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
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.
- Adult Constant Area Growth in sq. cm/yr The constant amount of basal area by which to increase a tree's basal area. Used in basal-area-increment-limited behaviors and constant basal area growth behaviors.
- Adult Constant Radial Growth in mm/yr The constant value by which to increase a tree's radius at breast height. Used in radial-increment-limited-growth behaviors and constant radial increment behaviors.
- Asymptotic Diameter Growth (A) Asymptote of the Michaelis-Menton growth function at high light in absolute and relative growth behaviors - A in the equations below. Used in absolute and relative growth behaviors.
- Asymptotic Height Growth (A) Asymptote of the Michaelis-Menton growth function at high light - A in the equations below. Used in the Relative growth - height only behavior.
- Basal Area NCI - BA Divisor The value by which to divide neighbor basal area. Used in the Basal area NCI growth behavior.
- Basal Area NCI - Use Only Larger Neighbors Whether to use all neighbors larger than the minimum DBH (false) or only neighbors larger than the target tree (true). Used in the Basal area NCI growth behavior.
- Browsed Asymptotic Diameter Growth (A) Asymptote of the Michaelis-Menton growth function at high light when a plant has been browsed. Used by the Browsed relative growth behavior behavior.
- Browsed Slope of Growth Response (S) Slope of the Michaelis-Menton growth function at zero light when a plant has been browsed. Used by the Browsed relative growth behavior behavior.
- Browsed Diameter Exponent The diameter exponent for growth when a plant has been browsed. Used by the Browsed relative growth behavior behavior.
- Double resource - Influence of Resource (C) The parameter governing the influence of the second resource on the double-resource Michaelis-Menton equation. Used by the Double resource relative growth behavior.
- Include Snags in NCI Calculations Whether or not to include snags when finding competitive neighbors for NCI. Used in the NCI growth behavior.
- Juvenile NCI Alpha NCI function exponent. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Beta NCI function exponent. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Crowding Effect Slope (C) The slope of the curve for the crowding effect equation. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Crowding Effect Steepness (D) The steepness of the curve for the crowding effect equation. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Diam10 Divisor (q) The value by which neighbor d10s are divided when calculating NCI. This can be used to make units adjustments. Used in the Juvenile NCI growth behavior.
- Juvenile NCI - Include Snags in NCI Calculations Whether or not to include snags when finding competitive neighbors for NCI. Used in the Juvenile NCI growth behavior.
- Species i Juvenile NCI Lambda Neighbors The competitive effect of neighbors of species i on the target tree species's growth, between 0 and 1. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Maximum Crowding Distance, in meters The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Maximum Potential Growth, cm/yr Maximum potential diameter growth for a tree, in cm/yr. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Minimum Neighbor Diam10, in cm The minimum d10 for trees of that species to compete as neighbors. Used for all species, not just those using NCI growth. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Size Effect "a" Size effect power function scaling factor "a" parameter. Used in the Juvenile NCI growth behavior.
- Juvenile NCI Size Effect "b" Size effect exponent "b" parameter. Used in the Juvenile NCI growth behavior.
- Length of Current Release Factor Controls the magnitude of the effects of release. Used in absolute growth behaviors.
- Length of Last Suppression Factor Controls the magnitude of the effects of suppression. Used in absolute growth behaviors.
- Linear Bi-Level - Intercept for High-Light Growth (a) The intercept of the linear growth function used in high-light conditions. Used in the Linear bi-level growth behavior.
- Linear Bi-Level - Intercept for Low-Light Growth (a) The intercept of the linear growth function used in low-light conditions. Used in the Linear bi-level growth behavior.
- Linear Bi-Level - Slope for High-Light Growth (b) The slope of the linear growth function used in high-light conditions. Used in the Linear bi-level growth behavior.
- Linear Bi-Level - Slope for Low-Light Growth (b) The slope of the linear growth function used in low-light conditions. Used in the Linear bi-level growth behavior.
- Linear Bi-Level - Threshold for High-Light Growth (0 - 100) The threshold between low-light and high-light parameters, as a value between 0 and 100. Used in the Linear bi-level growth behavior.
- Logistic - Asymptotic Diam Growth - Full Light in mm/yr (a) Asymptotic annual growth at full light, in mm/yr. Used by the Logistic growth behavior.
- Logistic - Asymptotic Height Growth - Full Light in cm/yr (a) Asymptotic annual growth at full light, in cm/yr. Used by the Logistic growth behavior.
- Logistic - Diam Shape Param 1 (b) Shape parameter 1. Used by the Logistic growth behavior.
