A non-asymptotic sigmoid growth curve for top height growth in forest stands
2012
Bontemps, Jean-Daniel | Duplat, Pierre
Since the height horizon remains undetected in the vast majority of height series sampled in forest stands, even of notable ages, the realism of the traditional asymptotic-size modelling assumption is questioned. The aims of the study were to present an original non-asymptotic growth model and to test its accuracy against asymptotic-size equations. The equation proposed is a first-order four-parameter autonomous differential equation. The related sigmoid size curve has a parabolic branch of time. It was tested on 349 old growth series of top height (1047 stem analyses) selected to explore the maximum observed ranges of age and site conditions in seven temperate tree species growing in pure and even-aged stands. The fitting accuracy of this equation and three classical asymptotic-size growth equations (Richards, Hossfeld IV and Korf equations) were compared, with parameterizations of increasing flexibility. For the different parameterizations, the proposed growth equation showed higher performances than asymptotic growth equations, attributed to its non-asymptotic property and to the mathematical independence between parameters related to the inflection point and late growth. Top height growth was therefore accurately modelled by a sigmoid curve not based on the asymptotic-size assumption. This equation may be of general relevance to tree growth modelling.
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