Robustness of Parametric and Nonparametric Fitting Procedures of Tree-Stem Taper with Alternative Definitions for Validation Data

Abstract

This study aims to evaluate the robustness of parametric and nonparametric procedures using alternative definitions of validation data for loblolly pine. Specifically, four data division strategies were implemented: random selection of one-third of the trees in the data set, selection of the smallest one-third of the trees by diameter at breast height (DBH), selection of the middle third of the trees by DBH, and selection of the largest third of the trees by DBH. Results indicate that tree taper was predicted reasonably well by both procedures when the smallest, medium-sized, or randomly selected trees were withheld for validation. However, when the largest trees were withheld for validation, diameters predicted by the nonparametric random forest algorithm were considerably less accurate than those predicted by the parametric models, especially for diameters near the tree top. When extrapolation is anticipated, a carefully designed data-partitioning strategy should provide some protection against poor results for given prediction objectives. Study Implications Parametric tree-stem taper models have been widely applied in forestry. Recently, nonparametric methods with computationally intensive algorithms were proposed for estimating tree taper, but reliability of the methods has not been explicitly examined. In practice, models are commonly applied to predict unknown populations, which may vary from the observations used in model development. This study provides insights for natural resource and forest managers to select appropriate validation procedures when developing models for predicting tree-stem taper and examining robustness of parametric and nonparametric fitting of tree-stem taper under varying levels of interpolation/extrapolation from fitting to validation of data.

Comparison of Data Grouping Strategies on Prediction Accuracy of Tree-Stem Taper for Six Common Species in the Southeastern US

“…As Figures 2 and 3 illustrate, MB and RMSE were similar among the different number of H-D ratio/DBH groups. Although H-D ratio has been shown to be related to crown/tree form, and tree taper usually varies by tree DBH, e.g., [8,9,19,20], we found that the uncertainty of prediction was not considerably reduced when grouping data based on H-D ratio or DBH. model fitting did not appreciably improve the prediction accuracy.…”

“…Max and Burkhart [11] proposed using the squared ratio d 2 /DBH 2 as the dependent variable, but Yang and Burkhart [9] found that the model with the first order ratio d/DBH provided more accurate predictions. To be comparable with the Kozak [12] model, the model with the first order ratio was used in this study, which is…”

“…In model evaluation, prediction accuracy is an important criterion and is commonly assessed using an independent validation dataset. It was found that parametric stem taper models produced reliable predictions for loblolly pine when the size distribution of the predicted populations deviated from the observations used in model development (i.e., high robustness) [9]. Although the data grouping approach has been implemented in forest and natural resources practice, to our knowledge, the accuracy of stem taper models fit by different data grouping approaches and calibration sample sizes has not been extensively investigated.…”

“…The LM algorithm is a compromise between the gradient-descent and Gauss-Newton approaches, which leads to more stable parameter estimates [18]. The initial values for parameter estimation were obtained from Yang and Burkhart [9]. The model evaluation statistics are given in Section 2.3.3.…”

Applying taper function models for black locust plantations in Greek post-mining areas

“…In turn, the primarily desired area of application in the Western Macedonian Lignite Center covers about 2500 ha. However, Yang and Burkhart (2020) found that withholding certain classes of DBH for parametric fitting approaches, i.e. the smallest or largest diameter trees, did not effectively influence the predictive ability of taper functions Eq.…”