BALANCE

a process based, spatially explicit forest growth model

by Thomas Rötzer April, 2015

Chair for Forest Growth and Yield Science, TU München

Email: thomas.roetzer@lrz.tum.de

1 Model history

A basic version of the growth model BALANCE was completed in 2002, when Grote and Pretzsch

(2002) published a first article about a process based model called BALANCE. Starting in 1998 with

the “SFB 607” BALANCE was developed, evaluated and validated within several further research

projects (e.g. IFOM, CSWH, EnForChange, ForeStClim, KROOF). This still ongoing process ensures that

the model is able to realistically simulate forest growth and productivity for several tree species in

diverse environments. Along with the carbon cycle the water balance and the nutrient cycle can be

simulated revealing environmental feedback and feed forward reactions.

BALANCE has been extensively validated for basic micro-meteorological and physiological processes,

for water balance, annual tree development, and entire stand development. Simulated values of

micro-meteorological and physiological processes like light distribution or photosynthesis were

compared to measurements (Rötzer 2006, Rötzer et al. 2010), as well as water balance parameters

(e.g. Rötzer et al. 2005, 2010), phenological phases (Rötzer et al. 2004, 2005, 2010) and data of the

stand development (Rötzer et al. 2005). At the site Kranzberger Forst, simulated parameter of single

tree segments and compartments, of tree individuals and of the entire stand were validated against

measured data (Grote and Pretzsch 2002, Rötzer et al. 2010). Other validations were carried out for

diverse Central European forest stands, particularly at level 2 sites (e.g. Rötzer et al. 2004, 2005, Liao

2011).

2 Short description

The process based growth model BALANCE calculates the 3-dimensional development of trees or

forest stands and estimates the consequences of environmental impacts. As an individual tree model

BALANCE simulates growth responses on tree level, which enables an estimation of the influence of

competition, stand structure, species mixture, and management impacts because tree development

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is described as a response to individual environmental conditions and environmental conditions

change with the development of each individual tree.

Dimensional tree growth is calculated once for each year based on the biomass increase of the

woody tissue that has been accumulated during the last year by the tree individual. Initial tree

biomass is calculated from the dimensional variables tree height, height to crown base, diameter at

breast height, tree position, and crown radii. Biomass increase is the result of the interaction

between physiological processes which are dependent on the physical and chemical micro-

environment. These are in turn influenced by stand spatial structure. Asymmetric crown shapes are

included and generate a spatially explicit representation of the environment. The calculation levels

vary from stand level to individual trees, from tree components (i.e. foliage, branches, stems, and

fine and coarse roots) to crown and root layers, which are spatially subdivided into segments.

Consequently, an increase in biomass is simulated based on the carbon and nitrogen uptake from

each segment, depending on its energy supply and resource availability.

The individual carbon-, water- and nutrient balances of the trees species European beech, Sessile

resp. Common oak, Norway spruce, Scots pine and Douglas fir are the fundamental processes for the

growth simulations. For each layer resp. each segment micro climate and water balance are

calculated by using temperature, radiation, precipitation, humidity and wind speed measurements

from climate stations. While these calculations are computed daily, the physiological processes

assimilation, respiration, nutrient uptake, growth, senescence and allocation are calculated in 10-day

time steps from the aggregated driving variables. This way, CO2-concentration, soil condition,

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competition between individuals, and stress factors, as for example air pollution and nutrition

deficiency, can be considered besides the weather conditions when modelling tree growth.

BALANCE includes different approaches for the estimation of the environmental conditions for each

individual tree. The Penman-Monteith equation (Allen et al. 1998) is the base of the water balance

calculations. Via the stomatal closure water balance is connected with photosynthesis, which is

calculated by using the approach of Haxeltine and Prentice (1996). This way, gross primary

production can be estimated depending on leaf surface, photosynthetically active radiation (PAR),

temperature, CO2 concentration, water and nitrogen supply, while total respiration is the sum of

maintenance losses and growth respiration.

To depict the relationships between the environmental influences and growth, the annual cycle of

foliage development must be known. Foliage biomass and leaf area as well as light availability and

PAR absorption change with the onset of bud burst. A tree’s foliage emergence date determines its

assimilation and respiration rate, but also alters the environmental conditions in the immediate

surrounding area. Bud burst of a tree species is estimated by using an air temperature sum model,

while foliage senescence is simulated depending on the respiration sum for each segment of a tree.

