Mapping the diversity of forest attributes: a design-based approach

Abstract

Forest attributes such as volume or basal area are concentrated at tree locations and are absent elsewhere. It is, therefore, more meaningful to consider the amount of forest attributes at a prefixed spatial grain, within regular plots of prefixed size centered at the points of the study area. In this way, the diversity of attributes within plots also can be considered and quantified by suitable indexes, giving rise to a diversity surface defined on the continuum of points constituting the area. We analyze the estimation of diversity surfaces when a sample of plots is selected by a probabilistic sampling scheme and diversity within nonsampled plots is estimated using an inverse distance weighting interpolator. We discuss the design-based asymptotic properties of the resulting maps when the survey area remains fixed and the number of sampled points increases. Because diversity surfaces share suitable mathematical properties, if the schemes adopted to select sample points ensure an even coverage of the study areas avoiding large portions of non-sampled zones, it can be proven that the estimated maps approach the true maps.

Functional estimation of diversity profiles

“…and riparian forests of common alder (Alnus glutinosa L.) are present. Renaturalization processes are ongoing at various degrees across the watershed, leading to different structural heterogeneities (i.e., tree size diversities) of the various stands (Fattorini et al, 2019). Forest attributes, such as volume and basal area, are concentrated at tree locations; thus, their diversity within the study area can be considered and quantified by suitable indexes (Corona, 2016;Corona et al, 2017).…”

“…In the Bonis forest watershed, stem diameters have been collected in 2016 from the population of trees in 36 circular plots of radius 20 m, randomly placed on the continuum of the study area by uniform random sampling (see Figure 5). For each plot, the basal area of each tree has been recorded and grouped into K = 5 diameter classes according to the following partition: trees with stem diameter at breast height less than 17.5 cm; from 17.5 to 35 cm; from 35 to 52.5 cm; from 52.5 to 70 cm; and greater than 70 cm (Fattorini et al, 2019). Thus, the dataset consists of the abundances of five diameter classes of trees at 36 replicated plots.…”

Increasing Precision for French Forest Inventory Estimates using the k-NN Technique with Optical and Photogrammetric Data and Model-Assisted Estimators

“…The forest contours were used to construct a forest mask. The mask was further intersected with the 30 m grid, and only the grid cells completely in the forest mask were considered for the analysis [10]. The FT map attributes were summarized for each grid cell and aggregated into three classes corresponding to pure broadleaved, pure conifers and mixed stands.…”

“…The objective of MSNFI methods is to infer population parameters [6,9]. Design-based estimators [10] are well adapted to NFI data because they rely on probability sampling designs as the basis for inference and are nearly design-unbiased [11][12][13][14]. A model-based approach is an alternative which assumes that the population under study is a random realization of a "super-population", but is subject to bias [15] and requires the use of a correctly specified model form [16,17].…”

Design‐based mapping of tree attributes by 3P sampling

“…On the basis of this assumption, the authors have adopted the inverse distance weighting (IDW) interpolator in which sample units are weighted on the basis of their vicinity to the unit to be interpolated rather than on the basis of their inclusion probabilities, as customary in most design‐based approaches. Subsequently, Fattorini, Marcheselli, & Pratelli (2018a) have adopted IDW for mapping finite population of spatial units, when the survey variable is the amount of an attribute within units, and continuous populations (Fattorini, Marcheselli, Pisani, & Pratelli, 2018b; Fattorini et al., 2019a) when, at least in principle, the survey variable is defined at each point of the continuum representing the area of interest. The IDW has been finally applied for mapping finite populations of marked units (Fattorini, Marcheselli, Pisani, & Pratelli, 2019b).…”