Theory predicts that rising CO2 increases global photosynthesis, a process known as CO2 fertilization, and that this is responsible for much of the current terrestrial carbon sink. The estimated magnitude of the historic CO2 fertilization, however, differs by an order of magnitude between long-term proxies, remote sensing-based estimates and terrestrial biosphere models. Here we constrain the likely historic effect of CO2 on global photosynthesis by combining terrestrial biosphere models, ecological optimality theory, remote sensing approaches and an emergent constraint based on global carbon budget estimates. Our analysis suggests that CO2 fertilization increased global annual terrestrial photosynthesis by 13.5 ± 3.5% or 15.9 ± 2.9 PgC (mean ± s.d.) between 1981 and 2020. Our results help resolve conflicting estimates of the historic sensitivity of global terrestrial photosynthesis to CO2 and highlight the large impact anthropogenic emissions have had on ecosystems worldwide.

Mechanistic vegetation models serve to estimate terrestrial carbon fluxes and climate impacts on ecosystems across diverse biotic and abiotic conditions. Systematically informing them with data is key for enhancing their predictive accuracy and estimate uncertainty. Here we present the Simulating Optimal FUNctioning rsofun R package, providing a computationally efficient and parallelizable implementation of the P-model for site-scale simulations of ecosystem photosynthesis, complemented with functionalities for Bayesian model-data integration and estimation of parameters and uncertainty. We provide a use case to demonstrate the package functionalities for modelling ecosystem gross CO2 uptake at one flux measurement site, including model sensitivity analysis, Bayesian parameter calibration, and prediction uncertainty estimation. rsofun lowers the bar of entry to ecosystem modelling and model-data integration and serves as an open access resource for model development and dissemination.

textlessptextgreatertextlessstrong class="journal-contentHeaderColor"textgreaterAbstract.textless/strongtextgreater Accurate predictions of environmental controls on ecosystem photosynthesis are essential for understanding the impacts of climate change and extreme events on the carbon cycle and the provisioning of ecosystem services. Using time-series measurements of ecosystem fluxes paired with measurements of meteorological variables from a network of globally distributed sites and remotely sensed vegetation indices, we train a recurrent deep neural network (Long-Short-Term Memory, LSTM), a simple deep neural network (DNN), and a mechanistic, theory-based photosynthesis model with the aim to predict ecosystem gross primary production (GPP). We test these models’ ability to spatially and temporally generalise across a wide range of environmental conditions. Both neural network models outperform the theory-based model considering leave-site-out cross-validation (LSOCV). The LSTM model performs best and achieves a mean textlessemtextgreaterRtextless/emtextgreater$^textrm2$ of 0.78 across sites in the LSOCV and an average textlessemtextgreaterRtextless/emtextgreater$^textrm2$ of 0.82 across relatively moist temperate and boreal sites. This suggests that recurrent deep neural networks provide a basis for robust data-driven ecosystem photosynthesis modelling in respective biomes. However, limits to global model upscaling are identified using cross-validation by vegetation types and by continents. In particular, our model performance is weakest at relatively arid sites where unknown vegetation exposure to water limitation limits model reliability.textless/ptextgreater