## 1 Introduction
At the site-scale an empirical relationship is created, typically between a vegetation index and field estimates of NPP or gross primary productivity (GPP) [14; 15], such relationships are generally image-specific, site-specific and specific to a particular vegetation type, which limits their application over wide areas. Typically, the key constraint is the limited availability of field data to generate the empirical relationships against, whereas at the global scale NPP is estimated using a combination of satellite data, meteorological data and modelling [13]. Country-scale NPP products from MODIS have also been explored for China [16] and recently methods have been developed to estimate Net Ecosystem Exchange from Landsat data via an upscaling approach that utilises flux tower observations [17]; however, this requires flux tower data for calibration. Prior to this, AVHRR data were used to produce ANPP estimates for large areas of grassland in the US [18]. However, for many applications the spatial resolution of the MODIS-, or earlier AVHRR-based products, is too coarse, especially for countries that are highly heterogeneous, such as the UK [19]. A widely-used indicator for deriving vegetation productivity from remotely sensed imagery is the Normalised Difference Vegetation Index (NDVI). Empirical models relating annually-integrated NDVI and ANPP have been shown to be relatively accurate in most environments [20]. NDVI is sensitive to the fraction of Absorbed Photosynthetically Active Radiation (fAPAR) and the exact relationship between NDVI and ANPP is dependent on several factors including the vegetation type and the climatological conditions. For this reason, physically-based, light use efficiency (LUE) models are commonly used for mapping vegetation productivity at a global scale, to deal with regional differences and a lack of sufficient in situ data for model calibration [21; 22]. Using this approach, Gross Primary Production (GPP) is estimated as:  
\[\text{GPP}=\varepsilon\times\text{fAPAR}\times\text{PAR},\]  
where \(\varepsilon\) is the efficiency of the conversion of absorbed PAR into dry biomass and fAPAR is estimated from NDVI imagery. NPP is then estimated as GPP minus autotrophic respiration losses. This approach requires accurate knowledge of \(\varepsilon\), which varies in response to environmental stressors such as drought and temperature extremes. Estimation of these variables from available coarse-scale meteorological data can introduce significant errors [23]. Hence, in cases where in situ ANPP data are available, simple empirical models relating vegetation indices and ANPP can be more robust than the LUE approach [15], particularly when mapping areas where climatic gradients are minimal. Typically, annually-integrated NDVI values are used for estimating vegetation productivity from sensors with high temporal sampling but low spatial resolution [20; 21]. To generate a product capable of mapping within-field variability in ANPP, high spatial resolution data are required and these typically have low revisit frequencies, which are further reduced by cloud cover. Estimating ANPP from annually-integrated NDVI precludes the use of Landsat-like sensors (with high spatial resolution and low revisit frequency), particularly in cloudy regions, because it is impossible to get cloud free imagery from enough time points in the year to produce a reliable estimate of integrated NDVI. Hence, a novel approach was developed in this study by using single-date NDVI imagery (rather than annually-integrated values) to overcome this challenge. We derive empirical models relating single-date NDVI to ANPP to demonstrate the feasibility of this approach. We also present results showing how the strength of this relationship varies with season and illustrating why the best relationships occurred during a narrow time window coinciding with the vegetation green up period, identifying for the first time, as far as the authors can ascertain, the optimum time period for predicting ANPP from single-date NDVI.