Site index models developed using the difference equation method, otherwise known as the algebraic difference approach (ADA) along with its generalization (GADA), play an important role in forest growth and yield modeling for operational use. Their projection accuracy tends to be reduced over increasing time intervals, a common modeling phenomenon not yet well understood. In this study, dominant height projections given one single prior observation using three (G)ADA models were examined in relation to pairwise height correlations on an empirical dataset consisting of height remeasurements taken on permanent plots of a second-rotation loblolly pine (Pinus taeda L.) plantation experimental study. The results indicated that the decline in projection accuracy in terms of RMSE or $Rp2$ (analogical to the coefficient of determination R²) with increasing time intervals is closely associated with the weakening correlations imbedded in distant height remeasurements. The squared coefficient of correlation (⁠$ρ2$⁠) between paired heights can be set as an upper bound of $Rp2$ in (G)ADA model prediction of heights conditional on prior observations. An examination of correlation over time interval will be informative of how projection accuracy is likely to change and what the maximal $Rp2$ might be for any potential (G)ADA model to be developed.

中文翻译：

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使用差异方程模型的主导高度投影精度的实证检验

使用差异方程法（又称为代数差异法（ADA）及其通用化（GADA））开发的场地指数模型在森林生长和可操作使用的产量建模中发挥重要作用。它们的投影精度会随着时间间隔的增加而降低，这是一种尚未很好理解的常见建模现象。在这项研究中，检查了使用三个（G）ADA模型在一次观测之前给出的主要高度投影，并与经验数据集上的成对高度相关性进行了比较，该数据集包括对第二轮火炬松（Pinus taeda L 。）人工林实验研究。结果表明，按RMSE或$[Rp2$（与确定系数R ²相似）（随着时间间隔的增加）与遥测高度中嵌入的弱相关性密切相关。相关系数的平方（⁠$ρ2$⁠）可以将成对的高度之间的上限设置为$[Rp2$在（G）ADA模型中以先前的观测为条件的高度预测。对时间间隔内的相关性进行检查将提供有关投影精度可能如何变化以及最大变化量的信息。$[Rp2$ 可能是要开发任何潜在的（G）ADA模型。