- Logistic - Diam Shape Param 2 (c) Shape parameter 2. Used by the Logistic growth behavior.
- Logistic - Height Shape Param 1 (b) Shape parameter 1. Used by the Logistic growth behavior.
- Logistic - Height Shape Param 2 (c) Shape parameter 2. Used by the Logistic growth behavior.
- Lognormal Bi-Level - Max Growth in High Light (m) The maximum height growth, in meters, under high-light conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Max Growth in Low Light (m) The maximum height growth, in meters, under low-light conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - X0 for High-Light Growth The X0 parameter to use under high-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - X0 for Low-Light Growth The X0 parameter to use under low-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Xb for High-Light Growth The Xb parameter to use under high-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Xb for Low-Light Growth The Xb parameter to use under low-light growth conditions. Used by the Lognormal bi-level growth - height only behavior.
- Lognormal Bi-Level - Threshold for High-Light Growth (0 - 100) Used by the Lognormal bi-level growth - height only behavior.
- Lognormal - Diam Effect of Shade (c) Effect of shade. Used by the Lognormal with exponential shade reduction behavior.
- Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) Annual growth increment at diameter 36, in mm/yr.Used by the Lognormal with exponential shade reduction behavior.
- Lognormal - Diam Shape Parameter (b) Shape parameter. Used by the Lognormal with exponential shade reduction behavior.
- Lognormal - Height Effect of Shade (c) Effect of shade. Used by the Lognormal with exponential shade reduction behavior.
- Lognormal - Height Growth Increment at Diam 36, in cm/yr (a) Annual growth increment at diameter 36, in cm/yr. Used by the Lognormal with exponential shade reduction behavior.
- Lognormal - Height Shape Parameter (b) Shape parameter. Used by the Lognormal with exponential shade reduction behavior.
- Michaelis-Menton Neg Growth - Alpha Alpha parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton Neg Growth - Autocorrelation Prob (0-1) Probability of autocorrelation from year to year, as a value from 0 to 1. Use 0 if there should be no autocorrelation. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton Neg Growth - Beta Beta parameter. Cannot be equal to zero. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton Neg Growth - Gamma Gamma parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton Neg Growth - Growth Standard Deviation Standard deviation of growth stochasticity, cm / yr. Use zero if growth should have no stochasticity. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton Neg Growth - Phi Phi parameter. Used by the Michaelis Menton with negative growth - height only behavior.
- Michaelis-Menton with Photoinhibition - Alpha Alpha parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - Beta Beta parameter. Cannot be equal to zero. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - D D parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Michaelis-Menton with Photoinhibition - Phi Phi parameter. Used by the Michaelis Menton with photoinhibition - height only behavior.
- Mortality Threshold for Suppression Defines the growth rate for suppressed status in terms of tree mortality. The value is expressed as the proportion of trees which die at the growth rate which defines suppressed status, expressed as a fraction between 0 and 1. For instance, if this value is 0.1, the growth
rate for suppressed status is one at which 10% of trees die with that growth. Used in absolute growth behaviors.
- NCI Alpha NCI function exponent. Used in the NCI growth behavior.
- NCI Beta NCI function exponent. Used in the NCI growth behavior.
- NCI Crowding Effect Slope (C) The slope of the curve for the crowding effect equation. Used in the NCI growth behavior.
- NCI Crowding Effect Steepness (D) The steepness of the curve for the crowding effect equation. Used in the NCI growth behavior.
- NCI Damage Effect - Complete Storm Damage (0-1) The fraction by which a tree's growth rate is reduced when it has sustained complete storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior.
- NCI Damage Effect - Medium Storm Damage (0-1) The fraction by which a tree's growth rate is reduced when it has sustained medium storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior.
- Species i NCI lambda neighbors The competitive effect of neighbors of species i on the target tree species's growth, between 0 and 1. Used in the NCI growth behavior.
- NCI Maximum Crowding Distance, in meters The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. Used in the NCI growth behavior.
- NCI Maximum Potential Growth, cm/yr Maximum potential diameter growth for a tree, in cm/yr. Used in the NCI growth behavior.
- NCI Minimum Neighbor DBH, in cm The minimum DBH for trees of that species to compete as neighbors. Used for all species, not just those using NCI growth. Used in the NCI growth behavior.
- NCI DBH Divisor (q) The value by which neighbor DBHs are divided when calculating NCI. This can be used to make units adjustments. Used in the NCI growth behavior.
