# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 3 Materials and Methods
### Images
#### 3.2.2 Daily GPP Images  
Daily GPP images at 1-km resolution were obtained for the period 2005-2012 following a procedure based on the optimization of [PERSON]'s approach, Equation (1), by adjusting the inputs (\(f_{\rm APAR}\), PAR and \(\varepsilon\)) for the study area. This optimized GPP product is driven by meteorological and satellite data (MODIS/TERRA and SEVIRI/MSG). Daily PAR was obtained as described above. \(f_{\rm APAR}\) was calculated by applying to MODIS data (at 1-km spatial resolution and 8-day temporal resolution) the algorithm that is actually used to derive the SEVIRI/MSG\(f_{\rm APAR}\) product, delivered by the LSA SAF network (EUMETSAT) ([[http://landsaf.meteo.pt](http://landsaf.meteo.pt)]([http://landsaf.meteo.pt](http://landsaf.meteo.pt))) at 3.1-km spatial resolution (sub-satellite point) and daily frequency over the geostationary MSG grid. This algorithm uses the Renormalized Difference Vegetation Index, RDVI [42]. Subsequently, the \(f_{\rm APAR}\) series were filtered and interpolated using an adapted (iteratively reweighted) local regression filter (LOESS) [43]. This procedure takes into account the data quality flags and has shown a very good performance; it is particularly resistant to outliers and offers an optimal reconstruction even in most extreme situations with long seasonal gaps. In order to assign a value of \(\varepsilon_{\rm max}\) to the different cover types, a hybrid land-cover map for Spain [44] was used (see below). Meteorological data were used to characterize the \(\varepsilon\) inter-annual variability due to water stress, which produces the most significant efficiency reduction in the study area. In particular, the water stress factor \(C_{\rm ws}\)[5], which accounts for limited photosynthetic activity in case of short-term water stress, was obtained from a local water budget based on actual and potential evapotranspiration.  
This daily GPP product was validated for 2008 and 2011 [4] by comparison with in situ GPP estimates from EC data (direct validation) and by inter-comparison with the MODIS GPP product (MOD17A3) [45], which will be also used in this work. The direct validation has evidenced an excellent agreement with correlations up to 0.98 in 2008 and 0.92 in 2011 in some sites. The inter-comparison has shown that the two GPP products are consistent temporally. However, a slightly decrease of the correlation has been observed in high precipitation areas (Northern Spain) and in semiarid areas(Southern Spain). Whereas the discrepancies on the northern region could be explained due to differences in the PAR (which seems to be better estimated in our approach), the discrepancies on the southern region could be related to the different way that the two GPP products account for the water stress. Our results evidence that the water stress factor \(C_{\text{ws}}\) outperforms the VPD (vapor pressure deficit) used in the official MODIS product. A further analysis on the explanatory power of the optimized GPP in terms of its inputs showed, as expected, that PAR and \(f_{\text{APAR}}\) are the most relevant inputs. Their relative importance depends on the location of the vegetation annual maximum so that the \(f_{\text{APAR}}\) plays a major role on the GPP estimation when that maximum is not reached during solar solstice. Nevertheless, \(\varepsilon\) has to be evaluated accurately in order to explain the GPP inter-annual variability associated with the water shortage typical of Mediterranean landscapes [4].