Growth behaviors

In this document:
How growth is applied
Growth parameters
Absolute growth behaviors
--Absolute growth limited to radial increment behavior
--Absolute growth limited to basal area increment behavior
--Non-limited absolute growth behavior
Allometric diameter growth - diam only
Allometric height growth
Basal area NCI growth
Constant basal area growth behavior
Browsed relative growth behavior
Constant radial growth behavior
Double resource relative growth
Juvenile NCI growth
Lagged post harvest growth
Linear growth
Linear bi-level growth
Linear growth w/ exponential shade reduction
Logistic growth
Logistic growth w/ size dependent asymptote
Lognormal bi-level growth - height only
Lognormal with exponential shade reduction
Michaelis Menton with negative growth - height only
Michaelis Menton with photoinhibition - height only
NCI growth behavior
Power growth - height only
Puerto Rico semi-stochastic - diam only
Puerto Rico storm bi-level growth - diam with auto height
Relative growth behaviors
--Relative growth limited to radial increment behavior
--Relative growth limited to basal area increment behavior
--Non-limited relative growth behavior
--Relative growth - height only
Stochastic gap growth
Weibull climate growth
Weibull climate quadrat growth

How growth is applied

Growth behaviors increase the size of a tree. A tree has two basic size dimensions: diameter and height. A growth behavior can increase tree size using one of three methods.

In the first method, the behavior calculates an amount of diameter increase, and then adds this amount to the tree's diameter. The tree's new height is calculated from the new diameter using the appropriate allometry equation. This is the way that growth has been applied in all previous versions of SORTIE, and is the method you should choose if you are in doubt about which one you want. Behaviors using this method have the tag "diam with auto height" in their name.

In the second method, the behavior calculates an amount of diameter increase, and then adds this amount to the tree's diameter. The height is not allowed to change. The rationale behind this is that tree diameter and height are not always strictly coupled by the allometry equations; sometimes, diameter and height should be allowed to vary independently. If you use a growth behavior of this type, it is required that you pair it with a separate behavior incrementing height. Behaviors using this method have the tag "diam only" in their name.

In the third method, the behavior calculates an amount of height increase, and then adds this amount to the tree's height. The diameter is not allowed to change. The rationale is the same as that for the second method. If you use a growth behavior of this type, it is required that you pair it with a separate behavior incrementing diameter. Behaviors using this method have the tag "height only" in their name.

Growth behaviors using the second and third method must work together in pairs. Behaviors using the first method work alone. If you pair a behavior using method one with a behavior using method three, the height-incrementing behavior will be ignored.

When incrementing a tree's diameter with new growth, seedlings and saplings have the amount of growth increase applied to their diameter at 10 cm. Adults have the amount applied to their DBH. For more on tree types and their measurements, see the trees topic. For more on tree size relationships, including how trees transition between life history stages, see the allometry topic.

Note: All behaviors convert growth to diameter growth in cm for internal consistency. The equations below reflect this. Some behaviors may take parameters in mm, or for radial growth. Take careful note of your behavior's parameters.

It is important to be careful when mixing different growth methods for different life history stages of a tree species. For instance: if tree seedlings or saplings get separate diameter and height increments, then their diameters and heights will be "uncoupled." This means that you cannot use one of the size dimensions to predict the other through an allometric equation. Trees with the same diameter will have different heights, and vice versa. Say that you do not have data on separate diameter and height growth for adults, so you assign the adults to a behavior that increments diameter and then automatically updates height according to the allometry equations. You are likely to notice strange results for new adult trees. You will lose the variability in height/diameter ratio that was developed. Suddenly, all trees with the same diameter will have the same height again, and vice versa. This means that individuals may suddenly jump in height, or even shrink.

The "Allometric height growth" and "allometric diameter growth" behaviors were developed to help bridge this gap. When used with a behavior that only increments diameter or height, they will preserve height or diameter differences that have developed across individuals in a species.

