

Mualem, Y. 1976. A new model for predicting the hydraulic ooonductivity
of unsaturated porous media. Water Reso. Res. 12: 513-522.

Nagpal, N. K. and J. deVries. 1976. An evaluation of the instantaneous
profile method for in situ determination of hydrologic properites
of layered soil. Can. J. Soil Sci. 56: 453-461.

Nagpal, N. K., L. Boersma and L. W. DeBacker. 1972. Pore size
distributions of soils from mercury intrusion porosimeter data.
Soil Sci. Soc. Am. Proc. 36: 264-267.

Phillips,R.E., R.L. Blevins, G.W. Thomas, W.W. Frye and S.H. Phillips.
1980. No-tillage agriculture. Science 208:1108-1113.

Richards, L. A. 1965. Physical condition of water in soil. In: Methods
of Soil Analysis, part I. C. A. Black (ed.) Agronomy 9: 128-152.
Am. Soc. of Agron. Madison, Wisconsin.

Richardson, C.W. 1981. Stochastic simulation of daily precipitation,

159
temperature and solar radiation. Water Res. Res. 17:182-190.

Rowse, H.R. and D.A. Stone 1978. Simulation of the water distribution
in soil; measurement of soil hydraulic properties and the model for
an uncropped soil. Plant Soil. 49:517-531.

Rowse, H.R., D.A. Stone and A. Gerwitz. 1978. Simulation of the water
distribution in soil ; the model for cropped soil and its
comparison with experiment. Plant Soil. 49:533-550.

Smucker, A.J.M. 1984. Carbon utilization and losses by plant root
systems. In: Roots, Nutrients, and Water Influx and Plant Growth.
(eds.) Barber and Bouldwin. ASA Special Pub. Madison,
Wisconsin.p27-45.

Van den Honert, T.H. 1948. Water transport in plants as a catenary
process. Faraday Soc. Discuss. 3:146-153.

Warrick, A.W. and D.0. Lomen. 1983. Linearized moisture flow with root
extraction over two-dimensional zones. Soil Sci. Soc. Am. J.

Warrick, A.W., D.0. Lomen and A. Amoozegarfard. 1980. Linearized
moisture flow with root extraction for three-dimensional steady
conditions. Soil Sci. Soc. Am. J. 44:911-914.

CHAPTER 6

SUMMARY AND CONCLUSIONS

A soil core seedling test (Asady _e_tL _a_l_., 1985) was used to obtain
multiple data sets which were incorporated into a root growth and water
uptake model (Huck and Hillel, 1983). This system could also be used to
study the main and interaction effects of several environmental
stresses on different cultivars. Root penetration ratios (RPR) of dry
edible beans cultured in the soil core seedling test decreased linearly
with mechanical impedance. When RPR approached a value of approximately
0.65, growth of plant shoots ceased. The xylem flow rate of stressed
plants was greatly decreased. The accumulation of toxic anaerobic
metabolites (eg., ethanol, acetaldehyde, etc.) increased with greater
mechanical impedance.

Mechanical impedance severely modified growth and distribution of
roots in these studies. Total root length of dry edible beans was 80%
lower after 30 days of growth in high density soils. Extension of new
roots into a deeper, compacted soil layer was significantly reduced,
and proliferation of the existing roots in the less compacted overlying
soil layers was greatly increased. Critical mechanical resistance
values of 5.5 MPa stopped the penetration of dry edible bean roots. The
inability of the roots to penetrate the compacted soils on one hand,
and the slow water movement in the compacted soils on the other hand,

160

161

created localized depletion of water and nutrients which could not be
replenished in spite of the large water content gradients.

The localized depletion of 02 in the root zone, decreased soil pore
diameter, slower root growth rate, and increased water film thickness
surrounding the roots in the impeded soil resulted in severe plant
stress. The 02 concentrations were low and the C02 concentrations were
high in the more compacted soils. High diffusive resistance of these
soils is attributed not only to smaller pores but also to pore plugging
by roots of air filled pores in the less compacted soil layers,
overlying the more compacted soil layer.

Severe mechanical resistance reduced the total carbon exchange rate
of the leaves but increased their specific carbon exchange rates. The
C02 concentrations in the rhizosphere of severely impeded soils were 6
to 8 times greater than in the nonimpeded soils.

