Tree Physiology 20, 477–484
© 2000 Heron Publishing—Victoria, Canada
Managing forests for wood yield and carbon storage: a theoretical
study
J. H. M. THORNLEY and M. G. R. CANNELL
Institute of Terrestrial Ecology, Bush Estate, Penicuik, Midlothian EH26 0QB, U.K.
Received August 24, 1999
Summary Which forest management regimes best achieve
the dual objectives of high sustained timber yield and high carbon storage, including the carbon stored in soil and wood products? A mechanistic forest ecosystem simulator, which
couples carbon, nitrogen and water (Edinburgh Forest Model),
was calibrated to mimic the growth of a pine plantation in a
Scottish climate. The model was then run to equilibrium (1) as
an undisturbed forest, (2) removing 2.5, 10, 20 or 40% of the
woody biomass each year (3) removing 50% of the woody biomass every 20 years, and (4) clear-felling and replanting every
60 years as in conventional plantations in this climate.
More carbon was stored in the undisturbed forest
(35.2 kg C m –2) than in any regime in which wood was harvested. Plantation management gave moderate carbon storage
(14.3 kg C m –2 ) and timber yield (15.6 m3 ha –1 year –1). Notably, annual removal of 10 or 20% of woody biomass per year
gave both a high timber yield (25 m3 ha –1 year –1) and high carbon storage (20 to 24 kg C m –2 ). The efficiency of the latter regimes could be attributed (in the model) to high light
interception and net primary productivity, but less
evapotranspiration and summer water stress than in the undisturbed forest, high litter input to the soil giving high soil carbon and N2 fixation, low maintenance respiration and low N
leaching owing to soil mineral pool depletion.
We conclude that there is no simple inverse relationship between the amount of timber harvested from a forest and the
amount of carbon stored. Management regimes that maintain a
continuous canopy cover and mimic, to some extent, regular
natural forest disturbance are likely to achieve the best combination of high wood yield and carbon storage.
Keywords: carbon, forest, management, model, nitrogen,
plantation, productivity, volume yield.
Introduction
Undisturbed forests yield no timber but have a high biomass
and so store large amounts of carbon (Harmon et al. 1990). On
the other hand, plantation forests—which are periodically
clear-felled—can give high timber yields, but, averaged over
the period from planting to harvesting, contain relatively little
biomass and carbon compared with undisturbed forests (Cooper 1983, Cannell 1995). At first sight, it may be supposed that
the more timber that is harvested from a forest the less carbon
is stored. But, if timber were removed by regularly thinning,
without clear-felling, would it be theoretically possible to obtain both a high sustained yield of timber and a large store of
carbon? Is there a simple trade-off between these two objectives or is there an optimum management regime? The purpose of this study was to explore these questions.
The answer is not self evident, because of the many interactions and feedbacks between plant and soil processes in a forest ecosystem, involving light, nutrients and water. Different
management regimes perturb the system in different ways.
Also, the answer would be difficult to derive by experimentation, because it would take centuries before valid estimates of
sustained yield and carbon storage could be made. Transient
responses would depend on the initial conditions and could
differ in sign as well as magnitude from the equilibrium response. A model that represents all the essential interacting
processes offers a way forward.
In this paper, we use the Edinburgh Forest Model to estimate sustained timber volume yield and carbon storage in forests subjected to different harvesting regimes. The model is
parameterized to simulate a pine forest in the climate of Scotland, but the principles elucidated may apply more widely.
Materials and methods
The Edinburgh Forest Model
The Edinburgh Forest Model is a mechanistic evergreen forest
ecosystem simulator that couples carbon, nitrogen and water
and runs with a 20 minute timestep. It is programmed in ACSL
(advanced continuous simulation language; Aegis Research
Corporation, Huntsville, AL—email: acsl-sales@aegisrc.
com) and is available by anonymous ftp (username: anonymous; password: email address) to budbase.nbu.ac.uk. The
source program is FOREST.CSL in /pub/tree/Forest/. The
model is generic, assumes horizontal homogeneity and is
composed of linked submodels, which are described elsewhere for the trees (Thornley 1991), soil and litter (Thornley
1998a, Chapter 5) and water (Thornley 1996, 1998a, Chapter 6). Flow diagrams of the submodel structures are shown as
Figures A1–A4 in the Appendix, and a synopsis of the processes represented is given by Thornley and Cannell (1996)
478
THORNLEY AND CANNELL
and Cannell et al. (1998). The model was calibrated to simulate a pine forest in a U.K. upland climate.
