Benchmarking and Calibration of Forest Vegetation Simulator Individual Tree Attribute Predictions Across the Northeastern United States

period (5 years) after updating the individual tree-mortality submodel in FVS’s Southern variant (Radtke et al. 2012). On the other hand, Rijal et al. (2012a, 2012b) recently found refitting FVS-NE tree height and crown ratio equations to be ineffective for improving predictions when compared to utilizing a different equation form for several species in Maine. This suggests that effectiveness of model calibration may depend on the performance of each submodel, the species examined, and the geographic extent of the evaluation data sets. It should be noted that although FVS-NE has an inherent self-calibration algorithm for some submodels (Dixon and Keyser 2008); calibration here is defined as improvements that can be applied to individual tree attribute predictions without requiring direct measurements such as tree diameter or height increment. Most importantly, the performances of key FVS-NE submodels have yet to be tested for the dominant species, ecoregions, site quality classes, and forest types that are found across the 13 northeastern states. The purpose of this analysis was to investigate the performance of key submodels within FVS-NE and to seek improvements of individual submodels. Specific objectives were to: (1) quantify the performance of the ht-dbh, dbh, and ht submodels within FVS-NE using independent data gathered across the northeastern United States (benchmarking), (2) examine predictions for individual tree attributes after making adjustments to submodel output using a modified site index or a suite of tree, stand, and climate variables (calibration), and (3) compare the accuracy of a noncalibrated and calibrated FVS-NE in predicting plot-level BA growth. Methods FVS-NE Submodels Total tree height (ht; ft) is estimated using tree dbh (in.) for trees where ht is missing in a tree list and is influential in estimating dbh for small trees in FVS-NE (Dixon and Keyser 2008). Model form of the ht-dbh equation depends on tree species. For the species examined in this analysis, conifer species are estimated with the Curtis (1967) form: ht 4.5 1 exp( 2dbh ) (1) where as hardwoods are estimated with the Wykoff et al. (1982) form ht 4.5 exp 1 2/ dbh 1.0 (2) where the regression coefficients i and i are species specific and derive from FVS’s Southern variant, while a separate set of coefficients are available for trees found in the Allegheny National Forest in Pennsylvania (Dixon and Keyser 2008). The dbh for trees 5.0 in. in FVS-NE is estimated using the potential-modifier approach initially outlined in Teck and Hilt (1991) but with some modification as implemented in FVS-NE. These modifications include a different interpretation of BA in larger trees, an adjustment factor (AF) (0.7), and bounds applied to the growth-modifier component. First, potential BA growth ( bapot) is estimated using dbh and site index (SI). Second, a growth modifier is estimated using the BA in larger trees two 1-in. diameter classes below the subject tree (bal). Lastly, predicted annual BA growth ( ba) is estimated by multiplying the potential and modifier components ba 1SI 1 exp( 2dbh * 0.7) * exp( 3bal ) (3) where i are species group-specific regression coefficients from the current implementation of FVS-NE (Dixon and Keyser 2008, Table 4.7.1.1). Data used to initially parameterize the large-tree dbh equation were collected from permanent sample plots in the 1960s through the 1980s from 14 states in the northeastern United States (Teck and Hilt 1991). Similarly, the potential-modifier approach is used in FVS-NE for predicting ht. First, growth effective age (GEA) is estimated using ht and SI with the equations of Carmean et al. (1989). Second, the tree is grown for 10 years and GEA is used to then predict an updated tree ht. The difference between these two ht values is assumed to be potential height increment (htpot). Modified ht increment is estimated using the growth modifier from Equation 3 and the subject tree’s ht divided by the 40 largest-diameter trees in the stand, termed relative ht (htrel) ht htpot * 1 1 exp 3bal 1 htrel * 0.8 (4) Forest Inventory and Analysis Data Tree and plot records were obtained from the USDA Forest Service’s Forest Inventory and Analysis (FIA) program (Forest Inventory and Analysis 2011). The majority of these inventory plots were remeasured (73% of all plots), with a mean remeasurement interval of 5.2 0.9 (mean SD) years. Data from 13 US states where the suggested FVS-NE geographic range lies were used. Measurements from 1998 onward were used, which was when the FIA’s annual inventory design was implemented across the United States (McRoberts et al. 2005). Data from the FIA plots were compiled from both subplots (trees 5.0 in. dbh) and microplots (trees 1.0–4.9 in. dbh). Only plots with no visible disturbance since the last remeasurement (or in the last 5 years for plots that were initially measured) were used in this analysis. Compiled data spanned seven ecoregions as defined by Bailey (1980). Ecoregions examined were (codes in parentheses): Laurentian mixed forest (212), eastern broadleaf (oceanic [221] and continental [222]), western Allegheny plateau (223), outer coastal plain mixed forest (232), Adirondack-New England mixed forest (M212), and central Appalachian broadleaf forest (M221). The primary forest type groups examined were: aspen-birch (A-B), elm-ashcottonwood (E-A-C), maple-beech-birch (M-B-B), oak-hickory (O-H), oak-pine (O-P), spruce-fir (S-F), and white-red-jack pine (W-R-JP). The five most abundant species in the compiled data included balsam fir (Abies balsamea [L.] Mill.), eastern hemlock (Tsuga canadensis [L.] Carr), red spruce (Picea rubens Sarg.), and red (Acer rubrum L.) and sugar maple (Acer saccharum Marsh.; Table 1). Assessments of model performances was limited to all trees with dbh 5.0 in. because (1) it is the threshold for measurement trees on FIA phase II plots, and (2) it is the threshold for the large-tree dbh and ht equations within FVS-NE. Plot-level metrics such as BA were computed for the conditions of each plot-year combination. Individual species were examined and their size and growth measurements analyzed. As most remeasurements occurred on a 4–6-year interval (84% of all plots), increments for dbh and ht were standardized for each tree that survived a remeasurement period inc5 size2 size1 Y2 Y1 5 (5) where inc5 is 5-year diameter ( dbh5) or height ( ht5) increment, size1 is dbh or ht at initial measurement year Y1, and size2 is dbh or ht at remeasurement year Y2. 76 NORTH. J. APPL. FOR. 30(2) 2013 FVS-NE Benchmarking Predicting tree ht was accomplished after employing the appropriate ht-dbh model form suggested for the individual species and if the FIA plot was located in the Allegheny National Forest (Dixon and Keyser 2008, p. 10–12). Only heights that were directly measured and displayed positive growth were used in this analysis. Tree records that contained ocular estimates of ht or records where ht was predicted with a model were omitted. Predicted annual BA increment from Equation 3 was first added to the current tree’s BA, and then converted to dbh. This process occurred iteratively until the 5-year cycle was complete. For the increment equations, the FIA SI for the condition of the plot was used. Per their protocol, FIA estimates SI from a single tree or by averaging SI values for multiple site trees (Woudenberg et al. 2010). For plot conditions where SI was not measured, the FVS-NE default setting of 56 ft at a base age of 50 years for sugar maple was used. For all species on the FIA plot, SI was then converted to species SI using the appropriate equation for a species group (Dixon and Keyser 2008, p. 6–7). For predicting ht, htrel was computed for each tree in predicting ht; if a tree’s actual ht was recorded in the FIA tree record, it was used. If not, the tree’s estimated ht from (Equation 1 or 2) was used. For each of the ht, dbh5, and ht5 equations for the 20 species, root mean squared error (RMSE) and mean bias (MB) were computed