Abstract
The main objective of this study was to explore the accuracy of Weise’s rule of thumb applied to an estimation of the quadratic mean diameter of a forest stand. Virtual stands of European beech (Fagus sylvatica L.) across a range of structure types were stochastically generated and random sampling was simulated. We compared the bias and accuracy of stand quadratic mean diameter estimates, employing different ranks of measured stems from a set of the 10 trees nearest to the sampling point. We proposed several modifications of the original Weise’s rule based on the measurement and averaging of two different ranks centered to a target rank. In accordance with the original formulation of the empirical rule, we recommend the application of the measurement of the 6th stem in rank corresponding to the 55% sample percentile of diameter distribution, irrespective of mean diameter size and degree of diameter dispersion. The study also revealed that the application of appropriate two-measurement modifications of Weise’s method, the 4th and 8th ranks or 3rd and 9th ranks averaged to the 6th central rank, should be preferred over the classic one-measurement estimation. The modified versions are characterised by an improved accuracy (about 25%) without statistically significant bias and measurement costs comparable to the classic Weise method.
Highlights
Exact mathematical descriptions of stand diameter distributions are one of the important tasks of forest growth modelling [1]
Stands were differentiated by mean diameter size intervals of 5 cm, from 10 to 50 cm, and three categories of degree of diameter dispersion (DoD)
The smallest, but still the most significant negative bias, was achieved for the 6th rank
Summary
Exact mathematical descriptions of stand diameter distributions are one of the important tasks of forest growth modelling [1]. Diameter structure is a basic modelling component of many complex forest growth and yield models linking individual tree characteristics with stand variables [2,3]; modelling stand diameter distribution is a rapidly evolving research field [4,5,6,7]. Several probability density functions based on statistical probability theory are used as a mathematical model of diameter distributions. (i) the parameter prediction method [15]; (ii) the parameter recovery and percentile-based parameter recovery method [16]; (iii) the non-parametric percentile-based distribution-free method [17]; and (iv) the quantile regression method [18]. The quantile regression method has gained increased attention in the last few years [19]
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