in the atmosphere).
- Combined forest model: developed from the addition of known processes and reliable experiments to create a new process model that can overcome the limitations of previous approaches.
The difficulty of building models is the scale of the model being simulated. One of the requirements that needs to be achieved is how to combine object heterogeneity with the model's ability to scale.
a. Scale of the model
The scope and detailed explanation of a model is expressed by the “Scale” factor. According to Ratze et al. (2007), Scale has 3 meanings:
- Meaning of observation
- Ontological meaning
- Representative meaning
Accordingly, the representative sense of scale is of particular importance in modeling because modeling involves representing a problem with limited precision. There are two approaches in ecological modeling that lead to different results: the individual variable-based approach and the aggregate variable-based approach.
The main difference between these two approaches is that instance-oriented models (IBMs) use the instance as the basic unit, which decouples the instances. This separation is often constructed for attributes of particular interest, such as size, spatial layout, spatial interactions, bioenergetic parameters, ecology, behavioral characteristics, etc.
Synthetic variable models (ASVs) typically model the possible behavior of individuals and average them over large numbers, in which case the individuals are assumed to be homogeneous. Therefore, the simulation results of ASVs cannot explain the existence of individual fluctuations compared to the IBM model.
To date, IBM has proven effective in simulating complex processes, especially when there are ecological factors in the calculation, while synthetic variable models do not achieve satisfactory results due to ignore differences between individuals.
The key issue for IBM is the relationship between the accuracy at the model run, the level of generality that can be simulated, and the degree of incorporation of mechanisms in the model.
models with spatial dynamics. IBM gives good results but not at the spatial scale which requires a large amount of computation. In forest ecology, the location and interactions between each tree are among the factors that cause differences between trees and cause self-thinning.
Some researchers have attempted to simulate forest dynamics in discordant groups, or forest growth models that focus on the complexity of individual trees within a group (Le Roux et al., 2001; Lischke et al. al., 1998, 2006). In this case, the model generally represents a tree as a collection of growth units.
Another trend is to use IBM to provide parameter values for variable aggregation models (Luan et al., 1996; Berninger, F. and E. Nikinmaa (1997); Le Roux et al., 2001). . Grimm (1999) called this application a “computer experiment” using IBMs. In this type of synthesis, detailed data is imported into IBM models to produce outputs (statistics from multiple IBM simulations). The output data are then used as input for the synthetic models.
b. Growth model
The difference between mangrove forests and terrestrial forests can be seen in the factors of salinity and tidal inundation. Therefore, the above two factors are the first conditions when mentioning factors affecting the development of mangrove forests. In this study, we ignore the influence of salinity factor and normalize the parameter salinity is equal to 1 and only calculates and simulates mangrove forest dynamics according to the inundation parameter (elevation factor).
The calculation equations are as follows:
* Growth equation:
· d0.3 · (1
d0.3 · H / D / H )
max max x MUL
dt 2b 3b · d0.3 4b · d0.3 2
1 2 3
H =b 1 +b 2 ·d0.3−b 3 ·d0.3 2 MUL=f s ×f el ×f c
d0.3: is the tree diameter at a height of 0.3 m
G opt : is the growth rate of a specific species under optimal conditions. H max : is the maximum height of the tree
D max : is the largest tree diameter
b 1 , b 2 , b 3 : is the growth constant of the species MUL: is the growth coefficient,
f c , f el , f s : are the competition, altitude and salinity coefficients. If the influence of this factor is not considered, they are given as 1.
The parameter G opt represents the growth rate of the tree, deciding how to achieve maximum growth for the tree.
The frequency and duration of tidal flooding affect the distribution and development of species. Some species can adapt well to long periods of tidal flooding (fish sauce), some species cannot tolerate flooding (sea date), Some species can tolerate moderate flooding (page). Elevation can be considered an indirect factor that reflects the frequency and duration of tidal flooding, so instead of considering two factors that affect plant growth (frequency and duration of tidal flooding), we integrate both indexes into one factor (submergence). Influence of factors
The degree of inundation on the development of mangrove forests is described by the following equation:
a 1 e (el/ el 1 ) a
e (el/ el 2 ) a
1 e (el/ el 2 )
el max e 1e 1e 2e
In which: a maxe is the maximum value of the altitude coefficient,
a 1e and a 2e are the minimum values of the altitude coefficient, el is the altitude in meters,
el 1 and el 2 are the optimal altitude types,
α and β are parameters that determine the slope of the elevation coefficient curve.
Data analysis results showed the influence of space competition on tree growth through density. Many researchers have developed models to explain this mechanism (self-thinning effect). In the research growth model, the assumptions of "Field of neighborhood" by Berger, U. and H. Hildenbrandt (2000) are applied.
Berger, U. and H. Hildenbrandt (2000) assumed that the size of a tree is influenced by surrounding trees, a process that is added to the model by the factor of FA competition . This factor is the portion of a tree's competitiveness in its total edge
pictures of neighboring trees. This process is described by the following equations:
FA i F ON . O FON o, ij
i j 1, j i
0 r rbh
l og F m in
rbh r R
0 r R
R=a 2 ×rbh c2
FA i : is the competitive power of the ith tree that is affected by the trees around it FON i : is the competitive influence area of the ith tree
N n : is the number of surrounding trees of a calculation tree
O FON o ,ij : is the coverage value of FON i on the ith tree under the influence of the jth neighboring tree
O: is the coverage area
R: is the radius of the affected area, a 2 and c 2 are the scaling factors
The growth competitiveness coefficient is calculated as follows:
f c = (a maxc − a 0c ) exp [−(FA/FA thr )] + a 0c
a maxc and a 0c : are the maximum and minimum values of the competitive effect on growth
FA thr : is the limit of FA.
