Introduction
In order for the user to fully understand the vegetation parameterizations
employed in the model a good understanding of certain concepts
would be beneficial. As mentioned before, electrical analog notation
is used as a concept to formulate the movement or transfer of
particular model variables, notably those of moisture and heat,
through the various model layers. Following on from this then,
we reintroduce the idea of a resistance to transfer and present
the concept of water potential which is used implicitly in the
plant canopy equations.
The Vegetation Parameterization
The vegetation component closely follows the description given
by Taconet et al. (1986)
with some modifications. Essentially, the model accounts for a
layer of vegetation between the atmospheric surface layer and
the ground surface. Heat and moisture fluxes are exchanged between
the foliage and the inter-plant airspaces and between the ground
and the inter-plant airspaces through resistances in the leaf
(for water vapour) and the air. The transition layer is replaced
by a shallow air layer just above the vegetation canopy.
Radiation Partition
Radiative energy penetrates the canopy to or from the leaves and
to or from the ground. Relative amounts absorbed in the vegetation
layer or at the surface are governed by a function that depends
upon the leaf area index. The radiative temperature of the canopy
is determined by a long-wave radiative balance equation that takes
into account the temperatures of the foliage and the ground.
Flux Partition
The partitioning of flux between the ground and the canopy is
parameterized as a function of the canopy characteristics, using
conductance and resistance formulations.
Sensible Heat Flux
The sensible heat formulation has two components; ie, the sensible
heat flux above the canopy, comprising that to or from the canopy
and that to and from the ground.
The part originating from the ground is obtained as for bare soil
where the analogous equations to that of bare soil are substituted
into the energy balance equation resulting in a similar expression
which resembles the Penman equation.
However, the sensible heat flux from the canopy is written as:
where raf (inter-leaf airspace resistance)
is the reciprocal of the conductance (the conductance Chf
is defined in Taconet et al); Cp stands for
the specific heat of air, r the density,
T1 & Taf are respectively
the temperatures of the leaf and the inter-leaf airspaces.
Latent Heat Flux
Similarly, latent heat transfer has two elements to it. Originating from the ground is formulated as:
In this equation the factor M, ie, the moisture availability
at the surface of the ground is assumed to be a fraction of the
field capacity; qs(Tg)
& qaf respectively represent the saturation
mixing ratio at the temperature of the ground and in the inter-leaf
airspaces, rag is the resistance between the
soil surface and the canopy.
The contribution to the total furnished by the vegetation, ie the transpiration, is given by equation and is unlike that presented in Taconet et al.
V being the difference between saturation vapor pressure at the
temperature of the leaf and the leaf-air boundary vapor pressure.
where
P
is the ambient pressure. r1 is the
leaf resistance. raf is calculated from a
knowledge of the friction velocity (ustar) and the size of the
leaf (Goudriaan 1977).
It is important to note that LeEf
is calculated first, so that Hf is really
a residual between Rn ( the foliage component
) and LeEf , this can
lead to a negative Hf if the demand for a
large LEf occurs.
Examination of this equation highlights the importance of the
resistance terms in the denominator, which play an important role
in the magnitude of the latent heat flux and in particular, the
part stomatal resistance plays in the overall leaf resistance.
This is central to the plant canopy structure and will occupy
much of the discussion that follows:
The Stomatal Resistance
The stomatal resistance constitutes an essential element of the
vegetation parameterization. Essentially it expresses the efficiency
of the vegetation to transpire. The energy partition between sensible
and latent heat is adjusted by the magnitude of Rst
per se. Many physiological and climatological factors are involved
in the foliage resistance to transpiration. The primary ones include
the variation in daylight, the evaporative demand imposed by atmospheric
forcing, the water supply to the plant's roots and the phenology
and type of vegetation.
Deardorff Formulation
To take account of these effects the model employs two stomatal
parameterizations. The first is the Deardorff formulation which
captures the gross aspects of stomatal behaviour as affected by
soil water content and sunlight. Yet it is important to state
that it ignores plant hydraulics which account for significant
shifts in transpiration rate over the diurnal period. These important
variations in transpiration rate are manifested by a change in
the stomatal resistance and can be correlated with variables that
reflect the physiological status of the plant. At this point in
the discussion the reader needs to become acquainted with the
concepts of water potential, vapour pressure deficits and osmosis.
