SIBYLA - Mortalitný model

How is natural mortality of trees simulated in the growth simulator SIBYLA ?

The model of natural tree mortality was adopted from the growth simulator SILVA 2.2 (Ďurský 1997, Ďurský et al. 1996). The model is always activated at the beginning of 5-year simulation interval, and consists of two parts: a model simulating the probability of tree survival, and a model simulating the threshold stand density.

Tree survival probability

This model is based on the logistic regression, which is a function of survival probability (function F-logit):

where L(x) is the logical value calculated for a particular tree:

The logical value depends on the tree diameter d_1.3, the annual increment of tree basal area i_g, the tree height h, and the absolute height (site) class AVB₅₀. Absolute height (site) class is expressed as a potential top height in the simulation plot reached at the age of t = 50 years:

where the coefficients A, k, p are derived from the ecological site classification.

The function of tree survival probability is then transformed to the function of tree mortality (in %) as follows:

where r(SD) is the value dependent on stand density (SD) determined by SDI according to Reineke (1933). If stand density is greater than or equal to 0.7 (0.8 for pine), r(SD) is equal to 1, otherwise it is equal to SD.

The obtained value Mrt% is then compared with the random number drawn from uniform distribution from the interval <0;100). The tree i dies if the calculated value exceeds the random number:

The age at which the tree dies is randomly generated from the 5-year interval. All coefficients are published in Fabrika (2005).

Threshold stand density

This model is based on the reduction of the stand basal area, if this exceeds the maximum possible level. First, maximum stand basal area is calculated as a weighted arithmetic mean of maximum basal areas of individual tree species (j) in the stand, while tree crown projections (cd_i²) are used as weights:

Maximum stand basal area of a particular tree species is calculated from its top height (h_95%) according to:

Next, stand basal area of dying trees is obtained from the actual stand basal area (G) and the stand basal area of dead trees (G_dead) as follows:

G_mort = G - G_max - G_dead; if G_mort > 0

Afterwards, the trees to be removed are selected according to the following rules:

The total basal area of selected trees has to be equal to or slightly greater than G_mort.

1. First, the trees with the greater probability of mortality than the predefined threshold (by default 50%) are selected, starting from the highest value Mrt%.

2. If it is necessary, the trees with the lower probability of mortality than the threshold value are also selected using random sampling.

The age of tree death is randomly generated from 5-year interval. All coefficients are published in Fabrika (2005).