A Computational Framework for Efficient Simulation of Chemical and Biological Tracers in the Ocean with Applications to Biogeochemistry and Paleoceanography

Numerical simulation of chemical and biological tracers has long played an important role in improving our understanding of ocean circulation and climate. However, the complexity of modern ocean general circulation models (GCMs) has prevented their more widespread use by the biogeochemical and paleoceanographic community. To address this, we have recently developed the "transport matrix method", a computational framework for tracer simulation that is significantly simpler and more efficient than full GCMs, yet retain the latter's accuracy. The essential idea is that the discrete tracer transport operator of a GCM can be written as a sparse matrix, which may be efficiently constructed by "probing" the GCM with a passive tracer. This empirical approach ensures that the circulation embedded in the transport matrix, by construction, satisfies the equations of motion, automatically incorporates transport due to all parameterized sub-grid scale processes (eddy-induced mixing, convective adjustment, etc.) represented in the GCM, and is entirely consistent with the geometry and numerics of the underlying GCM. Once the matrix has been derived, the GCM can be dispensed with: simulating a tracer simply involves a sequence of matrix-vector products (which can be performed, for instance, in MATLAB). The matrix method has two key advantages over GCMs or "off-line" tracer models. First, it is many orders of magnitude more efficient. Second, it can directly compute steady state solutions of the tracer equations, thus circumventing expensive, transient integrations. This is especially useful for tracers such as 14C, carbon, and nutrients. The method is illustrated by several realistic examples, including, (1) computation of steady state solutions of the OCMIP biotic carbon model and their sensitivity to various biogeochemical model parameters, (2) simulation of Ar-39, CFC-12, and SF6 in the ocean, (3) adjoint sensitivity analysis of anthropogenic carbon uptake with respect to the surface CO2 gas transfer velocity field, and (4) data-constrained simulation of epsilon-Nd, a paleoceanographic proxy tracer. These examples illustrate both the flexibility of the method, and the ease with which existing or novel biogeochemical parameterizations (sources and sinks) can be incorporated into the matrix framework. Simulation code and transport matrices derived from various global ocean configurations of the MIT OGCM (including the 1 deg data-assimilated ECCO model) are freely available.