Growth parameters

Relative growth behaviors

Several behaviors apply a relative growth version of the Michaelis-Menton function. Relative growth is calculated with the equation:


where:

Diameter growth is compounded over multiple timesteps with the equation:

G = ((Y + 1)T - 1) * diam X
where:

Relative height growth is calculated slightly differently. The details are discussed in the section for the Relative growth - height only behavior below. Relative growth is discussed in Pacala et al 1996.

Relative growth limited to radial increment

How it works

This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of the constant radial growth increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Relative growth limited to basal area increment

How it works

This behavior calculates an amount of diameter growth according to the relative growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" behavior.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Non-limited relative growth

How it works

The amount of increase returned by the relative growth equation is applied to the tree.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied.

Relative growth - height only

This behavior uses the Michaelis-Menton function to do height growth.

How it works

After the Michaelis-Menton function is used to calculate Y as described in the section above, the amount of height growth is calculated as:

G = Y * Height X

where:

If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior and a diameter growth behavior applied.

Allometric diameter and height growth

How it works

These behaviors are designed to be secondary growth behaviors. If you have a behavior that primarily updates one tree dimension (diameter or height), one of these behaviors can be used on the other dimension to ensure even growth. These behaviors calculate a growth amount based on the allometry equations. The amount of growth is:

Y = f(Xt+1) - f(Xt)

where Y is the amount of growth calculated by this behavior, f(X) is the allometry equation relating diameter and height, X t is the other tree dimension (either height or diameter) before the primary growth is applied, and X t+1 is the other tree dimension after primary growth is applied. The allometric diameter growth behavior can be paired with any height-only growth behavior, and the allometric height growth behavior can be paired with any diam-only growth behavior.

How to apply it

These behaviors can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a growth behavior applied that grows the opposite tree dimension.

Double resource relative growth

This behavior uses a double Michaelis-Menton function to calculate relative growth based on two resources: light and a second resource. The identity of the second resource is unimportant and could be anything, from exchangeable calcium levels to soil moisture. Relative growth is calculated with the equation:

where:

Growth is compounded over multiple timesteps with the equation:

G = ((Y + 1)T - 1) * diam

where:

Note that setting the C parameter in the equation above to 0 eliminates the second resource and makes this equivalent to the "Non-limited relative growth" behavior.

How it works

The amount of the second resource is captured in a grid object called Resource. Currently it is up to you to enter a map of the values for this resource grid; for instructions on how to do this, see the Grid Setup Window topic. This behavior does not in any way alter the values in this grid.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You must also enter a map of second resource values into the Resource grid. You can use either the diam with auto height or diam only version.

Absolute growth behaviors

Several behaviors apply an absolute growth version of the Michaelis-Menton function. Absolute growth is calculated with the equation:

where

Amount of diameter growth per timestep is calculated as

growth = (((10Y - 1) * 2 )/ 10) * T

where T is the number of years per timestep.

The absolute growth behaviors also take into account suppression status. A tree is considered suppressed if its growth rate for the previous timestep falls below a certain threshold. That threshold is the rate of growth at which X% of juveniles die, where X is a user-settable parameter. The threshold is calculated for each species by solving the BC mortality equation for G (growth), where m is the threshold growth rate.

A tree's suppression state is a multiplicative factor in its growth rate. If a tree is not suppressed, the suppression factor in the growth equation is set to 1 (no effect on growth). If the tree is suppressed, the suppression factor is calculated as follows:

SF = e((g*YLR) - (d*YLS))

where:

Details of this model are published in Wright et al 2000.

