Assuming volume equations with multiplicative errors, we derive simple conditions for determining when measurement error in total height is large enough that only using tree diameter, rather than both diameter and height, is more reliable for predicting tree volumes. Based on data for different tree species of excurrent form, we conclude that measurement errors up to ±40% of the true height can be tolerated before inclusion of estimated height in volume prediction is no longer warranted.
We consider the prediction of stem volume of a tree by means of simple linear regression wherein the explanatory variable is D2H; D is the bole diameter measured outside bark at breast height and H is the total height of the tree. Given a fitted equation, a tree whose volume is to be predicted must be measured for D and H. Two sources of error account for the deviation of predicted tree volume from V, the actual tree volume, i.e. (1) error in the estimated coefficients of the volume function and (2) variation of V around its expected value conditional upon D2H. Owing to the greater difficulty and expense of measuring H in forest conditions, a standard practice is to predict its value from a regression on diameter. Consequently the prediction of V, V say, is subject to additional sources of error due to (1) the error in the estimated coefficients of the height‐diameter function and (2) the variation of H around its expected value conditional on D. An empirical study of a population of more than 14000 loblolly pine trees was undertaken with the objective of quantifying the average proportion of overall prediction error which was due to these components. The exact mean square error of the vector of predicted volume, V, is also derived.
Fixed-area plot sampling, variable-radius plot sampling, and horizontal-line plot sampling performed similarly in estimating competition from adjacent trees if only plots were considered that had an adequate number of sample trees to compute the estimated indices. The percentage of plots for which the indices can be computed tends to be largest for variable-radius plot sampling, then line sampling, and last for fixed-area plot sampling. Variable-radius plot sampling performs about as well as fixed-area plot sampling in computing the competition measures used in the distance-dependent tree models evaluated in this analysis.
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