Above-ground modules in Hi-SAFE
(Tree phenology, tree C allocation, tree light interception,
microclimate)
Deliverable D.4.1 (SAFE European Research contract QLK5-CT-2001-00560)
Silvoarable Agroforestry For Europe (SAFE)
Christian Dupraz, Grégoire Vincent, Isabelle Lecomte, François Bussière, Hervé
Sinoquet
August 2004
Foreword
Hi-SAFE is the detailed 3D process-based biophysical model of the SAFE project. It
includes the main tree functions with regard to major resources (carbon, water,
nitrogen) and responses to the major climate variables (light, air temperature and
humidity). The present text shows how light and carbon acquisition by the trees has
been taken into account in the Hi-SAFE module. Requirements of the Hi-SAFE model
include sensitivity to a number of environmental and biological factors, and short
computation time.
THE TREE PHENOLOGY MODULE
This module should trigger other modules to give a fair representation of temperate
trees phenology.
BUDBREAK
We suggest to model budbreak date as a function of accumulated temperatures
above a threshold. Accumulation start after a starting date.
Budbreak module
Parameters
Date to start accumulation of
temperatures
Threshold
temperature
of
acronym
Value
suggested
for Hybrid
Walnut
Unit
Ph_Date_Start_Acc_T
(Ph_BB_DSAT)
01 January
DOY
10°C
°C
210
°C-day
effective Ph_Budburst_Effective_
T
(Ph_BB_ET)
Threshold of
temperatures
Budburst
accumulated
to
trigger
Ph_Budburst_Acc_T
(Ph_BB_AT)
This module triggers the Tree C photosynthesis, Tree water extraction, Tree C
allocation, tree growth modules.
Related questions :
This budbreak module initialises the Carbon pool of the leaves to a starting value.
What value? Has this absolute value an impact on the speed of leaf expansion right
after budbreak?
At the start of the growing season, tree leaf area is mostly formed with C reserves (C
labile pool). This is not accounted for by the C allocation module.
In what module is tree respiration accounted for? Tree respiration should be activated
all the year round, and should therefore not be triggered by the phenology module.
END OF LEAF AREA EXPANSION
This is a key phenology stage. According to our field observations, the end of leaf
extension is strongly dependent on water/nitrogen stress. Even in non limiting
conditions for water, nitrogen light and temperature, most temperate tree species
exhibit a limited period of leaf expansion. We describe here the end of the first flush
of leaf expansion, including preformated and neoformated phytomeres.
The C allocation module allocates every day some Carbon to the leaf pool, and will
apparently never predict the end of leaf expansion. This was already a poor feature
of HyPAR. This should be modified by the phenology module.
This phenology module should be able to fairly describe the following situations :
 A tree with no stress stops expanding leaves anyway at some date
 A tree with some stress stops earlier to expand leaves
It is not possible to use a simple date for stopping leaf expansion (even if this date is
predicted from tree stress indexes). Leaf expansion ceases gradually. The phenology
module, combined with the C allocation module should result in a sigmoid shape for
leaf expansion.
We suggest a module using 3 parameters :
 A fixed date of end of the leaf expansion in non limiting conditions (potential
expansion with no water stress, no nitrogen stress). This can be documented
by monitoring well cared trees (irrigated, fertilised…). Some tree species may
never stop (Eucalypts, Paulownia), but most temperate tree species will stop.
Some trees, after a pause, will resume a second flush, but this is beyond the
scope of HySAFE, as this is very unlikely in real conditions of AF plantations.
 A fixed delay between the beginning of the leaf expansion rate decrease until
the leaf expansion stop. This is necessary to avoid a sudden stop of leaf
expansion.
 A threshold for accumulated water and/or nitrogen stress to trigger the slow
down of leaf expansion.
Parameters
End of leaf expansion module
acronym
Date of end of leaf area
expansion in no stress
conditions
Delay for leaf expansion
slowing
Ph_Leaf
expansion_unstressed
(Ph_LE_U)
Ph_Leaf
expansion_delay
(Ph_LE_D)
Threshold of accumulated Ph_Leaf
water stress to trigger leaf expansion_Threshold
expansion slowing down
(Ph_LE_T)
Value
suggested
for Hybrid
Walnut
30 July
Unit
DOY
15
days
To be
discussed
To be
discussed
If no stress occur, at a date given by Ph_LE_D - Ph_LE_T, leaf expansion slows
down. The rate of leaf expansion can then be linearly decreasing until Ph_LE_U.
It must be discussed with Marcel van Oijen where in the C allocation module we
should include this impact. The sum of all C allocation coefficient must remain 1.
Related questions:
Most temperate trees have short shoots and long shoots. The leaf area of a single
tree is the sum of the leaf area of short and long shoots. Short shoots end expanding
in a short delay (usually less than a month, often about a week as in Wild Cherry).
Long shoots expand much more longer. The leaf area of a single tree can be
decomposed in two sigmoid curves describing short and long shoot area
respectively.
A possible strong impact of competitive stress is the demography of short shoots, as
was hypothesised in the MODELO approach. Should we include this approach in
HySAFE?
LEAF-FALL
A very simple module could be triggered by the average temperature of the last 15
days. When this temperature falls below a threshold, leafall starts. Using an average
temperature over a 15 days period is useful to avoid taking into account short periods
of cold days. Leafall is assumed to occur during a fixed maximum time lapse, but a
faster leafall will occur if some climatic events occur : high winds, frost.
Leafall module (temperature driven)
acronym
Value
Unit
suggested
for Hybrid
Walnut
Threshold of temperature Ph_Leafall_Threshold_T
15
°C
(average of air temperature
(Ph_LF_TT)
over the last 15 days)
Usual duration of leafall
Ph_LF_Duration
15
days
(Ph_LF_D)
Sensibility to frost or high
Ph_LF_Sensibility
If frost or
Y/N switch
winds
(Ph_LF_S)
winds>10
m.s-1 occur,
full leaf fall
Parameters
Related question
However, it must be noticed that our field observations show clearly that leafall is
much earlier for trees that experienced high water stress during the growing season.
This could be modelled by an accumulated stress index. But how to interfere with the
temperature signal? An other approach would be to consider a life expectancy for
leaves. This life expectancy would be diminished by accumulated stress. Leaf-fall
would occur at the earliest date predicted from the temperature driven module and
from the life-expectancy module.
Leafall module (life-expectancy driven)
Parameters
acronym
Value
suggested
for Hybrid
Walnut
Life expectancy of leaves
Ph_Leafall_Life_expectan
210
cy (Ph_LF_LE)
Factor
to
convert Ph_Leaf
To be
accumulated water stress in expansion_Stress factor discussed
a decrease of the life (Ph_LF_SF)
expectancy of leaves
Unit
DOY
Day.
Stress-1
ROOT PHENOLOGY
A similar approach could be developed for root phenology. The current C allocation
module will allow root growth all over the growing season, and will prevent any root
growth when the trees have no leaves (is that right?). This could be done in a similar
pattern as for the leaves phenology modules. For trees that display root growth
before budburst or after leaf-fall, C should be allocated from the C labile pool?
FRUIT PHENOLOGY
It was decided in Clermont-Ferrand to include a simple fruit sink for Carbon and
Nitrogen as a forcing variable.
Fruit sink volume is a forcing variable and should be provided as a time-series (one
value per year), or as a function of tree growth/vigour. It could include an alternate
bearing pattern.
Fruit sink inception date could be fixed in a first approach, or could depending on
climate.
Fruit sink end of filling date could also be fixed, or depend on accumulated stress
indexes.
Fruit phenology (forcing variable)
forcing
acronym
Value
suggested
for Hybrid
Walnut
Fruit sink volume C
Ph_Fruits_C (Ph_F_C)
Depends
on tree age
Fruit sink volume N
Ph_Fruits_N (Ph_F_N)
Depends
on tree age
Fruit sink inception date
Ph_Fruits_Start_date
150
(Ph_F_SD)
Parameters
variable
or
Unit
Kg C
Kg N
DOY
Fruit sink end of filling date
Ph_Fruits_End_date
(Ph_F_ED)
270
DOY
A high priority for fruits may be assumed, or may not be assumed. This has to be
decided within the C allocation module, and may involve other parameters.
CONCLUSION
Several phenology modules require accumulated stress indexes. Stress indexes are
a key component of the HySAFE model, but were not discussed up to now. They are
essential tools to introduce controls in the integrated model. They should be now
defined and agreed.
TREE RADIATION INTERCEPTION
1. OBJECTIVES:
The radiation interception module is aimed at computing:

Incident radiation available to the crop canopy: This is the spatial
distribution of the transmitted radiation below the tree canopy. The crop
canopy is likely to be divided into strips parallel and perpendicular to the
row direction, and the radiation model should compute incident radiation
above each crop area.

Radiation intercepted by each individual tree defined in the scene: Note
that the scene could include only one tree.
The radiation model provides inputs for the carbon acquisition module, the water
consumption and the canopy microclimate modules.
2. THE HYPAR SOLUTION:
In the HyPAR model, radiation interception is computed from the turbid medium
analogy, i.e. the model is based on Beer’s law. For computation of available light to
the crop canopy, the trees are modelled as simple shapes filled with leaf area turbid
medium, while the canopy is divided in cells (max. number 20 x 20). A transmission
coefficient of the tree canopy is computed for each canopy cell. Surprisingly,
computation of light interception by the trees is made by assuming that trees make a
multilayer canopy, i.e. not a discontinuous canopy.
Input parameters / variables include:

Incident radiation: The sky is assumed to be overcast, so that computations
can be made by using the only daily incident radiation (MJ m-2 day-1). Note
however that simulated radiation exchanges are insensitive to row
direction, day of year nor latitude.