Absolute growth limited to radial increment

How it works

This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of the constant radial increment for the species of tree to which it is being applied. The increment is calculated as described in the "Constant radial growth" behavior. Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Absolute growth limited to basal area increment

How it works

This behavior calculates an amount of diameter growth according to the absolute growth equation. Growth is limited to a maximum of a constant basal area increment. The amount of diameter increase is calculated by dividing the annual basal area increment of the tree's species by the diameter of the tree. The increment is calculated as described in the "Constant basal area growth" behavior.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Non-limited absolute growth - diam with auto height

How it works

The amount of diameter increase returned by the absolute growth equation is applied to the tree.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Constant basal area growth

How it works

The amount of diameter increase is calculated from a constant basal area increment. The increase is calculated as follows:

Y = (g / diam) * 100 * T

where

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

Constant radial growth

How it works

The amount of diameter increase is calculated from the constant radial increment. The increase is calculated as follows:

Y = (g4 / 10) * 2 * T

where

Note that the increment parameter specifies radial growth; the behavior makes all necessary conversions to diameter growth.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can use either the diam with auto height or diam only version.

NCI growth

This behavior uses the effects of neighbor competitiveness to influence growth rates ("NCI" stands for neighborhood competition index). A tree's maximum potential growth rate is reduced due to competitiveness and several other possible factors. You can use certain parameter values to turn these influences on and off to reflect the conditions appropriate for your run.

How it works

For a tree, the amount of growth per year is calculated as:


Growth = Max Growth * Size Effect * Shading Effect * Crowding Effect * Damage Effect

Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the NCI Maximum Potential Growth, cm/yr parameter. Size Effect, Shading Effect, Crowding Effect, and Damage Effect are all optional factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.

Size Effect is calculated as:

NCI size effect equation

where:

Shading Effect is calculated as:

NCI shading effect equation

where:

This effect is not required. To omit the Shading Effect, set the NCI Shading Effect Coefficient (m) parameter to 0.

Crowding Effect is calculated as:

NCI crowding effect equation

where:

The NCI value sums up the competitive effect of all neighbors with a DBH at least that of the NCI Minimum Neighbor DBH, in cm parameter, out to a maximum distance set in the NCI Max Radius of Crowding Neighbors, in m parameter. The competitiveness of a neighbor increases with the neighbor's size and decreases with distance and storm damage to the neighbor (optional). The neighbor's species also matters; the effect depends on the relationship between the target species and the neighbor species. Seedlings never compete. You set whether or not snags compete in the Include Snags in NCI Calculations parameter.

The crowding effect is optional. You can omit it by setting either the NCI Crowding Effect Slope (C) or NCI Max Radius of Crowding Neighbors, in m parameters to 0.

NCI is calculated as:

NCI equation

where:

The value of Damage Effect is optional. If you elect not to use storms in your run, set all values in the NCI Damage Effect - Medium Storm Damage (0-1) and NCI Damage Effect - Complete Storm Damage (0-1) parameters to 1. If you are using storms, then the value of Damage Effect depends on the tree's damage category. If the tree is undamaged, Damage Effect equals 1. If the tree has medium storm damage, the value is the NCI Damage Effect - Medium Storm Damage (0-1) parameter. If the tree has complete storm damage, the value is the NCI Damage Effect - Complete Storm Damage (0-1) parameter.

The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment DBH for one year. For each year, any portion of the growth equation with DBH as a term is recalculated with the previous year's updated DBH value. (NCI values are constant throughout this loop - for neighbors only the DBH at the start of the timestep is used.)

How to apply it

This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings. You can use either the diam with auto height or diam only version.

If the Shading Effect term is activated in the growth equation, then the trees to which this behavior is applied must also have a light behavior applied - the Sail light behavior is the one designed to work with the NCI behavior. The use of any other light behavior is at your own risk.

If any storm damage parameters are set to anything other than 1, it is recommended (but not required) that you have the Storm damage applier behavior applied.

Basal area NCI growth

This behavior uses the effects of neighbor competitiveness to influence growth rates ("NCI" stands for neighborhood competition index). In this case, the NCI is based on the basal area of neighboring trees. A tree's maximum potential growth rate is reduced due to competitiveness and several other possible factors.

