Abstract
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 PO 4 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 PO 4 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 PO 4 do not provide a significantly stronger constraint than the annually averaged data used in previous optimization studies.
Highlights
Ocean-biogeochemistry models have many uncertain parameters that cannot be directly measured in the field or laboratory
In their optimization study of the parameters controlling the cycling of phosphorus using the annual-average global PO4 climatology, KP06 found that the parameters controlling the mean lifetime of dissolved organic phosphorus (DOP) and the fraction of new production allocated to DOP were not well constrained independently
Some other important properties of P are that: (1) it is independent of the biogeochemistry model state as well as time independent and so needs to be constructed only once, (2) the numerical scheme used to construct hAi need not match exactly the numerical scheme used for the time dependent tracer transport model so that the time-dependent scheme could in principle use a high-order upwind scheme with flux limiters, and (3) the matrix Q has a block triangular structure which means that only the diagonal blocks of the form hAi À D, where D is a diagonal matrix whose coefficients are the linear Taylor series coefficients of the retained sink terms, need to be factored in order to apply P
Summary
Ocean-biogeochemistry models have many uncertain parameters that cannot be directly measured in the field or laboratory. The optimization study we conduct is motivated by the previous work of Kwon and Primeau (2006, hereinafter referred to as KP06) In their optimization study of the parameters controlling the cycling of phosphorus using the annual-average global PO4 climatology, KP06 found that the parameters controlling the mean lifetime of dissolved organic phosphorus (DOP) and the fraction of new production allocated to DOP were not well constrained independently. They speculated that perhaps the information in the seasonal variations of the PO4 climatology that was left out in the cost function for their steady-state model might help to better constrain the parameters.
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