Canopy structure: tree dimensions with regard to geometry used to
abstract tree shape, tree leaf area, extinction coefficient. Note that the
extinction coefficient globally accounts for the effect of leaf angle, foliage
clumping and optical properties of leaves. Note also that canopy
dimensions must be simulated by the model, namely tree growth and
development modules, but I am unsure that any model is able to cope with
dynamics of tree dimensions.
3. STATE OF THE ART:
The only two ways to simulate radiation exchanges in vegetation canopies are the
turbid medium analogy – as used in HyPAR – and ray-tracing and/or projection
techniques based on simulated 3D plants. None of the tree models proposed in the
literature is able to properly simulate dynamics of the 3D architecture in response to
environmental factors; and time needed for light computations on simulated 3D plants
is incompatible to the time requirements for Hi-SAFE simulations. The only way is
thus to adopt a turbid medium model, although projection models for 3D plants could
be used to derive parameters of the turbid medium model.
Improvement of the light HyPAR module could be:
1. To use discontinuous tree canopies for both the computations of available light to
the crop, and light interception by the trees.
2. To improve the flexibility of the scene definition, i.e. number and location of trees
on the scene, and discretisation of the crop canopy.
3. To better take into account the directional components of incident radiation: at
least direct radiation coming from the sun direction, and diffuse radiation obeying
a classical sky radiance distribution (e.g. Uniform or Standard OverCast
distributions).
4. To better define the extinction coefficient, as a function of leaf angle distribution,
foliage clumping and optical properties. The rationale to explicit the extinction
coefficient is well known, and Goudriaan’s expression (1977) accounting for both
leaf angle and optical properties could be used.
4. LIGHT MODEL IN HI-SAFE:
Courbaud’s light model (MOUNTAIN, 2003) meets most of the above requirements
(namely requirements #1, #2, #3). Moreover, it is written in Java, has been
incorporated in the CAPSIS system, and the author was available to help us for code
adaptations. The model MOUNTAIN has been therefore chosen to be included in the
Hi-SAFE model.
As mentioned by its author, this model was developed for spatially heterogeneous
coniferous forest canopies. Based on the interception of light rays by parabolic
crowns, it calculates simultaneously the energy intercepted by each tree and the
distribution of light reaching the ground. Slope and exposure are taken into account
as a function of the distribution of incident light rays. An optimisation process that
reduces the computing time needed to find trees which intercept a ray and to
manage plot boundaries was developed. A detailed description of the model is given
in Courbaud et al. (2003).
Small modifications to Courbaud’s model have included:
o the use of Goudriaan’s expression (1977) for the extinction coefficient. For a
given beam direction , the transmission T of light within a crown is computed
from Beer’s law as:
T  exp(  K  D  L)
(1)
Where the extinction coefficient K is modelled as:
K  G 
(2)
D is leaf area density within the tree crown (m 2 m-3). L is length on the beam path
within the tree crown (m). L is computed from geometry principles, from the
intersection points between the crown envelope and the beam line. G is the
projection coefficient of leaf area, which depends on both foliage inclination
distribution and direction .  is the leaf absorptance in the PAR (Photosynthetically
Active Radiation) waveband (400-700 nm).
Note that beams are regularly spaced, so that a given beam represents a small area
Ab. Average light interception I  by a tree is therefore expressed in square-meter,
i.e. as interception area of the tree
I 
 1  T   A
b
(3)
Beams
o The sky discretisation according to the turtle concept (Den Dulk, 1989) in order
to shorten the number of computed directions and then time computation. The
sky vault was characterised by a set of 46 directions.
o The computation of both sunlit and shaded leaf area: This is useful since the
photosynthesis response to light is not linear. Computation is based on the
following equation (see e.g. Sinoquet et al., 1993)
I sun  K  Dsun  L
(4)
Equation (4) simply means that leaf area intercepting light in the sun direction is the
sunlit leaf area.
Since leaf photosynthesis response is not linear, light interception in Hi-SAFE is
computed five times a day, according to the Gaussian integration proposed by
Goudriaan. This is a compromise between:
o A single simulation run at day scale, which has been shown to overestimate by
20% carbon acquisition by the trees (Fig. 1).
o Simulation runs at hourly scale, which would multiply computing time in a way
incompatible with simulation time requirements in Hi-SAFE.
In order to save more time, light computations are run only when (see Balandier et
al., 2000):

Trees are leafy.

The daily sun course significantly changes, i.e. every 2-3 days near the equinox
and every 10 days near solstices. Sensitivity analyses could be performed in
order to fit the time interval between light computations.

Tree structure shows significant changes, in terms of tree dimension and leaf
area.
Finally the model outputs are PAR interception by each tree in the vegetation scene
and PAR transmission to each crop zone, both for diffuse radiation and direct
radiation at the 5 time steps. As radiation variables are proportional to incident
radiation, only relative values (i.e. assuming that incident diffuse and direct radiation
is equal to 1) are stored in memory. They can therefore be used several days
showing different conditions of incident radiation, as long as the sun course or the
canopy structure does not significantly change. For each time step, sunlit and shaded
area of each tree are also computed (see equation 4).
5. INPUT PARAMETERS REQUESTED:
Input parameters for the radiation model are:

Incident radiation:
This includes at least the daily amount of global radiation (MJ m -2 day-1), and possibly
the amount of diffuse radiation (MJ m-2 day-1). If not available, daily diffuse radiation
is computed from empirical relationships, given that data of both global and diffuse
radiation are available from a weather station. Incident solar radiation is partitioned
into PAR (400-700 nm) and NIR (Near Infra Red, 700-1200 nm) components
according to coefficients found in the literature (e.g. Varlet-Grancher, 1975). The sun
course is computed from astronomical formulae involving site location (latitude) and
date in the year.

Canopy structure:
Canopy structure includes:

Dimensions and leaf area of the trees. These parameters must be computed by
the tree growth and development modules.

Leaf angle distribution, which could be surveyed from measurements in the field.
Data are already available for walnut (UMR PIAF, Clermont-Ferrand) and poplar
trees (Casella, Forestry Commission, UK).

Foliage dispersion parameters, which account for clumping. The dispersion
parameters should be derived from a comparison between simulated values of
the Hi-SAFE light model and a projection model applied to the 3D mock-ups of the
SAFE tree species (UMR AMAP, Montpellier).

Optical properties of the leaves:
They include leaf reflectance and transmittance. They usually do not show large
intra- and inter-species differences. They could however be surveyed in case of the
SAFE tree species by using a Li-cor 1800 spectrophotometer equipped with an
integrating sphere. Such a device is available in UEPF (INRA Lusignan, contact: C.
Varlet-Grancher).
Daily climate input : day D
Tmin, Tmax (°) - Rhmin, RHMax (%)
Global radiation (KW m-2) - PAR (moles m-2)
Rain (mm) - ETP (mm)
Wind Speed (m s-1)
Co2pressure (pa)
Daily climate input : day D + 1
Climate generator (using D and D+1)
Sun Declination (°) - Day Length (hours)
For each time step (X default =5) :
- Hour of each time steps
- Sun elevation and azimuth (°)
- Global PAR (µmol m-2) – Diffuse PAR (µmol m-2)
- Temperature (°) Relative Humidity (%) VPD (pa)
- Wind Speed (m s-1)
First
execution
YES
NO
Any leaf
in
trees ?
NO
YES
 leaf
NO
area >
threshold
 sun
declination
> threshold
YES
YES
Direct beams set position (X time steps)
Direct lighting computation (at each X time step)
- direct energy intercepted by each tree (unit?)
- direct energy remaining on each cell (%)
Diffuse lighting computation (once)
- diffuse energy intercepted by each tree (unit)
- diffuse energy remaining on each cell (%)
Result agregation to have :
- % of energy intercepted by each tree
(direct+diffuse)
- % of energy on each cell (direct+diffuse)
NO
For X time steps : Tree
photosynthesis (µmol m-2 s-1)
calculated for shaded leaves
(energy used is ....in which unit ?)
Aggregation of X results to
have a total daily photosynthesis
for each tree in µmol m-2 d-1
C allocation module
For X time steps : Tree
photosynthesis (µmol m-2 s-1)
calculated for shaded leaves
(energy used is .... in which unit ?)
THE CARBON ACQUISITION BY THE TREE
1. OBJECTIVES:
The carbon acquisition module is aimed at computing the whole net photosynthesis
of the tree at daily scale (gC tree-1 day-1). This module provides inputs to the carbon
partitioning module.
2. THE HYPAR SOLUTION
Photosynthesis in HyPAR is computed by scaling gas exchange from leaf to canopy.
The leaf photosynthesis model is Farquhar’s (1980), combined with Jarvis’ for
stomatal conductance. Farquhar’s and Jarvis’ models involve (e.g. see equations in
Le Roux et al., 1999):

Biochemical parameters which primarily varies with species and nitrogen content,
namely the maximal rate of carboxylation (Vcmax), the maximal rate of electron
transfert (Jmax) and dark respiration (Rd). The maximal stomatal conductance
(gsmax) could be included in this group.

Biochemical photosynthesis parameters which may vary with species, but are
usually assumed to be constant as their measurement is difficult. They include
activation and deactivation energy, Michaelis constants and specificity factors.
Values proposed by Jordan and Ogren (1984) are usually used, although
Bernacchi’s values (2001) are becoming more popular.

Environmental variables which influence both assimilation rates and stomatal
conductance, namely PAR irradiance, leaf temperature and vapour pressure
deficit at leaf surface.
Simulation of carbon acquisition by the whole tree at daily scale needs both space
and time integration of the leaf model, i.e. from leaf to tree and from minute to day,
respectively. In HyPAR, space integration follows Sellers et al. (1992), who assumes
full acclimation of leaf nitrogen content and then leaf physiological traits to timeaveraged light – i.e. relative variation in leaf physiological parameter scales with
relative variation in time-averaged light. In these conditions, carbon gain by the whole
tree is proportional to net assimilation and then physiological parameters of leaves in
a given location, mostly chosen at the top of canopy. Such a way shows two major
advantages:

Leaf models must be parameterised for the only top leaves, rather than assessing
variations within the canopy. This shortens the amount of field measurements
needed to parameterise the model.

Computing time can be saved.
This approach has been further tested in case of isolated tree crowns (Kruijt et al.,
1997) and has proved successful. Moreover, in case of a isolated walnut tree,
simulation with the RATP model (Sinoquet et al., 2001) have shown that carbon gain
is weakly sensitive to the nitrogen distribution within the crown, and that the observed
nitrogen distribution is close to the theoretical distribution leading to maximal carbon
gain (Le Roux and Sinoquet, unpublished data). This means that formalism adopted
in HyPAR is probably satisfactorily.
On contrast, the way the leaf scale model is integrated over the daytime is
unsatisfactory. HyPAR documentation implicitly suggests that the model runs with the
mean daily leaf irradiance. As shown in Fig. 1 from a simulation study with the RATP
model (Sinoquet et al. 2001) on a 20-year walnut tree, the single daily run results in a
20% overestimation of daily carbon gain, in comparison with a daily integration of
hourly simulation outputs.
3. ALTERNATIvES:
Photosynthesis modules for tree growth models have been recently reviewed by Le
Roux et al. (2001). Approaches used at the daily time step are the RUE concept
(Radiation Use Efficiency, Monteith, 1972) and empirical models, where the effect of
environmental factors (leaf irradiance, temperature, CO2 concentration, water stress,
N supply) is taken into account by empirical functions. Note that Le Roux et al.’s
review – which does not include the HyPAR model – does not report any model using
Farquhar’s model at time steps larger than one hour.
The approach used in HyPAR is good, because Farquhar’s model use
physiologically-sound parameters and the spatial integration process (after Sellers,
1992) avoids to parameterise the whole variations of leaf photosynthesis and
stomatal parameters within tree crowns.
The only questionable point in HyPAR tree photosynthesis is time integration at daily
scale. Farquhar’s model usually runs at short time steps. Because photosynthesis
responses to light and temperature are not linear, running the model with the mean
daily leaf irradiance provides a biased estimation of the daily carbon acquisition.
4. PHOTOSYNTHESIS MODEL IN HI-SAFE
Like in HyPAR, tree photosynthesis in Hi-SAFE is computed from Farquhar’s model
associated with Jarvis’ to take stomatal responses into account. In Jarvis’s model,
responses to leaf PAR irradiance, vapour pressure deficit, leaf temperature, CO2
concentration in the air are modelled from empirical relationships (see e.g. Le Roux
et al. 1999 for application to walnut trees). The environmental factors are assumed
not to interact, so that the empirical functions are multiplied to account for the overall
effect of climatic factors. The maximum stomatal conductance gs max is assumed to
depend on leaf nitrogen content. While there is no direct link between nitrogen
content and stomatal capacity of leaves, this way allows to take into account
differences in gsmax between sun and shade leaves (see e.g. Leroux et al. 1999).
Since the HyPAR model does not include a complete leaf energy budget which could
allow to compute leaf temperature, leaf temperature is assumed to be equal to air
temperature (as in Wang & Jarvis, 1990). This assumption is correct as long as water
stress keeps moderate. Otherwise coupling between leaf boundary layer, vapour
pressure deficit and stomatal conductance is analytically solved in a new elegant way
(see code lines XXX to YYY).
The effect of water stress on gsmax is also taken into account by introducing an
additional response to the soil water content. As soil water content shows spatial
variations in the Hi-SAFE model, the average soil water content of 50% of soil
volume occupied by the tree root system is used in the relationship. Note also that
this effect is computed once per day, and from soil water content of the previous day
in order to avoid to take into account interactions between soil water content and
transpiration.
The Harley et al. (1992) version of the Farquhar model (Farquhar et al. 1980) has
been used. It computes assimilation rate as limited by drak and light photosynthesis
responses, using a biochemical framework. All equations used are given in Le Roux
et al. (1999).
The model outputs are thus:
o Leaf boundary layer conductance, computed from wind speed in the canopy.
o Leaf stomatal conductance, computed from Jarvis’ model
o Leaf photosynthesis rate, computed from Farquhar’s model.
Computations are performed 5 times a day. For each time step, photosynthesis rate
is computed separately for sunlit and shaded area. This allows to satisfactorily take
into account the non-linear responses to environmental parameters (de Pury and
Farquhar, 1997).
5. INPUT PARAMETERS REQUESTED:
Input parameters for the carbon acquisition model are:

Microclimatic variables sensed by the leaves:

Leaf irradiance: as computed from the radiation interception model.