A mathematical model of growth for annual plants was introduced
which describes growth from the seedling stage to physiological
maturity. It takes into account the efficiency index of growth as well
as the environmental potential of growth. This model provides a new
opportunity for plant growth analysis..AImechanistic model of root
growth and water uptake in a layered homogeneous soil profile was
modified which accounts for the effects of mechanical impedance in the
soil. The PHASOL model takes into account the water supplying power of
the roots and soils and the evapotranspiration potential of the
atmosphere for its water balance. The balance of carbon is the result a
mass balance between the atmospheric C02 influx through photosynthesis,
and the C02 eflux through respiration and leakage of soluble root

exudates.‘The effects of mechanical impedance on root proliferation and

162

extension is simulated via a normalizing function which adjusts root
growth for the instantaneous level of mechanical impedance.

The results from several simulation runs demonstrated that this
model behaves as expected.‘The accuracy of the model needs more testing
with experimental results before it can be used for management
decisions. We, however support the statement forwarded by Huck and
Hillel (1983) that " a good model is not one that embodies a perfect
depiction of reality, for such is not possible, but one that spurs
further efforts toward the aquisition of more knowledge and greater
understanding ”.

In conclusion, the soil core seedling test appeared to be a quick
and inexpensive method for studying plant responses to multiple levels
of environmental stresses. This is analogeous to a small scale physical
model that an engineer uses to test his larger scale and real life
systems. Biological systems, however, are dynamic and interactive
systems which are much more complex. Their linkages and forces which
are acted upon are often invisible, even to a trained eye. Their
biochemical and enzymatic reactions further complicate the study of
these systems. Therefore, plant growth studies under confined
environments, such as the soil core seedling test, produce relative
results, and interpretations have to be made in the context of two

domains, time and space.

A P P E N D I X I

PHASOL MODEL

Computer Program

Input Data

Computer Output

Glossary of Variables

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NAME

A(3,3)

AA
ABS
AFGEN
AGFAC
AGING
ALOG
AHAX1
AMIN1
AMOD
AR
ARS
ATN
ATX
AVCOND
AVPET

B(3,3)
BB

BD
BGNDAY
BIRTH
BR
BRMIN

CAPRIS
CC
CEVAP
CF
CLOCK
COND
CONVRT
COS
COUNT
CRMI
CRTEX
CRTMRS
CSTMRS
CUMPET
CUMREM

GLOSSARY OF MODEL VARIABLES

DESCRIPTION UNIT
Matrices derived by Richardson(1981)+ to describe the
interaction between daily maximum and minimum tempe-
ratures and solar radiations in the continental U.S.
Coefficient for sigmoid root generation curve
Absolute value FORTRAN function
Table function generator subroutine
Aging factor parameter controlling leaf aging
Relative aging factor modifying shoot death rate d d”1
Natural log FORTRAN function
Maximum FORTRAN library function for real numbers
Minimum FORTRAN library function for real numbers
Modulo FORTRAN function for real numbers .
Amplitude of annual curves of daily solar radiation Ly (1"1
Axial (xylem) resistance to water flow through roots 3
Amplitude of annual curves of daily minimum temp. oF
Amplitude of annual curves of daily maximum temp. 0F
Average conductivity between two soil compartments m 3'1
Average potential evapotranspiration measured daily
The same as A(3.3)
Coefficient for sigmoid root generation curve
Soil bulk density Mg m 3
Julian day at the beginning of the simulation run
Root birth rate (formation within the same layer) m 3'1
Birth rate parameter
Minimum soil water potential for root birth m
Cumulative capillary rise (past the 8th soil layer) m
Coefficient of mechanical impedance function
Cumulative evaporation from soil surface m
Correction factor for iteration loop
Clock time
Soil hydraulic conductivity m 3'1
Relative growth efficiency (kg respired/kg biomass) kg kg'1
FORTRAN function for cosine
Counter for the leaf water potential iteration loop
Critical mechanical impedance m
Cumulative root extraction m
Cumulative root maintenance respiration kg m'2
Cumulative shoot maintenance respiration kg m'2
Cumulative potential evapotranspiration
Cumulative root water remaval from all soil layers m

