*3.3. Uncertainty and Variability of Biophysical Parameters for Diversity Ecosystems in Arid Regions*

Since the performance after calibration of all five parameters of the MOD17 model was better than after the calibration of only the parameter εmax, indicating the important role of temperature and water-constrained factors in the estimation of GPP in the arid region. We thus calibrated all the parameters of MOD17 algorithms (Table 3). Our study illustrated that variability of biophysical parameters not only exist across different ecosystems, but also within the same ecosystems, such as the diverse biophysical parameters of grassland ecosystems and the desert grassland ecosystems. The current version of MOD17 BPLUT does not consider the differentials of these two types—they shared the same BPLUT parameters of grassland. However, there are different climate conditions and species in these two ecosystems in the study region. Meanwhile, there are different photosynthesis paths between C3 cropland and C4 cropland, which have many differences in their biophysical properties. However, these two types are also shared in the current version of MOD17 BPLUT.

The value of εmax is biome specific, representing the maximum LUE of the corresponding vegetation in the process of photosynthesis. For a given biome type, the value of εmax is constant and assigned by the MOD17 BPLUT. While the newly released version of BPLUT has corrected and updated the εmax values, the εmax value were still significantly underestimated in the main ecosystems in arid regions (Table 3). The mis-estimation of their values inherently further reduced the accuracy of GPP estimations.


**Table 3.** Prior distribution (initial value and range) and posterior distribution (mean value and 95% confidence interval) of the parameters of the MOD17 model for all sites. For the parameters εmax (gC/MJ APAR), Tmin\_min ( ◦C), Tmin\_max ( ◦C), VPDmin (Pa), and VPDmax (Pa), we set the original values of MOD17 BPLUT as the initial values (with bold font).

Meanwhile, the large variations in the temperature and water-constrained stress factors also existed due to the diversity of climate conditions in different parts of HRB (Table 3). For example, the climate is cold and humid in the upstream HRB, therefore, the temperature stress factor has a great impact on GPP estimation in the grassland ecosystems in the upstream HRB. However, as Table 3 reveals, the original MOD17 BPLUT overestimated the parameters of the minimum temperature stress factors and the VPDmax values. In comparison, the climate is extremely arid in the downstream HRB, however, the original MOD17 BPLUT underestimated the parameters of the maximum temperature stress factors and the VPDmax values.

In addition, the Bayesian approach can estimate the posterior distribution of model parameters, which is a useful tool to reduce model uncertainty. Using the Bayesian approach, the uncertainty of model parameters was reduced significantly for some sites (e.g., the NTZ site) located in the extremely arid region (Figure 9).

**Figure 9.** Relative reduction of parameter uncertainty (95% confidence interval) from prior to posterior distribution. The green bar and blue bar represent the reduction of uncertainty in model parameters for the MOD17A2H model at the NTZ and DMZ sites.

#### **4. Discussion**