Leaf temperature assumed to be equal to air temperature.

Leaf nitrogen content: as computed from the tree model. Note that the spatial
distribution of leaf nitrogen within the tree crown is not taken into account. Indeed
RATP simulations on a 20-year walnut tree have shown that the daily carbon gain
at tree scale is weakly influenced by the spatial distribution of leaf nitrogen (see
Fig. 2).

Leaf physiological parameters: As previously mentioned, they include i) a set of
parameters available in the literature (Bernacchi et al. 2001), which are commonly
used for any plant species, and ii) leaf parameters – namely, Vcmax, Jmax, Rd and
gsmax -, the values of which mainly depends on leaf nitrogen content on an area
basis. The best way should therefore be to parameterise relationships between
these parameters and N content for the SAFE tree species. Such relationships
have already be established for walnut trees (Le Roux et al., 1999)

Stomatal responses of leaves to microclimatic variables: Namely, responses to
PAR irradiance, vapour pressure deficit, temperature and water stress. Such
responses exist for walnut trees (Le Roux et al., 1999), and should parameterised
for the other SAFE tree species.
INTRA-DAY WEATHER DATA GENERATOR
1. Objectives:
The Hi-SAFE model is fed from microclimate variables at daily scale, i.e. as
commonly available from standard weather stations. As the carbon acquisition model
is run 5 times a day, it needs meteorological data at intra-day scale. The intra-day
weather data generator was therefore developed to feed the light and carbon
acquisition modules with climatic data, namely air temperature, air humidity, global
and diffuse incident radiation.
2. Intra-day data computation:
Astronomical formulae dealing with the sun direction (namely sun elevation and
azimuth) have been included in the data generator, in order to compute the day
length, and sunrise and sunset times, as a function of latitude and day of the year.
This allows one to define the time for the 5 carbon gain computations, which are
regularly spaced during the day. As a consequence, time step #3 is TST midday.
Air temperature and humidity are computed from minimum and maximum daily
values which are supposed to be available from the weather station. Minimum
temperature and maximum air humidity are assumed to occur at sunrise, while
maximum temperature and minimum humidity are supposed to occur at midday.
Interpolation is made from a sine function, the amplitude of which is given by the
difference between two successive extremum values.
As daily diffuse incident radiation D is rarely measured in weather stations, estimation
from daily global (G) and extra-terrestrial (G0) radiations has been included in the
weather generator:
D / G  aG / G0  b
(5)
where a et b are empirical coefficients. Extra-terrestrial radiation G0 is computed from
astronomical formulae, as a function of latitude and day of the year.
Intra-day global and diffuse incident radiation (i.e. for 5 time steps in the day) is
computed by assuming that instantaneous radiation is proportional to the sine of sun
elevation (Perrin de Brichambault 1976). The data generator checks for conservation
of daily incident radiation.
Model structure
For each day
If trees are leafy
Generate the climatic data for the 5 time steps: Weather generator
Astronomical formulae
Air temperature and humidity
Global and diffuse radiation: Gi and Di
If canopy structure has changed
Update diffuse PAR variables (tree and crops): Light model
If sun course OR canopy structure has changed
For each time step
Update direct PAR variables (tree and crops): Light
model
For each tree
For each time step
Compute leaf irradiance of sunlit and shaded area
For shaded and sunlit foliage area
Compute assimilation rate: Photosynthesis model
Leaf boundary conductance
Leaf stomatal conductance
Net photosynthesis rate
Sum up contributions of shaded and sunlit area
Sum up contributions of 5 time steps
THE TREE GROWTH MODULE
1. INTRODUCTION STATEMENT OF OBJECTIVES
This module is part of the tree growth model (which as a whole also includes
simulation of water and N uptake mediated through a spatially explicit root growth
model and C uptake via a light interception and photosynthesis module). The present
module more specifically covers C and N allocation to (and from) the different
compartments identified, and provides a spatially explicit above ground tree
representation.
The tree growth model itself is part of the Hi-SAFE agroforestry biophysical model
which is designed to describe a 3-5 years growth period of the tree + crop agro
system in a temperate (seasonal) climate on a daily time step. It should be capable of
simulating early years of tree development as well as the functioning of large mature
trees. It should address pruning or root trenching which are considered to be
important management practices to orient the productive outcome of such systems.
2. PRELIMINARY REMARKS
(based on bibliographical review and discussions with Christian Dupraz, Marcel van
Oijen, Andre Lacointe, Martina Mayus, Nick Jackson and other members of the HiSAFE consortium)
2.1. Is carbon supply limiting tree growth?
Recent evidence based on repeated measurements of above ground tree nonstructural-carbohydrates stocks which have been conducted in a variety of climates,
suggest that growth of mature trees in natural stands may never be limited by carbon
availability (Hoch et al. 2003; Korner 2003). This may reflect the fact that trees have
not yet adapted to the elevated ambient CO2 levels and that the limiting step is
integration of carbon into functional tissues rather than carbon uptake per se. For
example at high elevations, it has been argued that temperature may limit growth
more than C uptake (Korner 1998) as “growth as such, rather than photosynthesis or
the carbon balance, is limited. In shoots coupled to a cold atmosphere, meristem
activity is suggested to be limited for much of the time, especially at night”. The same
type of restriction may play a substantial role at high northern latitude.
This idea that tree growth is not intrinsically limited by C-uptake is apparently
contradictory with the extensive experimental data that prove that access to light is of
paramount importance in determining relative competitive success of individual trees
in a forest stand.
More probably in most environments tree growth is co-limited by a number of factors.
The most limiting step may indeed not be C-uptake rate but biosynthesis rate of new
tissues, particularly so under cold climates or low nitrogen fertility.
In any case, in low-density tree stands as those we are dealing with, light availability
is unlikely to limit C uptake as severely as in denser forest stands. Hence it is
suggested that emphasis be put on N and H2O limitations to growth, be it at the Cuptake step or the biosynthesis of new functional tissues step.
2.2. Internal C flows and wood anatomy
Internal C flows are tightly linked to wood anatomy. There are four basic types of
wood, ring porous, diffuse porous, (semi diffuse), conifer without resin ducts and
conifers with resin ducts. In the SAFE project we are concerned with the first two
types only (Oak and walnut having ring porous wood and poplar and wild cherry
diffuse porous wood)
In a recent study (Barbaroux and Bréda 2002), NSC concentrations in ten outer rings
of sessile oak (sap wood only) were found to be about 4% of the total dry weight (vs
2% in beech) with a much more pronounced radial gradient as well as stronger
seasonal pattern in oak than in beech. In the latter study there was also
circumstantial evidence suggesting that radial growth was more sensitive than
photosynthesis to moderate water stress in both species as NSC accumulation was
not reduced when growth was, supposedly due to water shortage.
Growth temporal pattern of the various tree compartments is also related to wood
anatomy. Diffuse-porous trees have vessels of about equal size and diameter
arranged at about equal distances from each other throughout the growth increment.
These vessels are produced regularly during the growing season. Such vessel
anatomy permits moderate loading throughout the entire growing season, i.e.,
loading of free water and essential elements dissolved in it. There is no or negligible
heartwood in those species.
Ring porous trees such as, oak, elm, chestnut and black locust, have large diameter
vessels in the first portion of the growth increment and vessels of smaller diameter
later in the growth increment. Vessels are produced early in the season before leaf
expansion in spring. Ring-porous tree have no or little over-wintering functional
xylem. (See Shigo 1994).
2.3. Tree response to pruning
The few reviews found on the subject (Geisler and Ferree 1984; Stiles 1984;
Richards 1986) focus on fruit trees and are not recent. A quick Internet search was
also conducted to complement the information reported in the above-mentioned
horticultural reviews.
Overall, the literature consulted supports the view that response to pruning depends
on the timing of pruning and that the general response will be towards a redistribution
of growth to the pruned compartment. The extent to which remobilisation of NSC is
involved in fuelling compensatory growth and how this may relate to pruning severity
is unclear.
Root pruning and defoliation experiments in a broad range of species (Richards
1986) tend to support the interpretation that “in a constant environment the S/R ratio
tends to constancy and is restored following manipulative treatments that may initially
disrupt it”. This may imply an increased RGR of the severed compartment and a
reduced growth of the intact compartment as well as an extended growth period of
the pruned compartment.
For example effect of root pruning in peach seedling was quickly overcome by a
“redistribution of growth” in favour of roots. Similarly root pruning of trees have been
shown to induce reduced growth rate of above ground in many tree species (Geisler
and Ferree 1984). In one experiment conducted with 2 clones of coppiced 4 year old
poplar there was no evidence of root dye back after the above part was severed
during the dormant period (Dickmann et al. 1996). Growth rate of roots has been
sometimes observed to remain unaffected (noble fir, Monterrey pine) or to increase
(apple, peach) or to decrease in case root pruning was extremely severe. Restoration
of shoot:root ratio after pruning may take several months (as in the case of 22-year
old trees of white pine).
Timing of pruning is also known to affect significantly the tree response. Pruning in
winter (dormant pruning) produces the most new growth, pruning has the greatest
dwarfing effect in June and early July, “It first dwarfs the root system, and then the
whole tree”. Mid summer pruning has little or no effect on stimulating new vegetative
growth
(http://www.gov.on.ca/OMAFRA/english/crops/facts/00-005.htm).
Also
stressed in (Stiles 1984): pruning after terminal buds have formed minimizes the
possibility of stimulating renewed shoot growth during the same season. Sprouting in
poplars was also observed to be substantially less for trees pruned in May than in
March. (http://www.cropinfo.net/AnnualReports/2002/popprune2002.htm). Timing of
root pruning notably in apple also influences the response: pruning in July reduced
shoot growth but not if done in late summer (Stiles 1984).
Tree pruning is also known to affect the diameter/height relationship (height growth
being less affected than radial increment) and the tapering of the trunk
(http://www.for.gov.bc.ca/hfp/forsite/training/growth-and-yield/gy-07.htm).
2.4. C-uptake modelling
It was finally decided to replace the initially preferred Farquard type infra-daily time
step photosynthetic module a by a simple Radiation Use efficiency approach
((Bartelink et al. 1997). A number of reasons can be put forward to justify this
simplification
So much uncertainty exists in terms of C-allocation patterns that it would not make
much sense to use a lot of computer resources to – try and - estimate C uptake to a
great level of detail if further accounting of C the various pools is so grossly done.
