## Materials and Methods
### Model
#### 2.3.2 Representation of Temporal Variability of \(Re\)  
The seasonal dynamics of \(Re\) are reflected by \(f(T,P,W)\), which is mainly controlled by the temporal variability of temperature [48, 49], vegetation productivity [43, 50], and water [20, 21, 22, 40]. Especially in the arid and semi-arid ecosystems, water is the main limiting factor of the seasonality of \(RE\)[51, 52]. The values of \(f(T,P,W)\) are obtained by calculating the ratio of the observed \(RE\) from the flux tower and the site-specific _Reref_ partitioned from the observed \(RE\). Figure 4 displays the \(f(T,P,W)\) dependencies on the temporal variation of \(EVI\), \(LST\) and \(LSWI\). The form of \(f(LST,EVI)\) scalar was based on the \(LST\)-driven Lloyd-Taylor equation [48] and \(EVI\)-driven linear equation, while the form of _fw_ scalar was derived from a Michaelis-Menten equation firstly proposed by [PERSON] et al. [53]. During the growing season, we calculate the \(f(T,P,W)\) as follows:  
\[f(T,P,W)=f(LST,EVI)*f_{W}, \tag{5}\]  
Figure 3: Reference respiration (_Reref_) response to the mean annual springtime \(EVI\) (\(EVI_{mean}\)), mean annual \(LST\) (\(LST_{mean}\)) and mean annual growing season \(LSWI\) (\(LSWI_{mean}\)) for the Tibetan alpine grasslands and the Inner Mongolian temperate grasslands.  
\[f(LST,EVI)=p_{5}*\exp\left(E_{0}*(\frac{1}{\textit{Tref}-T_{0}}-\frac{1}{LST_{n}-T _{0}})\right)+p_{6}*EVI_{std}+p_{7}, \tag{6}\]  
\[f_{W}=\frac{(0.5+LSWI)}{k+(0.5+LSWI)}, \tag{7}\]  
where \(LST_{n}\) is nighttime \(LST\), \(EVI_{std}\) is the standardized \(EVI\) (8-day \(EVI\) divided by \(EVI_{mean}\)), \(p_{5}\) to \(p_{7}\) are the parameters to be sought, \(E_{0}\) is the activation energy, \(T_{0}\) is the minimum temperature for respiration, which is set to 227.13 k (\(-\)46.02 \({}^{\circ}\)C) as in the original Lloyd-Taylor model, \(k\) is the half-saturation constant of the hyperbolic relationship, and 0.5 is an empirically given value to maintain the numerator/denominator of \(\textit{fw}>0\).  
During the non-growing season, temperature, but not water, becomes the main limiting factor for \(RE\) in northern China's grasslands [24]. In addition, the surface covered by ice and snow in the non-growing season has a strong absorption of the shortwave infrared band that causes \(LSWI\) to increase sharply; thus, it cannot reflect the actual water content in the winter [54]. Therefore, the _fw_ scalar is only considered for the growing season (Equation (5)). During the non-growing season, we calculate the temporal variability of \(RE\) as follows:  
\[f(T,P,W)=f(LST,EVI)\, \tag{8}\]  
The different periods of MODIS indices (i.e., the mean springtime of \(EVI\), the mean annual of \(LST_{d}\) in _Reref_, and \(LST_{n}\) in \(f(T,P,W)\)) used here have already been selected by [PERSON] et al. [27] as the best index for fitting the relationship with RE. \(LSWI\), selected by us as the model driver, is a more direct proxy for moisture than \(LST_{diff}\), which was used in RECO but had no significant relation with the temporal dynamics of \(RE\) in our study (\(R^{2}<0.2\), \(p>0.05\)); in addition, land surface moisture was found to have greater influence on \(RE\) than deep soil water [20; 28], which is especially instrumental in northern China's grasslands with the large number of roots distributed in the soil surface [55]. Therefore, all these drivers appear to be chosen empirically but are based on the physiological dependencies of \(RE\), thereby ensuring reliable estimates from our model.  
Figure 4: \(f\) (_T,P,W_) response to nighttime \(LST\) (\(LST_{n}\)), standardized \(EVI\) (\(EVI_{std}\)), and \(LSWI\) for the Tibetan alpine grasslands and the Inner Mongolian temperate grasslands.