Comparison of Modeling Approaches for the Height–diameter Relationship: An Example with Planted Mongolian Pine (Pinus sylvestris var. mongolica) Trees in Northeast China

Abstract

In the process of modeling height–diameter models for Mongolian pine (Pinus sylvestris var. mongolica), the fitting abilities of six models were compared: (1) a basic model with only diameter at breast height (D) as a predictor (BM); (2) a plot-level basic mixed-effects model (BMM); (3) quantile regression with nine quantiles based on BM (BQR); (4) a generalized model with stand or competition covariates (GM); (5) a plot-level generalized mixed-effects model (GMM); and (6) quantile regression with nine quantiles based on GM (GQR). The prediction bias of the developed models was assessed in cases of total tree height (H) predictions with calibration or without calibration. The results showed that extending the Chapman–Richards function with the dominant height and relative size of individual trees improved the prediction accuracy. Prediction accuracy was improved significantly when H predictions were calibrated for all models, among which GMM performed best because random effect calibration provided the lowest prediction bias. When at least 8% of the trees were selected from a new plot, relatively accurate and low-cost prediction results were obtained by all models. When predicting the H values of Mongolian pine for a new stand, GMM and BMM were preferable if there were available height measurements for calibration; otherwise, GQR was the best choice.