## 1 Introduction  
Since the industrial revolution, the earth has entered an era in which human impacts on the fluxes of radiative energy through the earth system have demonstrable effects on climate (Intergovernmental Panel on Climate Change (IPCC) 2007). Net primary productivity (NPP), or the rate of assimilation of carbon dioxide (CO\({}_{2}\)) through photosynthesis, is the fundamental link between the atmosphere and the biosphere [1]. NPP contributes to human survival because it is not only the basis for food, fiber and wood production, but also affects composition of the atmosphere, the availability of fresh water, biodiversity, and the adjusting mechanisms of energy supply and distribution [2]. NPP is a sensitive indicator of climatic and other forms of environmental change [3], and is increasingly pertinent to land-use management [2; 4]. [PERSON] et al. found that the human appropriation of NPP (HANPP, which is an important indicator of environmental sustainability) amounted to 56% of the annual potential natural NPP in the territory of the Czech Republic [5]. In particular, urban ecosystem NPP is a key indicator of vegetation health in urban ecosystems, which provide critical services to urban residents, including the \"regulating services\" (e.g., purification of air and water, and regulation of climate and floods), \"cultural services\" (e.g., recreational, spiritual, religious and other nonmaterial benefits), and \"supporting services\" (e.g., nutrient cycling) [6]. For example, [PERSON] et al. found the observed diurnal cool island effect in hot desert cities could be largely explained by relative vegetation abundance [7]. Since human well-being in urban areas depends on the ecosystem services provided by urban vegetation, urban sustainability depends on the sustainability of urban ecosystems [8]. The ecosystem health of urban vegetation and the ecosystem services provided by them may be vulnerable because of the intensified environmental stresses (e.g., heat and drought) due to future climate change [9]. Multiple lines of evidence indicated that urban ecosystem NPP is sensitive to environmental changes at various spatiotemporal scales. Previous studies have investigated inter-annual variability of NPP in response to climate change [10; 11; 12; 13], the contributions of urbanization and climate change to NPP variations [14; 15; 16; 17], and the effect of urban land transformation on NPP [18]. Most research has been focused on the effect of land use/land cover change and historical climate change; however, the dynamic of NPP in response to future climate/CO\({}_{2}\) change effects are still unclear. To predict and manage urban ecosystem sustainability in the 21 st century, it is important to estimate the changes of urban ecosystem NPP in response to various future trajectories of climate and CO\({}_{2}\). Ecosystem process-based modeling is a powerful tool to quantitatively estimate and predict dynamics in terrestrial biogeochemical cycles and isolate/analyze associated control mechanisms in the context of global change [19; 20]. In this study, an urban ecosystem model, the Hierarchical Patch Mosaic-Urban Ecosystem Model (HPM-UEM), was used to predict the responses of the NPP of the Phoenix city, AZ, USA to climate and CO\({}_{2}\) changes in the 21 st century. The model simulations were conducted in 500-m spatial resolution, and the NPP changes under three representative concentration pathways--RCP2.6, RCP4.5 and RCP8.5--were compared. Numeric experiments and factorial analyses were designed to isolate and quantify the individual effects of temperature, precipitation, and CO\({}_{2}\) changes, and their interactive effects on NPP. The research objectives are: (1) projecting the trends of urban ecosystem NPP so as to evaluate the performance (growth, coverage, health, etc.)