The candidate photosynthesis model (which includes a Jarvis model of stomata
functioning) - which was developed for plants growing without water limitation - would
be relevant if the evaporative demand were to be computed on a infra-daily time step.
This again would imply a significant additional cost in term of computer time (and
would not be consistent with the crop daily time step yielding a number of additional
complications).
No human resources were available to calibrate this photosynthetic model for the tree
species under consideration.
RUE approach to simulate C-uptake and daily time step are congruent with the
STICS crop model
At this stage maximum RUE is a species-specific constant (g/MJ of intercepted PAR)
which is reduced through dimensionless modifiers to take into account water
stresses, nutritional stresses and possibly temperature effect.
2.5. Should respiration processes be explicit in the tree model?
There was considerable discussion about whether respiration should be explicitly
computed in the model. The model is meant to run under a variety of climate types.
The contribution of respiration fluxes to total C budget is considerable (as much as
half of the integrated daily net foliage carbon gain can be lost to respiration by the
whole plant) and largely influenced by temperature. Therefore it seemed justified to
consider including respiration in the model (as done in Hypar).
However as a Radiation Use Efficiency approach to C-uptake modelling implicitly
includes the growth and maintenance respiration costs by relating intercepted
radiation with net Carbon accumulation no explicit respiration modelling seemed
warranted. However it should be stressed that doing so, NSC accounting is done on
a 'Structural carbon unit' base as no conversion cost from NSC to SC is considered.
In addition to the above reason some more technical obstacles to incorporating
respiration in the model exist. Dependence of growth and maintenance respiration
rates on temperature in trees appear to be highly variable between sites and species
as illustrated for example in (Coleman et al. 1996; Lavigne and Ryan 1997). For a
given air temperature respiration rates further vary with tissue composition. Differing
organ thermal mass and organ location will also complicate the relation between
ambient air temperature and respiration rates. Seasonal variation has been reported
to occur (Desrochers et al. 2002) as well as rapid acclimation to temperature (Bostad
et al. 2003). Hence calibration of respiration parameters may be an extremely time
consuming and largely fruitless exercise as no site nor species- specific data will be
available from the project. It should be stressed that, in the absence of strict NSC
accounting, a number of situations won’t be correctly predicted as for example
mortality related to NSC exhaustion in seedlings or saplings following defoliation
(Canham et al. 1999). If respiration is incorporated in a later version, it is suggested
to implement a mechanistic approach to C allocation based on the transportresistance paradigm as proposed by (Thornley 1998).
2.6. Root phenology
Root and shoot growth are highly coordinated and patterns of root vs. shoot growth
appear to vary among species. Generally fine root production is halted during winter
resumes with leaf expansion in spring and stops with leaf fall (Pregitzer et al. 2000;
Cote et al. 2003).
(Friend and Coleman 1994) distinguish three fundamental C allocation patterns
between root and shoot in woody plants. The first one is associated with determinate
shoot growth limited to late spring and early summer during which most of the
assimilates are directed upward during the flushing episode and then downwards to
the lower stem and roots (eg Picea). The second pattern is associated with
indeterminate shoot growth which extends over most of the growing season (e.g.
Populus) where allocation to root and shoot largely overlap over the whole growing
season. The third pattern (e.g. Quercus) is associated with recurrent leaf flushing and
root and shoot growth peaks alternate. However this view is not entirely supported by
the data presented in Kramer and Kozlowski 1989 (from Lyr and Hoffmann 1967)
showing that root growth precedes shoot growth in Picea abies and Populus
trichocarpa by c. 3 weeks for example and that peak of root and shoot growth are
roughly concomitant in Quercus borealis…
In most fruit trees species examined in (Atkinson 1980) root growth in spring
precedes bud burst. Peak of root growth normally occur in early summer but
sometimes in spring or in autumn depending on species or cultivar. Some
observation of non-synchronous root and shoot maximum growth (notably in apple
trees) have been interpreted as a result of competition between both sinks for
assimilates. Noticeably in one-year-old apple one major peak of root growth
coincided with shoot growth while when the same trees where three years old the
main peak of root growth was delayed until the rate of extension shoot growth was
decreased. Suberized (brown) roots seem to be active in water absorption in apple.
Root longevity also appears to vary significantly with species and a number of biotic
and abiotic factors (Black et al. 1998).
3. THE POINT OF VIEW CHOSEN FOR THE C ALLOCATION MODULE
C allocation is governed by two types of rules
teleonomic (or goal driven) allocation rules based on allometric equations defining the
relative sizes of aboveground sub-compartments and below ground subcompartments. Allometric relationships are supposed to capture internal constraints
not explicitly dealt with in the model (e.g. architectural model and structural stability
constraints or hydraulic constraints) in relation to the tree dimensions.
an optimal allocation assumption (‘functional equilibrium’) between above ground and
below ground mediated through stress indices, which basically assumes that plant
allocates its biomass so as to maximise it’s growth rate under the given
environmental conditions.
Various tree phenological stages are considered, which govern the application of
different sets of rules for C allocation by switching on and off C sinks. Phenological
stage notably determines when NSC pool will act as a sink or a source of C.
Differences/similarities of some important features with some other models that were
considered are reviewed in appendix 1 (Hypar, Walnucas, Simplified SuperTree)
4. DESCRIPTION OF THE MAIN ALGORITHMS AND COMPONENTS
4.1. Tree parts considered
 Stem
 Branches (distinction between stem and branches is necessary because of
alteration of the branch / stem allometry following pruning)
 Foliage
 Coarse (structural) roots
 Fine roots (feeder roots)
C partitioning between fine roots and coarse roots is controlled by the root
development module and is not dependent on a fixed allometric relation but
depends on the tree root geometry, which is adaptive.
No distinction between sapwood and heartwood is considered. This distinction
would notably be important to include if maintenance respiration was to be
estimated correctly. It may also be important for the nutrient budget through
locking-up of nutrient in heartwood (cf Hypar).
4.2. C and N compartments
C and N pools are divided into structural and non-structural pools. N is allocated
to the tree parts according to target (structural) N contents.
a) Management of C reserves
Location
NSC is considered to be homogeneously spread and entirely located in woody tissues
(stem, branch and coarse roots) and reserve pool will consequently be affected by
branch pruning or root trenching in proportion to the severed woody biomass.
Note: reserve pools are not affected by senescence of woody biomass but could be
made so.
Flows to and from NSC pool
C flows from NSC pool to fuel growth may occur only if the following conditions are
simultaneously met
 There is significant imbalance in tree structure
 Phenological stage allows (from early spring to end of foliage expansion)
Only imbalance within aboveground compartments is considered here. A possible
extension of a similar concept to root:shoot imbalance following pruning is discussed
under section 4.8. Imbalance is here defined as the departure from the allometric rules
of the foraging organs (leaves in this case).
ImbThreshold= |1- (LF/LFtarget )| (i)
where
LF is the current Leaf carbon mass Fraction of the aboveground compartment
LFtarget is the predicted carbon mass fraction of leaf according to allometric equations
If ImbThreshold is more than a given threshold, (to be calibrated later and which may
be considered a parameter common to all species at first), then remobilisation of NSC
will occur at a fixed daily rate. This amount of daily mobilisation of NSC
(maxDailyNSC) can be set equal to a fixed percentage of the total structural C pool in
first approximation and will need to be adjusted per species based on observed
dynamics of growth on favourable sites.
Note that it is possible that not all the C potentially remobilised a given day is
converted into structural biomass as growth stresses may limit the actual conversion
rate. Hence even in the period when remobilisation is possible NSC pool may actually
increase if C-uptake is significant and growth much constrained.
The sensitivity of this maximum rate of NSC remobilisation (a parameter which will
not be measured…) will need to be assessed carefully. However C-uptake and stress
levels rather than NSC remobilisation rate will rapidly take over in governing the
overall growth dynamics, and this rate may not be very sensitive in fine.
Outside periods of possible remobilisation of NSC, the NSC pool acts as a sink. This
sink is set proportional to the total tree woody biomass (targetNSCFraction) and has
priority over growth of woody tissues. Alternatively allocation to NSC could set to be
proportional to the newly formed long-lived structural C (see paragraph on future
improvements). Even though reserves accumulation and woody tissue growth may be
non-overlapping in time (with more accumulation than growth towards the end of the
growing season) and differently affected by environmental stress they are functionally
and structurally linked and allocation of C to reserves as a fixed fraction of (new)
wood (and coarse root) tissue seems to be an acceptable simplification (Barbaroux and
Bréda 2002).
In addition to this minimum amount of daily C-uptake allocated to reserves, if growth
is limited more than C-uptake the surplus of C not incorporated into new biomass is
diverted to the NSC reserve pool. In this regard it seems important to include an
explicit dependence of growth rate on temperature, which is likely to be a significant
limiting factor at northern latitudes. The calibration of such a function remains
however problematic.
b) N uptake and allocation dynamics.
Within tree N recycling is quantitatively important as exemplified by the fact that 60%
of annual N demand in mature walnuts was shown to be derived from N redistribution
from internal pools (Weinbaum and Kessel 1998). In certain species up to 90% of the
leaf N may be derived from storage N (Millard 1996).
In deciduous trees, N is predominantly stored as protein in the bark and roots during
the winter and remobilized in the spring when the buds break. During the summer, N
is stored in the leaves and a proportion is withdrawn during senescence.(Millard et al.
1995).
N uptake does not necessarily cease with dormancy and can amount for as much as
50% of total annual N uptake in Nothofagus fusca (Stephens et al. 2001) and
substantial amounts were reported to be absorbed between leaf fall and bud break in
Pecan tree (Acuna et al. 2003). This suggests that including active N absorption
mechanisms and diffusion processes may be crucial to correctly estimate year-round
N balance in the system.
Due to lack of quantitative data for the various tree species under consideration and
consistent with the crude N repartition in the foliage adopted (supposedly
homogeneous), a simplistic N balance module is proposed.
Overall N demand is defined by the sum of the product of the various compartments
size with the N/C optimum ratios in each compartment multiplied by
targetNcoefficent (which defines the total tree demand). N absorption may occur
