A semi-analytical solution to accelerate spin-up of a coupled carbon and nitrogen land model to steady state

Abstract

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.