# Estimating Maize Yield from 2001 to 2019 in the North China Plain Using a Satellite-Based Method
## 3 Results
### Validation of the Estimated Yield  
Accuracy testing is crucial for agricultural yield estimation. We evaluated the model's performance in estimating maize yield at the county and municipal levels based on the statistical yield. Across all research years, the estimated yields can account for 64% of the spatiotemporal variation in yield at the county level (Figure 4a). The indicators of model performance were the RMSE, MAPE, and d\({}_{r}\), which were 830.97 kg/ha, 11.20%, and 0.67, respectively. Additionally, we contrasted each year's statistical yield with the estimated yield. The linear regression slope between the statistical and estimated yield varies from 0.75 to 1.08 (Figure 4b), and the average value is 0.88, indicating a lower deviation between the two yields at the county level. The R\({}^{2}\) values are higher than 0.57 every year, the RMSE values are between 555.47 kg/ha and 1018.53 kg/ha, all of the MAPE values are below 20%, and the majority of the d\({}_{r}\) values are above 0.5 (Figure 4c-f). However, there are still some years where the estimated and statistical yields diverge significantly. For instance, even though the R\({}^{2}\) values are higher than 0.57 and the MPEA values are lower than 20%, the d\({}_{r}\) in 2006 and 2012 is only 0.48 and 0.47, respectively, indicating that these two years saw poor performance. Figure 3: The spatial distributions (**a**) and coefficient of variation (**b**) in the maize HI at the county scale. The insert shows the frequency distribution in the HI. In addition, based on the HI calibrated at the county scale, the estimated yields and statistical yields were also contrasted at the municipal scale. On the city level, the estimated yields can account for 56% of the variation in the yield for all years (Figure 5a). The RMSE, MAPE, and d\({}_{\rm r}\) were 813.78 kg/ha, 11.21% and 0.61, respectively. Additionally, we ran regression analysis for each year's estimated and statistical yields. In general, the model predictions can also simulate how the statistical yield changes in the majority of the years. The linear regression's slope for statistical and estimated yields ranged from 0.6 to 1.22 for all years (Figure 5b). The R\({}^{2}\) values range from 0.37 in 2002 to 0.84 in 2015. Figure 5b-e shows that the model can still estimate maize production well at the city scale. The RMSE ranges from 420.14 kg/ha (2008) to 1523.37 kg/ha (2012), the MAPE values are less than 20%, except for 2012 (22.24%), and the d\({}_{\rm r}\) values are greater than 0.45, except for 2004 (0.38) and 2012 (0.28) (Figure 5c-f), which also shows that the model can still estimate the yield well at the city scale. All of these results imply that, despite its inconsistent performance in some years, the estimated yield accurately captures the changes in production over time, particularly at the county level. The model's accuracy met the requirements for assessing regional maize yield across the NCP. The crop output varies from region to region and is influenced by climate factors, soil characteristics, and management techniques [18]. As a result, we compared the model in different provinces to confirm how well it performed in various places. Overall, good performance was achieved in HB, HN, and SD; the R\({}^{2}\) values are 0.74, 0.57, and 0.58 at the county level and 0.61, 0.48, and 0.41 at the city level, respectively (Figure 6a-c). While it performed poorly in AH and JS, the R\({}^{2}\) are only 0.29 and 0.40 at the county level, and 0.20 and 0.33 at the city level, and all the MAPE values are larger than 14% for both levels (Figure 6d,e). There exist some differences between different provinces, and great uncertainties in the AN and JS provinces. Figure 4: County-level comparison of the statistical and estimated yields: (**a**) shows the model’s overall performance and (**b–f**) display the correlation coefficients (slope, R\({}^{2}\), RMSE, MAPE, and d\({}_{\rm r}\)) between the statistics and estimates on the yield from 2001 to 2019.