Concerning the precision of growth estimation using permanent horizontal point samples

Abstract

In forest inventories using horizontal point sampling with permanent sample plots, the composition of samples from successive measurements changes due to sample trees being selected with a probability proportional to their basal area at the time of measurement. For this reason, the variance of estimators of growth based on this type of data tend to be very high. In this paper, the precision of three growth estimators developed by (1) Van Deusen, Dell and Thomas, (2) Grosenbaugh and (3) Roesch, Green and Scott are evaluated. In order to perform the evaluation, a general expression was developed for the variance of growth estimators that is valid for point sampling as well as plot sampling. The variances for the three estimators were derived based on this general expression. The estmators were restricted to basal area growth, because of the strong relationship between the volume growth and basal area growth. Because the general expression contained covariance terms and takes into consideration the distribution pattern of the trees in a stand, the analytic comparison of the variances of the estimators was made by using some simplifying assumptions. For basal area growth smaller than the initial basal area, the analyses indicate a higher variance for Van Deusen's estimator than for Grosenbaugh's. Also, numerical comparisons were carried out on model stands with well-defined characteristics and including all covariance terms. The numerical comparisons confirmed the analytical results that for small growth rates, the variance of the Van Deusen estimator is considerably greater than the variance of Grosenbaugh's estimator. Only when the growth rates are approximately equal to the initial basal area are the variances approximately the same for the two estimators. Roesch's estimator showed little advantage when compared with Grosenbaugh's estimator. Priority should be given to Grosenbaugh's estimator in surveys where growth is less than the initial basal area, which is usually the case in practice.