Allocation of carbon and nitrogen into roots, branches, foliage and stem is computed according to

functional balance (Mäkela 1990) and pipe model principles (Shinozaki et al. 1964). Dimensional tree

growth is estimated annually, based on biomass accumulation during that year. Consequently, all

tissues within a segment, i.e. foliage and branches, fine and coarse roots, as well as the amount of

stem wood are mechanistically linked to each other. Volume expansion depends on the necessary

amount of twigs and transport branches and the amount of coarse roots within root segments.

Therefore, crown development is preferred in the direction of best assimilation conditions during the

previous year. If net assimilation rates are negative, the crown segment is regarded as dead. If no

segments contain living biomass, the tree is assumed dead and removed from simulations.

3 References

3.1 “BALANCE” articles

Rötzer, T. (2013): Mixing patterns of tree species and their effects on resource allocation and growth in forest stands. Nova Acta Leopoldina NF 114, Nr. 391, 239-254.

Rötzer, T.,Liao, Y.,Goergen, K.,Schüler, G.,Pretzsch, H. (2013): Modelling the impact of climate

change on the productivity and water-use efficiency of a central European beech forest.

Climate Research, Vol. 58:81-95.

Rötzer, T., Liao, Y., Klein, D., Zimmermann, L., Schulz, C. (2013): Modellierung des Biomasse-

zuwachses an bayerischen Waldklimastationen unter gegebenen und möglichen zukünftigen

Klimabedingungen. Allgemeine Forst- und Jagdzeitung, 184(11/12):263-277.

Rötzer, T., Pretzsch, H. (2013): Tree growth and resource allocation in forest stands: Empirical

evidence substantiated by scenario simulations. Austrian Journal of Forest Science, Vol. 130:187-218.

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Rötzer, T., Seifert, T., Gayler, S., Priesack, E., Pretzsch, H. (2012): Effects of Stress and Defence

Allocationon Tree Growth: Simulation Results at the Individual and Stand Level. In R. Matyssek et al. (eds.), Growth and Defence in Plants, Ecological Studies 220, DOI 10.1007/978-3-642-

30645-7_18. Springer-Verlag Berlin Heidelberg 2012. 401-432.

Rötzer, T., Leuchner, M., Nunn, A.J. (2010): Simulating stand climate, phenology, and photosynthesis

of a forest stand with a process-based growth model. Int J Biometeorol 54: 449-464.

Rötzer, T., Liao, Y., Pretzsch, H. (2010): Effects of climate change and adatation strategies for

Northwest European forest stands. Berichte des Meteorologischen Institutes der Albert-

Ludwigs-Universität Freiburg 20: 159 - 164.

Rötzer, T., Pretzsch, H. (2010): Stem water storage of Norway spruce and its possible influence on

tree growth under drought stress - application of ct-scannings -. Berichte des

Meteorologischen Institutes der Albert-Ludwigs-Universität Freiburg 20: 153 - 158.

Rötzer, T., Seifert, Th., Pretzsch, H. (2009): Modelling above and below ground carbon dynamics in a

mixed beech and spruce stand influenced by climate. Eur J Forest Res 128: 171-182.

Rötzer, T. (2006): Vom Baum zum Bestand. AFZ- Der Wald. 61(21): 1160-1161

Rötzer, T. (2005): Climate change, stand structure and the growth of forest stands. Annalen der

Meteorologie 41 (1): 40-43

Rötzer, T., Grote, R., und Pretzsch, H. (2005): Effects of environmental changes on the vitality of

forest stands. European Journal of Forest Research 124: 349-362.

Rötzer, T., Grote, R., Pretzsch, H. (2004): The timing of bud burst and its effect on tree growth.

International Journal Biometerology 48: 109-118.

Rötzer, T. (2003): Modellierung der Baumkronenentwicklung mittels eines ökophysiologischen Prozessmodells. Bundesministerium für Verbraucherschutz, Ernährung und Landwirtschaft ref.

533, Bonn: 73-42

Grote, R. (2003): Estimation of crown radii and crown projection area from stem size and tree

position. Ann. Forest Science 2003 60/5: 393-402.