- NCI Neighbor Storm Damage (eta) - Complete (0-1) The fraction to which a neighbor's competitive effect is reduced when the neighbor has sustained complete storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior.
- NCI Neighbor Storm Damage (eta) - Medium (0-1) The fraction to which a neighbor's competitive effect is reduced when the neighbor has sustained medium storm damage. Set this to 1 if you are not including storms in your run. Used in the NCI growth behavior.
- NCI Shading Effect Coefficient (m) The coefficient in the shading effect equation. Set this value to 0 if you do not wish to use shading. Used in the NCI growth behavior.
- NCI Shading Effect Exponent (n) The exponent in the shading effect equation. If you set the NCI Shading Effect Coefficient (m) parameter to 0, this value is ignored. Used in the NCI growth behavior.
- NCI Size Effect Mode, in cm (X0) The mode of the size effect curve. Used in the NCI growth behavior.
- NCI Size Effect Variance, in cm (Xb) The variance of the size effect curve. Used in the NCI growth behavior.
- NCI Size Sensitivity to NCI (gamma) The sensitivity of a tree's growth rate to its DBH. Set this to 0 to remove the DBH term altogether. Used in the NCI growth behavior.
- Post Harvest Growth - DBH Growth Effect The effect of DBH on growth. Used in the Lagged post harvest growth behavior.
- Post Harvest Growth - DBH NCI Effect The effect of DBH on the neighborhood competition index. Used in the Lagged post harvest growth behavior.
- Post Harvest Growth - Max Growth Constant Maximum annual radial growth, in mm. Used in the Lagged post harvest growth behavior.
- Post Harvest Growth - NCI Constant A constant adjusting the effects of NCI. Lagged post harvest growth behavior.
- Post Harvest Growth - NCI Distance (m) The maximum distance at which neighboring trees can have competitive effects.
- Post Harvest Growth - Time Since Harvest Rate Param A parameter controlling the rate at which the actual growth approaches the potential growth after a harvest.
- PR - "a" Parameter for Deterministic Growth "a" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - "b" Parameter for Deterministic Growth "b" parameter used to calculate deterministic growth when a tree is below the stochastic height threshold. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - DBH Standard Deviation for Stochastic Growth Standard deviation for DBH values when a tree uses stochastic growth. This is the standard deviation of the DBH value, NOT the amount of growth. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - Height Threshold for Stochastic Growth (m) The tree height threshold, in meters, between deterministic and stochastic growth. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR - Mean DBH (cm) for Stochastic Growth The mean for DBH values, in cm, when a tree uses stochastic growth. This is the mean of the DBH value, NOT the amount of growth. Used in the Puerto Rico semi-stochastic - diam only behavior.
- PR Storm Bi-Level - Threshold for High-Light Growth (0 - 100) The threshold between low-light and high-light equations, as a value between 0 and 100. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - High-Light "a" The "a" value in the high-light growth function. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - High-Light "b" The "b" value in the high-light growth function. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - Intercept for Low-Light Growth (a) The intercept of the linear growth function used in low-light conditions. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- PR Storm Bi-Level - Slope for Low-Light Growth (b) The slope of the linear growth function used in high-light conditions. Used in the Puerto Rico storm bi-level growth - diam with auto height behavior.
- Relative Michaelis-Menton Growth - Diameter Exponent The exponent to be used with diameter when calculating relative growth. Used in the Relative growth behaviors.
- Relative Michaelis-Menton Growth - Height Exponent The exponent to be used with height when calculating relative growth. Used in the Relative growth - height only behavior.
- Shaded Linear - Diam Intercept in mm/yr (a) Intercept of the size dependent growth potential, in mm/yr. Used by the Linear growth w/ exponential shade reduction behavior.
- Shaded Linear - Diam Shade Exponent (c) Effect of shading. Used by the Linear growth w/ exponential shade reduction behavior.
- Shaded Linear - Diam Slope (b) Slope of the size dependent annual growth potential. Used by the Linear growth w/ exponential shade reduction behavior.
- Shaded Linear - Height Intercept in cm/yr (a) Intercept of the size dependent growth potential, in cm/yr. Used by the Linear growth w/ exponential shade reduction behavior.
- Shaded Linear - Height Shade Exponent (c) Effect of shading. Used by the Linear growth w/ exponential shade reduction behavior.
- Shaded Linear - Height Slope (b) Slope of the size dependent annual growth potential. Used by the Linear growth w/ exponential shade reduction behavior.