How it works

For a tree, the amount of growth per year is calculated as:

Growth = Max Growth * Size Effect * Crowding Effect

Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the NCI Maximum Potential Growth, cm/yr parameter. Size Effect and Crowding Effect are factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.

Size Effect is calculated as:

NCI size effect equation

where:

Crowding Effect is calculated as:

CE = exp(-C * (DBH γ * BAn / BADiv) D)

where:

When calculating BAn, this behavior uses neighbors of all species out to the distance set in the NCI Max Radius of Crowding Neighbors, in m parameter. The neighbors must have a DBH larger than the values set in the NCI Minimum Neighbor DBH, in cm parameter. If the Basal Area NCI - Use Only Larger Neighbors parameter is set to true, they must also have a DBH larger than the target tree's DBH. Seedlings and snags never contribute to BAn.

The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment DBH for one year. For each year, any portion of the growth equation with DBH as a term is recalculated with the previous year's updated DBH value. (NCI values are constant throughout this loop – for neighbors, only the d10 at the start of the timestep is used.)

How to apply it

This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings. You can use either the diam with auto height or diam only version.

Linear growth

This behavior does either diameter or height growth as a linear function of GLI.

How it works

This behavior calculates an amount of diameter or height growth as:

Y = (a + (b * GLI)) * T

where

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.

Linear growth w/ exponential shade reduction

This behavior does either diameter or height growth as a function of GLI.

How it works

This behavior calculates an amount of diameter or height growth as:

Y = (a + (b * diam)) * (GLI/100)c * T

where

If calculating height growth: In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.

Logistic growth

This behavior does either diameter or height growth as a function of GLI.

How it works

The amount of diameter increase is calculated as:

where

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.

Logistic growth w/ size dependent asymptote

This behavior does either diameter or height growth as a function of tree size and GLI.

How it works

This behavior calculates annual diameter or height increases as:

where

For diameter growth: Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments.

For height growth: In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the logistic growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.

Lognormal with exponential shade reduction

This behavior does either diameter or height growth as a function of tree size and GLI.

How it works

This behavior calculates annual diameter or height increases as:

where

For diameter growth: Assume that the number of years per timestep is X. In order to find the total amount of diameter increase for a timestep, the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase for the previous year. The total diameter increment is the sum of the X individual diameter increments.

For height growth: In order to find the total amount of height increase for a timestep, the behavior takes as an input the amount of diameter growth increase. Assume that the number of years per timestep is X. The amount of diameter increase is divided by X. Then the lognormal growth equation is calculated X times, with the diameter incremented by the amount of diameter increase per timestep each time. The total height increment is the sum of the X individual height increments.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior applied. You can choose either a diam with auto height, diam only, or height only version.

Stochastic Gap Growth

This behavior uses a shortcut for simulating gap dynamics with very competitive conditions. This behavior causes rapid growth in high light, with a unique "winner"; low light produces no growth at all.

How it works

This behavior simulates high growth in gap conditions. It relies on the Gap Light grid created by the Gap Light behavior to tell it where the gaps are. In this grid, each cell is either in gap (with 100% GLI) or not in gap (with 0% GLI). If a cell is in gap, a tree in that cell is randomly chosen out of all the trees to which the behavior applies to be promoted directly to adult tree status (even if it is a seedling). This tree represents the "winner". All other trees in the cell do not grow. In cells that are not in gap, no trees grow.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have the Gap Light behavior applied.

Linear bi-level growth

This behavior increments growth according to a simple linear equation, with the possibility of two sets of parameters for each species: one for high-light conditions and one for low-light conditions. This can also be used alone without the light levels.

How it works

The equation used by this behavior to increment growth is:

Y = (a + b * diam) * T

where

Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of high-light and low-light parameters is set in the Linear Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.

This behavior can also be used without Storm Light. In this case, only the low-light growth parameters are used.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. If you wish to use the light-level parameter switch, also use the Storm Light behavior. You can use either the diam with auto height or diam only version.

