Application of a fast Newton–Krylov solver for equilibrium simulations of phosphorus and oxygen. (November 2017) - Fu, Weiwei; Primeau, François
Highlights: 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. Abstract: 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.