Grote, R., Patzner, K., Seifert, T. (2003): Modelling Water Availability in Individual Trees - a

Contribution of Process-Based Simulation to the Prediction of Developments in Heterogenous

Stands. Umwelt Informatik aktuell. 2003 (31). 804-812.

Grote, R., Pretzsch, H. (2002): A model for individual tree development based on physiological

processes. Plant Biology 4: 167-180.

3.2 Review articles of growth models (including BALANCE)

Priesack, E., Gayler, S., Rötzer, T., Seifert, T., Pretzsch H. (2012): Mechanistic modeling of soil-plant-

atmosphere systems. In R. Matyssek et al. (eds.): Growth and Defence in Plants, Ecol Studies

220. Springer-Verlag Berlin Heidelberg.

Fontes, L., Bontemps, J.D., Bugman, H., Van Oijen, M., Gracia, C., Kramer, K., Lindner, M., Rötzer,

T., Skovsgaard, J.P. (2010): Models for supporting forest management in a changing

environment. Forest Systems 19(SI): 8-29.

Pretzsch, H., Grote, R., Reineking, B., Rötzer, T., Seifert, S. (2007): Models for Forest Ecosystem

Management: A European Perspective. Annals of Botany 101 (8): 1-23.

3.3 Studies with BALANCE applications

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Pretzsch, H., Biber, P., Schütze, G., Uhl, E., Rötzer, T. (2014): Forest stand growth dynamics in

Central Europe have accelerated since 1870. Nature Communications, DOI: 10.1039/ncomms5967 .

Pretzsch, H., Rötzer, T., Matyssek, R., Grams, T.E.E., Häberle, K.-H., Pritsch, K., Kerner, R., Munch,

J.-C., (2014): Mixed Norway spruce (Picea abies [L.] Karst) and European beech (Fagus sylvatica

[L.] stands under drought: from reaction pattern to mechanism. Trees DOI 10.1007/s00468-

014-1035-9

Pretzsch, H., Biber, P., Schütze, G., Uhl, E., Rötzer, T. (2014): Veränderte Dynamik von süddeutschen

Waldbeständen seit 1870. LWF Wissen 76: 72-87.

Pretzsch, H., Biber, P., Schütze, G., Uhl, E., Rötzer, T. (2014): Beschleunigtes Waldwachstum

erfordert Anpassung Holz-Zentralblatt, 48: 1178.

Weigt, R.B., Häberle, K.H., Rötzer, T., Matyssek, R., (2014): Whole-tree seasonal nitrogen uptake and partitioning in adult Fagus sylvatica L. and Picea abies L. [Karst.] trees exposed to elevated

ground-level ozone. Environ Pollut. DOI 10.1016/j.envpol.2014.06.032

Hertel,C., Leuchner, M., Rötzer, T., Menzel, A. (2012): Assessing stand structure of beech and spruce

from measured spectral radiation properties and modeled leaf biomass parameters. Agric

Forest Meteorol. 165: 82 - 91.

Häberle, K.-H., Weigt, R., Nikolova, P.S., Reiter, I.M., Cermak, J., Wieser, G., Blaschke, H., Rötzer, T.,

Pretzsch, H., Matyssek, R. (2012): Case Study "Kranzberger Forst": Growth and Defence in

European Beech (Fagus sylvatica L.) and Norway spruce (Picea abies (L.) Karst). In R. Matyssek

et al. (eds.), Growth and Defence in Plants, Ecological Studies 220, DOI 10.1007/978-3-642-

30645-7_11 [Titel anhand dieser DOI in Citavi-Projekt übernehmen] . Springer-Verlag Berlin Heidelberg 2012. 243-271.

Leuchner, M., Hertel, C., Rötzer, T., Seifert, T., Weigt, R., Werner, H., Menzel, A. (2012): Solar

radiation as a driver for growth and competition in forest stands. Matyssek In R. Matyssek et

al. (eds.): Growth and Defence in Plants, Ecol Studies 220. Springer-Verlag Berlin Heidelberg.

Pretzsch, H., Dieler, J., Seifert, T., Rötzer, T. (2012): Climate effects on productivity and resource-use

efficiency of Norway spruce (Picea abies [L.] Karst.) and European beech (Fagus sylvatica [L.])

in stands with different spatial mixing patterns. Trees - Structure and Function.

Liao, Y. (2011): Modeling carbon dynamic and water balance for a beech stand under present and fu-

ture climate conditions. Master Thesis TU München.

