FORMIND - Introduction

FORMIND is an individual-based, spatially explicit and process-based model designed for simulating species-rich vegetation communities (Fischer et al. 2016).

In FORMIND, vegetation is simulated on an area of size $A_\text{area}$, which is a composite of regularly ordered, quadratic patches of size $A_\text{patch} \, \left[ \text{m}^2\right]$ described by their location within the area (figure below). Individual trees grow within the patches, but do not have spatially explicit positions within a patch (the gap model approach).

Patches <dic id="Patches">
Figure: Illustration of the simulated area and its composition of regularly ordered patches. Individual trees do not have spatially explicit positions within the patches. Only for an illustrative purpose, we show positioned trees on an exemplary patch.

The trees change their sizes during the simulation according to a set of ecophysiological and morphological parameters used within the modelled processes. The modelled processes are simulated on different levels: (i) area-level, (ii) patch-level or (iii) single-tree level.

The individual model components are described in the following subpages:

  • Geometry: trees are described via several geometric relationships. Tree types (in some projects we use the concept of plant functional types and in others real species) can differ in their parameter sets of these relationships.

Within each time step $\Delta t$ (e.g. one year), the following main processes considered:

  • Recruitment and establishment: Establishment of recruited seeds is modelled on the patch level, whereby the distribution of seeds is simulated on the area level.

  • Mortality: First, an event-driven mortality due to crowding can take place on the patch level. Afterwards, mortality rates affects each trees (e.g. base mortality). Finally, every dying tree may fall and damage other trees.

  • Environment: The patches of the simulation area are homogeneous regarding climatic input variables. Based on these input parameters, the environment of the trees is specified. For example, the radiation above canopy and day length are equal for all patches. The vertical attenuation of the incoming radiation (i.e. light climate) is calculated for each patch based on the vegetation state, so that light intensity at different heights can differ between patches dependent on the number of trees shading each other. Reduced light availability results in reduced gross photosynthesis of a tree. Limited soil water resources can also reduce the gross photosynthesis of an individual. In the same manner as the light climate, soil water contents can differ between patches during the simulation, although the initial soil water content and other soil properties (e.g. soil porosity) are equal for all patches. Differences in soil water content between patches are dependent on the number of trees per patch, which take up soil water resources. Further, type-specific effects of the air temperature can also limit gross photosynthesis and affect respiration of an individual.

  • Growth: growth of a single tree is determined by its gross productivity, respiration and type-specific morphological parameters. Respiration is calculated on the level of an individual. An increase in biomass per tree is modelled as the difference between gross photosynthesis and respiration. The allocation of the resulting biomass (including the increase of geometrical properties according to chapter Geometry) act on the level of a tree.

  • Disturbance: Fire and landslide events are simulated on the areaa level.

  • Logging: Selective logging of trees is simulated on the area level. The selection is based on tree-specific characteristics (e.g. stem diameter or tree type) and represent conventional or reduced impact logging.

The modelled processes, which are summarized within the above mentioned main processes, are scheduled in a serial way. For an overview on the modelled processes and their schedule, see the figure below:

Formind flow chart <dic id="FlowChart">
Figure: Block diagram of the modelled processes. Different colours indicate the spatial scale on which each process is calculated (blue = area, green = patch, orange= individual). Italic written boxes show processes which are simulated with time steps of higher resolution than $\Delta t$ (e.g one year). Numbers in brackets within each box show the serial order of their calculation within one time step $\Delta t$. Grey frames that underly these boxes group them according to the above mentioned main processes and their corresponding chapters. Rhombuses indicate climatic input parameters with the following abbreviations: PET – potential evapotranspiration, PPFD – photoactive photon flux density.

Periodic or open boundary conditions can be used. For periodic boundary conditions, that means processes leaving one side of the simulation area are entering the area on the opposite side again. For open boundary conditions, that means processes leaving the simulation area are lost. No migration entering the open boundaries would be considered.

For the purpose of calculations within the processes of light climate and crowding mortality, the above-ground space is discretized into vertical height layers of constant width $\Delta h$. The table below shows general input parameters.

DescriptionParameterUnitvalues range
Time step$\Delta t$$\text{yr}$$365^{-1} - 5$
Simulation area$A_{\text{area}}$$\text{ha}$$1-400$
Patch area$A_{\text{patch}}$$\text{m}^2$$400$
Width of height layers$\Delta h$$\text{m}$$0.5$