Numerous current efforts seek to improve the representation of ecosystem ecology and vegetation demographic processes within Earth System Models (ESMs). These developments are widely viewed as an important step in developing greater realism in predictions of future ecosystem states and fluxes. Increased realism, however, leads to increased model complexity, with new features raising a suite of ecological questions that require empirical constraints. Here, we review the developments that

Terrestrial gross primary production (GPP) is the basis of food production and 24 vegetation growth globally 1 , and plays a critical role in regulating atmospheric CO2 through its 25 impact on ecosystem carbon balance. Even though higher CO2 concentrations in future decades 26 can increase GPP 2 , low soil water availability, heat stress, and disturbances associated with 27 droughts could reduce the benefits of such CO2 fertilization. Here we analyzed outputs of 13 28 Earth System Models (ESMs) to show an increasingly stronger impact on GPP by extreme 29 droughts than mild and moderate droughts over the 21 st century. Due to a dramatic increase in 30 the frequency of extreme droughts, the magnitude of globally-averaged reductions in GPP 31 associated with extreme droughts was projected to be nearly tripled by the last quarter of this 32 century (2075-2099) relative to that of the historical period (1850-1999) under both high and 33 intermediate greenhouse gas emission scenarios. In contrast, the magnitude of GPP reduction 34 associated with mild and moderate droughts was not projected to increase substantially. Our 35 analysis indicates a high risk of extreme droughts to the global carbon cycle with atmospheric 36 warming; however, this risk can be potentially mitigated by positive anomalies of GPP 37 associated with favorable environmental conditions. 38 39 3 The terrestrial biosphere absorbed ~30% of anthropogenic carbon emissions from fossil 40 fuels during 1990-2007 3 , making it a critical component of the global carbon sink that mitigates 41 fossil fuel CO2 emissions and associated climate warming. GPP is a measure of fixation of CO2 42 into an ecosystem through photosynthesis and plays a key role in the net carbon balance of the 43 terrestrial biosphere and the terrestrial CO2 absorption. However, despite our knowledge of CO2 44 fertilization effects on plant productivity 2 , the future trend of GPP under elevated CO2 levels 45 remains highly uncertain due to the impact of many factors such as nutrient limitation 4 and 46 increasing frequency and intensity of drought 5 . Drought is already the most widespread factor 47

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.

The spin-up of land models to steady state of coupled carbon–nitrogen processes is computationally so costly that it becomes a bottleneck issue for global analysis. In this study, we introduced a semi-analytical solution (SAS) for the spin-up issue. SAS is fundamentally based on the analytic solution to a set of equations that describe carbon transfers within ecosystems over time. SAS is implemented by three steps: (1) having an initial spin-up with prior pool-size values until net primary productivity (NPP) reaches stabilization, (2) calculating quasi-steady-state pool sizes by letting fluxes of the equations equal zero, and (3) having a final spin-up to meet the criterion of steady state. Step 2 is enabled by averaged time-varying variables over one period of repeated driving forcings. SAS was applied to both site-level and global scale spin-up of the Australian Community Atmosphere Biosphere Land Exchange (CABLE) model. For the carbon-cycle-only simulations, SAS saved 95.7% and 92.4% of computational time for site-level and global spin-up, respectively, in comparison with the traditional method (a long-term iterative simulation to achieve the steady states of variables). For the carbon–nitrogen coupled simulations, SAS reduced computational cost by 84.5% and 86.6% for site-level and global spin-up, respectively. The estimated steady-state pool sizes represent the ecosystem carbon storage capacity, which was 12.1 kg C m⁻² with the coupled carbon–nitrogen global model, 14.6% lower than that with the carbon-only model. The nitrogen down-regulation in modeled carbon storage is partly due to the 4.6% decrease in carbon influx (i.e., net primary productivity) and partly due to the 10.5% reduction in residence times. This steady-state analysis accelerated by the SAS method can facilitate comparative studies of structural differences in determining the ecosystem carbon storage capacity among biogeochemical models. Overall, the computational efficiency of SAS potentially permits many global analyses that are impossible with the traditional spin-up methods, such as ensemble analysis of land models against parameter variations