Analysis of Different Base Models and Methods of Site Model Derivation for Scots Pine

Abstract

Abstract Using an example of averaged growth series data of Scots pine (Pinus sylvestris L.), we examine several approaches to site-dependent height-age model derivation. We consider several renowned base models (two-dimensional equations, such as Y = f(t)) and derive from them anamorphic and polymorphic dynamic site equations (three-dimensional site-height-age models, such as Y = f(t, t 0, y 0)) of different complexities. The considered base models were selected previously as suitable for Scots pine in other studies, and are different variations of exponential and fractional functions. We compare all of the base models fit to individual site classes and the derived base-age invariant anamorphic and polymorphic dynamic site equations fit to all sites pooled together. All the fits of site equations to the pooled data from different site productivity series were based on base-age invariant stochastic regressions, in which the global model parameters that are common to all data are estimated simultaneously with the site effects unique for each site productivity series. The results show that: (1) choice of definition describing changes across site qualities may be more important than the choice of base equation defining changes over time; (2) a base model with high cost of deriving self-referencing function may sometimes be better than a base model with low cost of deriving the self-referencing function; and (3) superior base models may not produce superior anamorphic or simple polymorphic site models, but can produce superior advanced polymorphic site models, which can describe the growth patterns in data better than either anamorphic or simple polymorphic models.