Analysis of biomass accumulation and stem size distributions over long periods in managed stands of Pinus sylvestris in Finland using the 3-PG model.

We tested the performance of a process-based model (PBM) in relation to long-term mensuration data from two sites in Finland where the stands were up to 90 years old and had been thinned at approximately 5-year intervals over the last 50 years. The PBM used was based on the 3-PG (Physiological Principles to Predict Growth) model developed by Landsberg and Waring (1997), with modifications in the biomass allocation routine, for which we used data and calculations by Vanninen (2003) to estimate the allocation coefficients and turnover rates. Site fertility was estimated in terms of known site-type characteristics. The model was evaluated in terms of stand development and its ability to simulate responses to thinning; stem numbers after thinning were specified at the dates when the thinning took place. Stand development in terms of basal area, volume and mean diameter at breast height, closely followed the measured characteristics of all stands. Foliage mass predictions were close to estimates obtained by an empirical method. The analysis shows that, under normal thinning regimes, a range of different thinning intensities can be adequately described using a simple multiplicative model relating the proportion of volume and foliage mass removed to the corresponding proportion of stem numbers. This model, together with stem allometry data, described the "growth" in mean diameter after thinning, which simply reflected the removal of the smaller trees. These results indicate that, with a single set of parameter values, 3-PG can provide good descriptions of the growth patterns of trees-in this case Pinus sylvestris L.-over long periods, including growth after repeated thinning. One of the outputs from the 3-PG model is mean stem diameter (B): we show that it is feasible to estimate stem size distributions, which changed considerably over the life of these stands, from B using the Weibull function. This shows that, given information about the Weibull parameters for particular species and cultural systems, it should be possible to use stem numbers and the B obtained from the 3-PG model to produce information about stem size distributions from simulated data.