## 3 VIs as Proxies for Other Canopy Attributes
### VIs and Roughness Lengths, Emissivity and Albedo  
Roughness length (z\({}_{0}\)) in meteorology is a measure of the roughness of the surface over which wind is blowing, and it is related to the height and shape of the surface objects that obstruct horizontal flow and convert it to turbulent flow [11]. It is defined as the height above the ground where the logarithmic wind profile goes to zero, and it is approximately 0.1 times the height of the surface elements (e.g., plants). It is a critical term in many SVAT and SEB models because flux rates of mass and energy in and out of canopies are dependent on turbulent flow, and these models require knowledge of z\({}_{0}\). Many remote-sensing SEB and SVAT models use VIs to estimate z\({}_{0}\), either with [e.g. 39,43] or without [e.g. 44] supplementary ground information. For example, the Two Source Time Integrated Model remote sensing model for surface energy fluxes in [39,43] combines NDVI with knowledge of plants heights (when available) to compute f\({}_{\rm c}\) and z\({}_{0}\). On the other hand, Surface Energy Balance Algorithm model for surface energy fluxes [44] sometimes assumes a fixed relationship between z\({}_{0}\) and LAI, which is estimated by NDVI.  
Unfortunately, the same reservations on using VIs to estimate LAI and f\({}_{\rm c}\) apply to roughness lengths. While vegetated surfaces have greater roughness lengths than bare soil, VIs do not adequately capture differences in canopy heights among different vegetation types in mixed scenes [45]. For example, a field of alfalfa 0.5 m tall (e.g., in Figure 3) will have a roughness length of approximately 0.05 m, whereas a saltcedar stand 5 m tall has a roughness length of 0.5 m, 10 times greater; yet, Figure 3 shows that a typical alfalfa field has 50% higher NDVI than saltcedar, which could lead to a large error in estimating turbulent flow by NDVI over a mixed riparian scene containing both agricultural fields and natural vegetation. As mentioned, corrections can be made by supplying plant height data into SEB models but given the complex canopy structure of mixed landscapes, the estimates are approximations.  
Emissivity (\(\varepsilon\)) is the ratio of energy radiated by an object to that radiated by a black body at the same temperature, in which \(\varepsilon=1\)for a perfect black body radiator [11]. This relationship is used to measure land surface temperature by satellite sensors in the thermal infrared bands; however, plant canopies and soils are not perfect black body objects (\(\varepsilon<1.0\)), and, therefore, estimates of \(\varepsilon\) are needed to correct satellite-derived land surface temperatures in SEB models that estimate ET by the difference between air temperature and land surface temperature. Albedo is a measure of the fraction of incident radiation diffusely reflected from an object [11], and it is required to calculate net radiation absorbed by the land surface and for other model parameters. Bare soil and vegetation have distinctly different values for emissivity and albedo. Hence, remote sensing models often use transformations of NDVI or other VIs to estimate these parameters. For example, the SEBAL model [44] uses different transformation of NDVI for fc, albedo, roughness length and \(\varepsilon\). Emissivity and albedo are closely correlated with VIs for the vegetated fraction of the landscape, but soils can differ more substantially in the relationship between NDVI, albedo and \(\varepsilon\)[46-48]. Models that use VIs to estimate these parameters generally first partition the landscape into bare soil and vegetation using VIs, then assign values for emissivity and albedo to each class, e.g. [44]; hence, they are subject to the same types of errors inherent in using VIs to estimate f\({}_{\rm c}\).