- Simple Linear - Diam Intercept in mm/yr (a) Intercept of the linear growth function, or growth at no light, in mm/yr. Used by the Linear growth behavior.
- Simple Linear - Diam Slope (b) Slope of the linear growth function. Used by the Linear growth behavior.
- Simple Linear - Height Intercept in cm/yr (a) Intercept of the linear growth function, or growth at no light, in cm/yr. Used by the Linear growth behavior.
- Simple Linear - Height Slope (b) Slope of the linear growth function. Used by the Linear growth behavior.
- Size Dep. Logistic - Diam Intercept (a) Intercept of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Diam Shape Param 1 (c) Shape parameter 1 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Diam Shape Param 2 (d) Shape parameter 2 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Diam Slope (b) Slope of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Height Intercept (a) Intercept of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Height Shape Param 1 (c) Shape parameter 1 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Height Shape Param 2 (d) Shape parameter 2 for shade reduction of annual growth. Used by the Logistic growth w/ size dependent asymptote behavior.
- Size Dep. Logistic - Height Slope (b) Slope of the size dependent annual growth potential. Used by the Logistic growth w/ size dependent asymptote behavior.
- Slope of Growth Response (S) Slope of the Michaelis-Menton growth function at zero light for relative and absolute growth behaviors - S in the equations below. Used in absolute and growth behaviors.
- Slope of Height Growth Response (S) Slope of the Michaelis-Menton growth function at zero light - S in the equations below. Used in the Relative growth - height only behavior.
- Weibull Climate Growth - Adult Competition Effect "C" The C parameter for the competition effect when the target tree is an adult. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Competition Effect "D" The D parameter for the competition effect when the target tree is an adult. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Competition Gamma The gamma parameter for the competition effect when the target tree is an adult. This controls the response of a target tree to competition as a function of its size. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Precip Effect "A" The A parameter for the precipitation effect when the target tree is an adult. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Precip Effect "B" The B parameter for the precipitation effect when the target tree is an adult. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Precip Effect "C" The C parameter for the precipitation effect when the target tree is an adult. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Temp Effect "A" The A parameter for the temperature effect when the target tree is an adult. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Temp Effect "B" The B parameter for the temperature effect when the target tree is an adult. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Adult Temp Effect "C" The C parameter for the temperature effect when the target tree is an adult. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Competition Effect "C" The C parameter for the competition effect when the target tree is a juvenile. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Competition Effect "D" The D parameter for the competition effect when the target tree is a juvenile. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Competition Gamma The gamma parameter for the competition effect when the target tree is a juvenile. This controls the response of a target tree to competition as a function of its size. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Precip Effect "A" The A parameter for the precipitation effect when the target tree is a juvenile. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Precip Effect "B" The B parameter for the precipitation effect when the target tree is a juvenile. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Precip Effect "C" The C parameter for the precipitation effect when the target tree is a juvenile. Units of precipitation are millimeters per year. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Temp Effect "A" The A parameter for the temperature effect when the target tree is a juvenile. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Temp Effect "B" The B parameter for the temperature effect when the target tree is a juvenile. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Juvenile Temp Effect "C" The C parameter for the temperature effect when the target tree is a juvenile. The effect is based on mean annual temperature in degrees Celsius. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Max Neighbor Search Radius (m) The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Max Potential Growth (cm/yr) Maximum potential diameter growth for a tree, in cm/yr. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Minimum Neighbor DBH (cm) The minimum DBH for trees of that species to compete as neighbors. Used for all species, not just those using Weibull Climate growth. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Size Effect X0 The mode of the size effect curve. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Size Effect Xb The variance of the size effect curve. Used in the Weibull climate growth behavior.
- Weibull Climate Growth - Size Effect Minimum DBH The minimum possible DBH for size effect. Trees with a DBH less than this value will use this value in the size effect calculation instead. Used in the Weibull climate growth behavior.
- Years Exceeding Threshold Before a Tree is Suppressed The number of years for which a tree's growth must be below the defined suppression threshold before it is considered to be suppressed. Used in absolute growth behaviors.
- Weib Clim Quad Growth - Competition Effect "C" The C parameter for the competition effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Competition Effect "D" The D parameter for the competition effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Max Neighbor Search Radius (m) The maximum distance, in m, at which a neighboring tree has competitive effects on a target tree. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Max Potential Growth (cm/yr) Maximum potential diameter growth for a tree, in cm/yr. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Minimum Neighbor DBH (cm) The minimum DBH for trees of that species to compete as neighbors. Used for all species, not just those using this growth behavior. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Precip Effect "A" The A parameter for the precipitation effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Precip Effect "B" The B parameter for the precipitation effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Precip Effect "C" The C parameter for the precipitation effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Temp Effect "A" The A parameter for the temperature effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Temp Effect "B" The B parameter for the temperature effect. Used in the Weibull climate quadrat growth behavior.
