## 5 Discussion  
### Performance of AGB Upscaling Model  
To meet various requirements of AGB estimation at grid scales in practice, coarser-spatial-resolution AGB estimates such as those at 1 km or 5 km resolution may be needed. In this study, to select the best AGB upscaling model, we used MODIS and AVHRR NDVI products and Ta, P, Rs, elevation, and AGB ground observations to establish the RF, ERT, and GBRT models for estimating the grassland AGB in the TRHR. The validation results illustrated that the GBRT model has the best performance among the three models, judging by the R\({}^{2}\) (0.74) and RMSE (57.8 g C m\({}^{-2}\)) of the AVHRR-derived estimated and MODIS-derived reference AGB with a 5 km spatial resolution (Figure 4d-f). Model validation demonstrated that the GBRT algorithm could improve the accuracy to prevent overfitting on the new data [64], which is corresponding to the reported results. [PERSON] et al. [65] used GBRT as the optimal algorithm to estimate global forest AGB after comparing the performance of ANN and multivariate adaptive regression spline (MARS) algorithms. The validation results showed that the R\({}^{2}\) and RMSE between the estimated and reference AGB with 1 km spatial resolution were 0.90 and 35.87 Mg/ha, respectively. [PERSON] et al. [78] used the GBRT algorithm to estimate the global monthly gross primary production (GPP) at a 5 km spatial resolution with the OCO-2 SIF product (GOSIF) and other explanatory variable data. Compared with the RF, MARS, light gradient boosting machine (LightGBM), and long short-term memory (LSTM) algorithms, GBRT was more suitable to estimate global GPP by GOSIF. The GBRT-based GPP estimations derived from GOSIF were validated by in situ measurements with highly accurate R\({}^{2}\) (0.58), RMSE (2.74 g C\(\cdot\)m\({}^{-2}\)), and bias (\(-\)0.34 g C\(\cdot\)m\({}^{-2}\)) values. Our conclusions are similar to previous findings. This may be  
Figure 12: Spatial pattern of P trends from **(a)** 1982-2018, **(b)** 1982–1998, and **(c)** 1998–2018 in the TRHR. The black solid dots refer to grids with 95% confidence. because the GBRT algorithm is an iterative decision tree that utilizes the additive model and the forward distribution algorithm to combine several weak classifiers into a strong classifier in different proportions [64; 79]. We compared estimated AGB errors to judge the performance of GBRT, RF, and ERT. Figure 13 illustrates the probability density distributions of the AVHRR-derived estimated AGB errors against the MODIS-derived reference AGB with a 5 km spatial resolution by the GBRT and the other two AGB upscaling models in the validation set. Figure 13 shows that all three predictive errors are closely centered on zero, even in the ERT model, which obtained the largest bias (0.6 g C m\({}^{-2}\)) (Figure 4f). The GBRT model shows a competitive and superior predictive performance compared to RF and ERT. This may be because the GBRT algorithm has the advantage of producing competitive, highly robust, interpretable procedures for regression [64]. Therefore, the GBRT algorithm can capture the AGB variance accurately and show the optimal estimation performance. Training samples with spatial representativeness were essential for modeling the relationships between AGB and remotely sensed data with a coarse spatial resolution. To generate reliable long-term grassland AGB datasets, we proposed upscaling AGB data from ground observations to a dataset with a 1 km spatial resolution using MODIS data and then from a 1 km to 5 km spatial resolution using AVHRR data. A previous study confirmed this upscaling strategy [80]. Fractional vegetation cover (FVC) is a basic indicator of biomass production in ecosystems [81]. To enhance the spatial representativeness of FVC training samples for spatial matching with AVHRR reflectance data, [PERSON] et al. [80] reprojected the Global LAnd Surface Satellite (GLASS)-MODIS FVC data from a spatial resolution of 500 m to 5 km as the training samples to generate a long-term GLASS-AVHRR FVC product since 1981 by MARS.