The cycling of nutrients and carbon in the ocean and land systems has adjustment timescales that extend out to centuries and millennia. For high-resolution models, these long timescales make it computationally infeasible to spin-up the biogeochemical components of Earth-system models (ESMs) by simply time-stepping them forward until transients die out. As a result, ESMs typically experience a drift for the first several hundred to thousand years of simulation as the oceans adjust to the surface forcing and the soil carbon and nutrient pools adjust to the drifting climate. Furthermore, biogeochemical modules in ESMs have many parameters that are calibrated by “fitting” the model to observations rather than from first principles. The biogeochemistry initialization problem therefore consists of finding a consistent set of parameters and biogeochemical state variables that minimize model drift and mismatch of the resulting model state with a sparse and noisy observational database. Here we propose to address this problem by: (1) fully implementing Newton-Krylov spin-up methods to the marine biogeochemical module (MARBL) in an offline approach using tracer-transport operators derived from Energy Exascale Earth System Model (E3SM)’s ocean component (MPAS-O), (2) extend the application of Newton- Krylov spin-up techniques to E3SM’s land model (ELM), (3) develop the computational infrastructure needed for an online spin-up of MARBL and ELM that is integrated with the Common Infrastructure for Modeling the EARTH (CIME), and (4) generate a fully coupled initial state for the Earth’s carbon cycle.

Previous efforts with Newton-Krylov based solvers for spinning up ocean tracers have been applied to O(100km) grid resolution and obtained orders of magnitude acceleration of spin-up times. Some aspects that will need to be addressed are the impact of internally generated variability (e.g. mesoscale eddies) on the definition of cyclo-stationarity and the impacts of finer grid resolution on the design of the preconditioner for the Krylov solver portion of the method. In addition to addressing these research topics, we will build on the recent development of cyclo-stationary solvers for the planetary-geostrophic equations to explore the extension of Newton- Kryolv techniques to dynamically active temperature and salinity tracers in MPAS-O.