even when demand is 0 as defined by the luxuryNCoefficient.
If total tree N concentration falls below the overall optimal N/C ratio (defined by the
weighted sum of all structural compartments) N stress occurs. Above the overall
optimal ratio N is assumed to be non-limiting.
N is freely remobilised from the NSN pool in case N uptake is insufficient to maintain
N/C ratios in the different structural compartments at target N/C levels, as is the case
in particular in spring. NSN is considered to be located entirely in and proportionally
to the woody biomass (and is affected by pruning proportionally to the woody
biomass severed).
Based on the general observation that under low nutrient supply starch accumulates
(Poorter and Villar 1997 in (Poorter 2001)) N stress is considered to affect both C
uptake and C conversion rate (in the latter case inducing higher rates of NSC
accumulation).
Partial N recovery by translocation from dying leaves is included (to be measured, set
to 50% at this stage (cf Kramer and Kozlowski 1979).
4.3. Above-ground allometric and geometric equations
Relative dimensions of the aboveground part of the tree are forcing functions in the
model (except for crown volume which may be altered by pruning) which serve as
guides to the distribution of biomass between compartments and in space within
compartments.
Diameter-height relations, stem profile and crown diameter
A first allometric equation links total tree height (H) to diameter at breast height (D)
H=cD^d (i)
This relation is known to be altered by tree density (Cabanettes et al. 1998) and
pruning
(http://www.for.gov.bc.ca/hfp/forsite/training/growth-and-yield/gy-07.htm).
Those parameters are therefore characteristic of a given context i.e. a combination of
a tree species, a tree spacing and a tree management regime. Those parameters are
not dynamically altered by pruning or thinning in the model.
Data from the French Inventaire Forestier National were used to calibrate those
relation for wild cherry, black walnut and poplar.
Only poplar data were adequate to assess impact of planting density on the heightdbh relation, as illustrated below. For the other two species data of tree growing in
55
50
45
density classes range from <100 trees per ha (lower most line)
to > 500 trees per ha (upper most line)
40
height (m)
35
30
25
20
15
10
5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
dbh (m)
hedges were used.
Figure 43-1: Height-dbh relationship adjusted for planting density (Poplar I214 clone)
Stem profile is known to be altered by pruning, planting density and age (Niklas
1995). However we considered a single equation per species to relate stem volume
to tree height and diameter, following the model proposed by (Pryor 1988) in which
log transformed values of stem volume are regressed against log transformed values
of D & H.
A linear relationship between crown width and dbh is assumed and parameterised for
each species (this relation is extremely stable and may be assumed to be
independent of planting density in first approximation).
900
800
CROWNDIAM
700
600
Fig 43-2: DBH and
crown
diameter
relation in walnut (data
courtesy of AMAP)
500
400
300
200
100
0
5
10
DBH
15
20
Crown length is derived from total tree height and crown base height. Crown base
height is set at initialisation and only altered by pruning (no natural branch shedding
considered)
In addition to the above “outer dimensions” description, it is necessary to estimate the
biomass relationships between the different compartments. The driving variable in
biomass allocation in the above ground tree part is the stem biomass. Biomass of
stem is fully determined from stem volume and wood density. From the stem size
and crown base height the crown volume is determined. However the biomass of
branches and leaves per unit crown volume is likely to depend on the tree
architectural characteristics and may vary with tree size and this will need to be
estimated.
The ratio of foliage biomass to wood biomass in beech has been to decrease
significantly with increasing tree size (Bartelink 1997).
To assess the variations in the relative size of the various compartments in relation to
crown volume, species and planting density, it was proposed to use AMAP mock-ups
to simulate typical trees of various sizes growing under various planting densities.
For the time being a common allometric relation is used for all species to relate
branch volume to crown volume. Parameters are based on data published by
Bartelink (1997).
BranchVolumeRatio= aBranchVolume * crownVolume^bBranchVolume
Leaf biomass is set to a fixed proportion of the crown volume (through a species
specific Leaf Area Density parameter which is also used in the light interception
module).
Alternatively a simple model could be derived from the pipe model theory if the
proportion of over-wintering functional xylem can be ascertained for each species
(see paragraph on future improvements)
Assuming a fixed “triaxial ellipsoid” to describe crown shape, the crown volume V is
related to the three half-axis values a, b and c by
V = 4/3*Pi*a*b*c (ii)
(or V= 4/6*Pi*a*b*c (ii’) in case of a half ellipsoid)
Parameters a and b (horizontal axes) are constrained respectively by inter-tree
distances on the line and inter line distances.
Figure 43-3: View from
above
illustrating
constraints
applied
to
lateral crown expansion by
inter-tree planting distance
Crown deformation as a function of planting pattern is only applicable to regular
planting patterns and assumes equivalent development of all trees.
Maximum values for a and b (horizontal radii) are defined respectively as on the line
inter-tree distance and inter-row distance (possibly adjusted during growth if stand
thinning occurs). In other words each tree is allocated a vital surface of a * b (m^2).
We assume that the allometric relationship linking dbh to crown width reflects the
relationship between crown projection and stem section for symmetric crowns. Hence
from dbh we infer the expected equivalent radius r if r > amax then b is defined as
r^2/amax. If b exceeds bmax lateral canopy expansion is halted. Growth in diameter
and growth in height will however continue based on diameter-height allometry hence
violating the dbh-crown_width relationship.
Another possibility considered would be to relax this spatial constraint by allowing
additional crown expansion to mimic the fact that as trees come into contact the
interstitial space between crowns will continue to be gradually filled until the full
projection of the space is saturated (completely closed canopy). Hence we could
tolerate further growth of horizontal axes until the equivalent section reaches the
surface = amax*bmax. This however may be difficult to reconcile with the light model
which does not consider crown intersection and hence this option is not implemented
at this stage.
4.4 Crown shape and crown volume alteration by pruning
Two types of crow shapes are considered: complete triaxial ellipsoid and half triaxial
ellipsoids (truncated on the vertical axis). The first type would apply to poplar (upward
general orientation of branches). The second type would be preferred for oak, wild
cherry and walnut.
Pruning is defined by a reduction of canopy length expressed a fraction of initial
length removed.
Let a and b be the horizontal radii and c be the vertical radius before pruning. And a’,
b’ and c’ the radii values after pruning.
Pruning will reduce vertical axis by a certain fraction X (between 0 and 1) and the
new vertical radius is simply computed as c’ = (1-X) c
The new horizontal radii are computed as half the width of the ellipsoid before
pruning measured at the height of new centre of ellipsoid (see 2D diagram below)
a’ = a * sin(acos(X)) and b’=b * sin(acos(X))
Fig: 44-1: Sketch of pruning effect
c’
a’
a
Fig. 44-2: fraction of volume removed
V(x) as a fraction of canopy length
removed (x)
c
1
1
0.5
V( x)
0
0
0
0.5
1
0
x
1
Canopy thinning is also possible and will alter the leaf area density and branch
volume without changing canopy shape.
4.5 Belowground allometric relationship
Coarse root-to fine root allocation ratios are governed by the root module and are not
discussed here.
Locally driven senescence (water logging), or root growth cessation may need to be
considered and fed back from the tree root growth model to the C allocation module.
4.6. Phenology
Phenology remains fairly crude. In particular no tree flowering or fruiting is yet
implemented. Change from one phenological stage to the next is based on
accumulated degree-days, or average minimum temperature over a time window.
Developmental stages considered are based on (Dupraz and Lecomte 2003)
Dormancy
End of dormancy is triggered when a threshold temperature sum has been reached.
Start of dormancy is concomitant to end of leaf fall
Growth
Growth starts with bud-burst and ceases with leaf fall. Leaf fall occurs at a given date
at a given location and may be hastened by lower than usual temperatures (but this
function has not yet been calibrated). Stem growth is known to precede budburst in
ring porous trees in relation to the lack of over wintering functional xylem. This is
neglected here and should not have major impacts on overall growth of the various
plant components as this growth is fuelled by internal remobilisation of C and N
resources. Probably more important to predict the outcome of competition between
tree and the crop would be to assess whether root growth is indeed synchronous (as
implemented by default) or rather precedes leaf flush by a significant period of time.
Active foliage expansion period
During the leaf expansion phase, almost all assimilates are allocated to non-woody
tissues, i.e., leaves and fines roots as those sink forces are much stronger since
those compartments start from zero (or much reduced values for fine roots) each
spring. Length of period of active foliage development is likely to depend on current
trophic conditions (see note mentioned above). This could be explicitly included
provided that we have a clear understanding of what kind of physiological stress
maybe used to trigger cessation of foliage expansion.
Growth without additional leaf growth
Once initial leaf flush has ceased all additional C will be allocated to roots, woody
biomass and NSC. During the wood production phase, only leaf sink is switched off
(by default fine roots sink is not but it may need to be adjusted as well).
4.7. Implementation of the optimal allocation assumption
The degree of “reactivity” in root:shoot equilibrium is species-specific and governed
by three parameters RSNoStressResponsiveness, NdesatResponsiveness,
WstressResponsiveness.
N and H20 limitations affect overall daily growth rate (conversion rate of available
NSC to new organs), C uptake rate per unit leaf area (negative impact of both water
stress and sub-optimal nitrogen content), and the relative allocation to above vs.
below ground.
An index of global N status is introduced which will affect relative allocation to aboveand belowground compartments. If N content is above the target overall nitrogen
content, C allocation to the aerial part is increased, whereas if N content falls below
this level allocation to roots is increased. Preliminary tests suggest that due to the
annual loss of N following leaf and root senescence and the fluctuating size of these
compartments, this target level should be set slightly above the N level defined by
the optimum N concentrations otherwise every other year the tree faces severe N
shortage once N starts becoming limiting. This is level of N content is controlled by
the targetNcontent parameter.
A Nitrogen saturation index (Nsat) is defined which may affect biomass allocation in
the absence of water (or nitrogen) limitations.
Let Ntot be the current total N pool size
Let Nmax be the maximum N pool size (defined as Nopti * targetNcontent
*NluxuryCoeff)
Let Ntarget be the base level of the N pool above which saturation is measured
(defined as Nopti * NtargetCoeff)
Then
Nsat = 1- ((Ntot-Ntarget)/(NMax-Ntarget)) if Ntot>Ntarget and 0 otherwise.
When saturation is above 0 the fraction of the structural biomass increment allocated