Two developments have been made in the model since it
was described (Thornley 1991, Thornley and Cannell 1996).
First, the physiology of tree growth has been improved by including the acclimation of photosynthesis to light, nitrogen,
carbon dioxide and temperature (Thornley 1998b), and by separating out some of the components of maintenance respiration, including those associated with phloem loading, uptake
of nutrients and nitrate reduction (Cannell and Thornley 2000,
Thornley and Cannell 2000).
Second, the model was modified for this application to run
in different management modes. As originally configured, it
simulated the growth of a conifer plantation of identical trees
of the same age, with an initial density of 2500 trees ha –1,
which was regularly thinned, clear-felled and replanted every
60 years. The model has now been modified to simulate an undisturbed, natural forest too. This was achieved by assuming a
proportional stem mortality rate that depended on tree nutrient
status (the product of the carbon substrate and nitrogen substrate concentrations), water stress, and leaf area index (LAI)
as a surrogate for between-tree competition. The proportional
stem regeneration rate was then assumed to depend on stem
mortality (as a result of the formation of gaps), tree nutrient
status, irradiance at ground level and leaf area per stem.
For the purposes of this study, which was to make comparisons between harvesting regimes rather than quantitative predictions, the carbon contained in wood products was estimated
on the assumption that thinnings had a half-life of 5 years and
clear-felled timber a half-life of 20 years.
Environment
The models were run in a constant annual climate simulating
the 30-year mean conditions at Eskdalemuir in northern Britain, latitude 55o19′ N, 242 m a.s.l. (Meteorological Office
1982). Wind speed (at 50-m height) was constant at 4 m s –1.
Other quantities varied sinusoidally throughout the year:
photosynthetically active radiation varied from a maximum of
7.1 MJ m –2 day –1 on June 21 to 0.5 MJ m –2 day –1 6 months
later; daily maximum and minimum air temperatures varied
from annual maxima of 18 and 9 °C on July 26 to minima of
4 and –1 °C 6 months later; soil temperatures were diurnally
constant and varied from 14.5 °C on July 27 to 1.5 °C 6 months
later; rainfall varied from 5.6 mm day –1 on November 20 to
2.8 mm day –1 6 months later (totalling 1530 mm year –1); daily
maximum (dawn) and minimum (1500 h) relative humidities
varied from annual maxima of 0.91 and 0.88 on December 30
to minima of 0.77 and 0.62 6 months later. Daily variation in
radiation was assumed to be a full sine wave between dawn
and dusk; daily variation in air temperature was sinusoidal,
with the minimum at dawn and the maximum at 1500 h.
The forest was assumed to receive 10 kg N ha –1 year –1 from
the atmosphere, evenly spread throughout the year. This is a
reasonable average for combined dry and wet deposition of
oxidized and reduced nitrogen in many areas of Britain and
Europe.
Model evaluation and calibration
During the development of the model (Thornley and Cannell
1992), the assumptions and ways in which processes are represented were progressively modified until the dynamics of the
system were stable and the model was capable of simulating
known trends during a 60-year rotation, in the relative mass of
tree parts, LAI, the main elements of the C budget (gross photosynthesis, respiration and carbon loss to litter) and the N
budget (N uptake and N loss to litter).
For this application, the parameters listed by Thornley and
Cannell (see Table 2A in Thornley and Cannell 1996) were
adjusted so that the values of the principal output variables
were within measured ranges for pine forests in the U.K. uplands, averaged over a 60-year rotation (Table 1). The Yield
Class was 15.6 m3 ha –1 year –1 (Christie and Lines 1979). Net
primary production varied from zero to 15 Mg C ha –1 year –1
over a rotation (averaging 4.5 Mg C ha –1 year –1) and at the end
of the rotation the mean tree height was 25 m, with LAI = 4.1
(Miller et al. 1980). Total plant respiration averaged 0.40 of
gross photosynthesis (within the 0.36–0.68 range for pines:
Ryan et al. 1997). The mean C:N ratios of soil organic matter,
harvested wood and of the whole ecosystem were 11, 289 and
24, respectively. Non-symbiotic N2 fixation averaged 7 kg N
ha –1 year –1 (Sprent and Sprent 1990). Gaseous losses of N averaged 2 kg N ha –1 year –1 as NH3 from foliage, 4 kg N ha –1
year –1 NH3 volatilized from the soil (Sutton et al. 1993) and
1 kg N ha –1 year –1 lost by both nitrification and denitrification
(Williams et al. 1992). Leaching losses were small, averaging
1 kg N ha –1 year –1, or 10% of atmospheric N deposition
(Binkley and Hogberg 1997, Wright et al. 1995, Emmett et al.
