# The Net Influence of Drought on Grassland Productivity over the Past 50 Years
## 2 Materials and Methods
### Model Applicability Evaluation  
Based on the model parameterization and sensitivity analysis, it is necessary to further evaluate the model's ability to be applied regionally. The validation of model applicability is mainly to evaluate the degree of agreement between simulated and observed values until there is no statistically significant difference between simulated and observed values. In this study, linear regression analysis, root mean square error (RMSE), and significance level (\(p<0.001\)) were used as evaluation indicators to validate the accuracy of model simulations, and the calculations using Equations (1) and (2) for each indicator were as follows:  
\[y=bx+a \tag{1}\]  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(C_{si}-C_{oi}\right)^{2}} \tag{2}\]  
where \(y\) is the simulated value, \(x\) is the observed value, \(b\) is the slope, and a is the intercept; the most ideal result of the model simulation should be \(a=0\) and \(b=1\). Therefore, the closeness of b to 1 in the linear regression equation directly reflects the effect of model simulation. \(N\) denotes the number of samples, \(C_{si}\) denotes the simulated result value, and \(C_{oi}\) denotes the measured result value. In this paper, the Biome-BGC model was calibrated according to different carbon and water fluxes using different grassland-type flux sites and literature data in Inner Mongolia. The data details are shown in Table 3. According to the aim of the study, the key carbon and water flux parameters such as GPP, Re, NEP, and ET were mainly calibrated and optimized. According to the data characteristics of different stations, the NPP data of corresponding periods were extracted for comparative analysis to evaluate the accuracy and applicability of the Biome-BGC model simulation. The meadow grassland carbon and water fluxes were verified mainly using the data from 2003-2007 at the Tongyu flux station, as shown in Table 3. The GPP of the Tongyu flux station is the synthetic data for 8 days from 2004 to 2006; the NEP and ET are the daily values from 2003 to 2007. According to the conversion relationship of aboveground and belowground biomass (belowground biomass = 5.26 \(\times\) aboveground biomass) and the NPP and biomass conversion relationship (carbon gC\(\cdot\)m\({}^{-2}\) = biomass \(\times\) 0.45 g\(\cdot\)m\({}^{-2}\)) for temperate meadow grasslands, the Ewenke Banner grazing NPP data were calculated from 1989-2005 at the weather station. From Figure 3, it can be seen that, generally, the model simulated values are in good agreement with the flux observations, and all the \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Grassland Type** & **Site Name** & **Site Location** & **Elevation (m)** & **Time Scale** & **Data Source** & **Application** \\ \hline \multirow{3}{*}{Meadow stepe} & Tongyu flux station & 44.42 N, 122.87 E & 184 & 2004-2007 & \multirow{3}{*}{COIRAS} & Calibration models \\  & Xing\(\cdot\)an League & 46.10 N, 123.00 E & 191 & 1981–1990 & & ORNL (Oak Ridge National Laboratory) & Validation of drought \\  & experimental site & 49.22 N, 119.75 E & 610.2 & 1989–2005 & Literature biomass & \\  & & & & & (Ma, R.F., 2007) & Calibration models \\  & Xilinhot flux station & 43.55 N, 116.67 E & 1125 & 2003–2007 & Literature biomass & \\  & & & & & ([PERSON] et al., 2010; \\ Typical stepe & & & & & & [PERSON] et al., 2008) & \\  & & & & & & ChinaFLUX and \\  & Xilinpole flux station & 43.63 N, 116.70 E & 1100 & 2004–2005 & Literature biomass & \\  & Xilinhot experimental & & & & ([PERSON] et al., 2003) & \\  & Station & 43.72 N, 116.63 E & 1200 & 1980–1989 & ORNL (Oak Ridge National Laboratory) & Validation of drought \\  & Xilinhot pilot site & 43.95 N, 116.12 E & 1063 & 1982–2006 & Literature biomass & \\  & & & & & (Ma, R.F., 2007) & Calibration models \\  & & & & & & (McGraw and Literature biomass \\ Desert stepe & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \end{tabular}
\end{table} 
Table 3: The details of fluxes and experimental sites.