# Incorporating Spatial Autocorrelation into GPP Estimation Using Eigenvector Spatial Filtering
## 5 Discussion  
### Advantages of SA-LGBM  
SA-LGBM significantly enhances the precision of GPP estimation. By combining the ESF method, sophisticated nonlinear model design, and an ample training dataset, SA-LGBM effectively reduces estimation errors, providing more precise results for remote sensing-based GPP estimation. The performance of common machine learning methods in GPP estimation is compared in our experiment, revealing that LGBM outperformed these other methods when not considering the spatial effects. Building upon this, we improved the model by incorporating spatial factors, resulting in the superior performance of the SA-LGBM model. The inclusion of EV led to an 8.5% increase in \(R^{2}\) and a 20.8% reduction in RMSE. This improvement was achieved through the synergistic combination of the ESF method, the nonlinear model structure, and the comprehensive training dataset, significantly reducing estimation errors and yielding more accurate remote sensing GPP estimates. Furthermore, within the footprint range near the flux tower sites, we compared GPP estimates produced by the SA-LGBM model with other GPP products. SA-LGBM demonstrated a notably higher overall correlation with flux data. Across all time scales, SA-LGBM consistently exhibited outstanding performance. Compared to MOD17 and GOSIF, SA-LGBM achieved a 0.21 and 0.17 average increase in \(R^{2}\) across different time scales. In conclusion, SA-LGBM has the capability to provide more accurate results across various time scales. In addition, the discrepancy in estimating flux tower GPP by MOD17 and GOSIF, resulting in underestimation, has been extensively documented in the literature [40; 58; 59], and SA-LGBM overcomes the underestimation of the existing GPP products to a certain extent and achieves better results.  
SA-LGBM, through the ESF method, effectively and succinctly extracted the inherent spatial autocorrelation between GPP flux sites, resulting in more accurate GPP estimates. In contrast, the residuals of LGBM without spatial factors exhibit statistically significant spatial autocorrelation, indicating the existence of spatial dependencies within the data that LGBM failed to capture. Ignoring these dependencies can lead to biased and inefficient estimates. By considering the intrinsic spatial organization within the dataset, SA-LGBM makes the model residuals more random and less spatially structured, which is a key assumption in many statistical analyses [29; 60; 61].These findings align with our expectations that incorporating spatial information should help capture spatial autocorrelation and improve accuracy, thereby reinforcing the results of previous related research [62; 63; 64].  
SA-LGBM is entirely based on remote sensing observation data, without considering plant functional types, multi-source data, or inherent parameters. Compared to other models that use precipitation and vapor pressure deficit data [65; 66; 67], SA-LGBM can reduce the uncertainties associated with interpolated meteorological data, and its input data have higher availability.  
Figure 11: Comparison of the spatial distribution of residuals and EV: (**a**) spatial distribution of residuals from LGBM and SA-LGBM models and (**b**) spatial distribution of EV.