- Weib Clim Quad Growth - Temp Effect "C" The C parameter for the temperature effect. Used in the Weibull climate quadrat growth behavior.
Relative growth behaviors
Several behaviors apply a relative growth version of the Michaelis-Menton function. Relative growth is calculated with the equation:
where:
- Y is the amount of annual relative growth
- A is the Asymptotic Diameter Growth (A) or Asymptotic Height Growth (A) parameter
- S is the Slope of Growth Response (S) or Slope of Height Growth Response (S) parameter
- GLI is the global light index, calculated by a light behavior
Diameter growth is compounded over multiple timesteps with the equation:
G = ((Y + 1)T - 1) * diam X
where:
- G is the amount of diameter growth for the timestep, in cm
- diam is the diameter of the tree in cm (at 10 cm height if seedling or sapling, or DBH if adult)
- T is the number of years per timestep
- X is the Relative Michaelis-Menton Growth - Diameter Exponent parameter
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:
- G is the amount of height growth for one year, in cm
- Height is the height of the tree in cm
- X is the Relative Michaelis-Menton Growth - Height Exponent parameter
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:
- Y is the amount of annual relative growth
- A is the Asymptotic Diameter Growth (A) parameter
- S is the Slope of Growth Response (S) parameter
- C is the Double resource - Influence of Resource (C) parameter, in units appropriate to the value of R
- R is the amount of the second resource, in units appropriate to the value of C
- GLI is the global light index, calculated by a light behavior
Growth is compounded over multiple timesteps with the equation:
G = ((Y + 1)T - 1) * diam
where:
- G is the amount of diameter growth for the timestep, in cm
- diam is the diameter of the tree in cm (at 10 cm height if seedling or sapling, or DBH if adult)
- T is the number of years per timestep
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
- Y = log10(radial growth + 1)
- SF is the suppression factor
- A is the Asymptotic Diameter Growth (A) parameter
- S is the Slope of Growth Response (S) parameter
- GLI is the global light index, calculated by a light behavior
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:
- SF is the suppression factor
- g is the Length of Current Release Factor parameter
- YLR is the length of the last (or current) period of release,
in years
- d is the Length of Last Suppression Factor parameter
- YLS is the length of the last (or current) period of
suppression, in years
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
- Y is the amount of diameter increase, in cm
- g is the Adult Constant Area Growth in sq. cm/yr parameter
- diam is the tree's diameter, in cm
- T is the number of years per timestep
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
- Y is the amount of diameter growth, in cm, to add to the tree
- g4 is the Adult Constant Radial Growth in mm/yr parameter
- T is the number of years per timestep
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:
where:
- DBH is of the target tree, in cm
- X0 is the NCI Size Effect Mode, in cm (X0) parameter
- Xb is the NCI Size Effect Variance, in cm (Xb)
Shading Effect is calculated as:
where:
- m is the NCI Shading Effect Coefficient (m) parameter
- n is the NCI Shading Effect Exponent (n) parameter
- S is the amount of shade cast by neighbors, from 0 (no shade) to 1 (full shade). This value should come from the Sail light behavior.
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:
where:
- C is the NCI Crowding Effect Slope (C) parameter
- DBH is of the target tree, in cm
- γ is the NCI Size Sensitivity to NCI (gamma) parameter for the target tree's species
- D is the NCI Crowding Effect Steepness (D) parameter
- NCI is this tree's NCI value (equation below)
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:
where:
- the calculation sums over j = 1...S species and k = 1...N neighbors of each species of at least a DBH of NCI Minimum Neighbor DBH, in cm, out to a distance of NCI Max Radius of Crowding Neighbors, in m
- ηk is the storm damage parameter of the kth neighbor, depending on the damage status (optional). If the neighbor is undamaged, the value is 1. If the neighbor has medium damage, the value is the NCI Neighbor Storm Damage (eta) - Medium (0-1) parameter for the target species. If the neighbor has complete damage, the value is the NCI Neighbor Storm Damage (eta) - Complete (0-1) parameter for the target species. To omit the storm damage term, set all values for the above two parameters to 1.
