## 2 Materials and Methods
### Chamber-Based Re Estimations  
Ecosystem respiration (\(Re\)) and its components, soil surface CO\({}_{2}\) flux (Rs) and Rm, were measured in each polyvinyl chloride (PVC) collar (diameter \(\times\) height = 20 cm \(\times\) 5 cm) by a LI-COR 8100 Automated Soil CO\({}_{2}\) Flux System (LI-COR Inc., Lincoln, NE, USA) in the growing season from 2010 to 2011. Chamber-based Re measurements are determined by the rate of change of trace gas concentration in the chamber headspace [76; 77; 78]. We selected 7 sample plots (3 m \(\times\) 3 m) near the EC flux tower for chamber-based Re measurements, which were basically along the local prevailing wind direction, thus were believed to be similar to the average characteristics of EC-based measurements (Figure 2b). Before the growing season, the PVC collar was randomly inserted into soil at depth of 3-5 cm in each plot for Re and Rs measurements. Re were measured with all plant material in the collar left intact, which includes both above (Ra_above) and belowground components (Rs) (Equation (16)) [45; 48].  
\[Re=Rs+Ra\_above \tag{16}\]  
After Re measurements, aboveground plant materials within those collars were removed. To avoid the disturbance of clipping and ensure relative steady measurements [12], one day later, we measured Rs, which included Rm and underground autotrophic respiration by plants roots (Ra_under) (Equation (17)) [5; 11; 43; 79].  
\[Rs=Rm+Ra\_under \tag{17}\]  
Root exclusion was used to estimate Rm, which is the soil CO\({}_{2}\) efflux rates without living plant roots respiration [5; 47; 80]. This alpine meadow had a shallow soil layer depth of about 30 cm, and over 95% of plant roots were contained in the top 0-15 cm of soil layer [47; 81]. As the gravel content is high (about 30%) and higher as one goes deeper [26], it is arduous to insert the PVC collars. Thus we selected 4 of 7 measurement plots to develop the root exclusion. The root-free soil quadrat (length \(\times\) width \(\times\) height = 0.5 m \(\times\) 0.5 m \(\times\) 15 cm) was developed by removing all aboveground and belowground plant materials separately in every 5-cm layer and backfilling the soil according to the original order before the growing season in each plot [47; 81]. Then, the PVC collars were inserted into these quadrats to about 13-15 cm depth. These were kept free of plant growth by frequent manual removal during the whole growing season. Rm measurements were identical to Re and Rs measurements [76; 77; 78].  
All chamber-based measurements were conducted with intervals of about 10 days from June to October [48], and each measurement was recorded between 9:00 and 11:00 a.m. for approximating the daily average estimation [82]. Therefore, we can calculate the Ra, the ratio of Rm and Rs (\(Rm/Rs\), \(\beta\)), \(Rs/Re\left(\gamma\right)\), \(Ra/Re\left(1-\beta^{*}\gamma\right)\) based on chamber-based \(Re\left(Re\_{\text{-}}\text{CAM}\right)\), \(Rs\left(Rs\_{\text{-}}\text{CAM}\right)\) and \(Rm\) measurements (\(Rm\_{\text{-}}\text{CAM}\)) as Equations (16) to (20).  
\[Ra=Ra\_above+Ra\_under \tag{18}\]  
\[Rm/Rs=\beta\quad Rs/Re=\gamma \tag{19}\]  
\[Ra/Re=1-\beta*\gamma \tag{20}\]