* Reproduction and dispersal of propagules
The number of seedlings of a tree depends on its biomass, we have the following equation:
dt r 2 .fR ep .Biom. 1 N
f Re p 1 exp B iom / Ec 2
Biom = a 1 . d0.3 c1
N 1 : is the number of seedlings planted
N 2 : is the number of seedlings produced by a tree at time tr 2 : is the reproductive rate
Biom: plant biomass
N 2max : maximum number of offspring a tree can produce
fRep: is a function of biomass and is included during the period when a tree produces trees
a 1 and c 1 and γ 2 : are scaling parameters.
A seedling spreads from the mother plant (located at (μ 1 , μ 2 )) to a point (x,y) at random.
naturally and is constructed by the probability density function h(x,y) . This probability density function is included in the calculation of the concavity process with a specified number of points N 2 . The overhanging distance is half the diameter of the tree, which means that one tree cannot grow inside another tree.
0 r rbh
kx, y , r rbh
s 1 2
For node k s (x,y|μ 1 , μ 2 ), a two-dimensional normal density function is introduced to describe the anisotropic distribution.
x 2 x . y 2 y 2 2
k x, y ,
. 1 2 . 1
s 1 2
2 . . . 1 2
2(1 2 ) 2
1 1 2 2
r: is the distance between the mother tree and the child tree x, y: is the child tree coordinates
function h(x,y) : ensures that a child tree cannot grow in another tree
* Dead trees
A tree's ability to die depends on its energy. We assume that during life, trees accumulate energy. This energy is determined as the biomass minus the energy consumed by respiration and reproduction. When biomass stops increasing
increases, this stored energy decreases over time because the plant has to use energy for respiration and reproduction, increasing the possibility of death.
d E r . dBiom r .N
0 .exp t
P m = P 0 . exp (−r 4 · E)
E: is the stored energy of a plant r 1 : is the rate of energy accumulation Biom: is the biomass of the plant
r 3 .N 2 and μ.Biom : is the energy the plant consumes for reproduction and respiration
μ: is the dependent function included in the calculation for the period of high energy consumption due to respiration
α μ : is the curve parameter of μ
P m : is the probability of the tree dying
P 0 : is the probability of the tree dying when not growing
r 4 : is the decay rate of the function.
220.127.116.11. CGMM model structure and model applied in the study area
CGMM is structured like a whole of elements, the elements play the role of a batch tree, the size of the elements can vary. Forest component and structural simulation attributes are stored in attribute data structures associated with each element. The heterogeneity between elements includes the difference of the d0.3 value and the species within it.
Environmental factors (flooding) are entered into the model directly through geographic information layers. Within a batch, environmental factors are assumed to be uniform.
Figure 2.3: Conceptual structure design diagram of the CGMM model
Two types of scale-level interactions are computed in CGMM: at the clustering level, the growth rate of each class d0.3 is determined by the interaction between trees (based on the neighborhood field assumption), and environmental conditions, at a general level.
Table 2. 1: Description of components and variables with different scales of CGMM
Lot and group level
Geographic information layers Spatial display of endemic habitats
Value group d0.3 Spatial statistics Endemic species
Salinity, altitude, recovery
Total number of plants, growth (d0.3, height), biomass, basal area
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The conversion processes applied are as follows:
- Aggregate the size (d0.3) of the individuals to structure the quantity (layers d0.3)
- Synthesize the explicit spatial state variables of the competitive factor (FA) to the target scale function.
- Synthesis of nodes disperses seedlings from the spatial positions of the mother tree in the IBM to the spatial positions of the source elements.
* Process dynamics implemented in CGMM Lifecycle
CGMM includes a set of different equations to describe the life cycle of a tree: Establishment - growth - reproduction - death.
At the initial time, the first number of subtrees is created in the element
N (x,y),t 1 ( N1 sp,(x,y),t Ns sp,(x,y),t Nd sp,(x,y),t )
- N: is the total subtree added to the element group (x,y)
- N1 is the number of seedlings planted, imported from the GIS database
- Ns is the number of seedlings increased due to reproduction
- Nd is the number of dead seedlings during the calculation period
- x, y are the positions of the elements in the matrix
- sp is species
- t is the calculation time
= f(z ) g (z , e )
sp, k,(x,y) ii=1
sp, k,(x,y) i,(x,y)
- f(z sp,k,(x,y) ) represents the growth rate under optimal conditions
- z sp,k,(x,y) is the diameter at breast height (d0.3) of species sp in the kth layer of d0.3 in element (x,y). The coefficient g i represents the influence of the dynamic variables e i,(x,y) on the growth rate. They are normalized to 1.
dN2 sp,(x,y) dt
f (N2 sp,k,(x,y) , Biom sp,k,(x,y) )
In which Biom sp,k,(x,y) =a 1 .d0.3 c1 is the biomass of trees in the kth DBH class of species sp in element (x,y).
The total number of risks (both large trees and saplings) Nd sp,(x,y),t of sp species in element (x,y) at time t is determined as the number of tree "lines" in class d0. The kth 3 species sp in element (x,y) multiplied by the probability of death Pm sp,k,(x,y),t