A relatively straight-forward survey of plant physiology is presented
in Raven et al (1981),
which may help those unfamiliar with the field.
Plant Canopy Formulation
The development of stomatal resistance then begins with a model conception as suggested by Jarvis (1976). Here the stomatal resistance (rs) is calculated from the product of two functions f(S) and f(ye ), according to the relationship:
where rmin is the minimum stomatal resistance
that can be observed; defined as that occurring with full sunlight
and at saturation leaf water potential. The functions f(ye)
and f(S) represent the stomatal resistance initiated due to leaf
potential and solar flux.
The solution for f(ye)
is analytical and is a function of soil moisture, vapour pressure
deficit, inter-foliage resistances and plant internal resistances.
The resistance structure of the plant is shown in Figure 2.
Attention is drawn to the fact that a variable resistor (Zstore)
is drawn at the mid-point along the stem of the plant, which is
an analogy representing the ability of the plant to store water
in its tissue ( root, stem or leaf ). This resistance
pertains to the flow of water to or from storage and governs the
ability of the plant to store water in its tissue ( root,
stem or leaf ). This capacity to store water, termed in our electrical
analogy scheme as the capacitance can be modelled such that any
flux of water resulting from storage is directly related to the
position of the resistor. For example, if the resistor ( branch
point ) is situated at the top of the plant, the implication is
that most of the stored water comes from the leaves. The choice
of the branch point position is left up to the user.
Solutions for f(S) & f(ye
)
The solution then to f(ye
) is two fold. The first is designated "steady-state"
and implies that there is no water storage in the plant or simply,
any water entering the plant at the roots is leaving through the
leaves. The second implies that water storage in the plant is
a contributing factor to the eventual transpiration at the leaves
and is called "capacitance".
The functions f(S) and f(ye
) exhibit exponential behaviour which can be represented
simply by a pair of straight lines whose intersection defines
sub-critical and super-critical regions separated by a critical
value of S or ye .
We term this a "discontinuous linear" model and maintain
that it captures the fundamental form of the functions without
any great loss of accuracy.
The equations are of the form:
The solution for f(S) is straight-forward where the solar flux
(S) is obtained from the radiation component of the model. However,
the function defined by f(ye)
requires greater elaboration.
For steady-state situations, transpiration from the leaves is considered equal to the flux of water from the root zone. It is therefore, possible to combine these equations into the form -
where the coefficients a b and c contain all of the independently specified or calculated variables listed in the equations. This quadratic equation is then solved for ye to yield two roots -
the negative root specifying the correct value for ye.
All that remains now is to establish whether ye
is above or below the threshold value to determine the value of
dy .
This is accomplished by defining a critical ground water potential
(ygc) as that minimum
ground water potential which can meet the evaporative demand without
ye becoming less
than yc . This
is done by setting the leaf water potential to that of the threshold
water potential, at which point rs is equal
to a critical resistance rct . We define sub-critical
simply to refer to the region where stomatal resistance varies
slowly with S or ye .
Super-critical signifies the region where rs
varies rapidly with S or ye
.
The critical value can be obtained by arranging the equations to yield the expression:
Where b is a constant describing the
difference between the mesophyllic and leaf epidermal water potential
divided by the vapor pressure and Zt is the
sum of the resistances from ground to, but not including, the
leaf. s = rLe
and the critical and cuticular resistances are rct
and rcut respectively.
If the critical ground water potential is less than the value
of the soil water potential, the sub-critical solution is correct
as ye is greater
than yc . Moreover,
when the critical ground water potential is greater than the value
of the soil potential, ye
is less than yc
, necessitating the super-critical solution.
The additional water supply from the plant's storage can be an
important contribution to the transpiration. The capacitance solution
though takes the same form but with the inclusion of substantially
more terms which account for the storage resistance, initial storage
volume and placement of the variable resistor. Further elaboration
on the capacitance parameterization is to be found in Carlson
and Lynn (1991).
The Canopy Resistance
It is possible to define a canopy moisture availability, which
is the ratio of evapo-transpiration to the potential evaporation
from a surface with radiometric surface temperature calculated
by the model. Indeed, if one chooses to ignore vegetation and
use the bare soil model ( which, strictly, is a general canopy
model rather than a specific bare soil model ), the moisture availability
is then the canopy moisture availability. Given this definition
of the canopy moisture availability, that is, the ratio of evapo-transpiration
to potential evaporation and the atmospheric resistance, one can
define a canopy resistance (instead of a soil resistance). This
canopy resistance is that which is often measured over vegetation.