Lognormal bi-level growth - height only

This behavior increments growth according to a simple linear equation, with the possibility of two sets of parameters for each species: one for high-light conditions and one for low-light conditions. This can also be used alone without the light levels.

How it works

The equation used by this behavior to increment growth is:

Lognormal bi-level equation

where

Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of high-light and low-light parameters is set in the Lognormal Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.

This behavior can also be used without Storm Light. In this case, only the low-light growth parameters are used.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a diam-only growth behavior applied. If you wish to use the light-level parameter switch, also use the Storm Light behavior.

Puerto Rico semi-stochastic - diam only

This behavior combines a deterministic growth function for small trees with completely stochastic growth for larger trees. It's meant to be used when a species uses a height growth behavior as the primary growth method.

How it works

The divide between the two growth functions is defined in the PR - Height Threshold for Stochastic Growth (m) parameter. Trees shorter than this use the following function:

Y = (A * exp(-B * Height)) - Diam

where:

Above the height cutoff, trees are assigned random diameters drawn from a normal distribution. The normal distribution is defined by the PR - Mean DBH (cm) for Stochastic Growth and PR - DBH Standard Deviation for Stochastic Growth parameters, and represents the distribution of DBH values, NOT growth values. The amount of growth for a tree is Y = D' - D, where Y is the amount of growth, D' is the new diameter chosen from the normal distribution, and D is the previous diameter. This means that growth can be negative. The effect is to create a tree population with normally-distributed diameters, where any individual tree may jump from place to place within the distribution.

How to apply it

This function can be applied to seedlings, saplings, or adults of any species. Any tree using this behavior must also use a height-only growth behavior.

Puerto Rico storm bi-level growth - diam with auto height

This behavior increments growth according to two possible growth equations, one to be used in low-light conditions and the other to be used in high-light conditions. This behavior was originally created for the Puerto Rico model.

How it works

Light levels come from the Storm Light grid produced by the Storm Light behavior. The threshold between the use of the high-light and low-light functions is set in the PR Storm Bi-Level - Threshold for High-Light Growth (0 - 100) parameter.

The function used in low-light conditions is:

Y = (a + b * diam) * T

where

The function used in high-light conditions is:

H = T * a * diam * e(-b * N)

where

H is expressed in centimeters of height growth. This is transformed into a number of cm of diameter growth, which is what this behavior passes along. This means that during tree life history stage transitions, the height the tree ends up with is not guaranteed to match the height calculated by the high-light growth function.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. You must also use the Storm disturbance and Storm Light behaviors.

Browsed relative growth behavior

This behavior simulates herbivory by allowing trees to grow at different rates when browsed versus unbrowsed.

How it works

Trees grow according to the relative growth version of the Michaelis-Menton function. The same function is used for both browsed and unbrowsed trees, but the parameters are different. The function is:

where:

Growth is compounded over multiple timesteps with the equation:

G = ((Y + 1)T - 1) * diam X

where:

Whether or not a tree is browsed is determined by the Random browse behavior.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior and the Random browse behavior applied. You can use either the diam with auto height or diam only version.

Michaelis Menton with negative growth - height only

This behavior uses a modified Michaelis-Menton function to do height growth. You can optionally add autocorrelation and a degree of stochasticity to the growth.

How it works

The amount of height growth is calculated as:

Michaelis Menton with negative growth equation

where:

Optionally, the value of Y can be randomized by adding to it a stochastic factor SF, which is a random draw on a normal distribution with mean zero and standard deviation set using the Michaelis-Menton Neg Growth - Growth Standard Deviation parameter. SF can be positive or negative and is in units of centimeters of height growth. If you do not want to add SF, set the value of this parameter to zero.

