## 2 Materials and Methods
### Experimental Design and Factorial Analysis  
The implementation of HPM-UEM simulation includes three steps: (a) equilibrium run; (b) spin-up; and (c) transient run. The main purpose of equilibrium run was to establish a baseline for the biomass, soil carbon and water pools. The model was driven by the initial climate datasets and CO\({}_{2}\) concentration in the year of 2000 at the equilibrium step. Then, a spin-up run of 1000 (200 spins \(\times\) 5 years/spin), driven by random data sequence of de-trend climate data of 2000-2005 was conducted to reduce biases in the transient simulations. Finally, the time series data for climate and CO\({}_{2}\) was applied to simulate the NPP dynamics in the 21 st century (2006-2099) under different RCP scenarios. To identify the magnitude and relative contribution of various environmental factors (temperature, precipitation, and CO\({}_{2}\) concentration), four numeric experiments were designed. The OVERALL experiment (multifactor) was set up to simulate the combined effect of climate and CO\({}_{2}\) change on NPP during the entire study period. The other experiments--CO\({}_{2}\), TMP, and PPT--were set up to project the relative devotion of CO\({}_{2}\) change (or CO\({}_{2}\) fertilization effect), temperature change, and precipitation change on NPP during the entire period, respectively. In the multifactor experiment (i.e., OVERALL), all environmental factors were allowed to change from day by day. In the three other factorial experiments, one factor was changed while the others were kept unchanged (to the level of equilibrium year); taking the CO\({}_{2}\) experiment for example, CO\({}_{2}\) concentration was transient during 2000-2099 while climate data (temperature and precipitation) were kept at the equilibrium level. Based on the simulation results, a serial of factorial experiments were conducted to quantify the individual effects of CO\({}_{2}\)/climate factors:  
\[Effect_{factor}=NPP_{factor,\;end}\;-\;NPP_{factor,\;start}(\text{where factor }\epsilon\;[CO2,\; TMP,\; PPT])\]  
where \(Effect_{factor}\) is the magnitude of NPP change during a certain time period as defined by the subscriptions of \"start\" to \"end\" in response to the changes in climate/CO\({}_{2}\) factors (including CO\({}_{2}\), temperature, precipitation). Following previous studies [41; 42], the NPP dynamics during \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Land-Use Type** & **Area (km2)** & **Percentage (\%)** & **Description** \\ \hline Industrial area & 157.45 & 5.43 & Industrial \\  & & & Other Employment-Landfill/Proving Grounds/Sand and Gravel/etc. \\ \hline  & & & Single Family Medium Density-1 to 4 du/ac \\  & & & Multi Family-Apartment/Condo \\  & & & Single Family Low Density-Less than 1 du/ac \\  & & & Single Family High Density-Greater than 4 \\  & & & du/ac-Includes Mobile Homes \\ \hline  & & & Cemetery \\  & & & Educational \\  & & & Medical/Nursing Home \\  & & & Mixed Use \\  & & & Office \\  & & & Public/Special Event/Military \\  & & & Religious/Institutional \\ \hline Transportation & 36.43 & 1.26 & Airport \\  & & & Transportation \\ \hline Waters & 52.75 & 1.82 & Water \\ \hline Recreation area & 93.03 & 3.21 & Golf Course \\ \hline Construction/transition & 39.36 & 1.36 & Developing Employment Generating \\  & & & Developing Residential \\ \hline Agricultural & 139.5 & 4.81 & Agriculture \\ \hline  & & & Vacant \\ \hline Vacant natural & 467.04 & 16.09 & Active Open Space \\  & & & Passive/Restricted Open Space/Undevelopable \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._the first-half, second-half, and the whole 21 st century were estimated by comparing the five-year averaged NPP of the early-21 st century (2006-2010), mid-21 st century (2048-2052), and late-21 st century (2059-2099). For example, the \"start\" was set to the 2006-2010 period, and \"end\" was set to \"2048-2052\", when estimating the NPP change during the first-half of the 21 st century.