DERIVATIVE BASED METHODS FOR CONSTRUCTING VOLUME-RATIO AND TAPER EQUATIONS

Methods for the construction of volume-ratio and taper functions based on taper derivatives are examined. Using such an approach, the modele r is required to specify the functional form of the second or third ta per derivative. The use of differential equation techniques gives an i ntegral expression for taper or volume ratio. The compatibility requir ements, that diameter at tree tip be zero and that it satisfy the diam eter at breast height measurement, can be met by imposing boundary con ditions. Similarly, in a volume ratio system, the requirements of zero at tree tip and unity at tree base, are formulated as boundary condit ions. The duality between volume-ratio and taper allows the developmen t of taper equations from volume-ratio equations. A parameter estimati on procedure that uses iteratively reweighted least squares is describ ed.