SPECIAL REPORT 96-13

Soil Physical Environment and

Root Growth in Northern Climates

Gurdarshan S. Brar and Charles M. Reynolds May 1996
Abstract

Understanding the growth and function of plant roots in cold climates is

critical, but examination of root systems to elucidate their link to production is expensive and labor-intensive. Limited information is available on

the root growth and functions of plants grown in northern climates. Our

objective is to present an overview of the influence of physical edaphic

factors on plant root systems with special emphasis on models that are

available for simulating root growth. This report summarizes the impact

of the soil physical environment (soil water, soil temperature, soil air,

physi-cal impedance, and spatial variability) on root uptake and growth.

Roots grow because new cells are formed in the meristematic tissue near

the root tip, and these newly formed cells increase in volume, pushing the

root tip forward if growth conditions are satisfactory. Rapid elongation of

primary roots, combined with well-developed secondary roots, allows the

plants to exploit moisture and nutrients from a greater soil volume. Root

and shoots are strongly interdependent. The roots receive photosynthates

and growth hormones from shoots and in return furnish water and nutrients to the shoots. Several root growth models have been developed during the past decade; however, none addresses the problems associated

with cold regions. The models reported in the literature can be classified

as 1) simple models, 2) carbon partition models, 3) growing degree daybased models, 4) soil parameter-based models, and 5) arctic plant

growth models.

For conversion of SI units to non-SI units of measurement consult Standard

Practice for Use of the International System of Units (SI), ASTM Standard E380-

93, published by the American Society for Testing and Materials, 1916 Race St.,

Philadelphia, Pa. 19103.
Special Report 96-13

Soil Physical Environment and

Root Growth in Northern Climates

Gurdarshan S. Brar and Charles M. Reynolds May 1996

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was prepared by Dr. Gurdarshan S. Brar, Research Physical Scientist,

Geological Sciences Division, and Dr. Charles M. Reynolds, Research Physical Scientist, Geochemical Sciences Division, Research and Engineering Directorate, U.S. Army

Cold Regions Research and Engineering Laboratory.

This project was supported by the Strategic Environmental Research and Development Project (SERDP), Project Number 712–94, U.S. Army, Enhancing Bioremediation

Processes in Cold Regions, Dr. John Harrison, Executive Director. Technical review of this

report was provided by Dr. Giles M. Marion and Antonio J. Palazzo, both of CRREL.

This publication reflects the personal views of the authors and does not suggest or

reflect the policy, practices, programs, or doctrine of the U.S. Army or Government of

the United States. The contents of this report are not to be used for advertising or promotion purposes. Citation of brand names does not constitute an official endorsement

or approval of the use of such commercial products.

ii
iii

CONTENTS

Preface .................................................................................................................................... ii

Introduction........................................................................................................................... 1

Root origin and distribution ............................................................................................... 1

Monocots ........................................................................................................................... 2

Dicots ................................................................................................................................. 3

Root growth and development .......................................................................................... 3

Root–shoot relationships ..................................................................................................... 3

Root functions ....................................................................................................................... 4

Water uptake .................................................................................................................... 4

Nutrient uptake ............................................................................................................... 8

Root growth under physical edaphic constraints ........................................................... 10

Soil water .......................................................................................................................... 10

Soil air ................................................................................................................................ 11

Soil temperature............................................................................................................... 12

Physical impedance ......................................................................................................... 14

Spatial variability............................................................................................................. 15

Overview of root growth models ...................................................................................... 15

Simple models .................................................................................................................. 15

Carbon partition models ................................................................................................ 15

Growing degree day-based models .............................................................................. 16

Soil parameter-based models ........................................................................................ 16

Arctic plant growth models ........................................................................................... 16

Conclusions ........................................................................................................................... 17

Literature cited ...................................................................................................................... 17

Abstract .................................................................................................................................. 25

ILLUSTRATIONS

Figure

1. Distribution of permafrost in the Northern Hemisphere..................................... 2

2. Gross morphology of two root types ....................................................................... 2

3. The growth of roots and shoots of high-input UK winter wheat crops in

relation to the number of days from sowing ..................................................... 4

4. Factors influencing the generation of chemical information, soil effects,

plant physiological and developmental processes in roots in drying soils.. 5

5. A root system in layered soil viewed as a resistance network ............................ 6

6. Water flow in the soil–root continuum ................................................................... 6

7. Effect of plant age on the hydraulic conductivity of hydroponically grown

and sand-grown cotton roots ............................................................................... 8

8. Main axis root length at ten days after planting as a function of temperature 13

9. Minimum soil temperature at 3-cm depth as affected by minimum air

temperature and depth of snow cover ............................................................... 13
Figure

10. Seasonal warming of air temperatures determines when temperatures are

favorable for plant growth ................................................................................ 13

11. Effects of pressure applied to the outside surface of a flexible container on

relative root elongation and shape of barley roots ....................................... 14

12. Types of arctic plant growth models based on relative degree of comprehensiveness and mechanism ............................................................................ 17

TABLES

Table

1. Maximum root length density in the topsoil for various field crops ................. 4

2. Root:shoot ratio of sorghum seedlings as affected by soil temperature and

soil water matric potential ................................................................................ 4

3. Plant resistance data of various crops extracted from literature ........................ 6

4. Specific water uptake rates for some tropical and temperate species ................ 8

5. Total length of cotton as affected by plant age and root medium ...................... 9

iv
INTRODUCTION

Plant roots grow because new cells form in the

meristematic tissues near the root tip and the

newly formed tissues expand in volume, pushing

the root tip forward. The amount of water and the

nature of nutrient uptake from the root zone are

established by the interactions of various physical, chemical, and biological processes. After

many years of scientific discoveries, we understand how water and chemicals enter the soil and

are transported through the root zone. However,

our understanding of the fundamental aspects of

growth and proliferation of plant roots within the

cold soil environment is still incomplete, because

of the vast complexity of the various interacting

processes involved.

During the last decade, root research has received its strongest emphasis from plant physiologists, ecologists, and soil scientists. Limited information is available on water and nutrient

uptake by roots in cold regions. Billings (1992) reported that in northern climates, plant metabolism, growth, and reproduction are controlled by

the interactions of the soil physical environment

and the genetic structure of cold-adapted flora. In

these cold regions, the major constraints to root

growth are the presence of continuous permafrost in the subsurface and the short growing season (Fig. 1). The literature provides information

on the genetic structure of cold-tolerant plants;

however, limited information is available on the

root growth and development in northern climates. Therefore, this review focuses on the soil

physical environment and its effect on root

growth in cold climates.

The soil physical environment will be characterized by temperature, water, aeration, mechanical impedance, and spatial variability. The soil

physical environment required for the development of an efficient root system must be free from

stresses caused by mechanical, water, oxygen,

and cold-temperature conditions. Soils, because

they vary texturally, structurally, in porosity, and

pore size distribution, differ greatly 1) in their resistance to root penetration, 2) how they collect,

store, and release water for root uptake, and 3)

how they maintain aeration by gas exchange with

the atmosphere.

The objective of this report is to present an

overview of plant root growth and development

under soil physical environments with special

emphasis on models that are available for root

growth simulation. The physical edaphic factors,

as they occur naturally or are created by human

activities, and their effects on root growth are presented, beginning with brief background information on root origin and distribution, growth,

development, and functions.

