Polymorphic height and site index curves for lodgepole pine in Alberta

Abstract

This new, biologically based, nonlinear regression model produces polymorphic site index and height curves as a function of prediction age and a height at any age. The curves are constrained to pass through the origin and appropriate heights at any index age. The model was parametrized on 970 stem-analyzed trees and tested on tree measurements from 147 permanent sample plots. Compared with other lodgepole pine (Pinuscontorta var. latifolia Engelm.) height models in Alberta, this model had fewer parameters, yet showed better accuracy and precision than the other models. Above all, the new model provides compatible site index and height estimates, and it can predict height without prior knowledge of site index.

Site quality equations for Pinus sylvestris L. plantations in Galicia (northwestern Spain)

“…Similar results were obtained by [1]. The best results for model M7 [19] were obtained when Asi = 30 was used. Models M1 (Sloboda [53]) and M4 (Bertalanffy-Richards solved by b 2 ) provided the best results for the goodness-of-fit statistics calculated, although models M2 (McDill and Amateis [37]) and M3 (Bertalanffy-Richards solved by b 1 ) represented the data almost as well, with both behaving similarly.…”

“…With the difference equation method (1) short observation periods of temporary plots or stem analysis from trees whose total age is under or over the reference age can be used, (2) the curves pass through site index at the reference age, and (3) they are base-age invariant [19,20]. The invariant or unchanging property refers to predicted heights: any number of points (A 1 , H 1 ) on a specific site curve can be used to make predictions for a given age A 2 and the predicted height H 2 will always be the same.…”

“…Model M7 was proposed by Cieszewski and Bella [19] from the Hossfeld IV equation (cited in [46]) by relating a model parameter to site index. The approach used to derive model M7 can be referred to as initialcondition site index substitution in expanded dynamic equations [17].…”

Modelling height and diameter growth of dominant cork oak trees in Spain

“…For model fitting, the "Difference Equation" method was chosen because it is base age invariant [12,17] and allows the use of any temporal series of data, whatever the length, such as those resulting from stem analysis. Furthermore, this method affords other advantages like the possibility of using data from trees which are younger than the base age [24].…”

“…Results indicate that a single height growth model could be used for both regions. Based on these results, the following difference form of the McDill-Amateis equation (MA) with same parameters was proposed as the height growth model for dominant cork oak trees in the Natural Park of "Los Alcornocales" and in Catalonia, equation (12): (12) where h i is the height (m) at age t i (years). Site index was defined as the top height reached at 80 years old and then five quality classes were defined ranging from 14 m for quality I to 6 m for quality V, with a 2 m step between each quality class.…”