### Leaf Area Index (LAI)  
LAI, in an ecological sense, is (typically) defined as the total canopy area per unit ground area (m\({}^{2}\). m\({}^{-2}\)) [11] and ranges from 0 (bare ground) to over 10 (dense forest). LAI determines the interception of solar energy (and thus the fAPAR) for photosynthesis, as well as the available area for gas and water exchange between plant and atmosphere. LAI in a remote sensing sense, in contrast, is (typically) defined as one-sided leaf area per unit ground area (m\({}^{2}\). m\({}^{-2}\)) _i.e._, 0.5 of the total [1; 12], primarily from the point of view of light interception. Projected leaf area is often the more general requirement for radiation interception, which is dependent on leaf angle distribution [13; 14]. Here, LAI is defined in the latter sense as half the total canopy area per unit ground area (m\({}^{2}\). m\({}^{-2}\)). Caveats: LAI  
Despite the (seemingly) relatively simple and physically-meaningful definition of LAI given above, two key issues must be considered in practice when using LAI derived from EO data. The first is to do with the problem of relating LAI inferred from satellite data to other indirect estimates of LAI [15]; the second issue is to do with the scale at which observations are made. LAI can only be measured directly via destructive harvest and scanning/weighing, which is impractical over anything other than very small areas (a few m\({}^{2}\)). Indirect methods are thus widely used to infer LAI, typically via upward-looking hemispherical photographs (hemiphotos) or bespoke instruments that compare light levels above and below the canopy (e.g., LI-COR LAI 2200c Plant Canopy Analyser [16]; the Delta-T SunScan Canopy Analysis System [17] and so on). In these cases, LAI is inferred based on assumptions of the canopy absorption properties (e.g., all canopy elements are black) and architecture (e.g., assuming the canopy is horizontally homogeneous, and/or leaf angle distribution is uniform or spherical) [18; 19]. LAI (and fAPAR) estimates from EO data are typically made by inverting RT models against estimates of surface fluxes or albedos (e.g., visible and NIR albedo here), resulting in model parameter estimates of (inter alia) LAI and fAPAR. Note that EO-derived albedo values are not direct observations per se, but are model-derived values produced from angular samples (observations) of surface reflectance, interpolated over viewing and illumination angles and time via RT model schemes to provide hemispherical integral fluxes (GlobAlbedo Algorithm Theoretical Basis Document: ATBD, 2013). Ideally, assumptions underlying the RT schemes used for both generating albedo (or surface reflectance) and for LAI retrieval should be the same; however this is rarely the case in practice. To achieve consistency of this sort [20] suggest adopting an \"effective\" LAI (\(\widehat{LAI}\)) such that \(\widehat{LAI}=\langle LAI\rangle\,\zeta\) where \(\langle LAI\rangle\) is the domain averaged LAI, and \(\zeta\) is a structural term that encapsulates the fact that real canopies are not turbid media but are clumped at multiple scales (from \(10^{-2}\) m within shoots, to \(10^{2}\) m at the stand level). Clumping acts to reduce \(\widehat{LAI}\) compared to the true value, \(\langle LAI\rangle_{\
u}\) as the degree of clumping increases. In contrast, very regular canopies (crops for example) will tend to have \(\widehat{LAI}>\langle LAI\rangle\)[19; 21]. The adoption of \(\widehat{LAI}\) permits a solution to the 1D limiting case of RT in a 3D canopy that is consistent with the assumptions made in many surface flux retrievals, as well as in large-scale Earth System Models (ESMs) (e.g., see [1; 22]). Using \(\widehat{LAI}\) also allows the use of a relatively simple two-stream 1D RT scheme that can be applied to large (global) datasets. In this case, \(\widehat{LAI}\) is then the equivalent of optical thickness.