ROOT ORIGIN AND DISTRIBUTION

Seeds germinate and primary roots originate

from the radicle. Roots also originate from stem

nodes on stolons, bulbs, and rhizomes of grasses,

or from the hypocotyl of certain dicotyledonous

plants (dicots, Fig. 2). As dicots grow, the laterals

of the first order emerge from the main root followed by laterals of second, third, fourth, and

even fifth order (Barley 1970). In monocotyledonous plants (monocots, Fig. 2), the seminal (primary) roots originate from primordia in the embryo, and crown (nodal, adventitious, or brace)

roots arise from foliar nodes of the growing plant

(Russell 1977, Klepper 1991). The growth rate of

Soil Physical Environment and Root Growth

in Northern Climates

GURDARSHAN S. BRAR AND CHARLES M. REYNOLDS
Figure 1. Distribution of permafrost in the Northern Hemisphere (after Péwé 1983).

the primary roots slows down after the initiation

of nodal roots. When the formation of crown roots

is delayed, the plants rely entirely on the seminal

root system for acquisition of water and nutrients

during the seedling establishment stage.

There is a continuous spectrum between the

two extremes of fibrous and tap root systems (Rendig and Taylor 1989). Monocot plants have fibrous

root systems, and dicots have some variant tap

root system.

Monocots

Under favorable conditions, monocot root extension rates are rapid. During the vegetative

phase of plant growth, root depth and root length

density (m roots m–3 soil) increase with time.

2

Figure 2. Gross morphology of two root types; a fibrous

root system (left) and a tap root system (right) in soil

(after Stem 1982).
3

However, even during seed sink initiation, roots

do not completely stop growing. Root length

density generally decreases with increased soil

profile depth.

Seminal and crown roots are different morphologically and functionally. For instance, in wheat

and grasses, seminal roots go deeper, are thinner

in size, and are more branched compared to

crown roots (MacKey 1973). The crown root system is more flexible regarding development under changed environmental conditions (Tennant

1976).

Dicots

The diameter of dicot roots decreases with increase in order (Rendig and Taylor 1989). The average functioning life of higher-order roots may

be 10 to 20 days. Higher-order roots form when

the environmental conditions are favorable and

die when water and nutrients are depleted in

their immediate vicinity. When soil water potential decreases below –0.2 MPa for 7 to 10 days,

about 80% of the roots can become senescent.

Time and environmental conditions substantially influence the initiation rates of new roots

and death of old roots. Therefore, the root length

density and root length per plant fluctuate during

the season. As observed in monocots, the root

growth of dicots continues during the reproductive phase.

ROOT GROWTH AND DEVELOPMENT

Roots grow because new cells are formed in

the meristematic tissue near the root tip, and

these newly formed cells increase in volume,

pushing the root tip forward if growth conditions

are satisfactory (Taylor and Brar 1991). Before the

cell starts expanding, the water potential inside

the cell, ψinside, is equal to the water potential outside, ψoutside, and ψinside = ψp + ψo, where ψp is

turgor potential and ψo is the osmotic potential.

Processes responsible for cell expansion are described by Hsiao and Bradford (1983) as

1. Cell-wall loosening or relaxation, i.e.,

ψoutside > ψinside;

2. Water flow into the cell, diluting its solutes;

3. Water influx causing the cell wall to expand

until ψinside and ψoutside are nearly equal.

These processes occur simultaneously and continuously in the plant root system.

Rapid elongation of primary roots, combined

with well-developed secondary roots, allows the

plants to exploit moisture and nutrients from

greater soil volume (Harris 1977). Main axis root

elongation rates of forage legumes were significantly correlated with seed weight (Brar et al.

1990a). Cultivars within the species had significant impact on root elongation rates. Similarly,

root growth also varied greatly among plant species (Stone and Taylor 1983, McMichael et al.

1985, Brar and Palazzo 1995). The rate of root

elongation may range from 0.5 to 3 cm day–1

(May et al. 1965) or more (Taylor and Ratliff 1969).

Elongation rates of main root axes, primary laterals, and secondary laterals of small grain cereals

grown in a relatively favorable laboratory environment were 20, 0.5, and 0.1 cm/day, respectively (Lungley 1973). The root extension rates decreased with increased plant age and were

negligible in perennial crops (Hillel and Talpaz

1976).

ROOT–SHOOT RELATIONSHIPS

Root and shoots are strongly interdependent.

The roots receive photosynthates and growth

hormones from shoots and in return furnish water and nutrients to shoots (Taylor and Arkin

1981). After seed germination, plants generally

contribute the major portion of the metabolites

towards root expansion. For instance, the radicle

grows faster than the plumule of wheat after germination; however, the trend is reversed at later

stages of growth. Root:shoot ratios differ depending on environmental conditions around the

plant.

Relationships of root and shoot growth for 22

winter wheat crops grown in the United Kingdom are illustrated in Fig. 3. Dry matter is equally

partitioned between roots and shoots in the early

stages of wheat growth, but at anthesis the rootper-plant ratio has fallen to 0.1 (Barraclough et al.

1991). The total shoot dry matter of 18 t ha–1 was

accompanied by a root dry matter of 1.5 t ha–1.

Winter crops with longer growing seasons produced more shoot dry matter compared with

spring crops, and similar trends were observed

for the root system. A well-developed root system was observed for winter wheat compared

with arable crops (Table 1).

Soil physical factors such as temperature and

soil water potential affected the root:shoot ratio

of sorghum seedlings (Brar et al. 1992). The ratio

significantly increased with increases in soil temperature from 15.9 to 25.2°C and declined at temperatures of 30.2 and 35.8°C (Table 2). Furthermore, the ratio was greater with –0.1 than –0.03
4

Figure 3. The growth of roots and shoots of high-input

UK winter wheat crops in relation to the number of

days from sowing. A = anthesis (after Barraclough et

al. 1991).

Table 1. Maximum root length density, MRLD,

(cm cm–3) in the topsoil for various field crops.

Crop MRLD Reference

Winter wheat 12.2 Barraclough et al. (1989)

Winter rape 9.7 Barraclough (1989)

Spring barley 4.2 Welbank et al. (1974)

Maize (US) 4.0 Mengel and Barber (1974)

Spring wheat 3.3 Welbank et al. (1974)

Sugar beet 2.6 Brown and Biscoe (1985)

Pea 2.5 Greenwood et al. (1982)

Potato (NL) 1.9 Vos and Groenwold (1986)

Soybeans (US) 1.0 Barber (1978)

Broad beans 0.8 Greenwood et al. (1982)

ROOT FUNCTIONS

The major functions of plant roots are water

transport, nutrient uptake, plant anchoring, and

plant metabolite storage. Roots absorb water and

nutrients simultaneously from deep and shallow

soil horizons and from moist and partially dry

soil (Rendig and Taylor 1989). Plant anchoring is

important for the shoot to emerge through crusted soils and for roots to force a path through a soil

matrix to keep the plant from falling. Storage capacity of metabolites is greater for fleshy roots

compared with grasses. Roots are believed to be

the primary source for growth regulators such as

cytokinin, gibberellin, abscisic acid, and ethylene.

