A generalized nonlinear mixed-effects height–diameter model for Norway spruce in mixed-uneven aged stands

Abstract Tree height measurements are laborious and require more time and effort compared to tree diameter measurements. That being the case, height-diameter (H-D) models are usually used to predict individual tree heights, which are necessary for estimating the tree volume and the site index, as well as for projecting the stand development over time. Using a permanent sampling network (400x400m) from Retezat National Park in Romania, twenty-one (H-D) functions were evaluated for their fit performance, sensitivity to outliers and prediction ability for Norway spruce in mixed uneven aged stands. A set of twenty-three stand variables, both spatial and non-spatial, were used to describe the stand structure, species inter-mingling and competition, in order to be used as stand predictors in a generalized H-D model. Nonlinear mixed effects model was used in modelling the H-D relationship of Norway spruce. We developed the first generalized height-diameter model in Romania using three stand predictors as measures of the stand vertical structure, density and competition. Random and fixed effects calibration techniques were compared, testing various sampling designs in order to improve the height prediction accuracy of the model on a new dataset. Measuring six trees around the median and the thickest tree gave the best result in calibrating both fixed and random effects. On average, the best calibration design increased the accuracy of the prediction by 50 cm compared to the fixed effects prediction. The use of the estimated coefficients and the calibration design will significantly decrease the amount of work done by forest management planners, while ensuring high accuracy and reducing costs.