1993). Over a rotation, 30% of the annual precipitation was
lost by evaporation of intercepted rain, 21% by tree
evapotranspiration and 49% by drainage to groundwater,
which is within the measured range for U.K. upland forests
(Johnson 1990).
Model runs
The model was run to equilibrium with the following management regimes: (1) undisturbed natural forest; (2) thinned natural forest, with 2.5, 10, 20 or 40% of the woody biomass
removed each year—simulating theoretical regular harvesting
of whole trees or prunings; (3) thinned natural forest, with
50% of the woody biomass removed every 20 years; and (4)
thinned plantation forest, clear-felled and replanted every 60
years, which is close to the rotation period for maximum mean
annual volume increment (cf. Thornley and Cannell 1996,
Cannell et al. 1998).
Results
Carbon sequestration and volume yield
The simulated effects of the seven forest management techniques are summarized in Table 2. At equilibrium, the undisturbed natural forest stored a total of 35.2 kg C m –2 in biomass
and soil organic matter (Figure 1). This is more than was
stored in any of the management scenarios in which wood was
TREE PHYSIOLOGY VOLUME 20, 2000
MANAGING FORESTS FOR YIELD AND CARBON STORAGE
Table 1. Parameters in the Edinburgh Forest Model were calibrated to
give the output values shown below, simulating a pine plantation in
the climate of Eskdalemuir, Scotland. All quantities are means for a
60-year rotation, unless otherwise stated. Net photosynthesis is gross
canopy photosynthesis minus whole-plant respiration. The simulated
Yield Class is 15.6 m3 ha –1 year –1 (stemwood yield at harvest divided
by 60).
Parameter
Output value
Carbon budget (kg C m –2 year –1)
Gross canopy photosynthesis
Net photosynthesis
Ratio (net/gross)
Local growth respiration
Residual maintenance respiration
Soil respiration
Leaching
Products
0.75
0.45
0.60 (dimensionless)
0.11
0.14
0.23
0.004
0.22
Nitrogen budget (kg N ha –1 year –1)
Deposition
Fixation
NH3 emission from foliage
Soil NH3 volatilization
Nitrification
Denitrification
Soil gaseous N emission
System gaseous N emission
Leaching
Products
10
7
2
4
1
1
5
7
1
8
Water budget (m year –1)
Annual rainfall
Intercepted and evaporated rain
Plant evapotranspiration
Drainage
1.53
0.46
0.32
0.75
End-of-rotation variables
Leaf area index
Stem height
Stem mass
4.1
25 m
1202 kg structural dry
mass stem –1
Some other variables
Stem height:diameter ratio (constant)
Stomatal conductance on July 1 at 1500 h
Soil mineral N concentration
60
0.0048 m s –1 (cf.
0.005 fully open)
0.00017 kg N m –2
Carbon sequestered (kg C m –2)
System
Soil (SOM, litter, biomass, Csol)
Tree
Products
C:N ratio of system:
C:N ratio of soil organic matter:
C:N ratio of total product pool:
14.3
6.4
3.8
4.0
23.5 kg C (kg N) –1
10.7 kg C (kg N) –1
289 kg C (kg N) –1
harvested, including the carbon stored in wood products (the
equilibrium product pool allowing for decay). In the natural
forest, biomass carbon reached an equilibrium of 13.2 kg C
m –2 , which occurred when tree respiration plus senescence
equalled gross production. Continuous high light interception
479
ensured moderately high canopy photosynthesis (despite low
stomatal conductance on summer days; Table 1) and all of the
net primary production was input to the soil, giving rise to a
relatively high equilibrium soil carbon store of 22.1 kg C m –2
(Figure 1).
