Biomass maps are valuable tools for estimating forest carbon and forest planning. Individual-tree biomass estimates made using allometric equations are the foundation for these maps, yet the potentially-high uncertainty and bias associated with individual-tree estimates is commonly ignored in biomass map error. We developed allometric equations for lodgepole pine (Pinus contorta), ponderosa pine (P. ponderosa), and Douglas-fir (Pseudotsuga menziesii) in northern Colorado. Plot-level biomass estimates were combined with Landsat imagery and geomorphometric and climate layers to map aboveground tree biomass. We compared biomass estimates for individual trees, plots, and at the landscape-scale using our locally-developed allometric equations, nationwide equations applied across the U.S., and the Forest Inventory and Analysis Component Ratio Method (FIA-CRM). Total biomass map uncertainty was calculated by propagating errors from allometric equations and remote sensing model predictions. Two evaluation methods for the allometric equations were compared in the error propagation—errors calculated from the equation fit (equation-derived) and errors from an independent dataset of destructively-sampled trees (n = 285). Tree-scale error and bias of allometric equations varied dramatically between species, but local equations were generally most accurate. Depending on allometric equation and evaluation method, allometric uncertainty contributed 30–75% of total uncertainty, while remote sensing model prediction uncertainty contributed 25–70%. When using equation-derived allometric error, local equations had the lowest total uncertainty (root mean square error percent of the mean [% RMSE] = 50%). This is likely due to low-sample size (10–20 trees sampled per species) allometric equations and evaluation not representing true variability in tree growth forms. When independently evaluated, allometric uncertainty outsized remote sensing model prediction uncertainty. Biomass across the 1.56 million ha study area and uncertainties were similar for local (2.1 billion Mg; % RMSE = 97%) and nationwide (2.2 billion Mg;  % RMSE = 94%) equations, while FIA-CRM estimates were lower and more uncertain (1.5 billion Mg;  % RMSE = 165%). Allometric equations should be selected carefully since they drive substantial differences in bias and uncertainty. Biomass quantification efforts should consider contributions of allometric uncertainty to total uncertainty, at a minimum, and independently evaluate allometric equations when suitable data are available.

中文翻译：

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从树木到景观尺度的森林生物量估计的变异性和不确定性：异速方程的作用。

生物量图是估算森林碳和森林规划的宝贵工具。使用异速方程计算单棵树生物量的估算值是这些图的基础，但是与单棵树估算值相关的潜在高不确定性和偏差通常在生物量图误差中被忽略。我们为科罗拉多州北部的黑松（Pinus contorta），黄松（P. pokerosa）和花旗松（Pseudotsuga menziesii）开发了等速方程。地块级生物量估计值与Landsat影像，地貌和气候层相结合，以绘制地上树的生物量。我们使用本地开发的异速方程，全美范围内的全国方程，比较了单个树木，地块和景观尺度的生物量估计值，以及森林调查和分析成分比率法（FIA-CRM）。总生物量图的不确定性是通过传播来自异速方程和遥感模型预测的误差来计算的。在误差传播中比较了两种异速方程的评估方法-从方程拟合（方程式得出）计算出的误差和从破坏性采样树的独立数据集中得到的误差（n = 285）。树种的误差和异速方程的偏差在物种之间变化很大，但是局部方程通常最准确。根据异形方程和评估方法，异形不确定性占总不确定性的30–75％，而遥感模型预测不确定性占25–70％。使用方程式衍生的异向误差时，局部方程式的总不确定性最低（均方根均方根误差百分比[％RMSE] = 50％）。这可能是由于样本数量少（每个物种采样了10–20棵树）的异速方程和评估结果并不能代表树木生长形式的真正可变性。当独立评估时，异速不确定性超出了遥感模型预测的不确定性。156万公顷研究区域的生物量和不确定性在本地（21亿Mg；％RMSE = 97％）和全国（22亿Mg；％RMSE = 94％）方程式中相似，而FIA-CRM的估计值较低且不确定性更高（15亿Mg；％RMSE = 165％）。异速方程应谨慎选择，因为它们会引起偏差和不确定性的巨大差异。