Data description

Data were made available by the second Italian NFI, namely National Inventory of Forests and Forest Carbon Pools, conducted in the years 2002-2006 and with reference year 2005 (acronym: INFC2005).

The inventory design is a three-phase sampling for stratification (Gasparini et al., 2010). In the first phase, the land cover/land use of approximately 301000 sample units is classified by photo-interpretation of aerial images. The second phase is mainly used to classify the forest type (21 forest categories and 77 forest sub-categories) and to collect data on qualitative attributes (site features, vegetation structure, management regime and others). The third phase is used to record quantitative data on trees, shrubs and deadwood. The second phase is carried out in the field, on a subsets of sampling units defined by land cover/land use and administrative region; also the third phase is carried out in the filed, on a subset of sample units further stratified by forest type. In INFC2005, the second phase sample consisted of approximately 30000 units, while the third phase sample of about 7000 units.

Relevant to this article, forest category, aspect (with a compass) and slope (with a clinometer) were recorded in the second phase (years 2004-2005) within a 25 m radius circular plot centred on the NFI sampling point. All trees with DBH ≥ 4.5 cm and ≥ 9.5 cm were callipered in two concentric circular plots with radius 4 m and 13 m, respectively, during the third phase (year 2006). Some of those were sampled for additional measurements, i.e. total tree height, crown base height (distance from ground surface to the lowest living branch) and tree coring. Sample trees were chosen following a protocol based on both random and representative criteria but discarding trees with visible faults. The five trees closer to the plot centre, the three larger ones in DBH and two of the less represented species (in mixed forests) or DBH class (in monospecific woods) were finally selected. As the trees in the last two categories may also be among the closer to the plot centre, the total number of sample trees ranged between five and ten per plot. One core per sample tree was taken at 1.30 m above ground level with a Pressler increment borer. The core was taken along the plot centre direction, to avoid systematic annual rings eccentricity due to site features, such as slope, prevailing winds and other. The width of the outermost 5 rings (excluding the current year ring) was measured as the five-year, inside bark, DBH increment (DI5). The DBH corresponding to five years before the survey year (DBH0) was calculated by subtracting DI5 from the measured DBH (DBHt) and the five-year periodic basal area increment (BAI) was then computed for each sample tree. Bark growth was considered null during the five-year interval; in European NFIs, the increment of bark is often omitted due to its difficult assessment (Gschwantner at al., 2016). The model developed in this study is based on the information recorded in 5162 NFI plots with complete data for all the variables tested as explanatory variables, and where no cuttings had occu-rred during the year before the survey; based on these se-lection criteria, the dataset resulted in 34638 sample trees.

 

Statistical analysis

The sample trees dataset was analysed and the exis-tence of outliers checked as recommended by Zuur et al. (2010). We first assessed singular observations graphically for each species through Cleveland dotplots and excluded less than 200 sample trees from the overall dataset that contained more than 35000 observations. We then discarded all the species with less than 200 observa-tions remaining. During the statistical analysis, fourteen additional singular observations were identified and ex-cluded. The remaining data were randomly divided into two subsets, one for model calibration (23091 sample trees) and the other for model evaluation (11547 sample trees). After the division, 4630 plots had either trees used for calibration and trees used for evaluation, 486 plots had only sample trees used for calibration, 46 plots had only trees for model evaluation. The model was constructed for 31 species that altogether constitute the 92% of the growing stock volume of the Italian forests; apart from Sorbus aria Crantz., they are all within the fortieth posi-tion in the list of the most important species in terms of tree volume (Gasparini & Tabacchi, 2011).

A set of potential predictors was built with variables related to plot location (geographical coordinates), site features (altitude, slope, aspect), stand attributes (basal area per hectare; dominant height, as the average height of the three largest trees in a plot), tree variables (DBH, total height, crown ratio) and with distance independent competition indices. The following competition indices were tested: basal area of trees larger than the subject tree (BALT); ratio of subject tree species basal area to stand basal area (BASPratio); ratio of subject tree basal area to stand basal area (BASTratio). Summary statistics on plot location and site features are reported in Table 1; summary statistics on trees and stand variables, as well as competi-tion indices, are shown in Table 2. Fig. S1 [suppl.] shows histograms for all the variables analysed. The stand attri-butes, also used for computing the distance independent indices, were those recorded at the time of measurement so assuming that stand and competition conditions remai-ned unchanged in the 5-year period. For some variables, also transformed values (log, squared or square root) were tested. The predictors were selected using OLS multiple regression analysis (stepwise forward procedures; Varian-ce Inflation Factor (VIF) = 5; F-to-enter/remove = 0.05); the analysis was undertaken using Systat 12.0 (Systat Sof-tware Inc., San Jose, CA, USA).