Partial Cover
In some cases, as with sparse vegetation, the user may wish to
blend in the bare soil and vegetation models. This is done by
setting a fractional vegetation cover in addition to the leaf
are index, the latter, however, pertains to the entire mixture
of bare soil and vegetation. At the level of the canopy, the model
then operates separately ( bare soil and vegetation ) and blends
the radiometric surface temperatures and the atmospheric fluxes
above the canopy according to the bare soil and vegetation fractions.
The parital routine is useful for studying the change in radiometric
surface temperature as a function of fractional vegetation cover.
Fractional vegetation cover is thought to be closely related to
the normalized difference vegetation index (NDVI) in the range
of fractional vegetation cover below 100%.
Dual Roughness regimes
When a stand of vegetation or other obstacles obstructs the flow
of air over surrounding clearings the logarithmic wind profile
in the air above the obstacles behaves differently from that below
the obstacles. Guyot and Seguin (Ag. And Forest Meteor.,
1978, p 411) show that widely separated tree rows can influence
the logarithmic wind profile in the spaces between the rows such
that the wind speed above the average height of the trees responds
to the average roughness height of the trees, which is typically
about 0.1 times the tree height. We will refer to this roughness
as the "global" roughness. Below the tree level, the
wind profile responds to the average roughness length of the surface
elements between the trees, e.g. the grass. We will refer to this
roughness as the "patch" roughness. Thus, two roughness
regimes exist at one point even when the trees are separated by
a distance several times the height of the trees and the latter
occupies only a small fraction of the surface area in a larger
region consisting of trees and surrounding bare or grassy terrain.
The importance of specifying two roughness regimes is that the
option will allow the surface temperature of clearings to become
more elevated because the roughness of the clearing will be much
less than that for the vegetation; an analogous situation exists
for the heating of the surfaces between buildings in urban areas,
where the obstacles are buildings rather than trees. For vegetation,
clearings may simply constitute the bare soil between rows of
a crop such as corn.
We generalize the result of Guyot and Seguin to include obstacles
such as trees, bushes or buildings, that may be surrounded by
flatter patches such as bare soil.. Five cases can be specified:
flat bare soil, bumpy urban landscape, uniform vegetation, uniform
vegetation but uses a patch roughness and trees and grass (or
urban with vegetation and). The users should first decide if they
want to have a dual roughness regime and whether the obstacles
are due to vegetation or buildings. The obstacle height and a
roughness are specified in the eighth and ninth slot in the data
statement, immediately after the parameter omega, which is the
precipitable water amount.
If no obstacle height is specified, the model assumes that there
is no dual roughness regime and uses only one roughness value,
even if a partial vegetation cover is indicated. This roughness
height must be specified in the slot for the roughness parameter.
A single roughness height would apply to the case of a bumpy bare
soil regime or a vegetation canopy with no clearings or for partial
vegetation cover if the user wanted to ignore the dual roughness
option. If both a zero roughness height and a zero obstacle height
are specified the model will fail.
If an obstacle height is specified the model assumes that the
global roughness is 0.1 times the obstacle height, e.g. 10 cm
if the obstacle height is 1 m; (obstacle height is specified in
meters). The user should note that the roughness length still
should be specified. If this parameter is specified as zero, the
model uses 0.1 times the obstacle height as the roughness height
and proceeds as if there were only one roughness regime.
If the user specifies an obstacle height and a roughness height,
the model assumes that there is a dual roughness regime. In this
case global roughness is computed as 0.1 times the roughness
height and patch (clearing) roughness is specified by a value
in the roughness parameter slot. Note, however, that the model
will fail if the obstacle height is less than 10 times the specified
roughness parameter. A typical example would be for a forest
canopy with partial bare soil patches. If the trees are 5 meters
high, an obstacle height of 5 meters is specified and the global
roughness would be calculated as 50 cm. If the tall grass surrounding
the forest is 10 cm high (essentially bare soil but with a sparse
grass cover), one might wish to specify a roughness of 1 .2 cm,
for example. The model will then calculate the fluxes in the partial
vegetation mode (if the partial mode is activated in the data
statement) or for an urban type setting if bare soil is indicated,
using the global and patch roughnesses.
