# Annual Gross Primary Production from Vegetation Indices: A Theoretically Sound Approach
## 5 Discussion  
The proposed semi-empirical model to estimate GPP does not require actual meteorological data. It exclusively relies on a vegetation index product commonly available--the MOD13A2 in this case--and on a representative PAR. The underlying assumption of the model is that VI is the main factor determining the GPP inter-annual variations. The use of a representative PAR in our model marks a qualitative distinction from those approaches based on a linear relationship between an annual cumulative or mean VI and the annual GPP [2; 48; 49]. The rationale of our model is also different from the greenness-radiation models that consider GPP equal to the product of a VI and PAR [50]. Certainly, a key factor accounting for the annual GPP is the annual cumulative or mean VI, but our model calculates a PAR-weighted annual mean VI. The use of the representative daily PAR as a weighting factor is important because VI gives the fraction of PAR absorbed but not the total absolute PAR absorbed. The same VI can produce different GPP depending on the incident radiation, and the latter shows a marked seasonal variability that affects differently the different vegetation types, depending on their phenology. The calibration/validation process, however, does require a reference GPP product and, obviously, the higher the quality of the reference GPP product, the better the performance of the semi-empirical model. In this study, a daily GPP product optimized for the study area has been used to calculate the reference annual GPP instead of using the annual GPP from MODIS (MOD17A3). Although both products show a temporal consistency [4], our product benefits from: an accurate PAR product, a land-cover map more adapted to the study area and a water stress factor that better accounts for the photosynthesis reduction during the summer water shortage. Nevertheless, the MOD17A3 product can be also used as reference to calibrate the model (and could even be recommended for a global study). In order to further test the methodology robustness, the calibration/validation process has been repeated using MOD17A3 as reference for both VIs and considering both constant regression coefficients and coefficients depending on the vegetation type (Table 6). Table 6 confirms that the MOD17A3 product can be also used as reference to calibrate the model, which significantly extends the range of applicability of the methodology. The additional requisite is the availability of a representative PAR image that could be estimated at the cost of a coarser spatial resolution from databases such as GMAO (Global Modeling Assimilation Office) or ECMWF (European Center for Medium-Range Weather Forecast). Since the results have shown a good agreement with reference data, the proposed methodology can be used to generate long series of annual GPP to detect regional changes without requiring actual PAR,\(f_{\text{APAR}}\) and \(\varepsilon\). As commented in the literature [27], the absorbed photosynthetic radiation and \(\varepsilon\) are somehow linked; in this work, the link is established by means of the vegetation indices NDVI