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

Compatibility of a volume-taper equation system is generally defined to mea n that volumes determined by integrating the taper curve from groundline to total tree height are algebraically identical to those obtained from the t otal volume or appropriate volume ratio equations. This constraint was appl ied to a previously published model as a boundary condition using the const ant of integration resulting from the solution of the differential equation . Four cases are discussed that apply to different solutions of the differe ntial equation. This set of models, all based on the same geometric assumpt ion, makes a very flexible system for modeling stem taper. We fitted the re sulting taper models and corresponding tip volume equations simultaneously to stem-measurement data for 23 tropical species growing on Hainan Island i n southern China. The simplest case among the four (case I-a) was acceptabl e for some species, but for some others, a more general case (case II-b) wa s needed. We compared the results for the simplest and the most general cas es of this system with a published geometric model having only a point cons traint at dbh and with a published variable exponent taper equation. We exa mined how well each one predicted upper-stem diameters, merchantable height for a given upper-stem diameter, and total stem volume. Our taper models a lways had the smallest bias and standard error of estimates for total volum e estimation. The variable exponent taper equation was the best for predict ing upper-stem diameter and merchantable height. The advantages of a taper system with a geometric rationale are discussed, and two examples of easy e xtensions of our taper model are shown in the appendix.