Water uptake

Soil water uptake is usually assumed to be

proportional to the product of the rooting activity, hydraulic conductivity, and potential energy

terms for any specific soil volume element of uni2000

1500

1000

500

0

0

50

100

150

200 0 100 200 300 400

Time (days)

A

Shoot Dry Weight (g/m2) Root Dry Weight (g/m2)

0.2

0.4

Table 2. Root:shoot ratio of sorghum seedlings as affected by

soil temperature and soil water

matric potential. Data are means

of three observations (after Brar et

al. 1992).

Soil Root:shoot ratio

temperature Soil water potential (MPa)

(°C) –0.03 –0.10

15.9 0.34b* 0.43ab

20.5 0.39b 0.60a

25.2 0.75a 0.66a

30.2 0.39b 0.44ab

35.8 0.36b 0.06

LSD (P ≤ 0.05) 0.035 0.42

* Within columns, means not followed

by common letter differ (P ≤ 0.05) according to Fisher’s Least Significant Difference Test.

MPa soil water potential at 15.9, 20.5, and 30.2°C.

Significant correlations (r2 = 0.96) were obtained

for shoot dry matter with root dry matter of tall

and fine fescues (Brar and Palazzo 1995). Furthermore, significantly greater root–shoot growth of

tall fescue was observed in silt loam compared

with sandy soil. Cool-season grasses (C3 photosynthesis) had lower root:shoot ratios compared

with warm-season grasses (C4 photosynthesis).

During the last seven years, plant water relation concepts have changed, and roots rather

than shoots are considered to regulate plant

growth and development in drying soil. Kramer

(1988) reported that 50 years of progress in our

understanding of plant water relations were lost

by shifting emphasis away from the soil to the

shoots of the plant. Recent evidence suggests that

root signals influence stomatal behavior, leaf initiation, leaf expansion, and other development

processes (Davies and Zhang 1991). Current

thinking in this area is summarized in Figure 4.
5

Leaf Water

Status

Leaf

Initiation

Leaf

Expansion

Leaf

Conductance

Soil Surface

Root Growth &

Physiological

Activity

ABA

in

Soil

Root Turgor, Cell

Volume or Pressure

on Membranes Nutrient

Status of

Rhizosphere

Soil

Strength

Soil Water

Availability

ABA, Ck, SIDAnions,

Cations, pH, Amino Acids

and Other Signals

Signalling from

Deep Roots

in Moist Soil

Signalling

From Roots

in Shallow

Drying Soil

Figure 4. Factors influencing the generation of chemical information

(dotted lines), soil effects (circles), plant physiological and developmental processes (rectangles) in roots in drying soils (after Davies and

Zhang 1991).

form properties (Taylor 1983). A shallow root system with a high root density in the surface soil

can result in rapid depletion of available water

and nutrients, while a deep root system can make

available a large volume of soil for root extraction

of water and nutrients (Chaudhery and Sandhu

1983). A deeper root system is more efficient in

water uptake compared with a shallow root system (Taylor and Klepper 1973).

In recent years, our understanding of the soil

water flow through the soil–plant–air continuum

has been strengthened by analogy with electrical

engineering concepts such as the flow of electricity through a network of resistances (Fig. 5). Axial

root resistance to water transport would increase

in a deep root system (Meyer and Ritchie 1980);

however, it is an insignificant component compared with radial resistance (Taylor and Klepper

1971). Feddes (1981) summarized plant resistances of various crops (Table 3). These data are empirical and can be applied to conditions from which

they were derived. It is evident from the pub-
6

Figure 5. A root system in layered soil viewed as a

resistance network. Water held in capacitors moves

through variable resistance. Diodes permit flow into the

roots but not from roots into the soil (after Hillel 1977).

lished literature that measurement of resistances

encountered in the soil–root–plant system is still

difficult or even impossible for many crops.

The pathway of water movement is from bulk

soil to the rhizosphere, across the rhizosphere

and the soil/root interface, across the cortex and

the endodermis, and then into the lumen of the

xylem. Water then moves along the xylem to the

substomatal cavities where it undergoes a phase

Source: Rain or

 Irrigation

Sink: Atmosphere V(t)

Leaves

Stem

Soil Surface

Conducting Roots

Absorbing

Roots

"Crown"

s1

s2

si

sn

Drainage

Bottom of Root Zone

r1

r2

ri

Darcian Flow

Figure 6. Water flow in the soil–root continuum. The

“valve” symbols represent water flow rates between

rectangular storage compartments or to external “sink”

in the atmosphere or groundwater (after Huck and Hillel

1983).

Water Vapor

Evaporation Transpiration

Plant Water

Rain/Irrigation

Root Uptake

Soil Water

Drainage Rate

H2O

 Root Length

 Resistance

 Potential Gradient

 Matric Potential

 Water Stress

LAI

Table 3. Plant resistance, Rp, data of various crops extracted from literature (after Feddes 1981).

Type of Root depth Rp

Crop experiment (cm) (103 cm) Source

Birds foot trefoil Lab 60 11.2 Gardner and Ehlig (1962)

Grass Field 26 10.4 Rijtema (1965)

Potatoes Field 40 10.3 Endrodi and Rijtema (1969)

Red cabbage Field 42–82 31.4–36.3 Feddes (1971)

Wheat Lab 45 9–21 Yang and de Jong (1971)

Wheat Lab 18 31–58 Yang and de Jong (1972)

Italian ryegrass Lab 22 5–17.5 Hansen (1974)

Maize Greenhouse — 13 Reicosky and Ritchie (1976)

Grain sorghum Field 100 11 Reicosky and Ritchie (1976)

Douglas fir Field 80 25 Nnyamah (1977)

change to vapor and diffuses through the stomata

and the leaf/air boundary layer. A generalized

overview of macroscopic water flow processes is

illustrated in Figure 6. Numerous water uptake

models are published in the literature and can be

classified as “macroscopic” or “microscopic.”

Macroscopic models

Macroscopic models assume the vertical tran-
H(z,t) = soil matric potential

S(z,t) = soil osmotic potential

RDF(z) = proportion of total active roots in

depth increments

Kw = soil hydraulic conductivity at

depth z

∆x = distance between roots at position

where H(z,t) and S(z,t) are measured

∆z = soil depth increment.

The major drawback of these models is that they

utilize a gross spatial average of matric and osmotic potentials and neglect the decrease in water

potential and change in the salt concentration at

the soil/root interface as well as the rhizosphere.

Microscopic models

Microscopic models consider the diffusion of

water towards a single root (Gardner 1960). The

models assume that liquid flow resistance in soil

is dependent on root geometry, rooting length,

and the hydraulic conductivity of the soil. Under

steady-state conditions, the rate of water uptake

per unit root length, qr, from the soil at a uniform

equilibrium water content can be estimated as

qr = –2ΠKw[Hp – Hs]/ln (rsoil/rroot) (6)

where Kw = soil hydraulic conductivity

Hp = matric head in root epidermis or total leaf water potential

Hs = matric head in soil surrounding root

rsoil = radius of soil cylinder surrounding

root

rroot = root radius.

Root water uptake of a specific soil volume can

be estimated by multiplying the qr with root

length density, Lv. The transpiration rate, T, is assumed to be equal to uptake rate and can be calculated as

T qL

i

= ∑ ri vi

1

. (7)

Taylor and Klepper (1975) proposed the following equation

θfinal = θinitial – (qr) (Lv) (Hp – Hs) (8)

where θfinal and θinitial are the volumetric water

contents at the end and beginning of a measuring

period.

