## 3 Results
### Environmental Effects on RE Spatiotemporal Variation
#### 3.3.3 Environment Effects on RE Spatial Variation  
The red fitting line in Figure 8 shows that annual RE was correlated with the annual average EVI across the seven grassland subtypes, and the R\({}^{2}\) reached 0.91. This indicates that EVI can best explain the spatial variation in RE in northern China's grasslands, compared with other environmental factors. In alpine grasslands, including AS, SW, KO, and SH, the mean 15-year EVI showed an increasing trend, and RE also showed an increasing trend (Figure 8c, Table 5). In temperate grasslands, EVI and RE also increased simultaneously from DS and TS to MS. These results highlight that RE and EVI changed synchronously in the same spatial direction in the same climate zone.  
In the temperate grasslands, including DS, TS, and MS, the mean annual RE increased synchronously with an increase in the mean annual PRE (Figure 8b). Within AS, SW, KO, and SH in the alpine grasslands, the mean annual PRE and the mean annual RE also increased simultaneously. However, simultaneous variation in the PRE and the RE was only observed in the same climate zone. Across grassland types in the same climate zone, the mean annual PRE controlled the magnitude of the mean annual RE.  
There was no significant correlation (R\({}^{2}\) = 0.004, \(p\) = 0.52) between annual RE and annual average Ta throughout northern China's grasslands (Figure 8a). In the alpine grasslands, including AS, SW, KO, and SH, the annual RE increased with an increase in the annual average Ta. However, in the temperate grasslands, there no synchronization phenomenon was observed. These results indicate that the dependence of annual RE on the annual average Ta tends to be stronger in regions with more moisture. The influence of Ta on RE in grassland ecosystems is regulated by moisture, and the regulation strength varies with different vegetation types.  
Across the seven grassland subtypes, the SOCD, clay, and silt content had positive effects on the mean annual RE, whereas sand content had a negative effect (Figure 9), which is consistent with previous research [27]. Within AS, SW, KO, and SH in the alpine grasslands and DS, TS and MS in the temperate grasslands, RE increased simultaneously  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Mean Annual Value**} & \multicolumn{4}{c}{**R\({}^{2}\)**} \\ \hline  & **Grassland** & **EVI** & **PAR (mol m\({}^{-2}\) yr\({}^{-1}\))** & **PRE (mm)** & **Ta (\({}^{\circ}\)C)** & **EVI** & **PAR** & **PRE** & **Ta** \\ \hline  & KO & 0.15 & 2723.14 & 628.23 & 0.10 & 0.44 & 0.00 & 0.07 & 0.91 \\ TP & SH & 0.17 & 2649.46 & 692.66 & 1.35 & 0.63 & 0.01 & 0.11 & 0.88 \\  & SW & 0.15 & 2673.11 & 508.06 & \(-\)0.21 & 0.48 & 0.00 & 0.00 & 0.80 \\  & AS & 0.10 & 2975.61 & 433.30 & \(-\)0.62 & 0.01 & 0.44 & 0.51 & 0.73 \\ \hline  & MS & 0.18 & 2182.35 & 431.45 & 3.48 & 0.28 & 0.08 & 0.20 & 0.17 \\ IM & TS & 0.14 & 2412.42 & 340.07 & 4.69 & 0.63 & 0.02 & 0.62 & 0.05 \\  & DS & 0.08 & 2728.92 & 275.18 & 2.13 & 0.62 & 0.03 & 0.64 & 0.12 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The mean annual values for the environmental variables and the interannual dynamic correlation (R\({}^{2}\)) between RE and the environmental variables in each grassland subtype.  
with the increase in SOCD and clay content. The R\({}^{2}\) between the RE and the SOCD, clay, silt, and sand content were 0.80, 0.68, 0.45, and 0.81, respectively, implying that soil factors also affect the spatial variation of RE.  
EVI and soil factors are critical environmental factors that determine the spatial variations in RE in northern China's grasslands. Their dominant roles illustrate the importance of grassland type and soil factors in regulating the spatial pattern of RE.