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    Tree crown ratio is useful in various applications such as prediction of tree mortality probabilities, growth potential, and fire behavior. Crown ratio is commonly assessed in two ways: (1) compacted crown ratio (CCR-lower branches visually moved upwards to fill missing foliage gaps) and (2) uncompacted crown ratio (UNCR-no missing foliage adjustment). The national forest inventory of the United States measures CCR on all trees, whereas only a subset of trees also are assessed for UNCR. Models for 27 species groups are presented to predict UNCR for the northern United States. The model formulation is consistent with those developed for other US regions while also accounting for the presence of repeated measurements and heterogeneous variance in a mixed-model framework. Ignoring random-effects parameters, the fit index values ranged from 0.43 to 0.78, and root mean squared error spanned 0.08–0.15; considerable improvements in both goodness-of-fit statistics were realized via inclusion of the random effects. Comparison of UNCR predictions with models developed for the southern United States exhibited close agreement, whereas comparisons with models used in Forest Vegetation Simulator variants indicated poor association. The models provide additional analytical flexibility for using the breadth of northern region data in applications where UNCR is the appropriate crown characteristic.

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    Westfall, James A; Westfall, Megan B E; Randolph, KaDonna C. 2019. Modeling Relations between Compacted and Uncompacted Crown Ratio for the Northern United States. Forest Science. 65(5): 593-601.


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    forest inventory, mixed models, heterogeneous variance, growth and yield, fire behavior

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