## 5 Discussion  
This study proposed an AVPM model to calculate the NPP. This model introduced a new indicator to quantify the impact of water stress (f(W)) on plant photosynthesis under the framework of the MOD17. This model was applied in the TRH region and showed good performance and indicated a lower bias, lower MAPE, and higher \(r\) than the MOD17. The average bias of the AVPM was \(-\)9.8 gCm\({}^{-2}\)yr\({}^{-1}\), which was reduced by 91.8% compared to the MOD17. The average MAPE of the AVPM was 57.0%, which was reduced by 68.2% compared to the MOD17. The average \(r\) of the AVPM was 0.4809, which was improved by 30.0% compared to the MOD17. The method showed better year-to-year generalization than the MOD17. From 2012 to 2019, the bias difference of the AVPM was 38.5 gCm\({}^{-2}\)yr\({}^{-1}\), which was 36.3% of the MOD17. The MAPE difference of the AVPM was 26.6%, which was 19.6% of the MOD17. The r difference of the AVPM was 0.2273, which was similar to the MOD17. Two aspects could be used to account for the improvements of f(W) in the AVPM method. First, there was a significantly improved correlation between the soil gravimetric water content (GWC) and the AVPM f(W). Second, there was a significant correlation between the GWC and the two indicators (RH\({}_{\rm min}\), VPD\({}_{\rm max}\)) used in the AVPM f(W). To argue this issue, this paper performed two time-series analyses at the Guide station (Figure 5a,c,e) and the Tuotuo River station (Figure 5b,d,f). To plot these two-time series, this paper collected 36 specific humidity (SH) images from the FLDAS dataset, 36 minimum temperature (T\({}_{\rm min}\)) images, and 36 maximum temperature (T\({}_{\rm max}\)) images from the TerraClimate dataset from 2014 to 2017 and calculated their RH\({}_{\rm min}\) (Figure 5a,b), VPD\({}_{\rm max}\), and VPD\({}_{\rm day}\) (Figure 5c,d), respectively, based on the equations in this paper (Figure 5e,f). First, there was a significant correlation between the two indicators (RH\({}_{\rm min}\) and VPD\({}_{\rm max}\)) and the GWC at these two stations. The correlations between the AVPM VPD\({}_{\rm max}\) and the GWC were significantly correlated at the Guide station (r = \(-\)0.42, \(p\)\(<\) 0.01, n = 25) and significantly correlated at the Tuotuo River station (r = \(-\)0.35, \(p\)\(<\) 0.01, n = 27). The correlations between the RH\({}_{\rm min}\) and the GWC were moderately significant at the Guide station (r = 0.46, \(p\)\(<\) 0.05, n = 25) and moderately significant at the Tuotuo River station (r = 0.39, \(p\) \(<\) 0.05, n = 27). The correlations between the MOD17 VPD\({}_{\text{day}}\) and the GWC were weakly significant at the Guide station (r = 0.37, \(p\) \(<\) 0.1, n = 25) and not significant at the Tuotuo River station (r = 0.17, \(p\) \(>\) 0.1, n = 27). Although the weak significance was presented in the Guide station, the larger the VPD, the lower the GWC should be. Therefore, the positive correlation (r \(>\) 0) could only indicate that the representation of VPD\({}_{\text{day}}\) was worse (Figure 5a-d). The correlation between the VPD\({}_{\text{day}}\) and the GWC was low because the correlation between the VPD\({}_{\text{day}}\) and the GWC was compromised during the low-temperature period, as discussed in the Introduction. Figure 5: Patterns of minimum relative humidity (RH\({}_{\text{min}}\)), soil gravimetric water content (GWC), vapor pressure deficit (VPD), daytime VPD (VPD\({}_{\text{day}}\)), maximum VPD (VPD\({}_{\text{max}}\)), MOD17 water stress (mf(W)), and AVPM water stress (af(W)) during 2014–2017 at Guide station (**a**,**c**,**e**) and Tuotuo River station (**b**,**d**,**f**). Second, there was a significant correlation between the AVPM f(\(W\)) and the GWC at these two sites. The AVPM f(\(W\)) and the GWC were significantly correlated at the Guide station (r = 0.62, \(p<0.01\), n = 25) and significantly correlated at the Tuotuo River station (r = 0.65, \(p<0.01\), n = 27).