## 3 VIs as Proxies for Other Canopy Attributes  
### VIs and LAI  
Leaf Area Index (LAI) values are required in many SVAT models to quantify the interception of light by the canopy. The canopy is conceptualized as a series of absorbing layers of leaves, each of which attenuates a fraction of the incident radiation according to the Beer-Lambert Law [16]. In early crop studies, LAIs were used as proxies for canopy light absorption, because fPAR itself was difficult to measure [17,18]. In the 1980s, it became feasible to measure photosynthesis and transpiration in the field on individual leaves enclosed in leaf chambers [19]. SVAT models were developed to scale these leaf-level measurements to whole canopies and stands of plants [16], and these models were then adapted to remote sensing studies [20]. LAIs were needed to scale leaf-level measurements to complete canopies. VIs or their derivatives are now often used as proxies for LAI in remote-sensing-based SVAT and SEB models, because LAI cannot be measured directly by satellite sensors [21]. In some applications, VIs are combined with look-up tables of vegetation classes to improve the accuracy of LAI predictions [22]. Multiple images taken at different times and over different sensor view angles can be combined to estimate leaf angles and LAI by Bidirectional Reflectance Factor (BRDF) models, which provide structural information about a canopy [23]. However, BRDF models of a canopy can be indeterminate, in that different combinations of LAI and leaf angles can produce similar results [24] (see below). Satellite estimates of LAI can be accurate in some cases [25] but off by a factor of 2 compared to ground estimates in other cases [26]. Furthermore, LAI is difficult to measure on the ground, and optical and leaf-harvesting methods often produce different results [27,28]. LAI is a mathematical construct that does not have a direct relationship to fPAR or processes that depend on fPAR [11]. LAI is usually defined as the one-sided area of leaves in a canopy per unit ground area of canopy cover but non-flat leaves complicate the definition [29]. LAI is related to light interception by a canopy (R\({}_{i}\)) by:  
\[\mathrm{R}_{i}=\mathrm{R}_{s}(1\mathrm{-exp}^{\mathrm{-kLAI}}) \tag{4}\]  
where k is a factor that accounts for leaf angles and other factors that affect absorption of R\({}_{s}\) within a canopy [11]. Plants with relatively vertical leaves (ereectophiles) typically absorb less light per unit leaf area than plants with relatively horizontal leaves (planophiles). The coefficient k also depends on the arrangement of plants within a stand, because isolated plants receive light from all sides of their canopy whereas a dense stand of plants is only illuminated at the top of the canopy. The fraction of light absorbed by the canopy (fPAR) depends not only on R\({}_{i}\) but also on the spectral properties of the leaves. Some leaves have reflective surfaces to minimize heat gain while others absorb nearly all of the incident radiation between 400 and 700 nm. Hence, LAI can be well correlated with NDVI for single plant species grown under uniform conditions [30], but not for mixed canopies, which often occurs in remote sensing studies in which a single pixel can contain several landscape units. As mentioned, some remote sensing methods to estimate LAI do include estimates of average leaf angle and canopy geometry for particular vegetation types. However, the complexity of using LAI to quantify biophysical processes is illustrated by studies of riparian vegetation on Colorado River in the U.S. [31-36]. Four plant species dominate the riparian corridor, and grow in mixed stands that cannot be easily resolved into individual species even by high-resolution aerial photography and not at all by multiband satellite imagery. Figure 1 shows the leaf structure and light absorption properties of the four species.