### Leaf Area Index (LAI)
Crucially however, values of \(\widehat{LAI}\) are not the same as \(\langle LAI\rangle\), which in turn are not the same as the LAI that would be measured on the ground (unless measured over some large, discrete canopy volume). That is, the resulting \(\widehat{LAI}\) is a model-dependent (effective) parameter that does not have a direct (physically-defined, measurable) meaning, but is determined via the inversion scheme such that observed fluxes can be reproduced by the RT scheme. The benefit is that this allows solution of the 1D RT problem by representing domain-averaged quantities that are forced to satisfy the constraints associated with a 1D representation of what is an inherently 3D system [20; 23]. We emphasize this point about effective parameters to highlight the fact that care must be taken in comparing and interpreting LAI values derived from different sources: key assumptions should always be made explicit in a particular model or application, so differences can be quantified and/or accounted for (e.g., via cross-calibration/transformation of LAI values). This is particularly important when the resulting parameters are intended for wide use, and users may have little interest in the subtleties of how the parameters were estimated. In this case, it is crucial to explain how and why differences arise between indirect estimates from different sources, despite apparently being measurements of the same, seemingly well-defined physical quantity. Here, LAI is derived from a two-stream inversion package (the JRC-TIP, outlined below) based on a 1D-equivalent LAI, for solving RT in a 3D medium. This is consistent with the method used to produce the albedo from which LAI is subsequently derived. It is not consistent with LAI derived using a more complex 3D RT scheme that allows some form of horizontal clumping (e.g., MODIS LAI), and will typically be lower than such a value. Neither of these EO-derived values is consistent with values measured in the field using indirect, optical methods at small scale. None of these indirect estimates are directly comparable with the real LAI that would be measured destructively. There is of course (fortunately) a high degree of correlation between these values. However, they still have to be locally calibrated, or generalised across biomes and scales (_i.e._, for a particular scale/type of clumping). The second issue, that of scale, must also be considered when comparing LAI estimates, and is related to clumping. The authors of [24] discuss this issue, where the same total amount of leaf material (LAI) may be present in each case, but clearly the arrangement of the material (even in simple cases) will determine the radiometric response [23]. The authors of [24] also highlight how the scale of observation alters the information available from a measurement at aggregation from 0.1 m (-leaf scale) to 30 m (-stand scale). Much, if not all, of the information on the spatial arrangement of the canopy is lost in moving from the leaf to the stand scale, even down to the number of trees in the scene, yet the underlying \"real\" LAI is the same. Models which allow us to relate radiometric variables measured at one scale, to ecological (structural/radiometric) properties at a (usually) finer scale do not in general scale linearly across space, and nor should we expect them to [14; 25]. A different approach has been to consider the EO parameter scaling issue from an information content perspective [26], as a possible alternative to simple aggregation.