## 4 Results
### Yield Forecasting Performance  
#### 4.2.1 Nuts-2 Level  
The best performance of end-of-season crop yield predictions is revealed for winter wheat (RRMSE = 8.15%), while predictions for maize and winter rapeseed are less accurate (RRMSE = 13%) (Table 3). For all three crops, the overall relative bias (RMBE) is below 1%. Yet, for individual NUTS-2 regions, these errors can be greater (Figure 7).  
Figure 8 reveals that forecasting quality metrics differ across years. Most evidently, the predictions tended to overestimate crop yields: for all three crops in 2006, for winter rapeseed in 2003, and for maize in 2015. [PERSON] and [PERSON] (2021) [41] reported these years as dry according to the Standardized Precipitation Index (SPI). In 2003, moderately dry conditions in May may have affected rapeseed development. In 2006, the very dry (SPI \(<-1.5\)) period in June-July impacted all crops. Finally, in 2015, drought lasted until the end of season limiting maize yields. Figures 9-11 reveal detailed year-by-year performance of the crop yield forecasts for all three crops. High performance of winter wheat yield forecasts for Mazowieckie, Swietokrzyskie, Podkarpackie, and Podlaskie NUTS-2 units can be related to low annual variability of yields ranging from 30 to 40 dt/ha (Figure 9) that can be well approximated by a monotonic trend.  
Figure 6: Monthly differences (May) for LAU units between cross-calibration error (RMSE) and the natural variability of the MODIS-derived predictors expressed as double standard deviation. The negative differences (blue colours) indicate that the calibration error is lower than the natural variability.  
The quality of the prediction models increases along the season when more predictors become available for the XGBoost model (after every 150 \({}^{\circ}\)C GDD step). According to correlation coefficient, for winter wheat and winter rapeseed, the prediction models on average outperform the Theil-Sen monotonic trend-model at 450 \({}^{\circ}\)C GDD (Figure 12). However, only after mid-season, this is valid for the vast majority of administrative units.  
Figure 8: Time series of quality metrics of crop yield predictions for NUTS-2 units after the vegetation season.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Crop Type**} & **MBE** & **RMSE** & **RMSE** & **RRMSE** & **R2** & **Correlation (r)** \\  & **(dt)** & **(\%)** & **(dt)** & **(\%)** & **(-)** & **(-)** \\ \hline Winter wheat & 0.25 & 0.60 & 3.43 & 8.15 & 0.84 & 0.92 \\ Winter rapeseed & 0.19 & 0.71 & 3.39 & 13.03 & 0.47 & 0.69 \\ Maize & 0.37 & 0.63 & 7.76 & 13.32 & 0.51 & 0.71 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Overall performance of crop yield forecasts at NUTS-2 level. MBE–Mean Bias Error, RMSE–Relative MBE, RMSE–Root Mean Square Error, RRMSE–Relative RMSE.  
Figure 7: Map of crop yield forecasts performance at the NUTS-2 level.  
For maize it is evident that after 600 \({}^{\circ}\)C GDD, the predictions models are significantly more accurate than the trend-model.  
Figure 10: Comparison of crop yield predictions with the reference statistics for winter rapeseed at NUTS-2 level. The RMSE and bias of this relationship is given in Figure 7.  
Figure 9: Comparison of crop yield predictions with the reference statistics for winter wheat at NUTS-2 level. The RMSE and bias of this relationship is given in Figure 7.  
Figure 11: Comparison of crop yield predictions with the reference statistics for maize at NUTS-2 level. The RMSE and bias of this relationship is given in Figure 7.  
Figure 12: Distributions of temporal correlations for different GDD levels between crop yield predictions and reference statistics. Additionally, the performance of linear trend models is shown on the rightmost box. Dashed line denotes median correlation of the linear trend-model.