A Comparison of Pine Height Models for the Crossett Experimental Forest
by D. Bragg. Journal of the Arkansas Academy of Science, Vol. 62, 2008, pp. 24-31
Many models to predict tree height from diameter have been developed, but not all are equally useful. This study compared a set of height-diameter models for loblolly (Pinus taeda) and shortleaf (Pinus echinata) pines from Ashley County, Arkansas. Almost 560 trees ranging in diameter at breast height (DBH) from 0.3 cm (both species) to 91.9 cm (for shortleaf) or 108.2 cm (for loblolly) were chosen for measurement. Height equations were then fit to four different functions (Chapman-Richards, modified logistic, exponential, and Curtis-Arney) with weighted nonlinear least squares regression using DBH as the only predictor. Models were evaluated using a series of goodness-of-fit measures, including fit index (R2), root mean square error (RMSE), bias, and corrected Akaike information criterion (AICc). All of the models fit the data very well, with 96 to 98% of the variation explained for loblolly pine, and 96 to 97% explained for shortleaf pine. Similarly, few differences were apparent in RMSE, bias, and AICc, although it was clear that the Curtis-Arney function fit both pine species slightly less well across the upper range of the diameters. Only subtle differences appeared in curve shape for small- to moderate-sized pines, with increasing departures predicted above 75 cm DBH. Given their overall similarity in performance, the modified logistic function was the preferred height-diameter model because of its more intuitive allometry at the upper extreme of pine size, especially when compared to the original FVS height dubbing equation. A unified height-diameter model capable of predicting total tree height for either pine taxa was also developed with a modified logistic function.
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