The thinned and clear-felled plantation forest stored a total
of 14.3 kg C m –2 (the sum of biomass, soil and product carbon;
bottom of Figure 1), less than half that stored in the undisturbed forest. Clear-felling every 60 years and regular thinning limited the mean standing biomass to 3.8 kg C m –2, less
than one-third of that in the undisturbed natural forest.
Clear-felling and thinning also limited light interception, so
that rotation-averaged canopy photosynthesis and net primary
production were less than in the undisturbed forest, although
the plantation forest suffered less water stress in summer (Table 1). Low net primary production and the removal of biomass in thinnings and at clear-felling decreased litter input to
the soil, so that equilibrium carbon storage in the soil was only
6.4 kg C m –2, less than one-third of that in the undisturbed forest. The sustained wood yield was quite large, at 15.6 m3 ha –1
year –1. Because the clear-felled timber had a half-life of
20 years (compared with 5 years for thinnings in this and the
other management scenarios), the time-averaged product carbon pool for the plantation was also quite large—similar in
size to the biomass carbon pool (4.0 and 3.8 kg C m –2, respectively; Figure 1). However, the carbon stored in wood products (clear-felled timber and thinnings) did not compensate for
the much smaller amounts of carbon stored in biomass and
soils in the plantation forest compared with the undisturbed
forest.
Thinning the natural forest to remove just 2.5% of woody
biomass each year yielded 12.2 m3 ha –1 year –1, 78% of that
yielded by the plantation forest, while storing a total of 28.1 kg
C m –2 in biomass, soil and products, twice that stored in the
plantation forest (Figure 1). Thinning the natural forest to remove 10 and 20% of the woody biomass each year yielded
25.4 and 25.7 m3 ha –1 year –1, respectively, about 60% more
than that yielded by the plantation forest (Figure 1) while storing a total of 23.7 and 20.5 kg C m –2, respectively, more than
stored in the plantation forest. Regularly thinning natural forests clearly resulted in stands that were considerably more efficient at generating, storing and yielding carbon than
conventionally clear-felled plantations.
The high performance of the 10 and 20% thinned natural
forests was associated with high canopy photosynthesis and
net primary productivity, resulting from a combination of
moderately high light interception (with sustained LAIs of
about 4), but lower evapotranspiration and less water stress on
summer days than in the undisturbed forest, plus a lower respiratory load (net/gross photosynthesis was about 0.65 compared with 0.60 in plantations and undisturbed forests;
Table 1). The biomass in these forests was decreased by thinning compared with the undisturbed forest, but even with 20%
of the biomass removed each year, there was 3.0 kg C m –2 in
biomass, about 80% of that in the plantation forest averaged
over a rotation. More importantly, high sustained net primary
production maintained a high input of litter to the soil, generat-
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480
THORNLEY AND CANNELL
Table 2. Simulated effect of seven scenarios of forest management on long-term (equilibrium) mean gross and net photosynthesis, and on water
relations indicated by stomatal conductance on July 1 at 1500 h.
Scenario
Gross photosynthesis
(kg C m –2 year –1)
Net photosynthesis
(kg C m –2 year –1)1
Stomatal conductance on
July 1 at 1500 h (m s –1)
Undisturbed natural forest
2.5% of woody biomass harvested each year
10% of woody biomass harvested each year
20% of woody biomass harvested each year
40% of woody biomass harvested each year
50% of woody biomass harvested every 20 years
100% of woody biomass harvested every 60 years (plantation)
0.95
1.02
1.19
1.17
0.34
1.05
0.75
0.59
0.64
0.76
0.77
0.23
0.65
0.45
0.0016
0.0027
0.0046
0.005 (fully open)
0.005
0.0030
0.0048
1
Equivalent to net primary production, equal to total litter input to the soil (because the system is at equilibrium) plus harvested wood products.
ing over twice as much soil carbon in forests subject to 10 and
20% annual thinning as in the plantation forest.
However, there is clearly a limit to the severity of annual
thinning, beyond which the forest has such a low LAI that it is
no longer productive. This limit was surpassed with the removal of 40% woody biomass every year, which resulted in
very low LAIs, yield and carbon storage (Figure 1).
Removing 50% of the woody biomass every 20 years gave
similar wood yields and carbon storage to removing 2.5% every year— the numerical equivalent (Figure 1). Similarly, removing 20% of the woody biomass every 4 years (not shown)
gave similar results to removing 5% every year. Thus, thinning does not need to be done every year to achieve a combination of high yield and carbon storage. Within limits, it is the
average removal rate that is important, giving flexibility to
adopt various thinning regimes.
