NPP were extracted from MOD17A3H product at a spatial resolution of 500 m by 500 m from 2005 to 2014 using the latitude and longitude of each site (S. Running 2015). To account for likely biases in the remote-sensing derived NPP for our forest sites, we selected the grid-cell at which the site was located and its eight surrounding grid-cells, and calculated mean NPP of each of those nine grid-cells from 2005 to 2014. We took the minimum, maximum range and average of the nine mean NPPs across 9 grid-cells as the prior range and initial value of NPP in an optimization framework to estimate the site-specific NPP. The optimization framework was based on the parsimonious framework developed by Wang et al. (2018b) that integrated above-mentioned observation-driven datasets, tracked C (N and P) allocations and transfers among different ecosystem compartments from a system viewpoint based on mass-balance. Through this framework, we optimized seven more parameters in addition to NPP (see Table S1), with detailed information in Supplementary Methods.

Direct measurements of N inputs (deposition and biological N fixation (BNF)) and P inputs (deposition and weathering) across these 127 sites were not available. To reasonably estimate these quantities, we extracted values from available resources that calculate these values through combining theoretical understandings (models) with observations. We obtained N and P depositions from Wang et al. (2017) that merged atmospheric transports and field measurements. BNF was derived from Peng et al. (2020) using simulations by the Australian Community Atmosphere‐Biosphere‐Land Exchange model (CABLE). Weathering P release was estimated through its relationships with runoff, lithology, temperature, and soil properties from Hartmann et al. (2014). Without site-level measurements, we considered those estimates as reasonable first order approximations for our study across space.