If the partial vegetation mode is not activated, the model proceeds
as if there is a 100% vegetation cover or bare soil (if LAI =
0), and uses the specified roughness parameter if obstacle height
is not specified and otherwise uses 0.1 times the obstacle height
as the roughness parameter if the roughness parameter is not specified.
If both roughness length and obstacle height are specified for
the case of vegetation, but the partial vegetation mode is turned
off, the model still calculates a dual roughness regime, although
this option is a bit artificial. However, the user may wish to
apply the dual roughness regime calculations to the case of bare
soil, e.g. urban areas, where buildings constitute the obstacles.
In that case, no partial vegetation mode is called for. The user
would specify bare soil conditions (zero LAI), an obstacle height
to represent the average height of the buildings and a roughness
height, which would apply to the spaces between the buildings.
One could consider a vegetated urban area in which the obstacle
height would be that of the buildings, but a vegetation fraction
and other vegetation parameters would be specified and the model
would execute in the partial vegetation and dual roughness modes.
Note that a vegetation height must be specified in the vegetation
mode, but that parameter has nothing to do with roughness, being
used only to calculate the water flow through the plant.
Finally, the user should note that the dual roughness concept
may be inapplicable if, for example, the percent of vegetation
is so small as to not influence the wind regime in the clearings.
A good rule of thumb might be that the vegetation must be greater
in height than about 0.1 the spacing between vegetation clumps
in order to affect the wind in the clearings. The existence of
a dual roughness regime depends on the wind direction with respect
to the roughness elements. A row of trees may not affect the
wind in the surrounding clearing if the wind blows along the direction
of the row rather than across it. Conversely, one would expect
the logarithmic profile laws to become invalid in the spaces between
vegetation clumps as the percentage of vegetation approaches 100%.
In that case a representative wind speed between the vegetation
elements is the interleaf wind speed, UAF, which is calculated
in VEGVEL.for.
Carbon Dioxide Flux
Carbon dioxide flux from the leaves is calculated in a similar
manner to that of transpiration, see Goudriaan (1977).
Stomatal and boundary layer resistances are scaled from those
of water to accommodate the differing diffusivity of CO2
. The gradients of the CO2
between the mesophyll and above the canopy must be specified;
As of 1991, the external concentration [Ca
] is about 330 ppmv
( parts per million per volume
) and the internal concentration [C i
] is thought to be about 120 ppmv
for C4 plants and 210
ppmv for C3
plants. The fluxes are output in Kgm-
² s-1 , typically
of the order of 100 x 10-8 .
They are scaled by the leaf area index divided by the shelter
factor to convert to fluxes per unit horizontal surface area.
Ozone Fluxes and Concentrations within a Plant Canopy
Ozone is destructive of plant tissues. Destruction occurs when
the ozone enters the leaf cells. The result is a reduction in
yield and in green leaf area and an increase in the root mass.
Fluxes of ozone to the plant consist of fluxes through the stomates
and through the cuticle. Fluxes also occur through the ground
beneath the big leaf and in the bare soil areas. One assumption
is that the contact concentration in side the leaf and at the
ground is zero. It is also assumed that no ozone is destroyed
at the leaf surface outside the stomates and the cuticle. In fact,
the efficiency of ozone destruction at dry surfaces is probably
not 100%.
Ozone fluxes from atmosphere to leaf move through an atmosphere
and canopy air resistance and then a leaf boundary layer, where
they split in parallel to go through the stomates and the cuticle.
A third branch bypasses the leaf and goes into the ground. Concentration
inside the canopy is calculated from a fixed ozone concentration
at 50 m. Ozone density is taken as 1.9 kg m-3, similar
to that of carbon dioxide. Molecular diffusivities are assumed
to be identical to those for carbon dioxide.
Ozone concentrations calculated in the model are assumed to be in the plant canopy, roughly near the top of the vegetation. Ozone concentration is prescribed at 50 m in units of parts per million by volume (ppmv); a typical value is 0.08. (In reality, ozone tends to be created in the boundary layer during the day as the result of photochemical effects on NO2, so that the maximum occurs during the early afternoon.) Even with the assumption of constant concentration at 50 m, that at canopy level tends to maximize at mid day because of increased turbulent transport. Fluxes are expressed in kg m-2 s-1; a typical value is about 1. Output is for both the plant fluxes alone and for the global fluxes, which includes that in the non-vegetated part of the canopy. 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