Water uptake rates of species differ even when

7

sient flow of water in a stable and uniform zone

of soil. The root system is considered as a diffuse

sink for water that permeates each depth of soil

layer uniformly, though not necessarily at the

same root length density through the root zone.

Macroscopic models are derived from Darcy’s

law, expressed in hydraulic head terms

Jw = –KwdH/dx (1)

where Jw = flux of water (L3 L–2 t–1)

Kw = soil hydraulic conductivity (L t–1)

dH = hydraulic head difference (L)

dx = distance along the flow path (L).

Incorporating the soil water diffusivity term,

Dw = Kw(dΨ/dθ), in eq 1

Jw = –Dw ∂θ/∂x. (2)

The vertical flow through a thin layer of soil

where water content changes with time and distance can be solved with Richards (1931) continuity equation

∂θ/∂t = ∂/∂z Kw∂H/∂z + ∂Kw/∂z

 = ∂/∂z D∂θ/∂z + ∂Kw/∂z. (3)

Equation 3 is further modified for water extraction by the plant roots

∂θ/∂t = ∂θ/∂z (Kw∂H/∂z) + A(z,t) (4)

where A(z,t) is the root water extraction in reference to soil depth, z, and time, t.

Several workers assumed that A(z,t) is a function of root activity. None, however, has assumed

that root activity is a function of water potential

difference between plant and soil, distance between the uniformly spaced roots, and some

measure of conductivity in the root–soil system.

The root water uptake model of Nimah and

Hanks (1973) can be written as

A(z,t) = Hroots + [RRES(z)] – H(z,t)

 –S(z,t)RDF(z)Kw/∆x∆z (5)

where Hroots = effective water potential in root at

z = 0

RRES(z) = root resistance equal to 1 + Rc

Rc = coefficient to account for longitudinal resistance in xylem
8

Table 4. Specific water uptake rates for some tropical and

temperate species (after Rendig and Taylor 1989).

Water

uptake rate

Species (m3 m–1 s–1) Source

Cotton 5 × 10–12 to 5 × 10–11 Bar-Yosef and Lambert (1981)

<1 × 10–14 to 8 × 10–12 Taylor and Klepper (1975)

Field pea 1 × 10–12 to 2 × 10–11 Hamblin (1985)

Lupin 3 × 10–12 to 8 × 10–12 Hamblin (1985)

Corn 3 × 10–12 to 2.4 × 10–10 Allmaras et al. (1975)

1 × 10–12 to 2.4 × 10–11 Taylor and Klepper (1973)

Oats 8 × 10–12 to 1 × 10–10 Ehlers et al. (1980)

Soybean 2 × 10–11 to 3 × 10–10 Allmaras et al. (1975)

2 × 10–12 to 3 × 10–10 Willatt and Olsson (1982)

2.8 × 10–11 to 2.2 × 10–10 Willat and Taylor (1978)

Wheat 1 × 10–12 to 2 × 10–12 Greacen and Hignett (1976)

Spring 4 × 10–13 to 1 × 10–12 Hamblin (1985)

Winter 2 × 10–13 to 2 × 10–12 Gregory et al. (1978)

Temperate about 1 × 10–12 Welbank et al. (1974)

grasses

Cortex

Intact Removed

Nutrient Solution

Sand

10 20 30 40 50

Plant Age (DAP)

50

40

30

20

10

0

Hydraulic Conductivity (cm2 min–1 Pa–1 1011) Figure 7. Effect of plant age on the hydraulic conductivity of hydroponically grown and sand-grown cotton roots (after Brar et al. 1990b).

they are grown under identical conditions (Table

4). For example, lupin and wheat were grown at

the same location and time, yet their maximum

uptake rates were 2 × 10–9 and 1 × 10–12 m3 m–1 s–1,

respectively. Root uptake models often assume that

hydraulic conductivity of the root system is a constant at all plant growth stages. Conversely, Brar et

al. (1990b) reported that hydraulic conductivity of

young cotton roots changed with plant age (Fig. 7).

Hydraulic conductivity decreased 45% in nutrient

solution-grown roots and 57% in sand-grown roots

between 12 days after planting (DAP) to the mean

of the 24, 36, and 48 DAP. Hydraulic conductivity

of sand-grown roots was 4 to 10 times lower than

that for roots grown hydroponically, whether

conductivity was compared at equal DAP or at

equal root length (Table 5).

Nutrient uptake

Nutrient uptake is related to diversity in nutrient mobility in soil as well as the surface characteristics of the roots. Root length, root radius, and

surface area are the important characteristics of

the roots that determine the rate of nutrient up-
9

Table 5. Total length of cotton

as affected by plant age and

root medium; hydroponic or

sand (after Brar et al. 1990b).

Root length

Plant Hydroponic Sand

age* (m) (m)

12 3.3† (1.0)** 2.6a (0.7)

24 13.4b (2.4) 14.4b (2.9)

36 28.8c (1.5) 17.4b (4.9)

48 93.9d (6.2) 17.1b (2.6)

* Days after planting.

† Means with the same letter are

not significantly different (P <

0.05).

** Standard error of mean.

the models to describe radial flux to the root by

mass–flow and diffusion as affected by uptake by

the root is

 

∂

∂

∂

∂

∂

∂

c

t rr

rD c

r

rvc

b

i c i ooi = + 



 





1 (12)

where ci = ion concentration in solution

r = radial distance from the root axis

r0 = root radius

Dc = apparent diffusion coefficient

v0 = flow velocity of soil solution to root

b = buffer capacity = (∂ci/∂t)/(∂ci/∂r)

t = uptake time.

Boundary conditions are required to find the

solution to eq 12. The initial boundary condition

of the equation is:

t = 0, r > r0, ci = cii (13)

where cii = initial nutrient concentration in the

soil solution.

The first boundary condition is

 

D b c

t

v c

J cc

K cc

rr t c i

o i

i min

m i min

at ∂

∂

+ = ( )

+ ( ) = > max –

– , 0 0

(14)

where cmin = ci when Jn = net flux is zero, Km =

Michaelis–Menten constant.

The second boundary condition, added by

Cushman to account for competition between adjacent roots, is

 

D b c

t

vc r r t c i

oi i

∂

∂

+= = > 0 0 , , (15)

where ri = mean half-distance between root axes.

In the absence of competition, ci = cii at r = ri and t

> 0.

Assumptions made in the Claassen-Barber

model are

1. Soil is homogeneous and isotropic;

2. Root zone has constant soil water content

that is maintained at field capacity;

3. Plant or root age has no impact on nutrient

flux;

4. Nutrient concentration has no impact on

convective component of flux;

5. Nutrients move to the root by diffusion and

mass–flow processes; roots are considered

as smooth cylinders that absorb nutrients

from the soil solution as per Michaelis–

Menten kinetics;

6. Apparent diffusion coefficient and buffer

take (Nye and Tinker 1969, Barber and Silberbush

1984). The relationship between solution concentration (ci ) of a given nutrient and its uptake by

plant roots intact with the solution was proposed

by Bouldin (1961) and modified by Nye (1966)

J = αci (9)

where J = rate of nutrient uptake (flux) expressed

in terms of quantity per unit root area per unit

time, and α = the proportionality term describing

the root absorbing power.

