## 2 Materials and Methods
### Terrestrial Biosphere Models  
We used four terrestrial biosphere models to analyze changes in GPP from 1982 to 2011. The models included BEAMS Version 1.3 [18, 41], Biome-BGC Version 4.2 [53], LPJ Version 3 [20, 54], and MOSES/TRIFFID [55, 56]. These models differ in terms of their model structure, parameters, and required input data. The BEAMS model is categorized as a diagnostic terrestrial biosphere model, which simulates spatial and temporal patterns in the carbon cycle more realistically using satellite-based LAI and FPAR inputs than prognostic terrestrial biosphere models. The model calculates GPP using a function of FPAR, shortwave radiation and an environmental regulation factor. The environmental regulation factor is calculated by combined [PERSON]'s photosynthesis model [57, 58] and the Ball-Berry-type stomatal conductance model [59, 60] using CO\({}_{2}\), temperature, soil moisture, and relative humidity. The Biome-BGC model is a prognostic terrestrial biosphere model with fixed vegetation cover. The model runs with only climate data as a time-variant input. The model calculates GPP using a function of the CO\({}_{2}\), shortwave radiation, temperature, soil moisture, and vapor pressure deficit using the Farquhar biochemical photosynthesis model [57] with a Jarvis-type stomatal conductance model [61]. LPJ and TRIFFID are dynamic global vegetation models that explicitly simulate vegetation types and run with only climate data as a time-variant input. The LPJ model calculates GPP using a function of CO\({}_{2}\), shortwave radiation, temperature, and soil moisture using the Farquhar biochemical photosynthesis model [62] with stomatal conductance estimated from a Ball-type conductance model [59]. The TRIFFID model calculates GPP as a function of CO\({}_{2}\), shortwave radiation, temperature, soil moisture, and relative humidity using a leaf-level photosynthesis model [58, 63] with a coupled photosynthesis and stomatal conductance model [64].  
The models were used under a consistent protocol. The 1901-1930 period was used for the spin-up period dependent on each model's spin-up setting. The models were run from 1901 to 2011 with time-variable inputs of climate data (for all models) and satellite-based LAI and FPAR data (for BEAMS only). BEAMS was spun-up for 3000 years using 1901 climate data. Biome-BGC was spun-up using the 1901-1930 climate data repeatedly until the soil carbon reached equilibrium, with 6,000 years as the maximum spin-up length. LPJ was spun-up for 1,000 years using the 1901-1930 climate data repeatedly with the fire module disabled. Finally, TRIFFID was spun-up for 1000 years using the 1901-1930 climate data repeatedly.  
In addition to the simulations with time-variable inputs for all climate parameters, we conducted sensitivity experiments based on an existing study to identify the causes of temporal GPP variations [65].  
For each simulation, the models were run using only one climate time-series with an interannual variability in temperature, precipitation, solar radiation and atmospheric CO\({}_{2}\) concentration; the other climate components were held at their 1901 values. We tested four climate parameters (_i.e._, temperature, precipitation, solar radiation and atmospheric CO\({}_{2}\) concentration) that are commonly incorporated in terrestrial biosphere models.