2. The model is unstable in terms of balanced
fragments, qualitative constraints, strength, aera-
growth;
tion, and temperature. The authors claim that the
model will work for mineral soils of temperate re-
3. The estimation of model parameters may
gions. However, the model does not account for
pose considerable experimental difficulties.
The drawbacks of the Reynolds and Thornley
soil situations such as variable-charge ion ex-
change capacity, wetness-dependent bulk density,
model were corrected by Johnson (1983). His
soil fertility effect on root growth, freezethaw im-
model is based on the partition of new growth
between shoot and root in terms of carbon or
pact on root growth, and root water uptake in tem-
nitrogen substrate levels and the shoot:root ratio.
perate climates.
The model considers the partitioning parameters
and dynamic responses to changing environment
ROOTMAP
ROOTMAP is a three-dimensional model to de-
and root- and shoot-specific growth rates.
scribe the growth and structure of fibrous root sys-
tems (Diggle 1988). Root growth is described in
Grass crop model
terms of growing time, number of axes, initiation
Johnson and Thornley (1985) developed a
time of axes, growth rate and branching charac-
model that divides root structure into four cate-
teristics of the roots, and characteristics governing
gories: growing, newly expanded, medium-aged,
the direction of root growth. A root system can be
and senescencing roots.
regarded as the result of the accumulated effects of
growth and branching responses of individual
SimRoot
root tips, the root tissues behind these root tips, lo-
SimRoot is a four-dimensional (i.e., space and
cal soil conditions, and overall state of the plant.
time) data structure model developed by Davis
The drawback of this model is that it cannot simu-
(1993) and used by Nielsen et al. (1994) to simu-
late the entire root system of a mature plant.
late root growth based on types of root branches,
Bengough et al. (1992) modified the ROOTMAP
branching angles, growth velocities of specific
model to allow the numerical output of the data on
types of branches, spatial distribution of respira-
root intersections with horizontal and vertical
tion, carbon exudation, and biomass along root
planes.
axes. They emphasized the importance of consid-
ering root architecture in relation to nutrient ac-
Arctic plant growth models
quisition efficiency and environmental factors,
Numerous whole-plant growth models for vas-
such as elevated CO2 concentration that affects
cular and nonvascular plants have been developed
below-ground allocation of carbon resources.
for arctic ecosystems. Reynolds and Leadley (1992)
reviewed 21 models based on a minimal set of pro-
Growing degree day-based models
cesses and variables that are critical to predict
WHTROOT (Porter et al. 1986), a winter wheat
plant growth under changing climatic conditions.
root growth model, was developed based on
Most of these models either ignored the roots or
cumulative thermal time with descriptions of the
provided limited information on root growth sim-
extension and branching of individual age classes
ulation. Reynolds and Leadley found greater vari-
of seminal and crown root axes. The model re-
ability in whole-plant growth simulations. They
quires sowing date and average monthly mean
classified these models into four general categories
air temperature as input parameters. Model out-
based on degree of mechanism and comprehen-
put provides maximum depth of penetration of
siveness: 1) budget, 2) flux, 3) semimechanistic,
each age class of root and root length density or
and 4) mechanistic (Fig. 12).
root weight in any 10-cm layer of soil contributed
Budget models are empirical in nature and ig-
by main axes, first order, and second order later-
nore any kind of mechanism or comprehensive-
als on any calendar date.
ness. These models describe plant growth as the
difference between input and output parameters.
Soil parameter-based models
In addition, budget models treat plants as "black
boxes" where plant biomass is lumped into a sin-
Root growth model
gle box. Semimechanistic models contain low to
Jones et al. (1991) developed a root growth
medium comprehensiveness. The plant growth is
model that simulates daily root growth of crops
described with a minimum number of compo-
grown in a layered soil. Model input parameters
are aluminum toxicity, calcium deficiency, coarse
nents, and heavy emphasis is placed on phenologi-
16
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