If the term “uptake per unit root area” in the

above equation is replaced with “root length,”

J = 2Παrci (10)

where r = root radius. Nye and Tinker (1969) combined the terms α and r and provided a new term

called root demand coefficient. For the evaluation

of total uptake, they incorporated the total root

length (L) in eq 10

J = 2ΠαrciL. (11)

The soil and plant factors affecting the root demand coefficient are

1. Nutrient demand for plant growth;

2. Operation of metabolically driven uptake

and transport mechanisms;

3. Functioning of physical and chemical processes in the root environment.

Mathematical models have been developed for

nutrient uptake by plant roots (Nye and Marriott

1969, Nye et al. 1975, Claassen and Barber 1976,

Barber and Cushman 1981, Tillotson and Wagenet 1982). These models help in understanding the

complex soil–rhizosphere–root–plant system and

in determining the significance of the parameters

involved. The basic transport equation used in
capacity are independent of the nutrient

concentration.

Parameters required for the Claassen-Barber

model along with one additional parameter required for the Cushman model are

1. Root morphology

a) Initial root length

b) Rate of root growth

c) Average root radius

2. Root uptake kinetics

a) Maximum influx Jmax of the nutrient

b) External nutrient concentration Km to obtain one-half Jmax

c) External nutrient concentration cmin

where net nutrient uptake is nil

3. Soil nutrient supply

a) Rate of water influx

b) Concentration of the nutrient in the soil

solution at the start of the plant growth

period

c) Apparent diffusion coefficient of the nutrient

d) Differential soil buffer capacity b for the

nutrient

e) Mean half-distance between root axes

The Cushman–Barber model, written in Pascal

and compiled for IBM PC, is available for educational purposes (Oates and Barber 1987).

ROOT GROWTH UNDER PHYSICAL

EDAPHIC CONSTRAINTS

Soil water

The most crucial edaphic factor in a plant’s life

is water, which links it to the soil via roots and

serves as a vehicle for nutrient transport. Water

also controls the exchange of gases and moderates soil temperature changes (Clothier and Scotter 1985). Soil absorbs, stores, and releases water

depending upon volume and size distribution of

pores as determined by texture, structure, organic

matter content, and the depth of the soil. Plant

available water is held in the soil between –0.01 or

–0.03 MPa potential (in coarse-textured and finetextured soils, respectively), known as the upper

limit or field capacity, and –1.5 MPa potential,

called the lower limit or permanent wilting point.

Water availability may not be limited to –1.5 MPa

potentials; plant roots can extract water at lower

potentials depending upon the plant type and the

aerial environment (Musick et al. 1976).

Root growth rates are controlled by the presence of continuing supplies of water to maintain

hydrostatic pressure in the elongating cells of the

root, metabolites for cell wall construction, and

growth hormone to loosen the bonds within the

cell wall constituents (Lockhart 1965). Water

flows radially into the elongating root cells only

when the cell’s total water potential is lower than

the combined osmotic and matric potentials of

the soil (Rendig and Taylor 1989). Furthermore,

lowered soil water content can shrink root diameter (Cole and Alston 1974), which reduces root/

soil contact, increases root senescence, lowers soil

hydraulic conductivity, reduces the water potential of the soil surrounding a specific root, and

decreases root hairs, thereby affecting the water

and nutrient uptake.

Water absorption is influenced by the geometric distribution of viable roots in the soil profile

and the availability of water at the root surfaces

(Smucker and Aiken 1992). Absorption of soil

water is not always linear with greater root

growth. Incomplete root contact with the soil

and/or declining soil water potentials reduce the

water absorption efficiencies, resulting in the production of excessive plant root surfaces. Weak

root contact with the soil matrix results as roots

are clustered within the macropores of soils and

smaller roots grow along soil aggregates or in

pores larger than the diameter of the roots (Lafolie et al. 1991, van Noordwijk et al. 1992). Greater

root/soil contact occurs as roots are exposed to a

compacted soil environment (Kooistra et al.

1992).

Lascano and van Bavel (1984) calculated the

partition of the water uptake rate over the root

zone as

Rj = (Ψsj – Ψe,i )RDj

/PHR (16)

where Rj = rate of water extraction from the root

zone or compartment j

Ψsj = soil water potential in that compartment

Ψe,i = effective leaf water potential

RDj = relative root density in the soil compartment

PHR = specific plant resistance.

The summation of Rj from each soil compartment

equals the total water uptake, provided there is

no change in water content of the plant. In nature,

this is not true because the plant water content

changes diurnally with radiation load and changing soil water content. Lascano and van Bavel

also assumed that the plant hydraulic resistances

are constant; conversely, the significance of plant

10
11

resistance in water transport was reported by Van

den Honert (1948). Under steady-state conditions, the pathway of water movement through

the soil–root–stem–leaves could be expressed as

resistances in series (Fig. 5) using the equation

T = Ψs – Ψr/Rs = Ψr – Ψl

/Rp (17)

where T = transpiration rate, Ψs, Ψr, and Ψl are the

water potentials in the soil matrix, at the root surface, and in the leaves, respectively; and Rs and

Rp are resistances of the soil and plant pathways.

Rp is considered to be dominant over Rs and decreases with increased transpiration rate (Feddes

1981).

Steady-state conditions rarely exist in the field.

Furthermore, the plant root system is dynamic

(root senescence occurs and new roots emerge),

root geometry is time-dependent, and water permeability varies with position along the root and

with time. Instead of considering water flow to

single roots, a more suitable approach might be

the macroscopic one, in which a sink term representing water extraction by a homogeneous and

isotropic element of the root system (volume of

water per volume of soil per unit of time) is added to the conservation mass equation (eq 4).

Variation in root diameter has long been observed, which further complicates the mathematical analysis of root function. Models of the transport of ions, water, oxygen, and other materials

from the soil to the root interior assume the root

has constant diameter, and transfer coefficients

remain constant with time.

The simulation of water transport through a

root system is complicated in cold regions because of the presence of permafrost and seasonally frozen soils. Furthermore, the soil freezing

front and ice formed in the frozen ground enhance runoff and reduce groundwater recharge.

A few workers (Taylor and Luthin 1978, Guymon

et al. 1980, Hromadka et al. 1981) studied the

complex processes of characterizing simultaneous heat and soil water transport in a freezing

soil without considering vegetation. The physics

of a frozen heterogeneous soil profile include the

terms of the soil energy balance and soil water

balance. The one-dimensional energy conservation equation for potentially freezing soils can be

written as

∂ ∂ θ∂ ∂ ρ ∂ ∂ ∂ ∂ / z T z c vT z S C T t h ll l [ ] ( ) // / + ( ) + = h s

(18)

The mass conservation equation can be written as

 

∂ ∂ θ ∂ ∂ ∂θ ρ ∂

∂θ ∂ ρ ∂θ ρ ∂

/ z K h z z Sm

t ii t

( )( / ) /

/ /

[ ] m v + + +

= +

1

1

l

(19)

where ρl = density of liquid water

cl = specific heat capacity of water

vl = downward liquid water flux

Cs = volumetric heat capacity of soil

ρi = density of ice

Lf = latent heat of fusion

θi = volumetric ice content

ρv = vapor density in soil pore space

θv = downward water vapor flux through

soil

Sh = heat sink/source

Sm = water sink/source

θ = volumetric soil water content

t = time

T = temperature

z = soil depth

 

h = thermal conductivity of soil.

