Evaluation of the Accuracy of an Offline Seasonally-Varying Matrix Transport Model for Simulating Ideal Age

Newton-Krylov (NK) solvers for ocean tracers have the potential to greatly decrease the computational costs of spinning up deep-ocean tracers, which can take several thousand model years to reach equilibrium with surface fluxes. One version of the algorithm uses offline tracer transort matrices to simulate an annual cycle of tracer fluxes. Here we present the impact of time-averaging the transport matrices on the equilibrium of an ideal-age tracer. We compared annually-averaged, monthly-averaged, and 5-day-averaged transport matrices with an online simulation using the ocean component of the Community Earth System Model (CESM) with a nominal horizontal resolution of 1^°x 1^° and 60 vertical levels. We found that increasing the time resolution of the offline transport model reduced a low age bias from 12% for the annual averaged operator, to 4% for the monthly averaged operators, and to less than 2% for the operator constructed from 5-day averages. The largest differences were in areas with strong seasonal changes in the circulation, such as the Northern Indian Ocean, and the Equatorial Eastern Pacific. For many applications the relatively small bias obtained using the offline model makes the offline approach attractive because it uses significantly fewer computer resources and is simpler to set up and run.