Many volume functions use diameter and height as input variables. Measurement and prediction errors in heights propagate into the error of the wood volume estimate for a tree or a plot. We quantified these errors (and bias) with census data of species, heights, and stem diameters in a 1.44 ha hardwood stand in Lower Saxony (GER) dominated by beech ( Fagus sylvatica L.) and with an understorey of hardwood species. We simulated simple random sampling with fixed area and variable radius plots and distorted the actual height measurements with three magnitudes of random Gaussian errors. The inventory protocol for height measurement results in a selection of three to four trees per plot, while heights for the remaining trees were predicted via two alternative models. Tree and plot level RMSE% of wood volume with a mix of measured and predicted tree heights were—across the three magnitudes of measurement errors, 18–81% greater than root-mean-squared errors obtained when all trees were measured for heights with errors. The results from this study contribute the statistical side of recommendations on the number of height measurements per forest inventory plot, where inferences on optimal numbers of height measurements will also depend on the costs.

中文翻译：

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测量和预测高度的木材体积误差

许多体积函数使用直径和高度作为输入变量。高度的测量和预测误差会传播到树木或地块的木材体积估计误差中。我们使用下萨克森州 (GER) 的 1.44 公顷硬木林分的物种、高度和茎直径的普查数据量化了这些误差（和偏差），该林分以山毛榉 (Fagus sylvatica L.) 为主，下层硬木物种。我们使用固定面积和可变半径图模拟了简单随机抽样，并用三个随机高斯误差幅度扭曲了实际高度测量值。高度测量的清单协议导致每个地块选择三到四棵树，而其余树木的高度则通过两个替代模型进行预测。树木和地块水平木材体积的 RMSE%，混合测量和预测的树木高度，在测量误差的三个量级中，比测量所有树木的高度有误差时获得的均方根误差大 18-81% . 这项研究的结果有助于对每个森林清单地块的高度测量数量的建议的统计方面，其中对高度测量的最佳数量的推断也将取决于成本。