## 4 Discussion
### Model Evaluation  
The model demonstrates that flux-tower observed \(RE\) can be estimated with an applicable degree of accuracy across grasslands using only remote sensing data. We first evaluate the precision of our model at a site scale by comparing it to other recent semi-empirical approaches, e.g., the two original developed-based models, T&P [22] and RECO [27] that achieved a mean site-level accuracy of \(R^{2}\) = 0.679 with RMSE =1.227 g C m\({}^{-2}\) day\({}^{-1}\) and \(R^{2}\) = 0.625 with RMSE = 0.969 g C m\({}^{-2}\) day\({}^{-1}\), respectively, for these 16 grassland sites, while our model performed better with a higher degree of explanation and a lower bias (Table 3), verifying the model improvements with better representation of _Reref_ and further incorporation of the moisture effect. An independent regional \(RE\) product from a popular process-based model CLM4 CN [56] was employed to further evaluate the model performance at a regional scale. The CLM4 CN presented a mean annual \(RE\) value (309.18 \(\pm\) 5.15) within an order of magnitude of this study, but it still resulted in an overestimation. The general spatial pattern of \(RE\) appeared similar but there were still distinct differences, especially in the water-deficit area. For example, in the southwest of the desert grasslands which is driest, the CLM4 CN failed to produce the lowest values. Moreover, the CLM4 CN unreasonably produced a higher \(RE\) in the alpine meadow steppe than the surrounding alpine meadow (Figure 7a,c). These distinct differences are likely associated with the different representation of _Reref_ in the models, which has been proven to largely determine the spatial pattern of \(RE\) (Figure 7a,b). _Reref_ was set as the same constant for all biomes in the CLM4 CN [72], as in the most process-based models [73; 74; 75]. However, more and more studies demonstrate that a large error would be introduced if a constant _Rerf_ is used [76]. In fact, _Rerf_ varies remarkably in space [9; 22; 60]. Therefore, the better representation of _Rerf_ makes our model more sensible for capturing the regional characteristics of \(RE\) in grassland ecosystems and arid and semi-arid areas, in particular. The consideration of moisture effects on both the spatial and temporal variabilities of \(RE\) is another major factor contributing to the better performance of our model. For the spatial variability of \(RE\) (_Rerf_), even though it has been gradually confirmed to vary systematically with the spatial variation of productivity (GPP or LAI) and temperature [8; 20; 22; 27; 20; 22], to our knowledge, this process has not yet been linked to moisture change in satellite-based \(RE\) studies at large scales and with a high resolution. Our findings reveal that _Rerf_ has a significant linear relation with \(LSW\!I_{mean}\) in both the Tibetan and Inner Mongolian grasslands (Figure 3, \(p<0.01\)), which is also supported by another recent study in northern China [24]. Considerable improvement was found in the explanation of _Rerf_ (12%, Table 4) in the temperate grasslands by the inclusion of the moisture effect, while the improvement is relatively small (4%) in the alpine grasslands due to the colinearity of plant biomass and soil moisture [62]. Moisture also exerts significant influence on the seasonal dynamics of \(RE\) in northern China's grasslands (Figure 4), which further explained a large proportion of \(RE\) in the arid and semi-arid vegetation types (Table 5). Obvious gaps would be found in the performance between the model without _fw_ and the model with _fw_ for the arid and semi-arid ecosystems. The simulated \(RE\) with _fw_ has a higher correlation coefficient with observed values (\(R^{2}\) increased by 12-24%) and a smaller bias from the observed values (RMSE reduced by 13-41%) in the desert steppe, typical steppe, and alpine meadow steppe.