## 3 Functional Diversity and Ecological Function
Metrics based on multiple functional traits use distance-based measures, geometric properties of the trait space, or the variability observed in trait probability densities (TPD) to estimate the various components of functional diversity [128; 129; 130; 152; 154; 155; 156]. Studies aimed at examining the potential of remotely sensed data to scale up functional diversity vary in terms of sources of field-based leaf and plant trait data, sources of remotely sensed data, sources of spectral features, derived spectral features, scaling methods, and metrics used (Figure 2b, Stage 5; Files S1 and S2: Table S2). One set of studies used pixel- and tree-level band indices and point-cloud data to derive variables representative of leaf physiological and tree morphological traits from which to calculate functional diversity metrics using the geometric properties of the trait space [15; 40; 47; 114; 157] or the variability of trait probability densities [158; 159]. A second set of studies used plot-level CWMs of field-based leaf and tree traits in combination with spectral features from multispectral, spaceborne sensors to estimate functional diversity metrics based on the geometric properties of the trait space [46]. These metrics provide a measure of the range of trait values in a community based on the area of a convex hull encompassing pixels in a neighborhood (functional richness; FRic), the variability of trait values based on the mean distance of the pixels to the trait space centroid (functional dispersion; FDis), the variability of trait values based on the mean distance to the convex hull centroid (functional divergence; FDiv), and the distribution of pixels in trait space (functional evenness; FEve). Further work based on these metrics has explored their sensitivity to changes in sources of trait data [157], spatial (changes in neighborhood size) and spectral (convolving airborne hyperspectral data) resolution [15; 40; 114], as well as their relationship with ecosystem-level processes [47] and spectral diversity [157]. The metrics just described provide a quantitative measure of functional diversity at local (within or alpha diversity) scales. Yet differences between communities, i.e., beta diversity, can help understand the role of environmental factors in structuring diversity at landscape and regional scales (Figure 2b, Stage 5; Files S1 and S2: Table S2). Using three structural variables derived from spaceborne and airborne LiDAR, [PERSON] et al. [159] used a TPD approach to investigate possible effects of data sources on estimates of alpha and beta functional diversity. Using airborne hyperspectral data and a subset of principal components, [PERSON] et al. [160] applied methods described in [PERSON] and [PERSON] [151] to estimate beta diversity and evaluate the extent to which image resolution, window size, and extent influenced this metric. Finally, [PERSON] et al. [66] and [PERSON] and collaborators [65; 161] developed different approaches to partition the total spectral diversity of a region (gamma; \(\gamma\)SD) into additive alpha (within community spectral diversity; \(\alpha\)SD) and beta (between community spectral diversity; \(\beta\)SD) components. The first author used band indices from a temporal series of Sentinel 2 and the Rao Q metric to calculate \(\gamma\)SD, whereas the second used a subset of principal components and the total variance to calculate SDy (Figure 2b, Stage 5; Files S1 and S2: Table S2). In sum, the development of functional and spectral diversity metrics from remotely sensed hyperspectral remains an active area of research.