- α is the NCI Alpha parameter for the target tree's species
- β is the NCI Beta parameter for the target tree's species
- DBHjk is the DBH of the kth neighbor, in cm
- q is the NCI DBH Divisor (q) parameter. Set this to a value greater than 1 to rescale the competitive effects of neighbors
- λik is the Species j NCI Lambda parameter for the target species relative to the kth neighbor's species
- distanceik is distance from target to neighbor, in m
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:
where:
- DBH is of the target tree, in cm
- X0 is the NCI Size Effect Mode, in cm (X0) parameter
- Xb is the NCI Size Effect Variance, in cm (Xb)
Crowding Effect is calculated as:
CE = exp(-C * (DBH γ * BAn / BADiv) D)
where:
- C is the NCI Crowding Effect Slope (C) parameter
- DBH is of the target tree, in cm
- γ is the NCI Size Sensitivity to NCI (gamma) parameter for the target tree's species
- D is the NCI Crowding Effect Steepness (D) parameter
- BAn is the sum of the basal areas, in square cm, of eligible neighbors
- BADiv is the Basal Area NCI - BA Divisor parameter
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
- Y = amount of diameter increase, in mm, or amount of height increase, in cm
- a = Simple Linear - Diam Intercept in mm/yr (a) parameter (for diameter growth) or the Simple Linear - Height Intercept in cm/yr (a) parameter (for height growth)
- b = Simple Linear - Diam Slope (b) parameter (for diam growth) or the Simple Linear - Height Slope (b) parameter (for height growth)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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
- Y = amount of diameter increase, in mm; or the amount of height increase, in cm
- a = Shaded Linear - Diam Intercept in mm/yr (a) parameter (for diameter growth) or the Shaded Linear - Height Intercept in cm/yr (a) parameter (for height growth)
- b = Shaded Linear - Diam Slope (b) parameter (for diameter growth) or the Shaded Linear - Height Slope (b) parameter (for height growth)
- c = Shaded Linear - Diam Shade Exponent (c) parameter (for diameter growth) or the Shaded Linear - Height Shade Exponent (c) parameter (for height growth)
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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
- Y = amount of diameter increase, in mm, or the amount of height increase, in cm
- a = Logistic - Asymptotic Diam Growth - Full Light in mm/yr (a) parameter (for diameter growth) or the Logistic - Asymptotic Height Growth - Full Light in cm/yr (a) parameter (for height growth)
- b = Logistic - Diam Shape Param 1 (b) parameter (for diameter growth) or the Logistic - Height Shape Param 1 (b) parameter (for height growth)
- c = Logistic - Diam Shape Param 2 (c) parameter (for diameter growth) or the Logistic - Height Shape Param 2 (c) parameter (for height growth)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- T = number of years per timestep
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
- Y = amount of diameter increase, in mm, or the amount of height increase, in cm
- a = Size Dep. Logistic - Diam Intercept (a) parameter (for diameter growth) or the Size Dep. Logistic - Height Intercept (a) parameter (for height growth)
- b = Size Dep. Logistic - Diam Slope (b) parameter (for diameter growth) or the Size Dep. Logistic - Height Slope (b) parameter (for height growth)
- c = Size Dep. Logistic - Diam Shape Param 1 (c) parameter (for diameter growth) or the Size Dep. Logistic - Height Shape Param 1 (c) parameter (for height growth)
- d = Size Dep. Logistic - Diam Shape Param 2 (d) parameter (for diameter growth) or the Size Dep. Logistic - Height Shape Param 2 (d) parameter (for height growth)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
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
- Y = amount of diameter increase, in mm, or the amount of height increase, in cm
- a = Lognormal - Diam Growth Increment at Diam 36, in mm/yr (a) parameter (for diameter growth) or the Lognormal - Height Growth Increment at Diam 36, in cm/yr (a) parameter (for height growth)
- b = Lognormal - Diam Shape Parameter (b) parameter (for diameter growth) or the Lognormal - Height Shape Parameter (b) parameter (for height growth)
- c = Lognormal - Diam Effect of Shade (c) parameter (for diameter growth) or the Lognormal - Height Effect of Shade (c) parameter (for height growth)
- GLI = global light index, as a percentage between 0 and 100, calculated by a light behavior
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
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
- Y = amount of diameter growth in cm
- a = growth intercept; in high-light conditions, this is the Linear Bi-Level - Intercept for High-Light Growth (a) parameter; in low-light conditions, this is the Linear Bi-Level - Intercept for Low-Light Growth (a) parameter
