## 2 Materials and Methods  
### Modeling of vegetation productivity  
During the last 20 years, several remote sensing based approaches have been developed to estimate vegetation productivity from global to regional scales [16]. The main concept for these approaches refer to experiments of [PERSON] [23] which showed that increase of plant biomass from well drained crops can be represented by the following equation:  
\[\text{GPP}=\text{FPAR}\times\text{LUE} \tag{1}\]where GPP is the gross primary production (gC m\({}^{-2}\) day\({}^{-1}\)), FPAR is the fraction of absorbed photosynthetically active radition (unitless) and LUE is an empirical light use efficiency factor (gC MJ\({}^{-1}\)). [PERSON] [24] and [PERSON] [25] have shown that FPAR can be derived from remote sensing data by using the normalized difference vegetation index (NDVI) which uses the reflectance (\(\rho\)) for the red (RED) and near-infrared (NIR) wavelength:  
\[NDVI=\frac{\rho_{NIR}-\rho_{RED}}{\rho_{NIR}+\rho_{RED}}\] (2a) and \[\frac{FPAR}{PAR}\,\alpha NDVI \tag{2b}\]  
where PAR is the incoming photosynthetically active radiation (MJ\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\)). Thus, spectral vegetation indices like the NDVI have a strong link to the fraction of photosynthetically active radiation that is absorbed (FPAR). When the FPAR is derived from NDVI and driven by the photosynthetically active radiation over a certain time step and converted by the LUE, the biomass production over this time step can be expressed as [26]:  
\[\text{GPP}=\text{NDVI}\times\text{PAR}\times\text{(LUE}\times\text{S}_{\text {Tmin}}\times\text{S}_{\text{VPD}}) \tag{3}\]  
where the scalars (unitless) for minimum temperature (\(\text{S}_{\text{Tmin}}\)) and water availability (\(\text{S}_{\text{VPD}}\)) are used to reduce the potential LUE to the actual efficiency [19]. LUE depends on the weather conditions which control the opening and closing of leaf stomata. Therefore, temperature and water stress were taken into account in the model.  
Both earth observation and _in situ_ sensor data sources were used for the parameterization of the variables of the regional scale GPP model (equation 3). Figure 1 gives an overview of the paths for the input datasets and the intermediate products for calculation of daily GPP for the surface area of the Netherlands. The NDVI as proxy for FPAR (equation 2b) was derived from daily remote sensing data provided by the medium-resolution sensor MODIS on the Terra platform. The MODIS surface reflectance product (MOD09) was used as input for calculation of NDVI. The required meteorological data for 16 stations in the Netherlands were taken from the KNMI SWE server hosted by the Royal Dutch Meteorological Institute (KNMI). Several studies have shown that maximum LUE (equation 3) varies for different vegetation types [27]. Therefore a look-up-table (LUT) was used to set biome-specific parameters related to the estimation of the actual LUE. By combining the biome-specific LUT with a remote sensing based land cover database, the spatial distribution of LUE related parameters could be established. Finally, the whole procedure was implemented as an automated processing chain which calculates a daily 250 m GPP product and makes the resulting maps available to the end-users through a dynamic web mapping service. In the following paragraphs, the different parts of the processing chain as presented in Figure 1 will be explained in more detail.