A Taper Equation for Loblolly Pine Using Penalized Spline Regression

Stem profile needs to be modeled with an accurate taper equation to produce reliable tree volume assessments. We propose a semiparametric method where few a priori functional form assumptions or parametric specification are required. We compared the diameter and volume predictions of a penalized spline regression (P-spline), P-spline extended with an additive dbh-class variable, and six alternative parametric taper equations including single, segmented, and variable-exponent equation forms. We used taper data from 147 loblolly pine (Pinus taeda L.) trees to fit the models and make comparisons. Here we show that the extended P-spline outperforms the parametric taper equations when used to predict outside bark diameter in the lower portion of the stem, up to 40% of the tree height where the more valuable wood products (62% of the total outside bark volume) are located. For volume, both P-spline models perform equal or better than the best parametric model, with taper calibration, which could result in possible savings on inventory costs by not requiring an additional measurement. Our findings suggest that assuming a priori fixed form in taper models imposes restrictions that fail to explain the tree form adequately compared with the proposed P-spline. Study Implications: Our semiparametric fitting approach translates into more precise stem diameter predictions compared with traditional parametric taper equations. In terms of volume, we show that the proposed method is flexible enough to accurately predict total and merchantable volume similar to calibrated segmented equations. Accurate diameter predictions and volume estimations at the tree level can add value to the data inventory process and reporting by reducing bias and allowing better management decisions for the most planted species in the southern United States. Although our sample size is only 147 trees, the method described here produces excellent volume prediction qualities without requiring calibration with extra upper-stem diameter measurement.