to roots β’ is computed as
 '    1  N sat 
NoStress
(iii)
where
β is the default allocation fraction of C to roots
Nsat saturation of the maximum admissible NSN pool
δNoStress a parameter governing the capacity of the plant to reallocate growth to
aerial fraction in case of nitrogen saturation (RSNoStressResponsiveness)
Note that in case of full saturation root growth is altogether stopped. Hence this
function is inactivated in early spring (during the first growth flush as initial root
growth will occur whatever the level of internal N reserves) i.e. when aboveground
imbalance is above 90%.
Similarly Ndesat measures the deficit of N (relative to the target level) and is defined as
Ndesat = Ntot/NTarget if Ntot<NTarget and 1 otherwise
N-demand (an input to the belowground competition module) is defined as
max(Ntarget-Ntot,0)
Daily water deficit is defined as (1-ETR/ETP). See below how water demand is
computed.
RUE is affected proportionally to this water deficit.
The same water stress index is used to modify growth rate (C conversion rate) and
RUE. The rational for this being that there are strong evidences that water may limit
growth directly (in addition to C uptake limitation) i.e. affecting the relative fraction of
C allocated to NSC. However contrary to the case of low nutrient availability, starch
does not seem accumulate in leaves at low water supply (Chaves 1991 in (Poorter
2001), but see (Barbaroux and Bréda 2002) and also (Chaves et al. 2002))
suggesting that a C conversion rate reducer based on water stress may not be
necessary or could at least be downplayed.
At present the modifier used to decrease growth rate (in addition to RUE) is a power
of the daily water stress index (default power coefficient = 0.2) that ensures that only
strong stresses have a significant impact on NSC conversion rate.
Root:shoot allocation is also considered to be affected by water availability (see this
section below) but a time-averaged value (over the last 10 days) is used instead of
the daily water stress.
Time-averaged water stress and N status index (referred to as
TimeAveragedWstress and Ndesat) may be compound (default implementation) or
alternatively only the maximum of both stresses may be applied when computing the
modification in the root:shoot grozth partitioning.
Both (Canham et al. 1996) working with tree seedlings and (Poorter and Nagel 2000)
in their quantitative review for plants observed that C allocation to roots was affected
more strongly by variation in soil nitrogen availability than it was by soil moisture
availability. Hence the general implementation proposed is the following:
 '    Ndesat 
Nstress
 TimeAveragedWstress Wstress
(iv)
or
 '    Max( Ndesat 
where
Nstress
, TimeAveragedWstress Wstress )
(iv’)
α’ is the new fraction of total C allocated to growth which is allocated to the
aboveground compartment
α is the default fraction of C allocated to shoot, which is equal to current shoot
fraction
N-desat and W-stress stand respectively for Nitrogen saturation deficit and Water
stress indices (both between 0 and 1). N desat is similar to a stress index in that it is
equal to 1 in the absence of deficit and decreases as deficit increases.
δNstress , δWstress are parameters characterising the species specific "responsiveness"
to N-stress or W-stress, which control the amplitude of the functional response to
stress
Introduction
of
the
δNstress
,
δWstress
parameters
called
NitrogenDesatResponsiveness and WaterStressResponsiveness will allow
simulating different plant strategies. For example seedlings of Quercus rubra
appeared more conservative than Acer rubrum seedlings in terms of there allocation
of C in response to limited N availability (Canham et al. 1996). It is also a way of
explicitly introducing the greater responsiveness of root:shoot allocation pattern to N
shortage than water shortage. Calibration of these parameters may however prove
uneasy.
4.8. Senescence
Within growing season turnover rates of coarse roots, branches and leaves (by
default set to 0.0005) are considered and determine daily senescence rate of both
compartments. Fine root senescence rate is computed in the root growth module.
Accelerated end of growing season mortality of leaves is triggered by phenology (as
described in (Dupraz and Lecomte 2003).
Exceptional senescence induced by pruning in the unprunned compartment is not
considered in the model due to lack of clear evidence and quantitative estimates, but
could be implemented if need be (see section below). Neither is accelerated leaf fall
triggered by prolonged stress included at this stage.
A default small turnover rate of stem compartment (to account for bark fall) could be
added.
4.9. C flow alteration following severe pruning
If frequency and severity of pruning remains moderate it is likely that the optimal
allocation paradigm governing above and belowground C apportioning will suffice to
describe tree response to pruning. If pruning becomes very intense (like in the case
of coppicing for example) and compensatory growth is expected to be largely fuelled
by NSC remobilisation (rather than by mere reorientation of steady state C flows)
then this would need to be included in the model.
It would then be necessary to introduce a new teleonomic assumption by which the
tree would seek to recover the root:shoot equilibrium prevailing before pruning, and
to define what level of pruning severity would determine dye-back of the overdeveloped compartment.
Such additional complexity is not deemed necessary or even desirable at this stage.
4.10. Tree water demand
The following notations are used throughout the present paragraph
∆ rate of change of saturating water vapour pressure with temperature evaluated at
ambient temperature
A energy available above canopy (Rn –S), with Rn net radiation above surface, S
subsurface heat flow (W. m-2 )
Rn net radiation = (1-a) Rs-Rl
a albedo (0.05 for water surface, 0.23 for green leaves)
Rl long-wave heat radiation (W m-2) computed as
5.67 10-8 (Ta+273,16)4 (0.56-0.08ea0.5) (0.1+0.9n/N)
with n duration of the number of sunshine hours (h)
n day length (h)
ea actual water vapor pressure in the air (hPa)
Ta temperature of the air (° Celsius)
γ psychometric constant ( = 0.67 hPa. K-1)
Lv Latent heat of vaporization for water (L=2.454 MJ. kg-1 at 20 °C)
ρw, density of water
ρ , density of air (1.2047 kg. m-3) .
cp specific heat of the unit mass of the air (cp = 1004 J. kg-1. K-1)
E evaporation rate (volume of water per unit land area per unit time); 1 W. m -2 ≈
0.0352 mm. d-1
Da water vapour pressure deficit in the air surrounding the plot (weather input)
rat tree canopy aerodynamic resistance, dependent on wind speed s.m-1
rst tree canopy stomatal conductance, s.m-1
Ts (tree) leaf temperature (° Celsius)
In the first version of the Hi-SAFE model tree and crop water demand are uncoupled
(the scene is treated as a patchy environment) and tree water demand is simply
computed based on Penman-Monteith formula
Lv ρw ETranspitree = (∆ Atree + cp ρ Da / rat)/ (∆ + γ + γ (rst/rat ))
(3)
In case the foliage is wet the potential transpiration is simply decreased by the
amount of water stored on foliage
Finally using actual transpiration rate (once competition has occurred) the tree
foliage temperature can be recomputed as
Ts = Ta + ra .(Rn - Lv ρw ETtree)/(  . cp)
(10)
Note: There exist numerous equations for calculating ra as a function of wind speed u (m. s-1)
and crop height Hc (m). One of them is
ra = [ln(z-dc)/z0]2/[k2 .uz]
where
dc = 0.63. Hc
z0 = 0.13. Hc
(14)
(15)
(16)
z is the reference height (m), usually 2 m taken here as being equal to tree height + 1 m, dc is a
so called zero plane displacement (m), z0 the roughness length (m), k is von Karman's
constant (k=0.41) and uz is wind speed (m. s-1) measured at height z (supposed to be equal to
measured wind speed at standard height) and Hc is the tree height.
5. FUTURE IMPROVEMENTS AND POTENTIAL ISSUES
5.1. Suggested future improvements to the C allocation
 Temperature effects
Calibrating impact of temperature on RUE and partitioning to reserve pool
(reflecting change in rate of C incorporation into functional or structural C) and
remobilisation rate will be uneasy though it may be important in explaining
between site and between year variations in tree growth.
Both the rate of conversion of NSC to new tissues, and the RUE are temperature
dependent. The latter may be roughly estimated from bibliographic search. The
former (much like the respiration parameters) is more elusive but should have
marginal effects on overall growth and may be neglected in first approximation.
After (Jones 1993) the following shape of temperature response may be used
(were k is the reduction in the rate under concern at a given temperature)
1.0
Fig 51-1: Proposed temperature
response curve
reducer
0.8
0.6
K(t) = max(
0.4
(2*(t+Tmin)^2 *(Tmax+Tmin)^2
-(t+Tmin)^4)/(Tmax+Tmin)^4,0)
0.2
0.0
0
10
20
30
40
temperature (deg C)
50
(e.g. Tmin=0, Tmax=30)
 Branch volume calculations – Pipe model application
Allometric relations between leaf surface (and crown volume) and branch
biomass may be derived by application of the pipe model theory. Next version
may include this functional constraint in the model allowing parameterising this
allocation fraction to woody biomass according to the type of wood (diffuse
porous, semi-diffuse or ring porous)
 Long term non-stomatal water stress
We may also need to introduce a water stress index to take into account the
nonstomatal limitation of photosynthesis during drought. According to Kozlowski
and Pallardy (Kozlowski and Pallardy 1996), the relative importance of stomatal
and non-stomatal inhibition of photosynthesis during drought varies with the
drought tolerance of the species, increasing in xeric plants under drought but
decreasing in mesic plants. Non-stomatal inhibition of photosynthesis are
considered by those authors to be especially important in the long term and
under severe water deficit. Some species show after-effects of water deficits on
photosynthesis that may last for weeks or months after irrigation resumes. This
calls for the introduction of a water stress index which could be used to reduce
further photosynthesis under severe drought and which recovery could be made
time dependent.
Such an index could be based on accumulated days of water deficit above a
certain threshold. An explicit time recovery function could be introduced (based
on a daily recovery fraction for example as done in (Noordwijk and Lusiana
2000)).
5.2. Potential issues
Even though we have tried to keep the number of parameters to a minimum some
calibration problems will undoubtedly arise.
The root:shoot equilibrium assumption combined with fixed allometric ratios within
above ground and below-ground compartment may prove awkward. If there is solid
evidence in support of the functional equilibrium assumption, it seems that this is best
expressed when dissociating foraging organs from structural organs. E.g. stem and
branch fraction are affected differently by limiting light availability (Korner 1994;
Poorter and Nagel 2000).
Linking phenology to extreme events e.g. early frost impact on N remobilisation and
leaf shedding, leaf fall triggered by water stress (a common reaction in black walnut
and poplar according to (Kozlowski and Pallardy 1996).
N balance is based on average values per compartment. However nitrogen content
in woody tree parts decreases with age and therefore the N balance as it is
computed presently is biased.
STELLA IMPLEMENTATION AND TESTING
Introduction
The model was first implemented under Stella (see full set of equations in Appendix)
to test the internal consistency of the proposed approach and explore the general
behaviour of the model.
A full assessment of this module cannot be conducted while it is disconnected from
the other modules. To conduct sensitivity analysis tests fixed resource capture
efficiencies were used as forcing variables
LUE = 3 g x m-1 x d-1 for light capture (0.003)
A default rate of 0.001 kg N per kg of C of fine roots was used for N absorption
efficiency
Water deficit was simulated by imposing a particular stress level throughout one (or
