Individual height–diameter models for young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations in New Brunswick, Canada

Abstract

Historically, height–diameter models have mainly been developed for mature trees; consequently, few height–diameter models have been calibrated for young forest stands. In order to develop equations predicting the height of trees with small diameters, 46 individual height–diameter models were fitted and tested in young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations between the ages of 4 to 8 years, measured from 182 plots in New Brunswick, Canada. The models were divided into 2 groups: a diameter group and a second group applying both diameter and additional stand- or tree-level variables (composite models). There was little difference in predicting tree height among the former models (Group I) while the latter models (Group II) generally provided better prediction. Based on goodness of fit (R2and MSE), prediction ability (the bias and its associated prediction and tolerance intervals in absolute and relative terms), and ease of application, 2 Group II models were recommended for predicting individual tree heights within young black spruce and jack pine forest stands. Mean stand height was required for application of these models. The resultant tolerance intervals indicated that most errors (95%) associated with height predictions would be within the following limits (a 95% confidence level): [-0.54 m, 0.54 m] or [-14.7%, 15.9%] for black spruce and [-0.77 m, 0.77 m] or [-17.1%, 18.6%] for jack pine. The recommended models are statistically reliable for growth and yield applications, regeneration assessment and management planning. Key words: composite model, linear model, model calibration, model validation, prediction interval, tolerance interval