- b = growth slope; in high-light conditions, this is the Linear Bi-Level - Slope for High-Light Growth (b) parameter; in low-light conditions, this is the Linear Bi-Level - Slope for Low-Light Growth (b) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- T = number of years per timestep
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:
where
- Y - amount of height growth in m
- MG - maximum growth, in meters; in high-light conditions, this is the Lognormal Bi-Level - Max Growth in High Light (m) parameter; in low-light conditions, this is the Lognormal Bi-Level - Max Growth in Low Light (m) parameter
- X0 - in high-light conditions, this is the Lognormal Bi-Level - X0 for High-Light Growth parameter; in low-light conditions, this is the Lognormal Bi-Level - X0 for Low-Light Growth parameter
- Xb - in high-light conditions, this is the Lognormal Bi-Level - Xb for High-Light Growth parameter; in low-light conditions, this is the Lognormal Bi-Level - Xb for Low-Light Growth parameter
- H - tree height in meters
- T - number of years per timestep
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:
- Y = diameter growth for the timestep, in cm
- a = PR - "a" Parameter for Deterministic Growth parameter
- b = PR - "b" Parameter for Deterministic Growth parameter
- Height = tree height in cm AFTER height growth in the current timestep
- diam = diameter of the tree at which to apply growth (before growth), in cm
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
- Y = amount of diameter growth in cm
- a = PR Storm Bi-Level - Intercept for Low-Light Growth (a) parameter
- b = PR Storm Bi-Level - Slope for Low-Light Growth (b) parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- T = number of years per timestep
The function used in high-light conditions is:
H = T * a * diam * e(-b * N)
where
- H = amount of height growth, in cm
- a = PR Storm Bi-Level - High-Light "a" parameter
- b = PR Storm Bi-Level - High-Light "b" parameter
- diam = diameter (diameter at 10 cm for seedlings and saplings, DBH for adults)
- N = number of years since the last storm, from the Storm Damage grid produced by the Storm disturbance behavior
- T = number of years per timestep
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:
- Y is the amount of annual relative growth
- A is the Asymptotic Diameter Growth (A) or Browsed Asymptotic Diameter Growth (A) parameter
- S is the Slope of Growth Response (S) or Browsed Slope of Growth Response (S) parameter
- GLI is the global light index, calculated by a light behavior
Growth is compounded over multiple timesteps with the equation:
G = ((Y + 1)T - 1) * diam X
where:
- G is the amount of diameter growth for the timestep, in cm
- diam is the diameter of the tree in cm (at 10 cm height if seedling or sapling, or DBH if adult)
- T is the number of years per timestep
- X is the Relative Michaelis-Menton Growth - Diameter Exponent or Browsed Diameter Exponent parameter
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:
where:
- Y is the amount of height growth for one year, in cm
- GLI is the light level
- α is the Michaelis-Menton Neg Growth - Alpha parameter
- β is the Michaelis-Menton Neg Growth - Beta parameter
- γ is the Michaelis-Menton Neg Growth - Gamma parameter
- φ is the Michaelis-Menton Neg Growth - Phi parameter
- H is the tree's height in cm
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:
where:
- Y is the amount of height growth for one year, in cm
- GLI is the light level
- α is the Michaelis-Menton with Photoinhibition - Alpha parameter
- β is the Michaelis-Menton with Photoinhibition - Beta parameter
- D is the Michaelis-Menton with Photoinhibition - D parameter
- φ is the Michaelis-Menton with Photoinhibition - Phi parameter
- H is the tree's height in cm
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:
- Y is the amount of height growth for one year, in cm
- n is the Power Height Growth - n parameter
- φ is the Power Height Growth - Exp parameter
- H is the tree's height in cm
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:
- PARG is potential annual radial growth (mm/y)
- DBH is in cm
- BA is the basal area (in sq m) of adult trees within the distance given in the Post Harvest Growth - NCI Distance (m) parameter
- α is the Post Harvest Growth - Max Growth Constant parameter, the maximum radial growth in millimeters per year
- δ is the Post Harvest Growth - DBH Growth Effect parameter
- η is the Post Harvest Growth - NCI Constant parameter
- ω is the Post Harvest Growth - DBH NCI Effect parameter
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:
- ARG is annual radial growth (mm/y) for the current timestep
- ARGpre is annual radial growth for the last timestep prior to harvest
- H is the number of timesteps since the last harvest
