Application of a fast Newton-Krylov solver for equilibrium simulations of phosphorus and oxygen

•Newton-Krylov solver applied to a 3-pool phosphorous model and oxygen model.•New preconditioning strategy to speed up the convergence of Newton-Krylov solver.•Seasonal varying equilibrium state of the cycling of phosphorous and oxygen.•By from their eventual equilibrium, model states after a 300 year spinup still drifting away.

Model drift due to inadequate spinup is a serious problem that complicates the interpretation of climate change simulations. Even after a 300 year spinup we show that solutions are not only still drifting but often drifting away from their eventual equilibrium over large parts of the ocean. Here we present a Newton-Krylov solver for computing cyclostationary equilibrium solutions of a biogeochemical model for the cycling of phosphorus and oxygen. In addition to using previously developed preconditioning strategies - time-averaging and coarse-graining the Jacobian matrix - we also introduce a new strategy: the adiabatic elimination of a fast variable (particulate organic phosphorus) by slaving it to a slow variable (dissolved inorganic phosphorus). We use transport matrices derived from the Community Earth System Model (CESM) with a nominal horizontal resolution of 1° × 1° and 60 vertical levels to implement and test the solver. We find that the new solver obtains seasonally-varying equilibrium solutions with no visible drift using no more than 80 simulation years.