Regression correlations between AGBobs and 13 corresponding annual NDVI values were analyzed, based on the preprocessed AGBobs and NDVI data, respectively. In total, 52 regression models were developed, including linear, exponential, power, and logarithmic models (Appendix S1). Coefficients of determination (R2 , Equation (2)), and root mean square errors (RMSE, Equation (3)) were employed to assess the performance of each of the 52 regression models.

(2)

(3)
In (2) and (3), R2 is the coefficient of determination between modeled AGB data (AGBmod ) and field-observed AGB data (AGBobs ), which denotes a similar pattern between AGBmod and AGBobs, and the fraction of AGBobs variation that can be explained by the model. RMSE is the root mean square error between AGBmod and AGBobs , which represents biases that cause modeled AGB data to differ from field-observed AGB data. The symbol n represents the number of field AGB observations included in the dataset for model validation.
The best AGB estimation model was identified as the model with the highest R2 and lowest RMSE, of the 52 regression models developed.26-27 The 52 models needed to be optimized when no model satisfied both maximum R2 and minimum RMSE criteria26, and this was achieved by calculating averaged results for AGB estimations obtained from the model with the maximum R2 , and the model with the minimum RMSE, at the pixel scale of this study.
As stated above, we developed AGB estimation models for the Chinese northern temperate and Tibetan Plateau alpine grasslands. Then, the performance of the models was assessed, based on the remaining 25% of the field AGB observations. Accuracy assessments indicated that the models with both the highest R2 and the lowest RMSE were not among the 52 regression models developed for either the northern temperate grasslands, or the Tibetan Plateau alpine grasslands of China (Appendix S1).
According to methods for developing an AGB estimation model, the optimal AGB estimation model was composed of the fitted regressions satisfying the highest R2 and meeting the lowest RMSE criteria, among the 52 regression models for both the northern temperate grasslands, and the Tibetan Plateau alpine grasslands, respectively (Appendix S1, bold fonts). More details on the development for grassland AGB estimation models have been reported in Jiao et al.,14 and a technical flowchart for the development of grassland AGB estimation models in this study can be seen in Figure 2.
Fig.2
Technical flowchart for developing AGB estimation models for Chinese northern temperate and Tibetan Plateau alpine grasslands Optimized AGB estimation models for the northern temperate grasslands (AGB-RSMNG, Equation (4)), and the Tibetan Plateau alpine grasslands (AGB-RSMTP, Equation (5)) were developed.

(4)

(5)
In (4) and (5),
x denotes the geographic position, and
t is the year, from 1982 to 2015.

and

separately denote the grassland AGB at position

in year

for the northern temperate grasslands, and for the Tibetan Plateau alpine grasslands, respectively.

,

,

and

denote, respectively, the averaged NDVI values of the period from July–October, from June–September, from April–August, and from May–August, for year
t.