STRATEGIES FOR STEM MEASUREMENT SAMPLING: A STATISTICAL APPROACH OF MODELLING INDIVIDUAL TREE VOLUME

ABSTRACT The aim of this paper was to evaluate different criteria for stem measurement sampling and to identify the criterion with best performance for developing individual tree volume equations. Data were collected in eucalyptus stands 58 to 65 months old. Schumacher-Hall model was applied using five sampling criteria with nine variations (45 in total): 1) number of trees per diameter class, being (a) fixed number, (b) proportional to the diameter class of the sample, or (c) proportional to the standard deviation of the sample; and 2) the width of the diameter class, which ranged from 1.0 up to 5.0 cm. We used the equations generated from each of the five sampling criteria to estimate stem volume of trees reserved for validation. This allowed us to obtain standard errors of estimates from this data-set. In addition, residuals of volume estimates were examined by means of statistical tests of bias, autocorrelation and heteroscedasticity. Better performances of volume equations occurred when smaller diameter class widths were used, i.e., when the sample size increased. There was no clear trend in increasing/decreasing residual autocorrelation and/or heteroscedasticity. Both methods of sampling proportional to the frequency of diameter class had the best performances, inclusive using only 36 trees. The ones where choice of trees was proportional to the standard deviation had the worst. In conclusion, the selection proportional to the frequency of the diameter class, under the condition that at least two trees per class are sampled, provides models statistically better than all the other criteria.

摘要 本研究旨在评估林木茎干测量采样的各类评判准则，并筛选出构建单木材积方程时综合表现最优的采样准则。试验数据采集自林龄58至65个月的桉树人工林分。本研究采用Schumacher-Hall模型（Schumacher-Hall Model），设置5类采样准则共9种变异形式（总计45组）：其一为径阶内林木株数准则，包含(a)固定株数、(b)与采样径阶成比例、(c)与样本标准差成比例三种形式；其二为径阶宽度准则，取值区间为1.0至5.0 cm。我们利用每类采样准则生成的材积方程，对预留的验证林木的茎干材积进行估计，由此得到该数据集下估计值的标准误。此外，通过偏差、自相关与异方差性统计检验，对材积估计残差展开分析。当采用更小的径阶宽度（即增大样本量）时，材积方程的统计学表现更优。残差自相关和/或异方差性的增减未呈现明确趋势。与径阶频数成比例的两类采样准则表现最优，即便仅选取36株林木亦是如此；而以林木选取比例与样本标准差成比例的采样准则表现最差。综上，当每径阶至少选取2株林木时，基于径阶频数比例的采样准则所构建的模型，统计学表现优于其余所有采样准则。