201

CUMTRN

DATA
DAY
DD
DELAY
DELT
DEPTH
DIF

DIFF

DIST
DR

DR
DRAIN
DRAING
DT
DTBL
DTHBGN
DTHFAC
DTRDEM

ERROR
EVAP
EXP
EXTENS
EXTMIN

EXTNRT

FA
FINTIM
FLPFLP
FLW
FLOWBN
FLOWBP
FRAC
FRACTB

GEN3
GROFAC
GROWTH

HOURC

I

18
ICHO
IFLAG
IFUN
IL

202
Cumulative transpiration

FORTRAN system data input
Cumulative days of simulation time
The same as CC
Delay time (half time for computing POTCRD)
Integration time step
Depth to midpoint of soil layers, from soil surface
Difference between total root extraction and
transpiration
Relative difference between total root extraction
and transpiration
Distance of flow between two adjacent soil layers
Leaf abaxial diffusive resistance
Function to adjust AR for julian day in SOLSIM
Cumulative internal drainage (past the 8th soil layer)
Instantaneous drainage rate (past bottom of 8th layer)
Function to adjust ATX, ATN for julian day in SOLSIM
Table of shoot death versus leaf area index
Relative shoot death rate
Relative root death rate
Minimum value of daily transpiration demand

Maximum allowable error in iteration loop
Evaporation from soil surface
FORTRAN function for exponentiation

Extension rate for root growth into the next soil layer

Minimum soil water potential for root extension into
the next soil layer

Extension rate parameter for root growth into the next
soil layer

Soil air filled porosity

Total duration of simulation run

Flipflop control statement for iteration loop

Hater flux density past the bottom of each soil layer
Capillary rise past the 8th layer(negative upward)
Internal drainage past the _8th layer(negative upward)
Fraction of carbohydrates remaining in the shoot
Table function for carbohydrate partitioning based
upon canOpy water potential

Temperature generating function
Relative consumption rate of carbohydrate reserves
Total plant growth (root and shoot)

hours of simulation time

Index of soil layer (integer number)

Vertical axix for graphic output of soil profile
Initial mass of carbohydrates

Flag set

Flag controlling the vertical gradient plots
Scale for vertical gradient plotting

8 k8-

kg kg'1 3:1
kg m'2 3'

kg m

IPER
IPOTM
IYEAR
IPRTL
IROOT
IRTL
ISHOOT
ITHETA
IVOLW
IX

J
JD
JDAY

K

LAI
LAIFAC

LAITBL

LEAFTH
LINE

LOCALE
LNGFAC

MAXFOT
MAXPOT
MAXRAD
MI
MIFAC
MIDIF
MNMIFC
MOD
HPANEV
MPOT
MSDPEV

NETGRO
NFL"
NJ

NJJ
NITTTL
NIPIL
NIPOL

OUTF

PCP
PET
PHOTSN
PHTCAR
PI

203

Initial percentage of soluble carbohydrates
Initial soil matric potential head

Calendar year

Initial partial root length(length per each layer)
Initial root mass per unit land area

Initial total root length per unit land area
Initial shoot mass per unit land area

Initial volumetric water content of the soil
Initial volume of water in each layer

Index for vertical plotting

Index of soil layers (integer number)
Integer value of JDAY
Julian day

Horizontal index of soil layer for vertical plotting

Leaf area index (leaf area per unit land area)

Leaf aera index factor for partitioning water

loss between plant and soil

Table function relating LAI and water loss betwee
plant and soil

Leaf thickness (leaf area per unit shoot mass)
Vertical plotting variable

Location #, a flag to read new data for new location
Length factor of the roots (length per unit mass)

Maximum photosynthetic rate

Maximum canOpy water potential allowed
Maximum light flux density (for one day)
Mechanical impedance in each soil layer
Mechanical impedance factor

Difference between instantaneous MI and critical MI
Minimum value of MIFAC

Integer remainder FORTRAN function
Measured daily pan evaporation

Matric potential of the soil in each layer
Measured daily pan evaporation

Net change in root length per layer(growth-death)
Net water flow into each soil layer (Darcian only)
Total number of layers comprising the soil profile
NJ + 1

Total number of iterations

Number of iterations per inner loop

Number of iterations per outer loop

Time interval for outputing vertical gradient plots

Measured daily precipitation values

Potential evapotranspiration

Photosynthetic rate (net carbon fixation)
Photosynthetic carbon conversion factor
Circumference of a circle divided by its diameter

m
m 111‘2

kg m'2

m m"2

k m“:

m m‘

m3 m'2

m2 m"2

m2 kg“1

m kg'1

kg m"2 s"1
m

N m'2

m

m

m 8‘1

cm

inch d-1
m -1

m 3'1

s

inch1

m 3'

kg m'2 3'1

POCR
POTCRD

POTCRE

POTH
POTM
POTRT
PRDEL
PRTL
PTOTL

RADN
RANGE
REFT
RESL
RESP
RESPRT
RESPSH
ROOTDY
ROOTW
RM(N)

