Comparisons of approaches to modelling tree taper, stand structure and stand dynamics in forest plantations
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This study addressed two general tree modelling topics: (i) taper, and (ii) growth and yield. Several modelling options were considered and evaluated in detail for each of the two topics. The use of various datasets (two and three, respectively) enabled sound conclusions to be drawn on a variety of methodological aspects.
In the first part of the study, several existing taper equations of different types were compared, and new variants were proposed. Variable-exponent equations exhibited the maximum levels of accuracy in terms of estimating diameter, height and volume. A variant of the classic segmented taper equation (Max and Burkhart 1976) was found to be best. This equation showed reasonably accurate diameter and volume estimations and was able to be inverted for height estimations and explicitly integrated for volume estimations. Bark models that predict under-bark diameters from over-bark diameters, dbh and total tree height were developed and used in a 2-step composite approach for predicting under-bark diameters. This approach has been proposed to minimise the number of under-bark measurements when collecting taper data (Gordon et al. 1995), but its validity has not been proved. The results obtained in this study showed that this composite approach was reliable for the two datasets used in this study. Practical suggestions for collecting taper data when adopting this approach were provided.
In the second part, three approaches for developing growth and yield models with comparable output resolution were compared. These approaches included: (i) diameter distribution models; (ii) relative-basal-area-based dis-aggregative approaches; and (iii) individual tree models. To facilitate comparisons, tree-level outputs from the latter two approaches were grouped by diameter class. Within each approach, a variety of equations and procedures was evaluated in order to obtain the best possible model for each approach. Diameter distribution models based on the reverse Weibull distribution with a parameter-recovery approach provided acceptable depictions of actual stand tables, and were more accurate than other methods over long projections. Nonetheless, the best representation of actual diameter distributions was achieved with individual-tree models. Between those modelling approaches that provided compatible tree-level and stand-level output resolution, the adjusted individual-tree model (ITMadj) approach exhibited lower error indices than the relative-basal-area-based dis-aggregative approach. This was attributed to the increased complexity of diameter increment equations, which relied on stand-level and tree-level variables, as opposed to the simple formulation of relative basal area equations.
Adjusted individual-tree models were preferred to unadjusted individual-tree models (ITM) for all three species studied. For the New Zealand grown species (Pinus radiate and Pseudotsuga menziesii), this decision was based on (i) more accurate basal area and stocking estimations from stand-level models as compared to basal area and stocking estimations derived by aggregating tree-level projections; and (ii) the lower error indices for depicting diameter distributions that were achieved with the ITMadj as compared to the ITM. For E. grandis grown in Uruguay, however, the main criterion for choosing the ITMadj was compatibility with the stand-level model, given that the ITM produced slightly lower error indices than the ITMadj for depicting diameter distributions.
Complete growth and yield models were built for all three species for the Central North Island of New Zealand and for Zones 7, 8 and 9 of Uruguay. These provided a range of options for performing forecasts of future stand conditions, depending on the type of input data available. Model options include fully compatible whole-stand, diameter-distribution and individual-tree models. User-friendly computer simulators including all these options were developed. These simulators allow comparisons of thinning schedules and rotation ages, providing information on the main stand variables, as well as tree-level (or diameter class) details and merchantable volumes by log type.
Regional models for estimating individual-tree heights from diameter and mean top height plot measurements, which form part of the growth models just described, can also be used independently. Their use would allow resources to be saved by minimising the amount of inventory height measurements.