Köhl, M., Kenter, B., Hildebrandt, R., Olschofsky, K., Köhler, R., Rötzer, T., Mette, T., Pretzsch, H.,

Rüter, S., Köthke, M., Dieter, M., Abiy, M., Makeschin, F. (2011): Nutzungsverzicht oder

Holznutzung? Auswirkungen auf die CO2-Bilanz im langfristigen Vergleich. AFZ- Der Wald 15:

25-27.

Köhl, M., Hildebrandt, R., Olschofksy, K., Köhler, R., Rötzer, T., Mette, T., Pretzsch, H., Köthke, M.,

Dieter, M., Abiy, M., Makeschin, F., Kenter, B. (2010): Combating the Effects of Climatic

Change on Forests by Mitigation Strategies. Carbon Balance and Management 5: 8.

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4 Detailed Description

4.1 Model Structure

The eco-physiological growth model BALANCE is able to calculate the 3-dimensional development of

trees and forest stands using environmental influences. Growth is simulated at individual tree level.

As tree development is calculated as a response to individual environmental conditions and

environmental conditions change with individual tree development, the influence of competition,

stand structure, species mixture and management impacts can be taken into account.

A tree’s initial biomass is calculated from a dimensional group of variables: tree position, tree and

crown base height, diameter and crown radii. Biomass increase is the result of the interaction

between physiological processes which are dependent on the physical and chemical micro-

environment. The latter is in turn influenced by the spatial structure of the stand. Thus, an increase

in biomass is simulated on the base of the carbon and nitrogen that is taken up from each segment,

dependent on the energy supply and resource availability. Stress conditions are measured by the

change of the specific below and above ground uptake rates.

BALANCE takes into account asymmetric crown shapes and generates a spatially explicit

representation of the environment. The calculation levels vary from stand level to individual trees,

from tree components (i.e. foliage, branches, stem, fine and coarse roots) to crown and root layers.

These layers are again divided into crown- resp. root segments.

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By using weather data, the microclimate and water balance are calculated for each layer resp.

segment. Thus, the spatial distributions of the light and water availability are both estimated on a

daily basis. Based on the aggregated driving variables, all physiological processes i.e. assimilation,

respiration, nutrient uptake, growth, senescence and allocation are calculated in 10 day time steps.

Therefore, the individual carbon, water and nutrient balances of the tree species beech, oak, spruce,

pine and Douglas fir can be simulated.

4.2 Micro-climate

Precipitation, temperature and radiation are the main driving forces of growth. While the water

supply of a tree is estimated in the water balance module, a temperature and radiation gradient from

the top of the canopy to the soil surface (and in case of temperature also within the soil) is calculated

for every individual tree in the climate-module.

Air temperature within the stand is calculated for every layer j of every tree on the base of the

distribution of the leaf area and the air temperature above the canopy and above the soil surface

(Eq. 1).

tj = tas + (tca - tas) * Σjn=0 (LAIj / LAI) Eq. 1

(tj= air temperature in layer j in °C, tca=air temperature above canopy (measured) in °C, tas=air

temperature above soil surface in °C, LAI=total leaf area index in m²/m², LAIj=leaf area index of layer j

in m²/m², j=layer number)

The leaf area index below the layer j is calculated as the sum of the single layers LAI which are in turn

calculated from the foliage area of every layer divided through the tree ground area. According to

the SWAT-model-approach (Neitsch et al. 2002) air temperature above the soil surface tas is

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estimated from the tree area, the crown area, as well as from the soil surface temperature of the

previous day and the temperature of the bare soil:

tas = Ac / At * tprev + (1 - Ac / At) * tbare Eq. 2

(Ac=crown area in m², At=tree area in m², tprev=soil surface temperature of the previous day in °C,

tbare=temperature of the bare soil in °C)

The temperature of the bare soil tbare is a function of the mean, minimum, and maximum

temperature of the current day and the solar radiation reaching the ground (Neitsch et al. 2002).

The sum of PAR a segment collects in a time step is essential for estimating growth. This calculation

of the relative light consumption was derived from the competition algorithm of the growth

simulator SILVA (Pretzsch 1992) and extended by a light extinction function of a Lambert-Beer type.

