## 4 Results
### Linear Regression Analysis  
Figure 8 shows the highest R\({}^{2}\) values for the relationship between the official yield statistics and each regional cumulative modified DMP computed with different stress factor combinations. In Belgium common wheat has the highest correlation with DMP, without any stress factors in the Polders and with DMP including CO\({}_{2}\) fertilisation effect in the Sandy Loam Region. In France common wheat has the highest correlation with DMP, with water stress in Eure-et-Loir and DMP with CO\({}_{2}\) fertilisation effect and temperature stress in Somme. In Morocco common wheat has the highest correlation with DMP, with all three stress factors in both El Jadida and El Kelaa des Sraghna. In Belgium silage maize has the highest correlation with DMP, with temperature and water stress factors in both the Loam and Liege regions. In France silage maize has the highest correlation with DMP, with all three stress factors in Ain and Haut-Rhin. The highest correlations for modified DMP per region and crop type (Figure 8) are compared with CGLS-DMP, fAPAR and NDVI in Figure 9. In each study region the modified DMP has a higher correlation than the CGLS-DMP, and in general performs better than fAPAR or NDVI. The correlations are significant for all study sites and BPs, except for fAPAR in the Sandy Loam Region (BE), NDVI in Somme (FR) and CGLS-DMP in Liege Region (BE). The correlations between observed yield and calibrated BPs were significant at the 0.01 level for modified DMP in all regions, but displayed a mixed picture in the case of CGLS-DMP, fAPAR and NDVI. Figure 7: Average \(\varepsilon_{\mathrm{AR}}\) calculated with CGLS-DMP (**a**); modified DMP (this study) (**b**) for the period 1999–2012; and MODIS NPP/GPP ratio from 2000–2013 (**c**) with the study sites extent. Figure 8: R\({}^{2}\) for a linear regression between official yield statistics and regional cumulative modified DMP computed with different stress factors or combinations. CO\({}_{2}\): with CO\({}_{2}\) fertilisation effect; H\({}_{2}\)O: with water stress factor; Temp: with temperature stress factor and combinations of these stress factors. The cumulative periods of modified DMP for each study region are presented in dekads. The best combination of BPs from the regression analysis were calibrated with a leave-one-out cross validation. The RMSE (t/ha), the RRMSE (%), MBE (t/ha) and \(E_{1}\) values calculated in the validation analysis are presented in Figure 10. The modified DMP has lower RMSE values than the other BPs which range from 0.25 t/ha-0.44 t/ha for common wheat and 0.68 t/ha-1.41 t/ha for sil  
Figure 9: Cumulative period of BPs (modified DMP, CGLS-DMP, fAPAR, NDVI), \(p\)-value (calculated by [PERSON]’s correlation for \(r^{2}\)) and coefficient of determination (R\({}^{2}\) for the linear model) for wheat and maize per region. maize. In general the RRMSE values are lowest for the modified DMP. The RMSE values followed a similar trend as RRMSE. The MBE values are between \(-0.05\) t/ha-0.05 t/ha except for the Liege Region (BE), Ain (FR) and Haut Rhin (FR) for all BPs. Overall, higher \(E_{1}\) values were recorded for modified DMP compared to the other BPs. In addition, \(E_{1}\) values show that the model is not performant for maize in Belgium and France (except Ain). Figure 11 presents the temporal trends of the actual crop yield and predicted yield of BPs calibrated by the leave-one-out cross validation throughout the study period from 1999-2012. In general, the  
Figure 10: RMSE (t/ha), RRMSE (%), MBE (t/ha) and \(E_{1}\) based on the correlation between the calibrated BP (modified DMP, CGLS-DMP, fAPAR, NDVI) and yield statistics per region for wheat and maize using a leave-one-out cross validation. modified DMP followed a similar trend as the observed yield although there are some discrepancies for maize in the Loam Region (BE), Liege Region (BE) and Haut Rhin (FR).