Scaling from individual trees to forests in an Earth system modeling framework using a mathematically tractable model of height-structured competition

Abstract. The long-term and large-scale dynamics of ecosystems are in large part determined by the performances of individual plants in competition with one another for light, water, and nutrients. Woody biomass, a pool of carbon (C) larger than 50% of atmospheric CO₂, exists because of height-structured competition for light. However, most of the current Earth system models that predict climate change and C cycle feedbacks lack both a mechanistic formulation for height-structured competition for light and an explicit scaling from individual plants to the globe. In this study, we incorporate height-structured competition for light, competition for water, and explicit scaling from individuals to ecosystems into the land model version 3 (LM3) currently used in the Earth system models developed by the Geophysical Fluid Dynamics Laboratory (GFDL). The height-structured formulation is based on the perfect plasticity approximation (PPA), which has been shown to accurately scale from individual-level plant competition for light, water, and nutrients to the dynamics of whole communities. Because of the tractability of the PPA, the coupled LM3-PPA model is able to include a large number of phenomena across a range of spatial and temporal scales and still retain computational tractability, as well as close linkages to mathematically tractable forms of the model. We test a range of predictions against data from temperate broadleaved forests in the northern USA. The results show the model predictions agree with diurnal and annual C fluxes, growth rates of individual trees in the canopy and understory, tree size distributions, and species-level population dynamics during succession. We also show how the competitively optimal allocation strategy – the strategy that can competitively exclude all others – shifts as a function of the atmospheric CO₂ concentration. This strategy is referred to as an evolutionarily stable strategy (ESS) in the ecological literature and is typically not the same as a productivity- or growth-maximizing strategy. Model simulations predict that C sinks caused by CO₂ fertilization in forests limited by light and water will be down-regulated if allocation tracks changes in the competitive optimum. The implementation of the model in this paper is for temperate broadleaved forest trees, but the formulation of the model is general. It can be expanded to include other growth forms and physiologies simply by altering parameter values.