The search cone used to estimate competition is separately calculated for each single crown

segment. Consequently, light intensity of each segment is obtained based on the global radiation, the

extinction coefficient of foliage and the competition factor of the segment.

To exactly calculate photosynthetic active radiation PAR, a ‘competition-cone’ is positioned over each

segment. All segments within this cone are counted and weighed by their content of leaf area. PAR

for each segment Is is obtained by:

Is = Io * exp[1-(cfs+1)ε] Eq. 3

cfs = Σ (LAIn *ρ) Eq. 4

(Io =incoming shortwave radiation in J/cm², ε=extinction coefficient of foliage)

The competition factor cf of a segment s is determined from the leaf area index of every competing

segment n accounting by self shading by adding half of the LAI in the specific segment (ρ=0.5).

Competing segments are defined as located within a cone above segment s, which is characterized by

the base angle (β1 = 10°). If the angle between the centre of segments s and n (βx) are smaller than

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β1, the segments are included in the calculation of Eq. 4 (Grote and Pretzsch 2002). These

calculations are carried out for the beginning of each year as well as for the start (bud burst) and the

end (leaf senescence) of the vegetation period of each tree species.

4.3 Phenological development

The temporal and spatial development of foliage defines the relationships between environmental

influences and growth i.e. with the beginning of bud burst foliage, biomass and leaf area as well as

light availability and PAR absorption change. Thus, not only does the date of foliage emergence of a

tree determine its assimilation and respiration rate but it also alters the environmental conditions in

a tree’s immediate surrounding area.

The day of bud burst bb of a tree species is calculated by using an air temperature sum model (Rötzer

et al. 2004) and can be described as:

bb = d if Σdsd (td -tb)*(d/dmax)

2 > ttsumd with td > tb Eq. 5

(d= day of the year, sd=starting date for summing up temperature (day 1 for deciduous trees, day 60

for conifers), dmax=latest observed date of the beginning of a phenological phase, td=daily maximum

temperature in °C, tb=base temperature in °C above which temperature contributes to bud burst

(0°C), ttsumd=threshold temperature sum)

Ttsumd is calculated based on the day of the year and species specific coefficients (a, b):

ttsumd = a + eb*d Eq. 6

Bud burst is calculated species specifically and not for each single tree or single canopy layer, using

the measured air temperature.

Foliage senescence is estimated in dependence on the respiration sum for each segment of a tree

(Rötzer 2003).

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Estimations of the potential respiration capacity related to leaf senescence are based on the studies

of Kikuzawa (1995), Pensa and Sellin (2002) and Niinemeets and Lukjanowa (2003), which inform of

the manifold parameters that influence leaf senescence. Reich et al. (1999) resp. Reich (2001) found

a relationship between the life span of leaves, the specific leaf area, the photosynthesis rate and the

respiration.

Thus, the potential respiration sum of the leaves of a tree species is derived by multiplying the

potential respiration capacity of leaves with the mean life span. If the actual respiration sum of a leaf

segment achieves the potential respiration sum, the leaves of this segment will die off. Due to stress

reactions such as drought stress or the impact of air pollution the respiration rates of leaves increase.

Hence, the respiration sum accumulates faster and the leaves will die off earlier.

4.4 Water Balance

The simulation of the water balance considers the soil conditions in different layers, for which the

number and thickness can be chosen. Field capacities and wilting points of each layer are derived

from measurements. A simple multi-layer bucket soil water model regards vertical water flows whilst

horizontal flows between the rooted and non-rooted fractions in each layer are considered, too. The

water within the rooted fractions is used to fulfil a tree’s transpiration requirements. At the end of

each day, the soil water content within rooted and non rooted fractions is equalized.

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This way, the water balance of an individual tree can be described as:

Δswc = prec - eta - int - ro + cr Eq. 7

(Δswc =change in soil water content in mm; prec=precipitation in mm; eta = actual evapotranspiration

in mm; int=interception in mm; ro= run off in mm; cr= capillary rise in mm)

The calculation of the evapotranspiration based on the Penman-Monteith approach (e.g. Allen et al.

1998, DVWK 1996) provides key information which allows the water balance simulation of a tree.

