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ŠUMARSKI LIST 1-2/2021 str. 35     <-- 35 -->        PDF

of 100 (5.1 m – ŽA and 4.6 m – RU), the dominant height-age data at the age of 100 of both regions was classified into 5 groups (site classes) of a 4 m “width” for each region separately (Table 1). The main statistical characteristics of the felled beech dominant trees used for site index curve modelling per determined site class are presented in Table 1.
Three well-known growth functions, the Korf, the Korsun and the Chapman-Richards (CHR) were used to establish polymorphic site growth curves. The tested functions were parameterized (Gauss-Newton procedure) for tree groups of each site class (SC) and the parameters a, b and c were calculated. During the parameterization procedure, the starting values of the growth function were set to initial values which satisfy the S-shape criteria with an asymptote corresponding to the site class (the more productive the site, the higher the value of the parameter a). In the case of the Chapman-Richards model, the initial value of the asymptote for the I site class was set to 40 m, while the b and c parameters were set to 0.015 and 2, respectively. Using these non-linear regressions we determined the dominant heights at the age of 100 (H100) for each group of trees per site class.
According to the parameter prediction method, which relates parameter estimates to site classes, the growth model parameters b and c of each site class curve were set in relationship to the height at the age of 100 (H100) and the parameters bSI and cSI were obtained using the equations 1, 2 and 3 (Schmidt 1969, Halaj 1978, Kindermann 2004).
The Korf function:
                ,              (1)
The Korsun function:
The Chapman-Richards function:
                ,              (3)
where: bSI and cSI are non-asymptotic parameters of the site class curves; b0, b1, b2, c0, c1 and c2 are parameters to be estimated, and H100 is the fitted value from the parameterized curve of the age of 100 for each site class.
By applying the Korsun function, the value of parameter aSI for each site index was calculated in the following form (for the Korsun function - eq. 4 and for the CHR function-eq. 5):
                ,               (5)
where: SI is the site index value for the base age of 100.
Construction of the site index curve for a particular site class using the Korsun, the Korf and the CHR growth functions was performed by the following equations (eq. 6, eq. 7, eq. 8), respectively:
Korsun:                 (6)
Korf:      (7)
Chapman-Richards:            (8)
where: aSI, bSI, and cSI are model parameters, and SI is the site index value at the age of 100 (SI16, SI20, SI24, SI28 and SI32).
For the selection of a growth function to be used, various criteria have been applied. The first ones are coefficient of determination (R2) and residuals standard error (RSE).