## 5 Discussion
These areas are beyond the scope of this study and should be disregarded. The modified DMP could explain more variation in irradiation conditions, short term environmental stresses and respiration costs compared to NDVI and fAPAR. Thus, it could be a more robust choice, although it has several modelling assumptions. Similar to the findings in [112; 113; 114], [PERSON] _et al._[115] found that NDVI underestimated productivity due to backscatter effects in the lower values and saturation in the higher values. Additionally, the frequency and intensity of extreme weather events could have significant impacts on biomass production and crop yields [116; 117]. For example, floods and droughts can harm crops, reduce yields and increase crop prices. The amplitude of extreme events can be much larger at regional scales than at global scales [118]. For example, the 2003 heat wave affected the local natural environment, society and economy in many parts of Europe. [PERSON] _et al._[67] reported that 2003 maize yield loss in France equalled 1.5 t/ha compared to the 2000-2006 average. This trend can also be seen in the study sites in France within BPs used in this study. The modified DMP is therefore better suited than CGLS-DMP to the extreme event in 2003 (e.g., for Ain, the predicted yield from the BPs calibrated for maize yields are 10 t/ha for modified DMP, 14 t/ha for CGLS-DMP, 10 t/ha for fAPAR and 9 t/ha for NDVI, while the actual yield is 8 t/ha). Although the proposed method shows promising results in crop yield forecasting for the study sites, there are a number of limitations. Cereal yields depend on the harvest index which is the fraction of the total aboveground biomass allocated to the grains [13]. Different yields for the same amount of aboveground biomass can be obtained because the harvest index varies with crop varieties, management practices, and water and nitrogen availability [13], all of which play at the field scale. For this reason, the harvest index was not in the scope of our regional study. A limitation to predicting yield is the amplitude of the inter-annual crop yield variability. [PERSON] _et al._[6] showed that the regression analysis performs better when the inter-annual variability is high, which is confirmed in this study: higher performance was seen in Morocco where the inter-annual variability is higher. In addition, many weeds, pests and fungi flourish under warmer temperatures, wetter climates and increased CO\({}_{2}\) levels [116], and affect yields. We used products derived from SPOT VEGETATION, a sensor with a coarse 1 km spatial resolution, and we applied a mask to these products using the GlobCover 2009 crop map in order to minimize the influence of non-agricultural land cover types. DMP is subsequently calculated per pixel located in cropland assuming wheat (C\({}_{3}\)) or maize (C\({}_{4}\)) cover. The two resulting maps could be combined using weights corresponding to the proportion of each crop, provided that the share per crop is known in a particular year. However, this proportion is not available before the end of the season, and it is beyond the scope of this paper to explore the feasibility of such extension. Furthermore, crop-specific maps could minimise the effects of mixed signals through unmixing techniques or by selecting subsamples of purer pixels [119], thus improving the yield estimations [120]. The impact of stress is important for estimating dry matter productivity of cereal crops. The research could be extended to include other agricultural regions and arable crops. The incorporation of new generation remote sensing products with higher spatio-temporal resolutions into the DMP model is likely to improve yield estimates.