Determination of optimal tree height models and calibration designs for Araucaria araucana and Nothofagus pumilio in mixed stands affected to different levels by anthropogenic disturbance in South-Central Chile
Authors: Zhou Xinying , Kutchartt Erico , Hernández Jaime , Corvalán Patricio , Promis Álvaro , Zwanzig Martin 
Published: April 2023

Abstract
Key message
Here, we present a workflow for determining the optimal tree height model and calibration design for forests affected to varying degrees by anthropogenic disturbance. For mixed Araucaria-Nothofagus forests, tree height predictions in newly surveyed stands are most accurate and effective when the height of up to five random trees is measured to recalibrate predefined nonlinear mixed-effects models.

Context
Araucaria-Nothofagus forests in Chile are affected by anthropogenic disturbances such as intentional forest fires, grazing, and seed harvesting, causing forest structure to become more heterogeneous. This also challenges tree height predictions, which are required for yield estimations, carbon accounting, and forest management, since height measurements of standing trees are often considered too costly, difficult, and imprecise.

Aims
How does the structure of these forests vary by different levels of anthropogenic disturbance? Which models for estimating tree height of Araucaria araucana and Nothofagus pumilio are most reliable and generally usable? And considering their application in stands they have not been fitted to, which calibration design is optimal for these models?

Methods
Twelve stands were surveyed and classified into four different intensities of anthropogenic disturbance. In 25 to 36 plots per stand, horizontal point sampling measurements of stem diameter as well as of height of selected trees were carried out. Different quantitative stand-level properties were calculated to determine forest structure, which was compared among stands by cluster analysis. To identify the optimal height-diameter (H–D) model, simple models including diameter only as well as generalized models including stand variables were tested, each additionally extended by a nonlinear mixed-effects (NLME) modeling framework accounting for nested and random effects. To further determine tree height in new stands, the optimal model calibration design was identified involving the empirical best unbiased predictor technique.

Results
Forest structure greatly varied among stands affected by different levels of anthropogenic disturbance, which challenged the development of tree height prediction models. Of all the simple H–D models considered, the Gompertz model was the best for A. araucana and the Näslund model for N. pumilio. The models progressively improved by adding stand variables and using NLME techniques. However, our final model comparisons indicate that a calibrated simple NLME model without stand variables should be preferred. It was further found that the optimal calibration design is to use five randomly selected trees.

Conclusion
Although anthropogenic disturbances can have a complex effect on height-diameter relationships, the same H–D model can be used for stands representing different anthropogenic disturbance levels and recalibrated by cost-effective measurements.