## 2 Materials and Methods
### Driving Variables for the P Model Simulations  
GPP simulations were generated using the P-model and implemented via the \(R\) package 'rpmodel' [15; 38]. Here, we used a formulation of the P-model that does not account for soil moisture stress, but with an updated formulation for the temperature sensitivity of quantum yield in C\({}_{4}\) plants (see below).  
Solar radiation and vapour pressure data were obtained from the ECMWF high-resolution forecast model. These data (available in 0.25\({}^{\circ}\) grid cells) are operational forecasts for the next 24 h obtained via the MeteoGroup operational forecast system: ([[https://www.ecmwf.int/en/forecasts/datasets/set-i](https://www.ecmwf.int/en/forecasts/datasets/set-i)]([https://www.ecmwf.int/en/forecasts/datasets/set-i](https://www.ecmwf.int/en/forecasts/datasets/set-i)), accessed on 11 May 2021). IPAR data were derived from global radiation and converted to PPFD using the conversion factor 2.04 \(\mu\)mol J\({}^{-1}\)[39]. The vapour pressure deficit was calculated from vapour pressure and air temperature following [PERSON] et al. [40].  
Daily temperature data were obtained from (a) gridded ECMWF meteorological data as described above (\(T_{\text{air}}\), \({}^{\circ}\)C); and (b) from remotely sensed LST using daily level 3C Sentinel-3A SLSTR [41] obtained via the ESA project Land Surface Temperature Climate Change Initiative ([[https://climate.esa.int/en/projects/land-surface-temperature/about/](https://climate.esa.int/en/projects/land-surface-temperature/about/)]([https://climate.esa.int/en/projects/land-surface-temperature/about/](https://climate.esa.int/en/projects/land-surface-temperature/about/)), accessed on 7 July 2021). Pre-processing of these LST data involved cloud/confidence masking, separating day- and night-time overpasses, and interpolation using a cubic smoothing spline (function smooth.spline () with parameter spar = 0.01 in \(R\)) to provide ten-day averages based on the daytime overpass (typically mid-morning _ca_ 10:00).  
fAPAR data were obtained from the operational Sentinel-3 ESA Full Resolution OLCI product (OL_2_LFR, [[https://sentinel.esa.int/web/sentinel/user-guides/sentinel-3-olci/product-types/level-2-land](https://sentinel.esa.int/web/sentinel/user-guides/sentinel-3-olci/product-types/level-2-land)]([https://sentinel.esa.int/web/sentinel/user-guides/sentinel-3-olci/product-types/level-2-land](https://sentinel.esa.int/web/sentinel/user-guides/sentinel-3-olci/product-types/level-2-land)), accessed on 12 May 2021). The OGVI (OLCI Global Vegetation Index) and \"OGVI_err\" band contain respectively the instantaneous green fAPAR and associated product uncertainties. Pre-processing implemented the associated LQSF layer (classification, quality, and science flags) to remove clouds and cloud shadows. The remaining data were further smoothed, and gap-filled, with a Gaussian process regression ([[https://scikit-learn.org/stable/modules/gaussian_process.html](https://scikit-learn.org/stable/modules/gaussian_process.html)]([https://scikit-learn.org/stable/modules/gaussian_process.html](https://scikit-learn.org/stable/modules/gaussian_process.html)), accessed on 13 May 2021) algorithm, that allows the propagation of the initial data uncertainties to the gap-filled time series. The resulting output series were mapped to a 10-day interval.  
Annual values of the CO\({}_{2}\) mole fraction were obtained from the monitoring station at Mauna Loa, Hawaii (Scripps Institution CO\({}_{2}\) monitoring network: [[http://scrippsco2.ucsd.edu/data/atmospheric_co2/mlo](http://scrippsco2.ucsd.edu/data/atmospheric_co2/mlo)]([http://scrippsco2.ucsd.edu/data/atmospheric_co2/mlo](http://scrippsco2.ucsd.edu/data/atmospheric_co2/mlo)), accessed on 1 September 2021) and converted to partial pressure units for input to the P model.