Department of Earth System Science

We present a computationally-efficient method for obtaining the fully spun-up state of a seasonally-varying global ocean biogeochemistry model. The solver uses a Newton–Krylov method to find the fixed points of the map that assigns to an initial state the value of the model state at the end of a one-year run. Apart from the preconditioner, which we describe in the paper, the method relies on a black-box public-domain Newton–Krylov solver that does not require the explicit construction of the model’s Jacobian matrix. Applied to the PO₄ plus dissolved organic phosphorus (DOP) cycle of an Ocean Carbon Model Intercomparison Project II (OCMIP-2) type model, the solver is more than two orders of magnitude faster than the traditional time-stepping method for spinning up the model. The efficiency of the solver is illustrated by using the seasonally varying globally-gridded PO₄ climatology to objectively optimize the parameters that control the mean lifetime of semi-labile DOP and the fraction of new production allocated to DOP. The optimization study demonstrates that the information in the seasonal variations of PO₄ do not provide a significantly stronger constraint than the annually averaged data used in previous optimization studies.