Effect of upper stem diameter and errors of measurement on the accuracy of volume equations

Measurements of DBH, upper diameters, merchantable height and total heights were made on 80 standing white oaks (Quercus alba) which were then felled for detailed measurements of the same parameters. The data obtained were used to evaluate the accuracy of standing tree measurements, to develop and compare volume equations that used upper diameter as one of the predictor variables and to examine the contributions of individual predictor variables to total volume prediction bias and precision.

Relative bias ranged from 0.85% for DBH measurement errors to 2.88% for total height measurement errors. Relative standard deviation ranged from 1.52% to 10.13% for DBH and total height errors respectively. When both bias and precision ( standard deviation ) were considered jointly, the relative root mean squared error ranged from 1.75% to 10.48% for DBH and total height errors respectively. Upper diameter and merchantable height showed negative bias.

A comparison of eight fitted models against the combined variable model revealed a gain in precision and a reduction in bias for models that used upper diameter as a third predictor variable. The improvement as based on the relative root mean squared error ranged from 28.8% to 71.3% for taped measurements. However, models that used upper diameter as a substitute for either DBH or merchantable height performed worse than the combined variable model.

An analytic examination of the impact of measurement error on volume prediction bias showed that merchantable height errors accounted for most of the bias and that DBH and upper diameter errors contributed almost equal amounts(in absolute terms) to the volume bias.