## 3 Results
### Seasonal Dependence of the Relationship between NDVI and ANPP  
In order to use NDVI as a predictor of ANPP, it was first necessary to investigate the form and strength of the relationship between Landsat 8 single-date NDVI and in situ ANPP. The relationship for all habitats showed a strong seasonal dependence, with the strongest relationship in the spring and autumn, while in the summer and winter months, the correlation was very weak (Figure 3). When only grassland habitats were considered, the R\({}^{2}\) values were higher and there was less scatter in the relationship. A similar seasonal dependence was observed, with the strongest relationship occurring in the spring and the weakest in summer and winter (Figure 3). The weak relationship between NDVI and ln(ANPP) in the July images (Figure 3) is consistent with saturation. Saturation occurs when changes in the variable of interest (in this case ln(ANPP)) no longer result in obvious changes to the variable being observed (in this case single-date NDVI). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Broad Habitat** & **No. Samples** & _Mean ANPP (Dry Mass_ **g-m\({}^{-2}\).year\({}^{-1}\))** \\ \hline Broadleaved Mixed and Yew Woodland & 44 & \(438\pm 67\) \\ Coniferous Woodland & 43 & \(399\pm 50\) \\ Arabic and Horticulture & 14 & \(664\pm 230\) \\ Improved Grassland & 204 & \(561\pm 49\) \\ Neutral Grassland & 166 & \(542\pm 55\) \\ Acid Grassland & 88 & \(354\pm 80\) \\ Bracken & 15 & \(430\pm 55\) \\ Dwarf Shrub Heath & 25 & \(363\pm 39\) \\ Fen, Marsh, Swamp & 30 & \(412\pm 97\) \\ Bog & 51 & \(299\pm 45\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean plot-level ANPP values (mean \(\pm\) standard deviation) for each broad habitat type, from GMEP data for 2013 and 2014. Variation in the slope and the R\({}^{2}\) value for the relationship between NDVI and ANPP is shown in Figure 4. This analysis was done for both TOA NDVI and surface NDVI and the results showed very little difference in the strength and form of the relationship between NDVI and ANPP (Figure 4; Table 3). This suggests that using the Landsat 8 surface reflectance product did not have a significant effect on the uncertainty of the NDVI values. Hence, the rest of the analysis uses TOA values. Figure 3: Scatter plots of Landsat 8 NDVI versus ln(ANPP) for all habitat types for: a spring image (**top left**); and a summer image (**top right**); and for grassland habitats in: spring (**bottom left**); and summer (**bottom right**). The strong correlations observed for spring images were due to differences in the \"greening up\" times of the different plots, i.e., the more productive habitats greened up earlier in the year than less productive ones. This can be seen in Figure 5, which shows the time series of NDVI for different grassland habitats. Sites with higher productivity had higher NDVI values during the green-up period (March-May) than lower productivity sites. Similarly, in the autumn, the highly productive habitats continued to be photosynthetically active later into the season than the lower productivity grasslands. In the summer images all grasslands reached a similar level of \"greenness\" and, hence, there was little variation in NDVI across the productivity gradient resulting in low correlations between NDVI and ANPP. The bottom panel of Figure 5 shows the within-habitat and between-habitat variance for grasslands. It also shows the optimum time window for relating NDVI to vegetation productivity (grey shaded areas), which occurs when there is high between habitat and low within habitat variability. The saturation effect observed in the summer images in Figure 3 is apparent in Figure 4 as low gradient and low R\({}^{2}\) values, and in Figure 5 as a low between habitat variance. For the time period observed in this study, the optimum window occurred in the months March-May.