## 2 Materials and Methods
### Selection of Variables and Multi-Sensor Satellite Data Productions
#### 2.3.2. Multi-Sensor Satellite Data  
The collected satellite data differ in their temporal and spatial scales (Table 1). For the _soum_-level analysis, all satellite data were spatially and temporally aggregated for each _soum_ district and for summer (June-August) and winter (December-February). In our  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Description** & **Spatial Resolution** & **Temporal Resolution** \\ \hline (a) Satellite data & & & \\ Temperature & Daily mean temperature (\({}^{\circ}\)C) measured by MODIS and AMSR-E & 5 km & Daily \\ Precipitation & TRMM precipitation (mm) & 25 km & Monthly \\ Evaportranspiration & Daily evapotranspiration (mm d\({}^{-1}\)) measured by MODIS and AMSR-E & 1 km & Daily \\ NDVI & Normalized Differenced Vegetation Index from MODIS & 1 km & 16 days \\ \hline (b) Ground data & & & \\ Livestock numbers & National census data from 2003 to 2010 & _Soum_ & Annual \\ Temperature and & Observed at 67 national weather stations in Mongolia & Point, & \\ Precipitation & from 2003 to 2010 & countrywide & Monthly \\ Evaportranspiration & Gap-filled daily ET (mm d\({}^{-1}\)) observed at the SKT flux tower from & & Daily \\  & 30 March 2003 to 29 December 2005 & Point & Daily \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of data sources used in this study.  
Figure 3: A study flowchart from data collection to the production of satellite-driven summer and winter variables, validation, and factor analysis and modeling.  
multivariate statistical analyses, the seasonal variables of the previous year were related to the rate of change in livestock numbers between the current and the previous years.  
The Aqua MODIS Atmospheric Profile Product (MYD07) was used to measure the daily mean temperature [41]. MYD07 records nighttime and daytime air temperature at multiple pressure heights, of which the lowest pressure-level air temperatures were averaged to the daily mean temperature [37]. For cloudy days, AMSE-E surface brightness temperature was used as ancillary information to produce nighttime and daytime temperatures [38].  
Continuous daily ET is a synthetic product calculated using both optical MODIS products and microwave AMSE-E surface brightness temperature, both of which are onboard sensors on the Aqua satellite. Both of the sensors provide data necessary for retrieving input variables for a modified Penman-Monteith equation for estimating instantaneous ET at Aqua overpass time, which is temporally extrapolated to daily ET [42; 43]. For cloudy days, AMSE-E brightness temperature was used to prepare air and dew point temperatures [24]. Incoming solar radiation was retrieved with a simple atmospheric radiative transfer model based on MODIS cloud cover information [42]. Total summer ET was divided by summer precipitation to derive a proxy of dryness. Finally, summertime Aqua MODIS NDVI was accumulated and used as a proxy for summer pastureland biomass [44]. Because a robust biophysical algorithm for grass biomass was not yet developed and tested in Mongolia, we adopted the empirical results of [45], which showed a statistically significant linear relationship between harvested biomass and accumulated NDVI for Sahel, Africa.  
Accordingly, six input variables were prepared for multivariate analyses: four summer variables, NDVI (NDVI\({}_{\text{s}}\)), temperature (T\({}_{\text{s}}\)), precipitation (P\({}_{\text{s}}\)), and dryness (ET/P\({}_{\text{s}}\)); and two winter variables, temperature (T\({}_{\text{w}}\)) and precipitation (P\({}_{\text{w}}\)). Then, the variables were converted to z-scores (Equation (2)) to standardize ranges and units. Due to gaps in either TRMM precipitation data or records of livestock numbers, our multivariate analyses were conducted for only 291 out of 331 _soums_.  
\[z=\frac{\text{x}-\text{x}_{\text{m}}}{\sigma} \tag{2}\]  
where z is the z-score; and x\({}_{\text{m}}\) and \(\sigma\) are the mean and standard deviation of the satellite-driven variable x for the study period, respectively.