## 3 Results
### Calculation of Green Vegetation Fraction  
The analyses of NDVI datasets and interannual phenology trends in Sections 3.1 and 3.2 show that there are significant differences in mean value and trend between the various datasets. While the easiest way would be to interpret these differences as the uncertainties of these datasets, a more interesting question is: Can we find a way to reduce these uncertainties? Here we address this issue using the Green Vegetation Fraction (_GVF_) algorithm from [41,42] that is dependent on land cover type and is independent of spatial resolution of the data:  
\[GVF=\frac{N-N_{s}}{N_{c,v}-N_{s}} \tag{1}\]  
where \(N\) is the NDVI for each pixel and time period, \(N_{s}\) is the bare ground NDVI computed annually and \(N_{c,v}\) is the NDVI that corresponds to 100% GVF calculated annually for each land cover. The MODIS 0.5 km Land Cover (MCD12Q1) from 2004 was upscaled to the 0.125 \({}^{\circ}\) grid and the most frequent type of all MODIS pixels within each coarse grid cell was used as the land cover type. First, the maximum annual NDVI (\(N_{p,max}\)) is calculated for each pixel then the histograms of \(N_{p,max}\) for all pixels of each land cover are calculated and the 75 th percentile of most types and 90 th percentile of closed shrubland and urban classes are used as the \(N_{c,v}\) for a given land cover class. The \(N_{c,v}\) of open shrubland and barren is prescribed the \(N_{c,v}\) of the closed shrubland class because these classes may not have any pixels that have reached full capacity or 100% GVF. The value of Nc,v, particularly for forest classes, was shown to be insensitive to percentile used in [PERSON] _et al._[41]. \(N_{s}\) is calculated as the 5 th percentile of \(N_{p,max}\) for the Barren class. Finally, GVF is constrained within 0 and 1. Physically, NDVI values greater than \(N_{c,v}\) should represent vegetation with higher leaf area index (LAI) or healthier vegetation and not a higher areal coverage of vegetation. More details on the GVF computation are provided in [41,42]. There are three assumptions underlying this formulation of GVF. First, this method assumes that all seasonal changes in NDVI are due to changes in GVF alone or in the concurrent changes of GVF and LAI. Changes in NDVI are not only due to changes in the fraction of green vegetation, but also LAI, vegetation health among other factors. Therefore GVF should be understood as a combination of factors that lead to higher overall vegetation greenness. The second assumption is that the bare soil in each pixel can be represented by one value \(N_{s}\) and the 100% GVF NDVI of each pixel can be represented by one value \(N_{c,v}\) based on a pixel's dominant land cover. In reality, the area of a pixel that is not green vegetation can be represented by soil of different textures and soil moistures, leaf litter, and dormant vegetation. The green vegetation for a given land cover would ideally be represented by the same combination of vegetation for each pixel but in reality even within the same class the composition of vegetation would vary, not to mention that pixels often are composed of other non-dominant vegetation classes. This assumption would be most valid in the interior of a land cover class. The final assumption is that the interannual variations of \(N_{c,v}\) and \(N_{s}\) are due to spurious changes in NDVI that result from errors contained within the NDVI datasets and that they are not due to true changes in the surface NDVI. In order to check for the temporal consistency in \(N_{p,max}\) and validate the utility of calculating \(N_{c,v}\) and \(N_{s}\) separately each year, we analyzed the time-series of \(N_{c,v}\) for each land cover category as well as \(N_{s}\) for each of the long-term NDVI products from 1982-2008 (not shown). For the VIP product, jumps in \(N_{s}\) as well as \(N_{c,v}\) are evident and occur at the year 2000 when this product switches to using MODIS as the main source of information for NDVI.