## 3 Methods
### GPP Estimation Considering the Vertical Structure  
In situ meteorology data for the height of each sub-ecosystem are available for the DHS and TMK sites. Thus, the GPP of every sub-ecosystem can be described by the GPP model with the meteorology data and model parameters from each height. In this research, we assumed that each sub-ecosystem would have a different LUEi, which is defined as the LUE of the sub-ecosystem. LUEi is affected by only certain environmental factors, such as temperature and the VPD at the corresponding height. LUEi was calculated using Equation (4), and the LUEmax of the sub-ecosystems (such as those of shrubs and grasses), temperature, and the VPD stress functions are provided in the Supplementary Material. At the ecosystem scale, using temperature and the VPD scalar produces the LUEmax, which characterizes carbon sequestration from the LUE. Moreover, different vegetation types, such as the tree, shrub, and grass layers, have various LUEmax values. Table 2 presents the various LUEmax inputs for the GPP estimation results from four different articles. The results of [PERSON] and [PERSON] stated that overstory layers, such as the overstory tree layer, have an average LUEmax of 0.28 gC/m\({}^{2}\)/MJ, which is higher than the LUE of the understory layer (grass). To analyze the effect of vertical structure on GPP estimation, we calculated GPP considering vertical layers using the following function:  
\[\text{GPP}\text{m}=\sum_{i=\text{sub-ecosystem}}\text{LUE}_{i}\times\text{ APAR}_{i} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Tree (DHS)** & **Overstory (TMK)** & **Shrub** & **Grass** \\ \hline Zhou [32] & 1.120 & 1.180 & 0.930 & 1.520 \\ MODIS [67] & 1.268 & 1.051 & 0.841 & 0.860 \\ Yuan [31] & 1.680 & 1.640 & 0.660 & 1.520 \\ Madani [76] & 0.980 & 1.171 & 0.631 & 1.294 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tree, shrub, and grass maximum light use efficiency (LUEmax) parameterization values (units: gC/m\({}^{2}\)/day) (EBF and DNF were defined as the LUEmax values of the tree layer in the GPP simulations). where GPPm is defined as the modeled sum of GPP in two (overstory and understory) or three (tree, shrub, and grass) sub-ecosystems. The ecosystems were divided into overstory and understory groups at TMK and into tree, shrub, and grass groups at DHS using in situ LAI measurements. The meteorology data can provide in situ air temperature and VPD stress values for each sub-ecosystem. Temperature sensors at different heights measured the air temperature, while the VPD was calculated from the relationship between VPD and both temperature and humidity [77; 78]. APARI is the absorbed PAR for the LUE of a specified height, and was calculated from FPAR and PAR. At the DHS site, the whole ecosystem can be divided into three sub-ecosystems, namely, the tree, shrub, and grass layers; thus, the GPP was calculated for the EBF, shrub, and grass layers (sub-ecosystems) using the in situ temperature, VPD, PAR, and long-term LAI data for each layer, and specific LUEmax input values for each sub-ecosystem. At the TMK site, we divided the ecosystem into DNF and grass sub-ecosystems, and used the GPP input parameters for each layer, as used in the approach for DHS:  
\[\text{GPPs}\ =\ \text{LUEs}\times\text{APARs} \tag{6}\]  
GPPs represents the GPP of a specific ecosystem that was estimated using the big-leaf model, which assumes that the entire ecosystem is a single leaf. At the DHS site, the LUE was calculated as an EBF ecosystem with an EBF-based LUEmax (Table 3), and the temperature and VPD stress were given by the mean canopy temperature and VPD. At TMK, the DNF-based LUEmax (Table 3) was used, and the temperature and VPD stress were given by the mean canopy temperature and VPD. \[\text{GPPdif}\ =\ \text{GPPm}-\text{GPPs} \tag{7}\]  
The GPP bias (GPPdif in Equation (7)) is the multilayer GPP result (GPPm) minus the single-layer GPP result (GPPs), which represents the difference between the two models.