Modelling the Crown Profile of Western Hemlock (Tsuga heterophylla) with a Combination of Component and Aggregate Measures of Crown Size

Abstract

Research Highlights: We present statistical methods for using crown measurement data from multiple destructive sampling studies to model crown profiles in the Tree and Stand Simulator (TASS) and evaluate it using component (branch-level) and aggregate (tree-level) predictions. Combining data collected under different sampling protocols offered unique challenges. Background and Objectives: The approach to modelling crown profiles was based on Mitchell’s monograph on Douglas-fir growth and simulated dynamics. The functional form defines the potential crown size and shape and governs the rate of crown expansion. With the availability of additional data, we are able to update these functions as part of ongoing TASS development and demonstrate the formulation and fitting of new crown profile equations for stand-grown western hemlock (Tsuga heterophylla (Raf.) Sarg. Materials and Methods: Detailed measurements on 1616 branches from 153 trees were collected for TASS development over a 40-year period. Data were collected under two different sampling protocols and the methods were designed to allow the use of data from both protocols. Data collected on all branches were then introduced through the application of the ratio of length of each of the selected branches to the largest branch in the internode (RL). Results: A mixed-effects model with two random effects, which accounted for tree-level variation, provided the best fit. From that, a model that expressed one parameter as a function of another with one random effect was developed to complement the structure of the Tree and Stand Simulator (TASS). The models generally over-estimated crown size when compared to the projected crown area recorded from field measurements, and a scalar adjustment factor of 0.89 was applied that minimised mean-squared error of the differences. The new model is fit from direct measures of crown radius and predicts narrower crown shapes than previous functions used in TASS.