Several other workers used eq 18 and 19 and

developed the following types of water transport

models (Kung and Steenhuis 1986).

1. Models based on an analogy between the

mechanism of water transport in unsaturated

soil and in frozen soil (Harlan 1971).

2. Models based on the theory that the pressure

jump is due to the curvature in the liquid

water/ice/air interfaces (Bresler and Miller

1975; Miller 1973, 1977, 1978; Miller et al.

1975).

3. Models based on the theory of irreversible

thermodynamics (Kay and Groenevelt 1974,

Groenevelt and Kay 1974, O’Neill and Miller

1982).

4. Models simulating temperature distribution

in a partially frozen soil (Miller et al. 1984).

These models were developed without considering the plant root system. During thawing season, soils without vegetation in cold regions are

susceptible to degradation processes of soil erosion, nutrient losses, and organic matter depletion.

Soil air

Roots and soil organisms capture energy from

the oxidation of organic substances in a series of

enzyme-catalyzed reactions. Plants need molecular oxygen to respire and convert carbohydrates

to carbon dioxide and water. This is an exother- − ρ ∂θ ∂ ∂ρ ∂ ∂θ ∂ iL tL t vz f ( ) i vv / / /. + + ( )
mic reaction and releases respiratory energy that

is utilized for many plant processes. The disappearance of molecular oxygen triggers a sequence of changes in the physico-chemical properties of the soil (Gambrell and Patrick 1978,

Ponnamperuma 1984). Such changes include accumulations of reduced metal ions, organic acids,

and volatiles that are potentially harmful to plant

roots (Drew and Lynch 1980). Such accumulation

to phytotoxic levels requires time. The absence of

oxygen alone is sufficient to profoundly alter the

plant metabolism (Drew 1983).

In cold climates, cool autumn or early spring

temperatures result in a slow rate of depletion of

dissolved soil oxygen by respiration of roots and

soil organisms (Drew 1992). The root apical meristem, the zone of fastest oxygen consumption, is

particularly sensitive to oxygen deficiency and

the sequence of metabolic events leading to cell

death (Roberts et al. 1984a,b). In summer, crops of

cold climates consumed oxygen at the rate of 1.7

L m–3 day–1; furthermore, oxygen consumption

rates reduce to 1.5 L m–3 day–1 in winter, and to

about half in the absence of plants (Currie 1970).

Suboptimal oxygen concentrations in the soil

air occur because of interactions among soil properties such as porosity, water content, temperature, surface water movement, and continuity of

air-filled pores with biotic activity (Drew 1983,

Grable 1966). Jones et al. (1991) developed a root

growth simulation model and considered the effect of soil water content, bulk density, texture,

and plant genotype on soil air. Increased soil water content or bulk density reduce the oxygen diffusion rate and affect air-filled porosity. The

diffusion coefficient of oxygen in air is approximately 10,000 times greater (0.23 cm2 s–1) than

that in water (0.26 × 10–4 cm2 s–1) at 26°C (Rendig

and Taylor 1989).

A mathematical model for the relationship of

root respiration, soil oxygen supply, and internal

oxygen supply was first developed by Luxmoore

et al. (1970). Measurements used to predict the effect of a reduced soil oxygen supply on root

growth and function are

1. Oxygen diffusion rate;

2. Oxygen concentration in the soil;

3. Air-filled porosity percentage;

4. Redox potential;

5. Air permeability.

Soil air that is low in oxygen can contain high

concentrations of ethylene, which is a growth regulator rather than a toxin. Elevated concentration

of ethylene inhibits root elongation, cambial

activity, and stellar differentiation in roots (Rendig and Taylor 1989). An ethylene concentration

of ≤ 0.4 ppm can inhibit nodule formation on legume roots. Furthermore, ethylene has some advantageous impact on roots and stimulates lateral branching as well as root hair initiation

(Rendig and Taylor 1989).

Soil temperature

Temperature influences plant processes at the

cellular level, such as osmotic potential, hydration of ions, stomatal activity and transpiration,

Gibbs free energy available for work, membrane

permeability, solute solubilities, diffusion, and

enzymatic activities (Voorhees et al. 1981). The final shape of the root system is determined from

root branching and elongation of individual root

axes. Several reviews indicate that most plant

species exhibit an optimum temperature for maximum root elongation rates (Nielson and

Humphries 1966, Cooper 1973). Furthermore, the

species within a genus (Heinrichs and Nielsen

1966) and cultivars within a species (Johnson and

Hartman 1919) varied in root elongation and

branching rates in response to temperature. For

instance, Brar et al. (1990a) reported high variability among legume cultivars in main axis root

length at different specific temperatures (Fig. 8).

Low temperature reduces water absorption by

increasing the water viscosity and decreasing cell

membrane permeability. Furthermore, low temperatures also decrease metabolic activity and

decrease the root growth (dry matter production). The addition of fertilizer, particularly phosphorus, may compensate to some extent for the

reduced growth in cold soils (Nielsen and

Humphries 1966).

Snow cover has a large influence on soil temperature. Snow cover decreases heat conduction

to the soil surface (Legget and Crawford 1952)

and serves as a sink for heat fluxes at both upper

and lower surfaces of the cover (Granger et al.

1977). Relationships between air temperature and

snow depth can be used to predict the minimum

soil temperatures (Fig. 9). The pattern of seasonal

warming of air temperature is predominantly

temporal at the ground surface; however, its effect is temporal as well as spatial below ground

and causes temperature limitations on root

growth (Fig. 10). During the growing season, as

the warming front moves downward, temperatures of the deeper soil layers become suitable for

root growth. The depth of soil thermally suitable

for appreciable root growth is a function of both

12
13

A

B

C

G

H

I

D

E

F

J

K

L

200

100

0

200

100

0 10 20 30 0 10 20 30

Temperature ( °C )

Main Axis Root Length (mm)

Temple, Texas

18

20

22

24

26

28

80 120 160 200 240

Day of Year

30

20

10

0

1

2

Temperature (°C) Depth (m)

Soil Temperature

Isotherms (°C)

Figure 10. Seasonal warming of air temperatures (5-

year average of daily means) determines when temperatures are favorable for plant growth. Soil temperatures

favorable for root growth vary with time and depth (modeled thermal regime) (after Kasper and Bland 1992).

0

–10 –20 –30

Minimum Soil Temperature at 3cm Depth (°C)

Minimum Air

Temperature (°C)

–10 –20 –30

–40

–50

60

40

20

Snow Cover Depth (cm)

Figure 9. Minimum soil temperature at 3-cm

depth as affected by minimum air temperature and depth of snow cover (after Shul’gin

1967).

soil temperature regimes and root temperature

response (Kaspar and Bland 1992).