If you are using the stochastic factor SF, you can also introduce autocorrelation in the growth stochasticity. Each year, for each tree, a random number is compared to the value in the Michaelis-Menton Neg Growth - Autocorrelation Prob (0-1) parameter for that tree's species to determine if the stochastic factor will be autocorrelated for that year. If it is autocorrelated, the previous year's stochastic factor SF is added to Y to determine height growth. If it is not autocorrelated, a new value for SF is drawn. If you do not wish to use autocorrelation, set the value of the autocorrelation parameter to zero. Autocorrelation is ignored if there is no growth stochasticity.

If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time. Stochasticity and autocorrelation are also evaluated on a yearly basis.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior and a diameter growth behavior applied.

Michaelis Menton with photoinhibition - height only

This behavior uses a modified Michaelis-Menton function to do height growth.

How it works

The amount of height growth is calculated as:

Michaelis Menton with photoinhibition growth equation

where:

If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a light behavior and a diameter growth behavior applied.

Power growth - height only

This behavior uses a power function to do height growth.

How it works

The amount of height growth is calculated as:

Y = n H φ

where:

If the timestep is more than one year long, growth is recalculated for each year of the timestep, increasing the height each time.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. Any tree species/type combination to which it is applied must also have a diameter growth behavior applied.

Lagged post harvest growth

This behavior increments growth as a function of DBH and neighboring basal area, and incorporates a lag period after harvesting during which trees acclimate to their post-harvest growing conditions.

How it works

A tree's potential growth is calculated by:

PARG = α * exp(-δ * DBH) * exp(-η BA * exp(-ω * DBH))

where:

If no harvest has occurred yet in this run, then the tree's actual growth, ARG, equals PARG. If a harvest has occurred at some point during this run, then ARG is calculated by:

ARG = ARGpre + (PARG - ARGpre) * (1 - exp(-τ * H * t))

where:

Annual radial growth ARG is used to calculate timestep diameter growth using

DG = ARG * t * 2/10

where t is the number of years per timestep.

Model forms are based on those in Thorpe et al. 2010.

How to apply it

This behavior can be applied to saplings and adults of any species.

Juvenile NCI growth

This behavior uses the effects of neighbor competitiveness to influence growth rates for juvenile trees ("NCI" stands for neighborhood competition index). A tree's maximum potential growth rate is reduced due to competitiveness and other possible factors. This is very similar to NCI growth, but adapted for juveniles.

How it works

For a tree, the amount of diameter growth per year is calculated as:

Growth = Max Growth * Size Effect * Crowding Effect

Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the Juvenile NCI Maximum Potential Growth, cm/yr parameter. Size Effect and Crowding Effect are factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.

Size Effect is calculated as:

SE = a * d10b

where:

Crowding Effect is calculated as:

CE = exp(-C * NCI D)

where:

The NCI value sums up the competitive effect of all neighbors with a d10 at least that of the Juvenile NCI Minimum Neighbor Diam10, in cm parameter, out to a maximum distance set in the Juvenile NCI Maximum Crowding Distance, in meters parameter. The competitiveness of a neighbor increases with the neighbor's size and decreases with distance. The neighbor's species also matters; the effect depends on the relationship between the target species and the neighbor species.

Unlike NCI growth, this competitiveness index uses d10 instead of DBH; so seedlings can compete. For adults, the d10 is calculated from DBH using the DBH - diameter at 10 cm relationship. You set whether or not snags compete in the Juvenile NCI - Include Snags in NCI Calculations parameter.

NCI is calculated as:

where:

The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment d10 for one year. For each year, any portion of the growth equation with d10 as a term is recalculated with the previous year's updated d10 value. (NCI values are constant throughout this loop – for neighbors, only the d10 at the start of the timestep is used.) The final total growth amount is added to the tree's d10.

How to apply it

This behavior can be applied to seedlings and saplings of any species. You can use either the diam with auto height or diam only version.

