Merging a model of optimal allocation of carbon and nitrogen with one of photosynthesis and respiration

Abstract. Knowledge of the evolution of the terrestrial carbon cycle in a changing climate is important for many reasons, including allowing for an assessment of the extent to which the land can partially offset carbon dioxide (CO₂) emissions due to human burning of fossil fuels. However, understanding some characteristics of the response of terrestrial ecosystems to different environmental forcings remains limited. Future detailed measurement campaigns may advance our understanding of ecological processes, but many measurements that are needed to improve model representation have not yet been collected. Furthermore, a prerequisite of large-scale land surface models is their ability to accurately estimate change in all locations, and so will inevitably include places for which data may never be available. This global requirement is due to the need to develop robust predictions of the overall response of how land carbon stores will evolve in response to climate change, despite incomplete information and related unknowns. Global carbon storage on land still continues to increase, compensating for a substantial fraction of anthropogenic carbon dioxide (CO₂) emissions. Quantifying the magnitude of future CO₂ drawdown is critical to determining emissions pathways compatible with climate targets, including limiting global warming to two degrees above preindustrial levels. Designed to reduce uncertainty in terrestrial carbon storage and its interactions with biogeochemical cycles, optimisation hypotheses propose that ecosystems maximise specific attributes such as carbon uptake. If validated, these hypotheses offer a mathematical framework that can replace unknown mechanistic equations in land system models. Furthermore, optimal calculations that represent plant responses to local environmental conditions can capture geographical variations, substituting for spatially incomplete data, and, in particular, additionally provide expected responses to climate change forcings. Here, we substantially extend an existing description of the optimal carbon allocation between the three stores of wood, foliage, and fine root biomass (Makela et al., 2008). This extension incorporates an established model of the photosynthesis response (Farquhar et al., 1980) and the stomatal response (Medlyn et al., 2011) to near-surface meteorological conditions. The original optimal algorithm (Makela et al., 2008) maximises net primary productivity (that is, photosynthesis minus maintenance respiration) by determining how available nitrogen is allocated, which then influences the simulated size of the three carbon stores. In our extended mathematical framework, we first present how optimal allocation and resultant wood, foliage and fine root store sizes additionally depend on individual changes to near-surface meteorological and climatological drivers. We then estimate projected changes in allocation for the simultaneous increase in temperature and atmospheric CO₂ concentration, representing the effects of global warming. Finally, we evaluate the performance of the revised model in a temperate mature deciduous oak forest, contrasting with its original development for mature boreal evergreen pines. This forest is located at the BIFoR FACE (Birmingham Institute for Forest Research Free Air Carbon Dioxide Enrichment) facility, where continuous monitoring of the response of temperate forest trees to CO₂ has been carried out since 2018 (Foyer et al., 2025). Such data reveal that our enhanced simulation structure performs well in projecting the allocation of carbon to different stores. A key aim of our analysis is to create a mathematical structure for potential inclusion in the terrestrial carbon cycle components of Land Surface Models (LSMs). These models, in turn, may be used in Earth System Models (ESMs), to aid projections by the latter of the global carbon cycle in response to prescribed scenarios of CO₂ emissions.