Nitrogen inputs and outputs
Figure 1. Simulated effects of seven forest management regimes on
forest biomass (continuous line), leaf area index (LAI, dashed line),
and long-term equilibrium values of carbon sequestration and woody
volume yield.
In addition to the 10 kg N ha –1 year –1 received from the atmosphere, the forests received N as a result of non-symbiotic N2
fixation. Fixation was assumed to be positively related to the
amount of soil organic matter (which determined the biomass
of N2 -fixing microbes) and the amount of carbon entering the
soil (which influenced microbial N2 fixation rates). The plantation forest fixed only about 7 kg N ha –1 year –1, primarily because it had a relatively small amount of soil organic matter
(6.4 kg C m –2), whereas the undisturbed natural forest fixed
over 8 kg N ha –1 year –1. Natural forests that were thinned to
remove 10 or 20% of the woody biomass each year, fixed
about 9 kg N ha –1 year –1, more than that fixed by the undisturbed forest, owing to their high net primary production (Figure 2, Table 1).
By definition, at equilibrium, ecosystem N outputs equaled
N inputs (Figure 2). However, the fraction of N lost by leaching, in wood products and as gases (by nitrification,
denitrification and volatilization), differed greatly among the
forest management scenarios. In the undisturbed natural forest, leaching losses were small, because soil water drainage
was small, and the N balance was maintained by gaseous loss.
In the plantation forest, almost half of the N output was in harvested products, but leaching losses were also relatively high,
owing to mineralization of litter and high drainage during the
years after clear-felling, In the 10 and 20% annually thinned
natural forests, about 47% of the N output was in harvested
products, whereas leaching losses were no greater than in the
undisturbed forest, owing to low drainage and continued depletion of the soil mineral pools by root uptake (driven by tree
growth). Thus, these thinned natural forests avoided the N loss
to groundwaters that occurred in plantations and yet captured
TREE PHYSIOLOGY VOLUME 20, 2000
MANAGING FORESTS FOR YIELD AND CARBON STORAGE
481
Figure 2. Simulated effects of seven forest management regimes on
long-term (equilibrium) system N inputs and outputs. Definitions: N
deposition = atmospheric N deposition; N2 fixation = non-symbiotic
N2 fixation; products = N removed in harvested wood; gas = losses of
N2, NO, N2O and NH3 from denitrification, nitrification, volatilization from the soil, and emissions by foliage through the stomates; and
leaching = losses to ground water from the soil nitrate pool.
Essential features of undisturbed, thinned natural and
plantation forests
Figure 3. Summary of the main features of simulated forests, managed in three ways, when at equilibrium. No marking indicates a relatively small value of the process or quantity, underlining a moderate
value, and bold type a large value. Abbreviations: LAI = leaf area index; GPP = gross primary production or gross photosynthesis; NPP =
net primary production or net photosynthesis; SOM = soil organic
matter; C seqn. = carbon sequestration or storage in kg C m –2; and
harvest = woody volume removed in m3 ha –1 year –1.
The essential features of the simulated undisturbed, thinned
natural and plantation forests are illustrated in Figure 3. Differences between these forest types in mean LAI and biomass
affected evapotranspiration and light interception, which in
turn affected the C and N dynamics.
The undisturbed forest maintained a high LAI and biomass,
resulting in high light interception, but also high evapotranspiration and summer water stress, so that net primary production was only moderately high. However, leaching losses
were small (because of low drainage) and, because no biomass
was removed, soil organic matter levels and N2 fixation rates
were moderately high. The net result was high carbon sequestration in biomass and soils, but no yield and a high loss of N
as gases.
Averaged over a rotation, the LAI and biomass of the plantation forest were relatively small, resulting in relatively low
light interception, low evapotranspiration, high drainage and
N leaching, leading to low net primary production, despite relatively little summer water stress. Low net primary production, combined with the removal of wood, resulted in low soil
organic matter levels and N2 fixation rates. The outcome was a
combination of moderate carbon sequestration, moderate
wood yield, and considerable N loss to groundwaters.