Based on air temperature, radiation, air humidity and wind speed, potential evapotranspiration etp

can be calculated by

etp = 1/L * [ (s * rnet + δair * cp *vpd/ra) / ( s + p *(1+ rc/ra) )] Eq. 8

(L=specific vaporization heat of water in W m-², s=slope of the saturation curve for vapour pressure

deficit in hPa K-1, rnet=net radiation in W m-², δair=air density = 1.202 kg m-³ [20°C], cp=heat capacity of

the air = 1005 J kg-1 K-1, vpd=vapour pressure deficit in hPa, ra=boundary layer resistance in m s-1,

rc=canopy resistance in m s-1, p=psychrometer constant = 0.662 hPa K-1).

Boundary layer resistance ra is a function of stand height and wind speed. Canopy resistance rc is

calculated based on the leaf area index and the species specific maximum conductivity for water.

Actual evapotranspiration of a tree or of the ground cover is estimated using the potential

evapotranspiration and the maximum water uptake, which is derived from the water content within

the soil volume that contains fine roots. Thus, the relation of actual to potential evapotranspiration is

closely linked to the relation between water supply and water demand, the increase of this relation

above a threshold -defined by the species specific water deficiency coefficient- determines drought

stress for photosynthesis.

Interception int is calculated by using leaf area, the species specific interception capacity and the

degree to which the interception storage is filled. It evaporates potentially according to the Penman-

Monteith equation for wet surfaces. Stem flow is not regarded explicitly. Crown extensions depicted

as the ground covered area of each tree crown are estimated dynamically by BALANCE. For these

crown covered areas interception can be calculated while throughfall is equal to precipitation in

remaining gaps between trees. Throughfall precipitation in gaps between trees can refill the soil

water content of the rooted fraction within the same layer. Water can therefore be exchanged

between rooted and un-rooted soil layers of a tree. However, a horizontal water exchange between

the different trees is not yet realized.

Total soil water content is reduced by drainage ro, which is equivalent to the percolation from the

deepest soil layer. Percolation of a layer only occurs if its soil water content exceeds field capacity.

Consequently, using the daily actual evapotranspiration sum along with the precipitation, the

interception and the daily percolation, the change in the soil water content can be calculated.

Via stomatal closure the water balance of a tree is linked with the nutrient and carbon cycles.

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4.5 Nutrient cycle

Nutrient uptake is the result of the minimum demand, supply and absorption capacity (Grote 1998).

Initially, only the nitrogen cycle as the most important nutrient is taken into account. The demand is

based on the difference between the actual nitrogen concentration and a given optimal

concentration.

The supply however, is defined by the soil characteristics of the rooted volume, the uptake capacity

by the root surface and its specific absorption rate.

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Dependency of gross primary production from temperature and radiation (a), temperature and CO2 concentration (b), temperature and N-supply (c), radiation and CO2 concentration (d), N-supply and CO2 concentration (e), and N-supply and radiation (f); (1 x CO2 = current atmospheric CO2 concentration; 1.5 x CO2 and 2 x CO2 = increase in CO2 concentration by 50% and 100%)

0

2

4

6

8

10

12

0 10 20 30

g C

/ m

² d

temperature in °C

500

1000

1500

radiation in J cm-² d-1

0

2

4

6

8

10

12

0 10 20 30

g C

/ m

² d

temperature in °C

1xCO2

1.5xCO2

2xCO2

0

2

4

6

8

10

12

0 10 20 30

g C

/ m

² d

temperature in °C

severe deficiency

deficiency

optimal

N supply

0

2

4

6

8

10

12

0 400 800 1200 1600 2000

g C

/ m

² d

radiation in J /cm2 *d

2xCO2

1xCO2

0

2

4

6

8

10

12

0.4 0.6 0.8 1

g C

/ m

² d

N-supply

1xCO2

1.5*CO2

2xCO2

severe deficiency optimal

0

2

4

6

8

10

12

0.4 0.6 0.8 1

g C

/ m

² d

N-supply

1000

1500

500

severe deficiency optimal

radiation in J cm-² d-1

1050

1000

500

a b c

d e f

4.6 Photosynthesis

Physiological processes are calculated in 10 day time steps using results from the daily environmental

conditions (e.g. radiation, temperature). By using the simulation routine suggested by Haxeltine and

Prentice (1996), these time steps are essential for the calculation of the photosynthesis because it

assumes linearity between radiation and assimilation that is not applicable with shorter time steps.