Soil temperature usually limits root system expansion and proliferation. Root expansion is a

function of temperature-dependent processes

such as growth and development. Growth processes include cell elongation, root length increase, and root diameter. Developmental processes generally control growth duration of cells

(Burstrom 1956, Beauchamp and Lathwell 1966),

A) Paraponto gama medic

B) Mt. Baker subterranean clover

C) Chief crimson clover

D) Kenstar red clover

E) Vanguard vetch

F) Woodford vetch

G) Austrian winter pea

H) Maxidor alfalfa

I) Amclo arrowleaf clover

J) Cahaba white vetch

K) Hairy vetch

L) Eski sainfoin

Figure 8. Main axis root length at ten days after planting as a function of temperature (after Brar et al. 1990a).
organs, and whole plants (Beauchamp and Lathwell 1967). The number of lateral roots, distance

from a root tip to first visible lateral root, lateral

root density, root hairs, and root plagiotropism

(growth at angles from the vertical) are temperature-sensitive (Atkin et al. 1973, Engels et al. 1992,

Mozafar and Oertli 1992).

Root dry weight is the most commonly measured parameter that follows a typical growth response curve (Cooper 1973). Root length, surface

area, and extension of roots into deeper soil layers

are important parameters that influence water and

nutrient uptake. Present technology has the capability to measure these parameters. Root diameter

is another important parameter influenced by

temperature; it substantially reduces water and

nutrient uptake (Barber et al. 1989) as well as the

amount of carbohydrates required for root growth

(Fitter 1991).

Most plant growth models related to water and

nutrient transport require soil temperature with

depth as input for the model. Temperature simulation models published in the literature are

1. Mechanistic models that need detailed initial

and boundary inputs (Richtmeyer and Morton 1967, Wierenga and DeWit 1970, Hanks et

al. 1971, Rosema 1975, Van Bavel and Hillel

1976, Grant et al. 1990);

2. Functional models that require weather station information and soil information at one

depth (Neild 1971, Hasfurther and Burman

1974, Cruse et al. 1980, Gupta et al. 1984, Parton 1984, Brar and Unger 1994);

3. Statistical models of a regression type that

were developed at a particular site from a

limited data set (Meikle and Treadway 1979,

Ghuman and Lal 1983, Langholz 1989, Dwyer

et al. 1990).

The timing of snowmelt and above-freezing

temperatures are the major factors controlling the

onset of plant growth. Root elongation begins as

soon as the soil is thawed and elongation is possible, depending on the depth of the individual root

tips.

Physical impedance

Physical impedance, sometimes called mechanical impedance or excessive soil strength, can severely affect normal root growth patterns. Such

impedances result from increased soil bulk density, increased cohesion between soil particles, increased friction between soil particles, reduction

in soil water content, frost-heave action of soil, and

presence of permafrost within the root zone. The

157

69

16

Minimum Pore Diameter (μm)

––––––––––––––––––––––––

100

80

60

40

20

0 20 40 60 80 100

Applied Pressure (kPa)

Relative Root Elongation (%)

Figure 11. Effects of pressure applied to the outside surface of a flexible container on relative root elongation

and shape of barley roots (after Russell and Goss 1974).

adverse physical impedances can severely affect

the plant’s ability to emerge from crusted soils, to

extend its root system into unexplored soil volumes, to transport photosynthates from shoots to

roots, and to transport water from roots to shoots.

These impedances restrict below-ground expansion

of root crops, e.g., turnip, sugar beet, or radish.

Under an excessive soil strength environment,

roots enter the soil volume where pore sizes are

larger than the root tip. Conversely, if the pore

sizes are too small for the entry of the main root

but not for laterals, then laterals proliferate and

produce a highly branched root system (Russell

and Goss 1974). Furthermore, if the pore sizes are

too small and prevent entry of laterals, a stunted

root system can result. Maximum pressures that

roots can exert on the surrounding soil matrix

range from 900 to 1500 kPa. Different species exert

different maximum root growth pressures (Taylor

1983). The impeded roots are thicker in diameter

and distorted in shape (Fig. 11).

Physical impedances result from

1. Natural consolidation during soil forming

processes;

2. Trampling by animals, including humans;

3. Natural shrinkage of soils upon drying;

4. Soil response to pressures and deformations

imposed by vehicle wheels;

14
15

5. Actions of overburden and water droplets on

water-weakened aggregates during rainfall;

6. Frost heave actions.

Physical impedance can be measured with penetrometers, shear vanes, shear rings, triaxial shear

cells, and unconfined compression cells. As far as

we know, no mathematical model is available to

predict soil yielding under load using fundamental

parameters.

Spatial variability

Considerable research has been reported in

the literature during the past decade on the spatial variability of soil physical properties. However, in cold environments a computer literature

search has revealed limited published studies on

the spatial variability of solute and temperature,

and none with respect to root water uptake.

Therefore, this section is limited to reporting solute and temperature-related variability studies

from cold environments.

Spatial variability has a significant effect on

field-scale solute movement through the unsaturated zones. The effect of spatial variability in

soil hydraulic properties has been investigated

using either parametric models (Dagan and Bresler 1979, Bresler and Dagan 1981, AmoozegarFard et al. 1982, Simmons 1982, Destouni and

Cvetkovic 1989) or transfer function models (Jury

et al. 1986, Butters and Jury 1989). Few workers

studied the temperature spatial variability in relation to soil water content (Vauclin et al. 1982,

Davidoff et al. 1986).

OVERVIEW OF ROOT GROWTH MODELS

Several root growth models were developed

during the past decade, but none is geared to the

problems associated with root growth in cold regions. The models reported in the literature are

classified as simple models, carbon-partition

models, growing degree day-based models, soil

parameter-based models, and arctic plant growth

models.

Simple models

Root distribution with depth

The model of Gerwitz and Page (1974) is empirical in nature and simulates root density as a

function of soil depth. The model makes no

attempts to define the relative age classes of the individual root axes in each layer or the proportion of

those axes that are first- or second-order laterals.

Root depth with time

Borg and Grimes (1986) developed a model to

simulate actual root depth as a function of time.

For a given crop and location, the model requires

an estimate of the maximum rooting depth to be

achieved and the number of days to reach maturity.

Root depth with temperature

The model is two-dimensional and was developed from data that explain the effect of root zone

temperature on soybean root development (Stone

et al. 1983). The model predicts the extension of the

taproot and ten primary lateral roots for two

groups of soybean cultivars. The simulation emphasizes the importance of soil temperature, but

ignores many other factors responsible for root

elongation.

Carbon partition models

Carbon partition models are complex compared

to simple models. These models partition carbon

between the above- and below-ground biomass.

The partitioning coefficient is assumed to be a constant fraction of the daily photosynthetic production. Following are a few examples of carbon partition models.

Root:shoot ratios

Numerous studies have shown that plants tend

to adjust their root:shoot ratio to maintain an internal carbon-nitrogen balance favorable for growth

(Davidson 1969, Reynolds and Thornley 1982,

Skiles et al. 1982, Johnson 1983, Coughenour et al.

1984, Fishman et al. 1984). Davidson (1969) developed a model based on a hypothesis that a functional balance exists between the size and activity

of the shoot (which supplies carbohydrates) and

the size and activity of the root (which supplies

water and essential nutrients). His model suggested the partitioning of photosynthates.

Partition models were reviewed by Reynolds

and Thornley (1982). They developed a model

based on the assumption that the partition of new

growth is controlled by whole-plant substrate concentrations. Their model partitioned the photosynthates between root and shoot on the basis of

the nitrogen:carbon ratio in the plant’s labile pool.

