## 2 Materials and Methods
### Experimental Procedures and Measurement of \(R_{\rm s}\) and the Related Environmental Factors  
Soil respiration (\(R_{\rm s}\)) was measured once a month during April to November from August 2007 to November 2015. The diurnal variation of \(R_{\rm s}\) was measured to eliminate the influence of diurnal range on seasonal variations. The \(R_{\rm s}\) rate between 8:00 and 11:00 AM was almost equal to the daily average \(R_{\rm s}\) in the study site [26]. Thus the measurements were conducted during 9:00 to 11:00 local time to minimize the influence of the daytime temperature fluctuations. Furthermore, all measurements were conducted on rain-free days. Soil respiration was measured using a LI-COR 6400 portable photosynthesis system (LI-COR, Environmental Division, Lincoln, NE, USA) equipped with a LI-COR 6400-09 soil chamber with an area of 71.6 cm\({}^{2}\) that calculated soil CO\({}_{2}\) efflux in the chamber using optical absorption spectroscopy in the infrared range. Detailed information regarding the system is available elsewhere [19]. The spatial heterogeneity of \(R_{\rm s}\) at the study site has been studied previously [25; 26], which facilitated design of the sampling strategy and determination of the optimal sample size for the study site. At least 15 collars from PVC pipe were inserted 2-3 cm into the soil and the soil chamber was mounted on each collar at the time of observation. Three cycles of consecutive measurements on the collar were conducted to prevent any systematic errors, and the average \(R_{\rm s}\) value was used for each collar. The plants were cut off inside the collars manually to avoid the effects of photosynthesis on \(R_{\rm s}\). To minimize the effects of soil disturbance during installation, all collars were installed at least 1 day before measurement. Hence, it was assumed that there was no disturbance caused by operation of the flux chamber or plant growth. The average soil CO\({}_{2}\) efflux rate from all PVC collar measurements was recorded as the mean daily \(R_{\rm s}\) at the measuring time in study site. The measuring frequency was once a month. The monthly \(R_{\rm s}\) was computed by averaging all daily measured data in the corresponding month from August 2007 to November 2015 (n = 4 for April, 8 for May, 8 for June, 8 for July, 9 for August, 9 for September, 7 for October, and 5 for November) to get a representative monthly value. The frequency of the determination of related environmental factors were the same as for \(R_{\rm s}\). The soil temperature (\(T_{\rm s}\)) at depth of 5 cm was recorded using a thermocouple probe equipped with a portable photosynthesis system (LI-COR 6400) at locations near where \(R_{\rm s}\) was measured. The soil moisture (\(M_{\rm s}\)) was measured using soil samples collected from depths of 0-10 cm at the time of efflux measurement. Briefly, samples were returned to the laboratory and oven-dried at 105 \({}^{\circ}\)C until a constant mass was reached, and \(M_{\rm s}\) was expressed as a percentage of dry soil mass. MODIS eight-day surface reflectance products and eight-day land surface temperature (LST) products (MOD09A1, 0.5 km and MOD11A2, 1 km) in accordance with the in situ measuring time from NASA's Earth Observing System Data and Information System ([[https://wist.echo.nasa.gov/api/](https://wist.echo.nasa.gov/api/)]([https://wist.echo.nasa.gov/api/](https://wist.echo.nasa.gov/api/))) were downloaded. To match the measuring time of \(R_{\rm s}\), we obtained the LST and normalized  
Figure 1: A sketch map of the study area in the Loess Plateau, China. difference vegetation index (NDVI) of the measuring day by linear interpolation of two consecutive eight-day spatial products. The pixel containing the study site was extracted based on the geo-location information (latitude and longitude). All the 15 or more sampling points in study site were in one pixel for retrieving the MODIS data based on the geo-location information.