The observed individual trees are nested within plots, and hence do not satisfy the OLS basic assumption of in-dependence of observations. Failing to address this issue may lead to downward biases of the standard errors of the estimates, which in turn can result in wrong inferen-tial conclusions about the model parameters. Therefore, a two-level mixed-effects model with trees i nested within plots j has been estimated using R software (R Core Team, 2014). The number of trees observed per plot varies be-tween 1 and 10. Such a small average group size at the se-cond level is not an obstacle for estimating the plot effect because what matters is to have a sufficient sample size of plots (e.g. Snijders, 2005) and, in the calibration sub-set, the total number of sampled plots is 5116. The natural logarithm of BAI was selected as the dependent variable and the model formally described as

 

where lnBAI is the vector containing the values of the dependent variable, X is a matrix containing the tree level and plot level predictors, 𝒖 is the random effect vector at plot level and 𝜺 is the model residual vector at the tree level. According to the model specification expressed by Equation (1), the only coefficient allowed to vary randomly was the intercept. In other words, the average tree basal area increment can vary across the different plots. This modelling framework allows not only having correct inference, but also control over the non-measured unob-served plot-level local conditions. The fixed-effects com-ponent is a composite linear model (Wykoff, 1990) with tree, stand and site variables as predictors as shown in the following more explicit form:

where a₀ is the intercept, b_k, c_l, d_m, e_n f_o and g_p are the vec-tors of the regression coefficients for the k-tree variables, l-stand variables, m-competition variables, n-site varia-bles, o-plot location variables and p-dummies dummies (the species), respectively. Interactions among variables were also tested. The models resulting of different sets of predictors were compared according to their goodness-of-fit (adjusted R²) and performance assessment using the evaluation data. The variables that were finally retained for model calibration are shown in Tables 1 and 2. While the OLS methodology has helped selecting the predic-tors, the linear mixed model framework was required to consider the hierarchical structure of the data. When re-transforming the predicted lnBAIij back from natural log scale, the logarithmic bias correction factor suggested by Snowdon (1991) was used. Among the various alternative corrections proposed in the literature, this approach has proved to be the most efficient for this empirical cir-cumstance. Snowdon’s multiplicative correction factor, which represents an estimate of the proportional bias in logarithmic regressions, consists of the ratio between the sample mean of BAI_ij and the mean of the back-trans-formed values predicted from the model, say 𝐵AI𝑖j .

Model performance was assessed through cross-va-lidation on the evaluation data computing the following statistics: the mean error (ME), the mean absolute error (MAE), the root mean squared error (RMSE), the mean percent deviation (MPD) and the mean percent stan-dard error (MPSE) (Zeng, 2015). These were calculated on back-transformed and real scale (cm2) BAI values, as follows:

 

where 𝑒𝑖=𝑦𝑖−𝑦̂𝑖𝑦𝑖 are observed values, 𝑦̂𝑖 are va-lues estimated with the model.

The mean absolute error was also computed at plot level. For the 46 plots that had just evaluation sample trees, BAI predictions were obtained using the unconditional (population-level) intercept.

 

Table 1. Number of plots where the species were recorded and summary statistics of plot location (latitude and longitude of the sampling grid cell in which the INFC plot is located, WGS84) and site features (altitude, slope and aspect), by species and total

 

Table 2. Summary statistics of fitting data. Number of trees (n), five-year periodic basal area increment (BAI, cm²), initial DBH (DBH0, cm), crown ratio (CRATIO); dominant height (HDOM, m); basal area per hectare (BA, m² ha^-1); basal area of trees larger than the subject tree (BALT, m² ha^-1); ratio of subject tree species basal area to stand basal area (BASPratio); ratio of subject tree basal area to stand basal area (BASTratio)