- t is the number of years per timestep
- τ is the Post Harvest Growth - Time Since Harvest Rate Param parameter
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:
- d10 is the diameter at 10 cm height of the target tree, in cm
- a is the Juvenile NCI Size Effect "a" parameter
- b is the Juvenile NCI Size Effect "b" parameter
Crowding Effect is calculated as:
CE = exp(-C * NCI D)
where:
- C is the Juvenile NCI Crowding Effect Slope (C) parameter
- D is the Juvenile NCI Crowding Effect Steepness (D) parameter
- NCI is this tree's NCI value (equation below)
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 calculation sums over j = 1...S species and k = 1...N neighbors of each species of at least a d10 of Juvenile NCI Minimum Neighbor Diam10, in cm, out to a distance of Juvenile NCI Maximum Crowding Distance, in meters
- α is the Juvenile NCI Alpha parameter for the target tree's species
- β is the Juvenile NCI Beta parameter for the target tree's species
- D10jk is the d10 of the kth neighbor, in cm
- q is the Juvenile NCI Diam10 Divisor (q) parameter. Set this as necessary to rescale the competitive effects of neighbors
- λik is the Species j NCI Lambda parameter for the target species relative to the kth neighbor's species
- distanceik is distance from target to neighbor, in m
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:
where:
- DBH is of the target tree, in cm
- X0 is the Weibull Climate Growth - Size Effect X0 parameter; this is the mode of the function, expressed in cm
- Xb is the Weibull Climate Growth - Size Effect Xb parameter; this is the variance of the function, expressed in cm
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 =
where:
- A is either the Weibull Climate Growth - Adult Precip Effect "A" parameter or the Weibull Climate Growth - Juvenile Precip Effect "A" parameter, depending on whether the tree is a sapling or an adult
- B is either the Weibull Climate Growth - Adult Precip Effect "B" parameter or the Weibull Climate Growth - Juvenile Precip Effect "B" parameter, depending on whether the tree is a sapling or an adult
- C is either the Weibull Climate Growth - Adult Precip Effect "C" parameter or the Weibull Climate Growth - Juvenile Precip Effect "C" parameter, depending on whether the tree is a sapling or an adult
- P is the plot's annual precipitation, in millimeters, as entered for the Plot
Temperature Effect is calculated as:
TE =
where:
- A is either the Weibull Climate Growth - Adult Temp Effect "A" parameter or the Weibull Climate Growth - Juvenile Temp Effect "A" parameter, depending on whether the tree is a sapling or an adult
- B is either the Weibull Climate Growth - Adult Temp Effect "B" parameter or the Weibull Climate Growth - Juvenile Temp Effect "B" parameter, depending on whether the tree is a sapling or an adult
- C is either the Weibull Climate Growth - Adult Temp Effect "C" parameter or the Weibull Climate Growth - Juvenile Temp Effect "C" parameter, depending on whether the tree is a sapling or an adult
- T is the plot's annual mean temperature, in degrees Celsius, as entered for the Plot
Crowding Effect is calculated as:
where:
- C is either the Weibull Climate Growth - Juvenile Competition Effect "C" parameter or the Weibull Climate Growth - Juvenile Competition Effect "C" parameter, depending on whether the tree is a sapling or an adult
- DBH is of the target tree, in cm
- γ is the Weibull Climate Growth - Juvenile Competition Effect gamma parameter or the Weibull Climate Growth - Juvenile Competition Effect gamma parameter, depending on whether the tree is a sapling or an adult
- D is the Weibull Climate Growth - Juvenile Competition Effect "D" parameter or the Weibull Climate Growth - Juvenile Competition Effect "D" parameter, depending on whether the tree is a sapling or an adult
- ND is the number of neighbors with a DBH greater than the target tree's DBH
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 =
where:
- A is the Weib Clim Quad Growth - Precip Effect "A" parameter
- B is the Weib Clim Quad Growth - Precip Effect "B" parameter
- C is the Weib Clim Quad Growth - Precip Effect "C" parameter
- P is the plot's annual precipitation, in millimeters, as entered for the Plot
Temperature Effect is calculated as:
TE =
where:
- A is the Weib Clim Quad Growth - Temp Effect "A" parameter
- B is the Weib Clim Quad Growth - Temp Effect "B" parameter
- C is the Weib Clim Quad Growth - Temp Effect "C" parameter
- T is the plot's annual mean temperature, in degrees Celsius, as entered for the Plot
Crowding Effect is calculated as:
CE = exp(-C * ND D)
where:
- C is the Weib Clim Quad Growth - Competition Effect "C" parameter
- D is the Weib Clim Quad Growth - Competition Effect "D" parameter
- ND is the number of neighbors
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