Compatible volume and taper models with coefficients for tropical species on Hainan Island in southern China

Abstract

Compatibility of a volume-taper equation system is generally defined to mean that volumes determined by integrating the taper curve from groundline to total tree height are algebraically identical to those obtained from the total volume or appropriate volume ratio equations. This constraint was applied to a previously published model as a boundary condition using the constant of integration resulting from the solution of the differential equation. Four cases are discussed that apply to different solutions of the differential equation. This set of models, all based on the same geometric assumption, makes a very flexible system for modeling stem taper. We fitted the resulting taper models and corresponding tip volume equations simultaneously to stem-measurement data for 23 tropical species growing on Hainan Island in southern China. The simplest case among the four (case I-a) was acceptable for some species, but for some others, a more general case (case II-b) was needed. We compared the results for the simplest and the most general cases of this system with a published geometric model having only a point constraint at dbh and with a published variable exponent taper equation. We examined how well each one predicted upper-stem diameters, merchantable height for a given upper-stem diameter, and total stem volume. Our taper models always had the smallest bias and standard error of estimates for total volume estimation. The variable exponent taper equation was the best for predicting upper-stem diameter and merchantable height. The advantages of a taper system with a geometric rationale are discussed, and two examples of easy extensions of our taper model are shown in the appendix.