Natural forests that were thinned to remove about 10% of
the biomass each year (or 50% every 5 years) maintained a
moderately high, continuous LAI and biomass, giving moderate light interception and evapotranspiration, resulting in relatively little summer water stress. Consequently, net primary
production was high, sustaining both a high yield and litter in-
a substantial fraction of the N that was otherwise lost as gases
in undisturbed forests.
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482
THORNLEY AND CANNELL
put to the soil, resulting in moderately high soil content of organic matter and high N2 fixation rates. The outcome was
moderately high carbon sequestration and high wood yield.
Discussion
The salient conclusion from this study is that there is no simple
inverse relationship between the amount of timber harvested
from a forest and the amount of carbon stored in the ecosystem
and wood products. The method of harvesting is important. In
particular, regular removal of timber from a forest (annually or
every few years) in a way that maintains a continuous canopy
is likely to give substantially higher sustained yields and
amounts of carbon storage than periodical clear-felling, as in
conventional plantations. Runs of the model in other temperate climates and with different calibrations and N deposition
rates suggested that, qualitatively, this conclusion might apply
in a wide range of forest types. It should be stressed, however,
that we claim only to have elucidated a principle, not to have
made quantitative predictions, much less to have considered
the practicalities, costs and other implications of different harvesting regimes.
The study suggested that, if the objective were simply to
maximize timber volume yield (regardless of cost or value) the
order of optimal management system would be regularly
thinned forest > plantation > undisturbed forest, whereas if the
objective were to maximize carbon storage, the order would be
undisturbed forest > regularly thinned forest > plantation. If
the objective were to minimize uncontrolled N emissions to
the environment, the order would be the same as that to maximize timber volume yield.
In the simulations, more carbon was stored in the undisturbed forest than in any management regime in which wood
was harvested, including wood products, supporting previous
analyses that compared plantations with undisturbed forests
(cf. Cannell 1995) and suggesting that any biomass removal
from a forest will lower carbon storage, without unrealistic assumptions on the rates of decay of harvested wood.
Plantations offered the worst combination of yield and carbon storage and regularly thinned forests the best, provided
thinning removed not less than about 5% and not more than
about 25% of the woody biomass each year. There seemed to
be some scope for flexibility in thinning frequency, in that, for
instance, harvesting 5% of the woody biomass per year gave
similar results to harvesting 25% every 5 years.
Why were regularly thinned forests so efficient in the
model? The main features were as follows: (1) the continuous
canopy and moderately high LAI (about 4) gave high light interception and NPP; (2) there was no period of slow recovery,
which occurs after clear-felling; however, the LAI was less
than in an undisturbed forest and so evapotranspiration was
less, with less risk of water stress on dry summer days, also enhancing NPP; (3) high NPP ensured high litter input to the soil
and a large equilibrium soil carbon store, also favoring
non-symbiotic N2 fixation; (4) regular thinning meant that the
forest had a lower biomass than an undisturbed forest and was
continually growing, resulting in less maintenance respiration;
and (5) continuous growth also meant that the soil mineral ni-
trate pool remained depleted and N losses by leaching were
reduced.
The conclusion that regular thinning is better than
clear-felling is in keeping with much of the current discussion
regarding forest management to sustain multiple functions, including the maintenance of biodiversity, preserving soil fertility, and preventing erosion (Gale and Cordray 1991, Wiersum
1995). It is increasingly recognized that the many demands
made on forests may best be met by maintaining an intact forest ecosystem or ecological integrity (Armstrong 1999). This
analysis offers some scientific basis for those terms, with regard to carbon dynamics in the soil–plant system, as affected
by nitrogen dynamics and the water balance.
Finally, the regular thinning regimes that were optimal in
this study may be viewed as emulating the natural regular disturbance that many forests experience from insects, other animals, storms and minor fires. Simulating nature may, by
chance or design, be an optimal strategy to maximize yield
and carbon storage, as it may be in the natural disturbance
model of boreal forest management proposed by Hunter
(1993).
Acknowledgments
This work was supported in part by the U.K. Department of Environment, Transport and Regions in Contract EPG1/1/39.
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Figure A1. Overall structure of the Edinburgh Forest Model
Appendix
Figure A2. Flow diagram of
the tree submodel of the Edinburgh Forest Model.
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Figure A3. Flow diagram of
the soil submodel of the Edinburgh Forest Model.
Figure A4. Flow diagram of
the water submodel of the Edinburgh Forest Model.
TREE PHYSIOLOGY VOLUME 20, 2000