## 2 Materials and Methods
### Input Data Description  
The model inputs include 500-m resolution spatial datasets of climate, atmospheric CO\({}_{2}\), land-use and land-cover, and base maps for the study area. The base map datasets contain: (a) the topographic maps (elevation, slope, and aspects) derived from the 7.5-min US Geological Survey (USGS) National Elevation Dataset (NED); (b) the soil maps contain bulk density (g/cm\({}^{3}\)), volumetric content of sand and clay (%), depth (m), and acidity (pH), which are generated from 1-km resolution digital general soil association map; and (c) spatial map of nitrogen deposition based on the study of [PERSON] et al. (2005), [PERSON] et al. (2001), and [PERSON] et al. (2008) [33; 34; 35]. A detailed description of sources and the development of the base map datasets are found in [PERSON] et al. [21]. Future climate trends were based on the fifth phase of the Coupled Model Intercomparison Project (CMIP5) projections [36] ([[https://esgf-data.dkrz.de/search/esgf-dkrz/](https://esgf-data.dkrz.de/search/esgf-dkrz/)]([https://esgf-data.dkrz.de/search/esgf-dkrz/](https://esgf-data.dkrz.de/search/esgf-dkrz/))). The CMIP5 strategy includes several types of long-term climate change modeling experiments. The core simulations within the suite of CMIP5 long-term experiments include future projection simulation forced with specified concentrations [referred to as \"representative concentration pathways\" (RCPs)]. The labels for the RCPs provide a rough estimate of the radiative forcing in the year 2100 (relative to preindustrial conditions). For example, the radiative forcing in RCP8.5 increases throughout the twenty-first century before reaching a level of about 8.5 W m\({}^{-2}\) at the end of the century. In addition to this \"high\" scenario, RCP4.5 is intermediate, and there is a low, so-called peak-and-decay, scenario, RCP2.6, in which radiative forcing reaches a maximum near the middle of the twenty-first century before decreasing to an eventual nominal level of 2.6 W m\({}^{-2}\)[36; 37]. The future climate projections from different general circulation model (GCM) models could be very different. Because of the large number of simulation unit (over 11 thousand grid pixels) and long simulation time-period (100 years with a daily time-step) in this study, it was practically impossible to conduct multiple simulations for each RCP scenario (currently, each round of simulation takes more than one month, not including the additional time for data processing). Therefore, different GCM model products were evaluated using historical (2000-2005) climate datasets developed based on observational climate records from local meteorological stations [21] (Table 1). Then, based on the evaluation result, the best GCM product was selected to develop the high-resolution future climate dataset to drive the model simulation. In total, there are only eight GCM model products meet the data requirement of this study (Table 1). Our evaluation indicated the MPI-ESM-MR model products have the best performance in the study area, with highest correlation (R\({}^{2}\) = 0.85) and least bias of \(-\)81. Therefore, the future climate and CO\({}_{2}\) datasets for the Phoenix (2006-2099) were developed based on the MPI-ESM-MR model products and the RCP protocol, which were statistically downscaled to 500-m resolution based on a high-resolution historical (2000-2005) climate and CO\({}_{2}\) dataset of the Phoenix city [21] using the Localized Constructed Analogs (LOCA) method [38; 39]. The LOCA spatial downscaling procedure includes four steps: (a) develop analog pool points and spatial masks; (b) select analog days at the regional scale; (c) find the one best matching analog day at the local scale; and (d) construct final downscaled field using scale factors. Another detailed description of the LOCA methodology can be found in [PERSON] et al. [40].