In spite of good features and the high complexity

of the model, however, it has the following drawbacks:

1. The carbon:nitrogen (C:N) substrate concentration ratio is always considered a fixed value

not influenced by the external environment;
16

2. The model is unstable in terms of balanced

growth;

3. The estimation of model parameters may

pose considerable experimental difficulties.

The drawbacks of the Reynolds and Thornley

model were corrected by Johnson (1983). His

model is based on the partition of new growth

between shoot and root in terms of carbon or

nitrogen substrate levels and the shoot:root ratio.

The model considers the partitioning parameters

and dynamic responses to changing environment

and root- and shoot-specific growth rates.

Grass crop model

Johnson and Thornley (1985) developed a

model that divides root structure into four categories: growing, newly expanded, medium-aged,

and senescencing roots.

SimRoot

SimRoot is a four-dimensional (i.e., space and

time) data structure model developed by Davis

(1993) and used by Nielsen et al. (1994) to simulate root growth based on types of root branches,

branching angles, growth velocities of specific

types of branches, spatial distribution of respiration, carbon exudation, and biomass along root

axes. They emphasized the importance of considering root architecture in relation to nutrient acquisition efficiency and environmental factors,

such as elevated CO2 concentration that affects

below-ground allocation of carbon resources.

Growing degree day-based models

WHTROOT (Porter et al. 1986), a winter wheat

root growth model, was developed based on

cumulative thermal time with descriptions of the

extension and branching of individual age classes

of seminal and crown root axes. The model requires sowing date and average monthly mean

air temperature as input parameters. Model output provides maximum depth of penetration of

each age class of root and root length density or

root weight in any 10-cm layer of soil contributed

by main axes, first order, and second order laterals on any calendar date.

Soil parameter-based models

Root growth model

Jones et al. (1991) developed a root growth

model that simulates daily root growth of crops

grown in a layered soil. Model input parameters

are aluminum toxicity, calcium deficiency, coarse

fragments, qualitative constraints, strength, aeration, and temperature. The authors claim that the

model will work for mineral soils of temperate regions. However, the model does not account for

soil situations such as variable-charge ion exchange capacity, wetness-dependent bulk density,

soil fertility effect on root growth, freeze–thaw impact on root growth, and root water uptake in temperate climates.

ROOTMAP

ROOTMAP is a three-dimensional model to describe the growth and structure of fibrous root systems (Diggle 1988). Root growth is described in

terms of growing time, number of axes, initiation

time of axes, growth rate and branching characteristics of the roots, and characteristics governing

the direction of root growth. A root system can be

regarded as the result of the accumulated effects of

growth and branching responses of individual

root tips, the root tissues behind these root tips, local soil conditions, and overall state of the plant.

The drawback of this model is that it cannot simulate the entire root system of a mature plant.

Bengough et al. (1992) modified the ROOTMAP

model to allow the numerical output of the data on

root intersections with horizontal and vertical

planes.

Arctic plant growth models

Numerous whole-plant growth models for vascular and nonvascular plants have been developed

for arctic ecosystems. Reynolds and Leadley (1992)

reviewed 21 models based on a minimal set of processes and variables that are critical to predict

plant growth under changing climatic conditions.

Most of these models either ignored the roots or

provided limited information on root growth simulation. Reynolds and Leadley found greater variability in whole-plant growth simulations. They

classified these models into four general categories

based on degree of mechanism and comprehensiveness: 1) budget, 2) flux, 3) semimechanistic,

and 4) mechanistic (Fig. 12).

Budget models are empirical in nature and ignore any kind of mechanism or comprehensiveness. These models describe plant growth as the

difference between input and output parameters.

In addition, budget models treat plants as “black

boxes” where plant biomass is lumped into a single box. Semimechanistic models contain low to

medium comprehensiveness. The plant growth is

described with a minimum number of components, and heavy emphasis is placed on phenologi-
Gas-exchange Processes

Growth Processes

Death Processes

Budget

Flux

Semimechanistic

Mechanistic

Low High Degree of Mechanism

Degree of Compression Low High

Figure 12. Types of arctic plant growth models based

on relative degree of comprehensiveness and mechanism. Comprehensiveness refers to the number of processes considered (e.g., gas exchange, growth, and

death), whereas mechanism refers to the level of detail at

which each of these processes is treated (after Reynolds

and Leadley 1992).

cal modeling. Mechanistic models are based on

the high mechanism and comprehensiveness that

provide very detailed information. Flux models

are a special kind of semimechanistic model. The

models contain a high degree of mechanism and

comprehensiveness in terms of gas exchange per

se, but tend to have low overall comprehensiveness

in terms of other plant growth processes.

It is evident from the literature reviewed that

whole plant models combine mechanistic principles with empirical observations to predict mass

as a function of various edaphic factors. Root uptake is usually treated in a highly simplified submodel, the root system acting as a zero-sink for

nutrients, and the uptake is controlled by soil water potential and transpiration rate or by diffusion flux rate.

CONCLUSIONS

Our understanding of the fundamental aspects of growth and proliferation of plant roots

within the temperate soil environment is incomplete. During the last seven or eight years, concepts of plant-water relations in dry soil have

changed and consider the roots rather than the

shoots to regulate plant growth and development. Recent evidence suggests that root signals

17

influence stomatal behavior and regulate leaf initiation, leaf expansion, and other development processes.

LITERATURE CITED

Allmaras, R.R., W.W. Nelson and W.B. Voorhees

(1975) Soybean and corn rooting in southwestern

Minnesota. II. Root distribution and related water

inflow. Soil Science Society of America Proceedings,

39: 771–777.

Amoozegar-Fard, A., D.R. Nielsen and A.W. Warrick (1982) Soil solute concentration distributions

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May 1996

Soil Physical Environment and Root Growth in Northern Climates SERDP 712-94

Gurdarshan S. Brar and Charles M. Reynolds

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road Special Report 96-13

Hanover, New Hampshire 03755-1290

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161.

Understanding the growth and function of plant roots in cold climates is critical, but examination of root systems to elucidate their link to production is expensive and labor-intensive. Limited information is available

on the root growth and functions of plants grown in northern climates. Our objective is to present an overview of the influence of physical edaphic factors on plant root systems with special emphasis on models that

are available for simulating root growth. This report summarizes the impact of the soil physical environment

(soil water, soil temperature, soil air, physical impedance, and spatial variability) on root uptake and growth.

Roots grow because new cells are formed in the meristematic tissue near the root tip, and these newly

formed cells increase in volume, pushing the root tip forward if growth conditions are satisfactory. Rapid

elongation of primary roots, combined with well-developed secondary roots, allows the plants to exploit

moisture and nutrients from a greater soil volume. Root and shoots are strongly interdependent. The roots

receive photosynthates and growth hormones from shoots and in return furnish water and nutrients to the

shoots. Several root growth models have been developed during the past decade; however, none addresses

the problems associated with cold regions. The models reported in the literature can be classified as 1) simple models, 2) carbon partition models, 3) growing degree day-based models, 4) soil parameter-based models, and 5) arctic plant growth models.

Impedance Root system Water uptake

Physical environment Soil temperature

Root growth models Spatial variability

28

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