Tree mortality
Note: In version 2.0, a new mortality model is added ("Elfving") which replaces Bengtsson and Fridman & Ståhl below.. The new model is described here (Swedish only): HeurekaMortality-PM140317.pdf
The mortality level in self-thinning stands is predicted with functions presented by Söderberg (1986) and in stands of lower density with functions presented by Bengtsson (1978). The distribution of the mortality on species and dimensions is based on functions presented by Fridman & Ståhl (2001). Mortality of old trees and shelter trees is especially accounted. Mortality in young stands, as well as damages that result in height growth reduction, is modelled with Näslund (1986).
Söderberg (1986) presented one function for basal area and one function for mortality in selfthinning stands. Mortality was expressed as annual percent of the basal area that is selfthinned. At application in Heureka mortality is a weighted average of predictions by Söderberg and Bengtsson, depending on the relative density of the stand. Relative density is actual basal area related to basal area of self-thinning stands according to Söderberg.
The functions by Söderberg were based on data from 532 observation periods on 82 yield plots in non-thinned stands.
The functions by Bengtsson (1978) were based on the NFI inventory of dead trees in the period 1973-1975. Dead trees with dbh>49 mm were classified according to the season when they died and trees that died in the last 3-year period were accounted. For technical reasons data was grouped before regression which limits the interval for application to mean dbh (D) 7-30 cm and stand age (A) 30-120 years. For D and A values outside the valid values the use of closest limit value is recommended. For pine in southern Sweden site productivity, expressed in m²sk per hectare and year (MAI) was included as an independent variable. Dependent variable is annual mortality in percent of standing volume.
Fridman & Ståhl presented a mortality model with three steps:
- Predict probability of mortality on a plot during the next 5 yr period
- Predict proportion of basal area that die on plots with mortality
- Predict probability of mortality for trees of different species and size
The functions were based on data from the second and partly from the third observation period on the permanent NFI-plots, up to the 1998 inventory. Only trees with dbh> 99 mm were included. In Heureka only step3 functions are utilised. Estimated mortality as a function of diameter for different species is shown below.
The mortality of old trees is calculated as a function of their nearness to maximum age (not implemented yet). The latter was expressed as a function of tree species and site index as described in the following document.
Function parameters can be found here, page 63: Heureka_prognossystem_%28Elfving_rapportutkast%29.pdf
References
Bengtsson, G. 1978. Beräkning av den naturliga avgången i avverkningsberäkningarna för 1973 års skogsutrednings slutbetänkande. I: Skog för framtid, SOU 1978:7, bilaga 6.
Fridman, J. & Ståhl, G. 2001. A three-step approach for modelling tree mortality in Swedish forests. Scan. J. For. Res. 16: 455-466.
Näslund, B-Å. 1986. Simulering av skador och avgång i ungskog och deras betydelse för beståndsutvecklingen (Simulation of damage and mortality in young stands and associated stand development effects). Dissertation, Rapporter / Sveriges lantbruksuniversitet, Dept of Silviculture, No. 18. Sveriges lantbruksuniversitet, Umeå.
Söderberg, U. 1986. Functions for forecasting timber yields. SLU, Section for forest mensuration and management, Report 14.