more) growing seasons or on a series of days of the growing season. Nuptake was
reduced by a factor equal to the water stress value.
In addition, a simple allometric relation was used to link fine roots biomass to total
below ground biomass and a fixed fine root mortality rate was used to simulate root
development (as substitute of the input from the root growth module in the full
model).
Extensive tests were conducted leading to the conclusion that the models prediction
are sensible and that all parameter tested are sensitive at least under a particular set
of values of the other parameters. A few examples are given below to illustrate the
general behaviour of the model.
Sensitivity Analysis Test Runs
Example 1: Nresponsiveness – 20 year run
Input variables
NResponsiveness Run #
0.5
1
1
2
1.5
3
2
4
Output variables: DBH, root:shoot allocation; Nstress
1: TreeDBH
1:
2: TreeDBH
3: TreeDBH
4: TreeDBH
0,65
3
4
2
1:
0,40
3
4
2
2
3
4
1
1
1
1:
0,15
1
0.00
2
3
4
1825.00
Graph 1: p2 (Untitled)
3650.00
5475.00
Time
18:32
7300.00
mer 8 sep 2004
Figure SA1-1:
Tree diameter
at breast height
1-4: Root:Shoot ratio v . TotalStructuralC
0,30
Figure SA1-2:
Root:shoot ratio
0,15
0,00
0,00
1000,00
2000,00
Graph 1: p1 (Untitl… TotalStructuralC
1: NStress
1:
2: NStress
18:32
3: NStress
mer 8 sep 2004
4: NStress
1,05
1
2
3
4
1
2
3
4
3
4
3
4
Figure SA1-3 :
Nstress
2
2
1:
0,95
1
1
1:
0,85
0.00
1825.00
Graph 1: p3 (Untitled)
3650.00
5475.00
Time
18:32
7300.00
mer 8 sep 2004
Discussion
With the parameter values and initial state variable values used in this series of test
runs, tree dbh is severely constrained by an NResponsiveness value of 0.5. At this
level of the parameter, the tree fails to alter its root:shoot allocation fraction
sufficiently (figure 2) and suffers systematic nitrogen stress throughout the growing
season (figure 3) leading to a gradually decreasing annual growth after year 5
Example 2: LUE – 20 year runs
LUE (g. m-2. d-1) # run
0.0015
1
0.002
2
0.0025
3
0.003
4
Output variables: DBH, total structural C, root:shoot ratio
1: TreeDBH
1:
2: TreeDBH
3: TreeDBH
4: TreeDBH
0.65
4
4
1:
Fig.
SA2-1:
Tree diameter
3
0.40
3
4
2
3
2
4
1:
0.15
1
0.00
2
3
1
1825.00
Graph 1: p2 (Untitled)
2
1
3650.00
Time
1
5475.00
7300.00
11:17 PM Wed, Sep 08, 2004
1: TotalStructuralC
1:
2: TotalStructuralC
3: TotalStructuralC
4: TotalStructuralC
2000.00
4
1:
1000.00
4
Fig.
SA2-2:
Total
Structural C
accumulation
3
3
4
1
1:
3
2
4
1
2
3
1
2
2
1
0.00
0.00
1825.00
3650.00
Graph 1: p4 (Untitled)
5475.00
Time
7300.00
11:17 PM Wed, Sep 08, 2004
1-4: Root:Shoot ratio v . TotalStructuralC
0.30
Figure SA2-3:
root:shoot ratio
0.15
0.00
0.00
1000.00
Graph 1: p1 (Untitl… TotalStructuralC
2000.00
11:17 PM Wed, Sep 08, 2004
Discussion
Effect of LUE on tree dbh is almost linear resulting in an additional increment in dbh
of ca. 12 cm after 20 years per 0.0005 unit increment in LUE (fig 1) whereas the
effect on total structural C is exponential (figure 2) as expected. Faster growing trees
invest more C into roots (figure 2) as they experience earlier and stronger N stresses
(data not shown).
Slow growing trees (runs # 1 & 2) actually show a gradual decrease in annual dbh
increment. This decreasing return is associated with a steady decrease of the
root:shoot ratio. Slow growing trees experience later and milder N stress (data not
shown) and fail to increase significantly their below-ground C allocation fraction (N
responsiveness was set to 1 for this series of run, but qualitatively similar results are
obtained by setting Nresponsiveness to 2). Trees simply dry out of carbon when LUE
is set to 0.0015 or lower.
Example 3: Canopy pruning intensity
Canopy pruning is set to occur on year 3. Runs are made for five years. Three
pruning intensities are compared
1-9: TreeDBH
1:
0.23
1:
0.20
1:
0.16
Fig.
SA3-1:
impact
of
canopy
pruning (0%,
25% and 50
% intensity on
tree dbh)
0.00
456.25
Graph 1: p2 (Untitled)
912.50
Time
1368.75
1825.00
12:20 AM Thu, Sep 09, 2004
1-9: AGAllocFrac
1:
0.90
1:
0.70
1:
0.50
Fig SA3-2: alteration
of Above ground
allocation
fraction
following
canopy
pruning
0.00
456.25
Graph 1: p5 (Untitled)
912.50
Time
1368.75
1825.00
12:20 AM Thu, Sep 09, 2004
Discussion
Canopy pruning of 50% intensity reduces dbh increment on year 3 clearly less than
50% (fig 1) due to an increase in the above ground allocation fraction (fig 2) as
determined
by
the
functional
equilibrium
implemented.
Appendix 1 : List of the main parameters used in C allocation module
PARAMETER
DEFINITION
Def Value Range
(wild
cherry)
NSC pool management
targetCLabilePoolSize (kg)
steadyStateSavingFraction
imbalanceThreshold
controls growth rate when growth is fuelled by reserve remobilisation 0.005
fraction of C allocated to NSC pool under normal (autotrophic)
growth conditions
0.05
Level of relative imbalance in C partitioning between foraging and
structural organs above which growth becomes strictly autotrophic
(no more C remobilisation from NSC reserves)
0.7
Root:shoot ratio
waterStressResponsiveness
power coefficient
nitrogenStressResponsiveness power coefficient
RSNoStressResponsiveness
power coefficient
0.0010.05
0.01-0.10
0.1-0.9
1
2
0-2
0-2
Nitrogen balance
OptiNCBranch
optiNCCoarseRoot
OptiNCFineRoot
OptiNCFoliage
OptiNCStem
targetNCoefficient
functional optimum N/C concentration
functional optimum N/C concentration
functional optimum N/C concentration
functional optimum N/C concentration
functional optimum N/C concentration
coefficient applied to optimum to define target concentration
0.01
0.01
0.02
0.04
0.01
1.2
1-1.3
luxuryNCoefficient
Coefficient applied to optimum to define maximum concentration
2
1.5-3
leafNRemobilisationFraction
fraction of LeafN remobilised before leaf fall
fineRootNRemobilisationFraction fraction of fineRootN remobilised before root death
0.5
0.5
Tree size and allometries
aTree
bTree
aCrownVolume
bCrownVolume
AStemVolume
BStemVolume
cStemVolume
allometric coefficient linking diameter to height
allometric coefficient linking diameter to height
allometric coefficient linking diameter to crown width
allometric coefficient linking diameter to crown width
allometric coeff. linking stem volume to height and dbh -1.984 (P)
allometric coeff. linking stem volume to height and dbh 1.846 (P)
allometric coeff. linking stem volume to height and dbh 1.2148 (P)
126
0.692
15.8
1.19
-8.821
2.131
0.4723
aBranchVolume
bBranchVolume
Allometric coeff. Linking branch volume ratio to crown volume
Allometric coeff. Linking branch volume ratio to crown volume
0.0005
0.2
Carbon content
leafCarbonContent (g/g)
specificLeafMass (kg/m2)
woodDensity (g/dm3)
Leaf carbon content (g C g total dry biomass)
Leaf dry mass per unit leaf area
Dry wood density
0.6
0.05
500
Default senescence rates
LeafSenescenceRate
Daily leaf senescence rate
0.0005
0.0005
(?)
0.0005
branchSenescenceRate
coarseRootSenescenceRate
fastSenescenceRate
FineRootSenescenceRate
MISCELLANEOUS
Daily branch senescence rate
Daily coarse root senescence rate
leaf senescence rate once leaf fall has started (see phenology
module)
0.1
Daily fine root senescence rate
0.005
0-1
0-1
Radiation Use Efficiency (g/MJ
solar radiation)
Maximum RUE (no stress)
2
Maximum daily NSC remobilisation rate (expressed per unit
maxDailyNSC
structural C)
0.001
1-3
Appendix 2
Table comparing selected features of different tree growth modules in different models: Wanulcas version 2.0 (Noordwijk and
Lusiana 2000); Hypar version 3.0 (Mobbs et al. 1999); "Simple SuperTree" (van Oijen 2003)
Features
Aboveground
geometry
Hi-SAFE (this draft)
Tree Triaxial ellipsoid
Tree organs
Phenological stages
Foliage, stem, branches,
coarse roots and fine
roots
(Fruits to be added later
on)
Dormancy,
foliage
expansion, tree growth
without additional foliage
growth
Walnucas
Cylinder +
Ellipsoid
Hypar
Truncated Ellipsoid
Leaves+twigs,
bare
stem, branches, coarse
roots and fine roots
(+ fruit, latex…)
SimpleSuperTree
None
Foliage
(multilayered), Foliage, stem, coarse
sapwood +bark, heart roots and fine roots
wood, coarse roots and
fine roots
(Sexual
immaturity), Dormancy, growth
Flowering, fruiting
None
Non Structural Carbon Explicit NSC pool, size Explicit « carbohydrate Implicit NSC pool (C Explicit C labile pool
pool
linked to tree size
reserve pool » in stem
remobilisation
from
sapwood)
Non
Structural Explicit
NSN
pool, Implicit (limited luxury Implicit (limited luxury Explicit
NSN
pool,
Nitrogen pool
maximum size of which consumption allowed)
consumption allowed)
(unbound N uptake);
is controlled by tree size
C allocation
Above and belowground Above and belowground
partitioning based on partitioning based on
dynamic
functional dynamic
functional
equilibrium (an explicit equilibrium (an explicit
Allometric
relation
between tree diameter
and
total
woody
biomass; Fixed ratio
Above and belowground
partitioning based on
dynamic
functional
equilibrium
mediated
response to sub-optimal
water
and
nitrogen
availability);
Separate
allometric rules drive
partitioning between AG
sub compartments and
BG sub compartments;
response to sub-optimal
water
and
nitrogen
availability);
Separate
allometric rules drive
partitioning between AG
sub compartments and
BG sub compartments
N flows
Follow
C
flows;
Saturation
levels
of
nitrogen in all organs
vary in parallel;
Remobilisation
occurs
from senescing leaves
and fine roots
Follow
C
flows;
Saturation
levels
of
nitrogen in all organs
vary in parallel;
No remobilisation from
senescing organs
Maintenance
Respiration
None
None
Growth respiration
None
None
between
aboveground
and below ground woody
biomass; Fixed C ratio
between fine root and
foliage biomass; Fixed
ratio between sap wood
area and subtended leaf
area
Follow
C
flows
;
Saturation
levels
of
nitrogen in all organs
vary in parallel;
Optimal allocation of N in
the foliage; Rubiscobound,
chlrorophyllbound
and
other
“structural”
N
distinguished;
Remobilisation
from
senescing leaves and
fine roots
through relative size of
labile C & N pools;
Allometry driven in AG
and
BG
sub
compartments (?)
Follow C flows;
Leaf N dynamics largely
independent from other
organs N content via a
routine
simulating
dynamics of leaf protein
synthesis and break
down; Organs N content
unbound;
Depends on organ size, None
N
content
and
temperature
Explicit (single value for None
all organ types)
REFERENCE CITED
Acuna, M. L. E., M. W. Smith, N. O. Maness, B. S. Cheary, B.
L. Carroll and G. V. Johnson (2003). "Influence of
nitrogen application time on nitrogen absorption,
partitioning, and yield of pecan." Journal of the
American Society for Horticultural Science 128(2): 155162.
Atkinson, D. (1980). "The distribution and effectiveness of
the roots of tree crops." Horticultural Reviews 1: 424490.
Barbaroux, C. and N. Bréda (2002). "Contrasting distribution
and seasonal dynamics of carbohydrate reserves in stem
wood of adult ring-porous sessile oak and diffuse-porous
beech trees." Tree Physiology 22: 1201-1210.
Bartelink, H. H. (1997). "Allometric relationships for biomass
and leaf area of beech (Fagus sylvatica L)." Annales des
Sciences Forestieres 54(1): 39-50.
Bartelink, H. H., K. Kramer and G. M. J. Mohren (1997).
"Applicability of the radiation-use efficiency concept
for simulating growth of forest stands." Agricultural and
Forest Meteorology 88(1-4): 169-179.
Black, K. E., C. G. Harbron, M. Franklin, D. Atkinson and J.
E. Hooker (1998). "Differences in root longevity of some
tree species." Tree Physiology 18(4): 259-264.
Bostad, P. V., P. Reich and T. Lee (2003). "Rapid temperature
acclimation of leaf respiration rates in Quercus alba and
Quercus rubra." Tree Physiology 23: 969–976.
Cabanettes, A., D. Auclair, W. Imam and C. Dupraz (1998).
"Diameter and height growth curves for widely-spaced
trees in European agroforestry." Agroforestry Systems
43(1-3): 169-181.
Canham, C. D., A. R. Berkowitz, V. R. Kelly, Lovett, G.M. , S.
V. Ollinger and J. Schnurr (1996). "Biomass allocation
and multiple resource limitation in tree seedlings."
Canadian Journal of Forest Research - Revue Canadienne de
Recherche Forestiere 26(9): 1521-1530.
Canham, C. D., R. K. Kobe, E. F. Latty and R. L. Chazdon
(1999). "Interspecific and intraspecific variation in
tree seedling survival: effects of allocation to roots
versus carbohydrate reserves." Oecologia 121(1): 1-11.
