## 5 Discussion  
The modified DMP, the empirically identified model, is in general more efficient in describing the yield variability for maize and wheat yield across the study sites when different combinations of stress factors are included in the BPs regression analysis together with official statistics. Overall, the modified DMP correlates better with crop yield statistics than the CGLS-DMP, fAPAR and NDVI. On average, R\({}^{2}\) values increased from 0.49 for CGLS-DMP to 0.68 for the modified DMP, RMSE (t/ha) decreased from 0.84-0.61, RRMSE (%) reduced from 13.1-8.9, MBE (t/ha) decreased from 0.05-0.03 and \(E_{1}\) increased from 0.08-0.28. In general, the cumulative BPs with the highest correlations coincide with periods that include the reproductive stage, which is in agreement with previous studies [14; 99; 100; 101]. These periods are the most critical stages where any water stress may result in reduced crop yields [14]. In Canada, [PERSON] _et al._[14] reported RMSE values ranging from 104 kg/ha-697 kg/ha from arid zones to sub-humid zones when relating MODIS-NDVI and spring wheat yield. In China, [PERSON] _et al._[102] reported a RMSE value of 214 kg/ha when relating MODIS-NDVI and wheat yield. The values for maize in Figure 10 are similar to those recorded by [103] when relating MODIS WDRVI (Wide Dynamic Range Vegetation Index) and maize yield in the US. However, \(E_{1}\) values demonstrated that for maize the modified DMP model is performant only in Ain, which is also evident for the other BPs. In general, \(E_{1}\) values for the modified DMP are higher than the CGLS-DMP. [PERSON] & Indeje [104] reported RMSE values ranging from 0.962 t/ha-1.195 t/ha when predicting field-scale maize yields simulated by CERES-maize in Kenya. In agro-ecological zones of Belgium, [PERSON] [105] reported RMSE values fluctuating from 550 kg/ha-1430 kg/ha when relating the simulations of the B-CGMS crop growth model and winter wheat, and from 2150 kg/ha-7730 kg/ha for maize. The modified DMP includes plant specific parameterisations for C\({}_{3}\) and C\({}_{4}\) plants, introduces potential water limitation and incorporates the impact of different stress factors during the most sensitive cropping periods. According to the results, the inclusion of different stress factors can improve local empirical models. The results indicate that the stress factors play different roles in different climate regimes and for different C\({}_{3}\) and C\({}_{4}\) plants. For instance, the water stress index in CGLS-DMP proved to be a limiting factor, particularly in Morocco. AgroMetShell was used to generate AET estimations for each crop during different stages of the growth period of 1999-2012; this water balance model requires time for collecting the necessary data and computation. An alternative to AgroMetShell is LSA-SAF MSG AET [106] which has been available at the continental scale since 2009 and provides estimations closer to eddy covariance (EC) measurements [107]. Since the available years from MSG derived AET are too few for this study, we used AgroMetShell to compute AET. Another stress factor is the CO\({}_{2}\) fertilisation effect which is highly dependent on plant species, soil properties and soil nutrient status [108; 109; 110]. Study sites in Belgium were more responsive to this stress factor compared to the poor soils in Morocco. Irrigation can alleviate the effect of stress factors such as drought and temperature, while fertilisation alleviates plant nutrition stress [111]. However, the model approach used in this study did not take into account either irrigation or fertilisation. The autotrophic respiration fraction is overestimated in the CGLS-DMP model. We therefore proposed a new \(\varepsilon_{\text{AR}}\) which followed a similar trend as the findings in [98]. For example, densely vegetated areas in Europe have lower \(\varepsilon_{\text{AR}}\) values. However, the values in sparsely vegetated and high altitude areas are different than the values in [98].