Assimilation is

estimated as a function of leaf surface, absorbed PAR, temperature and CO2-concentration. The

internal CO2 supply depends on the stomata conductivity which is a nonlinear function of the soil

water supply, given relative soil water content is smaller than the species specific threshold i.e. the

water deficiency coefficient. Therefore, photosynthesis of each segment can be reduced by lack of

water as well as altered by the nutrient supply and pollutants.

4.7 Respiration

Total respiration is the sum of maintenance losses and growth respiration. Therefore, maintenance

respiration is calculated separately for each segment and compartment as a function of biomass,

specific respiration rate and temperature. Growth respiration however, is estimated as a constant

fraction of the maximum photosynthesis (Penning de Vries et al. 1989). To fulfil the requirements of

maintenance respiration, we assume that every compartment contains free available carbon. The

maximum free available carbon for each compartment is set as 20%.

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4.8 Allocation and biomass increment

The fixed carbon that is not needed for respiration is used for the distribution into the plant

compartments foliage, branches, stem and roots. This amount of available carbon for allocation is

distributed into the different compartments according to their growth and respiration demands

(Grote 1998). These demands are defined by the relationships between the compartments according

to the functional carbon balance theory (Mäkela 1990) and the pipe model theory (Shinozaki et al.

1964, Chiba 1998). Consequently, all tissues within a segment i.e. foliage and branches or fine roots

and coarse roots, as well as the amount of stemwood are mechanistically linked to each other. As a

result, specific leaf area as well as leaf area density depend on the individual competition situation of

the segment. Similarly to the functional balance theory, the nitrogen that is taken up is distributed

across the compartments according to the estimated demand from the optimum concentrations.

Therefore, an increase in biomass is the result of the interaction between physiological processes

which depend on the physical and chemical microenvironment that in turn is influenced by the stand

structure. It is calculated on the basis of the amount of carbon and nitrogen that is taken up from

each segment. The proportion is dependent on the local energy supply (PAR, temperature) and

resource availability (CO2 concentration, nitrogen availability). Stress conditions like restricted water

availability can decrease the uptake rates below and above ground.

Above ground biomass babove is calculated from the stem biomass bste, the free carbon pool bres and

the sum of the foliage biomass bfol, the twig biomass btwi, the branch biomass bbra, and the bud

biomass bbud of all segments i and layers j:

babove = bste + bres + Σ n,m ij=1 (bfol + btwi + bbra + bbud) Eq.9

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Below ground biomass bbelow, on the other hand, is the sum of the fine root bfro and the coarse root

biomass bcro of segments and layers:

bbelow = Σ n,m ij=1 (bfro + bcro) Eq.10

On the base of the foliated volume of the segment vfol, the foliage density δfol and the specific

foliage area sfa, the foliage biomass of each segment can be estimated:

bfol = vfol * δfol / sfa Eq.11

For the calculation of both the foliage density δfol and the specific foliage area sfa of a segment the

competition factor of the segment is needed. Additionally, maximum foliage density and maximum

volume is required to calculate δfol and maximum resp. minimum specific foliage area to calculate

sfa.

Twig biomass btwi is calculated as a specific ratio of foliage biomass. Branch biomass bbra as well as

stem biomass bste can be simulated from their specific wood density and biomass volume. Bud

biomass bbud is estimated as a function of the carbon required to produce the foliage for the next

year. Bres, the free available carbon, is defined as a fraction of the living woody tissue. By using

species specific fine root to foliage biomass ratios, fine root biomass bfro can be calculated. Analogous

to the branch biomass estimation, coarse root biomass bcro is derived from the coarse root density

and the coarse root volume. Coarse root volume just as branch volume is computed from the fine

root biomass resp. foliage biomass and the fraction of sapwood area needed to supply the fine root

biomass resp. the foliage biomass within the segment.

Dimensional tree growth is estimated at the end of every year, on the basis of the increase in

accumulation of biomass during that year. The increase in the proportion of biomass that every

crown resp. root segment receives is defined by its relative contribution to the net carbon and

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16

nitrogen increase. The volume development depends on the necessary amount of twigs and

transport branches resp. on the amount of coarse roots within the root segments. Therefore, crown

expansion is favoured in the direction towards the best assimilation conditions during the previous

year. If net assimilation rates are negative, the crown segment is regarded as dead. If no segments

contain living biomass, the tree is assumed to be dead and removed from calculations.

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17

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