RRL
RRS

RSPFAC
RSRT
RSSL
RTDTH
RTEX
RTGRES
RTGRO
RTMRES
RUN
RUNS

SATCON
SCALE
SHGRES
SHMRES
SHOOTD
SHOOTW
SIN
SLEVAP
SMAX
SHIN
SOLI
SOLCHO
SOLSIM
SRBAR

SRL1

204

Water potential of plant

Delayed plant water potential, allowing time for
growth recovery after stress

Effective plant water potential, stopping instantly
but recovering slowly

Hydraulic potential head in each soil layer
Matric potential of the soil in each layer

Water potential of the roots

Time inteval for outputting results

Partial root length

Total soil water potential (grav. + osm. + matric)

Radiation intensity

Range between average andlninimum or maximum temp.
Reference or average temperature

Reserve level of carbohydrates in the plant

Total respirstion of both root and shoot system
Total root respiration

Total shoot respiration

Root death rate

Total mass of living roots

Mean annual daily solar radiation for dry(N=1)

and wet (N=2) days

Relative root length per layer

Radial resistance to root water uptake (tissue
permeability)

Relative shoot maintenance respiration rate

Root system resistance to water flow, total per layer
Soil resistance to water flow, total per layer
Root death rate per layer

Root water extraction rate from each layer

Root growth respiration rate

Root growth rate per soil layer

Root maintenance respiration rate

Real number counting number of passes through update
Integer number of “RUN"

Saturated conductivity of soil

Scale factor for vertucal gradient plots

Shoot growth respiration rate

Shoot maintenance respiration rate

Shoot death rate

Mass of living shoot tissues

FORTRAN function for sine

Soil evaporation rate

Maximum scale factor for vertical gradient plots
Minimum scale factor for vertical gradient plots
Solar radiation intensity

Soluble carbohydrate reserves(Starch) in plant
Solar radiation simulator subroutine

Solar radiation mean for a given julian day (see
eqns. ua or Nb of Richardson, 1981)

Lag 1 serial correlation coeff. for solar radiation (
see eqn. 5 of Richardson, 1981)

B

BBQBSBB

kg kg"1 3‘1

kg m"2 3"1

kg m"2 3'1

-2 -1
-2 3-1
-1

m s'1

Ly (1‘1
kg m'

Ly d'1

SRSD1

STEMP
SUMR

SUMRD
SUMRG

TCOM
TEMP
THETA
THETST
TMAX
THIN
TMPFCR
TMPFCS
TN
TNBAR

TNL1
TNM
TX
TXBAR
TXL1
TXM(N)
TOPGRO
TOTRG
TRANSP
TRNTBL

UARS
URRS

VOLW
W
HATRST

X
XX

Y
YY

205

Standard deviation of daily solar radiations ( see
eqns. Ma or Nb of Richardson, 1981)

Temperature of the soil

Sum of water removal by roots in all layers
Estimated root death rate for the whole plant
Estimated root growth rate for the whole plant

Thickness of a soil layer

Temperature

Volumetric water content of each soil layer
Saturated volumetric water content

Maximum daily'temperature

Minimum daily temperature

Temperature factor for roots, biological Q10-value
Temperature factor for shoot, biological Q10—value
Minimum daily temperature

Mean minimum temperature for a given julian day (
see eqns. 4a or Nb of Richardson, 1981)

Residual series of daily minimum temperature (see
eqns. ua or Nb of Richardson, 1981)

Mean annual daily minimum temperature

Maximum daily temperature

Mean maximum temperature for a given julian day (
see eqns. Ha or Nb of Richardson, 1981)

Residual series of daily maximum temperature (see
eqns. Ha or Nb of Richardson, 1981)

Mean annual daily maximum temperature for dry (N=1)
and wet (N=2) days

Total growth rate of the shoot system

Total growth rate of the root system

Transpiration rate

Unit axial resistance (along the xylem)

Unit radial resistance per unit root surface

Volume of water in each soil compartment

Hater potential difference for extension of new roots
into second soil compartment

Hater stress factor for plant tissue

Water potential difference for new roots branching
Water potential difference for new roots extension

Index for vertical gradient plotting
Index for vertical gradient plotting

+ Richardson, C.V., 1981. Stochastic simulation of daily
precipitation, temperature, and solar radiation.

Water Reso.

Res. 17:182-190.

* For 12 hours daylight, 1 Langley/day ; 1 W/mz

oF
oF

oF
oF
oF

oF
oF

oF
kg m
kg m

ms

-2 E,5-1
-2 -1

S
1

A P P E N D I X II

OTHER DATA

206

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