Weibull climate growth

This behavior calculates tree growth as a function of climate and larger neighbor trees. A tree has a maximum potential growth rate that is reduced due to several possible factors. Different parameter values can be used for adults and juveniles (saplings).

How it works

For a tree, the amount of diameter growth per year is calculated as:


Growth = Max Growth * Size Effect * Precipitation Effect * Crowding Effect * Temperature Effect

Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the Weibull Climate Growth - Max Potential Growth (cm/yr) parameter. Size Effect, Precipitation Effect, Crowding Effect, and Temperature Effect are all factors which act to reduce the maximum growth rate and will vary depending on the conditions a tree is in. Each of these effects is a value between 0 and 1.

Size Effect is calculated with a lognormal function, as follows:

NCI size effect equation

where:

You can set a minimum DBH for the size effect in the Weibull Climate Growth - Size Effect Minimum DBH parameter. Any target tree whose DBH is less than this value will get a size effect based on the minimum DBH instead. This allows you to avoid problems with very small trees that can occur because of the shape of the lognormal function.

Precipitation Effect is calculated as:

PE = Weibull climate growth precipitation effect equation

where:

Temperature Effect is calculated as:

TE = Weibull climate growth temperature effect equation

where:

Crowding Effect is calculated as:

Weibull climate growth crowding effect equation

where:

The ND value is a count of all larger neighbors with a DBH at least that of the Weibull Climate Growth - Minimum Neighbor DBH, in cm parameter, out to a maximum distance set in the Weibull Climate Growth - Max Neighbor Search Radius (m) parameter. The value is a straight count - it is not scaled or relativized in any way. Seedlings never compete.

The amount of growth is in cm/year. For multi-year timesteps, the behavior will calculate total growth with a loop. Each loop iteration will increment DBH for one year. For each year, any portion of the growth equation with DBH as a term is recalculated with the previous year's updated DBH value.

How to apply it

This behavior can be applied to saplings and adults of any species. It cannot be applied to seedlings. You can use either the diam with auto height or diam only version.

Weibull climate quadrat growth

This behavior calculates tree growth as a function of climate and neighbor trees. For processing efficiency, growth is calculated for each species on a per grid cell basis. There is a maximum potential growth rate that is reduced due to several possible factors.

How it works

This behavior tracks growth using the Weibull Climate Quadrat Growth grid. Each tree gets the growth rate calculated for the grid cell in which it is found. You can set the grid cell size to set the balance between neighborhood composition resolution ( smaller grid cells) and processing time ( larger grid cells).

For a given species in a given grid cell, the amount of diameter growth per year is calculated as:


Growth = Max Growth * Precipitation Effect * Crowding Effect * Temperature Effect

Max Growth is the maximum diameter growth the tree can attain, in cm/yr, entered in the Weib Clim Quad Growth - Max Potential Growth (cm/yr) parameter. Precipitation Effect, Crowding Effect, and Temperature Effect are all factors which act to reduce the maximum growth rate and will vary depending on the local and plot-wide conditions a tree is in. Each of these effects is a value between 0 and 1.

Precipitation Effect is calculated as:

PE =  Weibull climate growth precipitation effect equation

where:

Temperature Effect is calculated as:

TE =  Weibull climate growth temperature effect equation

where:

Crowding Effect is calculated as:

CE = exp(-C * ND D)

where:

The ND value is a count of all neighbors with a DBH at least that of the Weib Clim Quad Growth - Minimum Neighbor DBH (cm) parameter, out to a maximum distance from the center of the grid cell set in the Weib Clim Quad Growth - Max Neighbor Search Radius (m) parameter. The value is a straight count - it is not scaled or relativized in any way. Seedlings never compete.

The amount of growth is in cm/year. For multi-year timesteps, the annual growth rate is multiplied by the number of years per timestep.

How to apply it

This behavior can be applied to seedlings, saplings, and adults of any species. You can use either the diam with auto height or diam only version.



Last updated: 28-Sep-2010 02:13 PM