Chaves, M. M., J. S. Pereira, J. Maroco, M. L. Rodrigues, C.
P. P. Ricardo, M. L. Osorio, I. Carvalho, T. Faria and C.
Pinheiro (2002). "How plants cope with water stress in
the field. Photosynthesis and growth." Annals of Botany
89(Special Issue): 907-916.
Coleman, M. D., R. E. Dickson, J. G. Isebrands, D. F.
Karnosky, D. Whitehead and F. M. Kelliher (1996). "Root
growth and physiology of potted and field-grown trembling
aspen exposed to tropospheric ozone." Tree Physiology
16(1-2): 145-152.
Cote, B., N. Belanger, F. Courchesne, J. W. Fyles and W. H.
Hendershot (2003). "A cyclical but asynchronous pattern
of fine root and woody biomass production in a hardwood
forest of southern Quebec and its relationships with
annual variation of temperature and nutrient
availability." Plant and Soil 250(1): 49-57.
Desrochers, A., S. M. Landhausser and V. J. Lieffers (2002).
"Coarse and fine root respiration in aspen (Populus
tremuloides)." Tree Physiology 22(10): 725-732.
Dickmann, D. I., P. V. Nguyen and K. S. Pregitzer (1996).
"Effects of irrigation and coppicing on above-ground
growth, physiology, and fine-root dynamics of two fieldgrown hybrid poplar clones." Forest Ecology and
Management 80(1-3): 163-174.
Dupraz, C. and I. Lecomte (2003). Proposal for a simple
phenology module in Hi-SAFE. Montpellier, INRA: 4.
Friend, A. L. and M. D. Coleman (1994). Carbon allocation to
root and shoot systems in woody plants. Biology of
adventitious root Formation. T. D. D. a. B. E. Haissig.
New-York, Plenum Press: 245-273.
Geisler, D. and D. C. Ferree (1984). "Response of plants to
root pruning." Horticultural Reviews 6: 155-188.
Hoch, G., A. Richter and C. Korner (2003). "Non-structural
carbon compounds in temperate forest trees." Plant Cell
and Environment 26(7): 1067-1081.
Jones, M. B. (1993). Plant microclimate. Photosynthesis and
production in a changing environment. D. O. Hall, J. M.
O. Scurlock, H. R. Bolhar-Nordenkampf, R. C. Leegood and
S. P. Long. London, Chapman & Hall: 47-64.
Korner, C. (1994). Biomass fractionation in plants: a
reconsideration based on plant functions. A whole plant
perspective on carbon-nitrogen interactions. J. R. E.
Garier. The Hague, SPB Accademic Publishing: 173-185.
Korner, C. (1998). "A re-assessment of high elevation treeline
positions and their explanation." Oecologia 115(4): 445459.
Korner, C. (2003). "Carbon limitation in trees." Journal of
Ecology 91(1): 4-17.
Kozlowski, T. T. and G. S. Pallardy (1996). Physiology of
woody plants, Academic Press.
Lavigne, M. B. and M. G. Ryan (1997). "Growth and maintenance
respiration rates of aspen, black spruce and jack pine
stems at northern and southern BOREAS sites." Tree
Physiology 17: 543-551.
Millard, P. (1996). "Ecophysiology of the internal cycling of
nitrogen for tree growth." Zeitschrift fur
Pflanzenernahrung und Bodenkunde 159(1): 1-10.
Millard, P., M. Tagliavini and G. H. Neilsen (1995). Internal
cycling of nitrogen in trees. Mineral nutrition of
deciduous fruit plants.
Mobbs, D. C., G. Lawson, A. D. Friend, N. M. J. Crout, J. R.
M. Arah and M. G. Hodnet (1999). HYPAR Model for
agroforestry systems, v 3.0, Institute of Terrestrial
Ecology: 113.
Niklas, K. J. (1995). "Size-dependent Allometry of Tree
Height, Diameter and Trunk-taper." Annals of Botany
75(3): 217-227.
Noordwijk, M. v. and B. Lusiana (2000). WaNulCAS v2.0,
Background on a model of water, nutrient and light
capture in agroforestry systems. Bogor, ICRAF.
Poorter, H. and O. Nagel (2000). "The role of biomass
allocation in the growth response of plants to different
levels of light, CO2, nutrients and water: a quantitative
review." Australian Journal of Plant Physiology 27(6):
595-607.
Poorter, L. (2001). "Light-dependent changes in biomass
allocation and their importance for growth of rain forest
tree species." Functional Ecology 15: 113-123.
Pregitzer, K. S., J. S. King, A. J. Burton, S. E. Brown, R.
Norby, A. Fitter and R. Jackson (2000). "Responses of
tree fine roots to temperature." New phytologist 147(1
(Special issue: Root dynamics and global change: An
ecosystem perspective)): 105-115.
Pryor, S. N. (1988). The silviculture and yield of wild
cherry. Forestry Commission Bulletin: No. 75, 23 pp.
Richards, D. (1986). Tree growth and productivity - the role
of roots. Acta Horticulturae.
Stephens, D. W., P. Millard, M. H. Turnbull and D. Whitehead
(2001). "The influence of nitrogen supply on growth and
internal recycling of nitrogen in young Nothofagus fusca
trees." Australian Journal of Plant Physiology 28(3):
249-255.
Stiles, W. C. (1984). "Effects of pruning on growth and size
of trees." Acta Horticulturae 146: 225-229.
Thornley, J. H. M. (1998). "Modelling shoot: root relations:
the only way forward?" Annals of Botany 81: 165-171.
van Oijen, M. (2003). An allocation module for simulation of
trees in SAFE. Edimburgh, CEH: 14.
Weinbaum, S. and C. v. Kessel (1998). "Quantitative estimates
of uptake and internal cycling of 14N-labeled fertilizer
in mature walnut trees." Tree Physiology 18(12): 795-801.
THE MICROCLIMATE MODULE CONCEPT
RAINFALL INTERCEPTION MODULE
Experimental data on stemflow for several species showed that the stemflow
depends on tree crown architecture and is somehow proportional to the tree leaf area
index. This provide a relationship that was implemented in the crop model STICS
(Brisson et al., 2004). The same relationships were proposed for the HiSAFE model.
The rain interception is governed by two equations:
Stemflow ratio:
First, for each tree, a part of the incident rainfall is diverted as stemflow:
Stemflow  Rain  KstemflowM axTree  1- exp - KstemflowT ree  LAI 
Eq. 1
Were Rain is the incident rainfall (mm), Stemflow is the part of the incident rainfall
that reached the soil as stemflow (mm) and LAI is the Leaf Area Index of the tree.
Therefore, the stemflow is governed by 2 parameters :
KstemflowMaxTree : represents the upper limit of the stemflow which means that
over a given crown size, the stemflow no longer increased
KstemflowTree : that represents the proportionality between stemflow and tree leaf.
Crown water storage :
A part of the remaining rainfall is stored in tree crowns. This water contributed to so
called “interception loss” in hydrological models. The volume of water stored per tree
crown depended on surface storage properties of the different organs of the tree :
crown, leaves, branches, bark and on the arrangement between these surfaces
depending on tree architecture.
The storage of water in tree crowns was simply expressed as :
Storage Capacity  Wettabilit yTree  LAI
Eq. 2
Where WettabilityTree expressed the storage capacity of the tree crown per unit of
leaf area (mm).
In the model, the water volume stored in the crown is considered as a tank with a
storage capacity that is daily filled with available rainfall (i.e. rainfall that reached the
crown and was not diverted as stemflow) and emptied by direct evaporation
calculated in the microclimate module. Once the tank is full the additional rainfall is
transmitted to the cells below the tree as throughfall.
Parameters estimation :
For some species stemflow parameters were calculated from published data. For
other species, not studied until now, parameters were calculated using data for
morphologically similar species.
A protocole was proposed for the estimation of storage capacity of the tree crowns.
(see “Rainfall interception parameterisation.doc” for details).
NEW MICROCLIMATE MODULE
Theoretical background
The new microclimate module was implemented in the HiSAFE daily loop, in Java
language under CAPSIS environment. As the previous one, this module used the
Shuttleworth and Wallace formalism (Shuttleworth and Wallace 1985)(see previous
reports for more details). Each water vapour flux is then expressed as :
E i 
sR ni  C p D o / rai
Eq. 3
s   (rci / rai )
Were Ei is the water vapour flux (MJ day-1 m-2), D0 is the saturation deficit of the air
within the canopy (mbar) and Rni is the net radiation of the canopy (MJ day-1 m-2), rci
and rai are canopy and aerodynamic resistances, respectively (s m -1). The other
symbols representing thermodynamic constants
Reciprocally, D0 depends on the actual air saturation deficit (Da) and the sum of all
the radiation and water vapour fluxes (Rn=∑Rni, E=∑Ei) :
D 0  D a  sR n  (s   )E
raa
C p
Eq. 4
As a consequence of that coupling between E fluxes and D 0, a first estimate of D0
must be implemented at the beginning of the daily loop according to the available
information from weather data of the day and actual evapotranspirations of the
previous day. Then, as the fluxes and interactions between trees and crop were
calculated, more accurate estimation of D0 can be provided. Finally the actual value
can be calculated at the end of the daily loop accounting for all the stresses. (full
details of The C++ code skeleton developed for those purpose were in
“MicroclimatHiSAFE.doc”).
Initial D0 estimate
At the beginning of the daily loop, after the radiative transfer module, the first
implementation of Eq. 4 needs estimates of Rni and Ei for each components of the
system, namely trees, crop transpirations, water stored on trees an crops direct
evaporation and soil evaporation.
Each Rni, (one per tree , crop and soil ) was calculated from weather data, solar
radiation absorbed by trees and transmitted to cells. We used, as in STRICS
standard Brutsaert (1975) estimate for long wave radiation. When the canopy
temperature is not available, air temperature is used. These R ni represent the total
available energy per component i.
Rni = Rvi + εi(Ra-σTs4)
Eq. 5
where Rvi is the visible available radiation, calculated by the radiative transfer module
for trees and estimated for cells by
(1-ai)Rgi
Eq. 6
with Rgi , the visible radiation received by the cell calculated by radiative transfer
module and ai, the cell albedo (implemented).
Ra is the atmospheric radiation following Brutsaert (1975) currently implemented in
STICS, εi is the emmissivity of the component i, σ the Stephen-Boltzman constant
and Ts the canopy temperature replaced by Ta , mean daily air temperature from the
weather data.
The available energy is first used for direct evaporation of water present on
vegetation according to Prestley-Taylor equation (1972), hence
E i  
sR n i
s
Eq. 7
Were α is a coefficient calculated by Brisson et al. (1998).
The remaining energy, if any, is then used for trees and crops transpiration according
the rates of the previous day following :
E id  E i ( d 1)
R n id
R n i ( d 1)
Eq. 8
were subscripts d and d-1 means “of the day” and “of the day before” respectively.
Then the water vapour fluxes, E=∑Eid is used for D0 estimation in Eq; 4.
In order to account for tree canopy effects on crop microclimate, D0 is used as Da in
the following STICS instances.
Second D0 and fluxes calculation after the STICS runs
As STICS provide for each cell, crop an soil water vapour fluxes and canopy
temperature estimates. These variables are then used, for providing new estimates of
Rni and Ei that are both used for a D0 calculation : actual Ts replaced Ta in Eq. 5 and
actual crop and soil evaporation and transpiration from STICS are used in Eq. 4 for
an updated D0 estimation.
Then trees direct evaporations and potential transpirations are calculated by Eq. 3
with the updated values of the other variables.
The potential transpiration of trees (from here) and crop (from STICS) are now all
available for the water competition module.
Final canopies energy budget and canopy temperatures estimates
The trees canopy temperatures are calculated using the same formalism as in STICS
to be consistent with crop temperature estimates. In that formalism, the average tree
canopy temperature (TS) is the average of the minimum tree canopy temperature
occurring in the morning before sunrise (T Smin) and the maximum tree canopy
temperature occurring at midday (TSmax). In both cases, the canopy temperature TS
come from the canopy energy budget equation.
H + E + Rn = 0
Eq. 9
with
H
C p
ra
(T  Ts )
Eq. 10
soit
Ts  T  (R n  E)
ra
C p
Eq. 11
For TSmin :
T = Tm (Tm = Minimum temperature of the day from weather data) ; E = 0; Rn
calculated by Eq. 5 with Rvi = 0
For TSmax :
T = Tx(Tx Maximum daily temperature from weather data); E = Emax.