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Subsections


5.3.1 Overview of the experiment

We describe an adjoint sensitivity analysis of out-gassing from the ocean into the atmosphere of a carbon-like tracer injected into the ocean interior (see [29]).


5.3.1.1 Passive tracer equation

For this work the MITGCM was augmented with a thermodynamically inactive tracer, $ C$. Tracer residing in the ocean model surface layer is out-gassed according to a relaxation time scale, $ \mu$. Within the ocean interior, the tracer is passively advected by the ocean model currents. The full equation for the time evolution

$\displaystyle \frac{\partial C}{\partial t} \, = \, -U\cdot \nabla C \, - \, \mu C \, + \, \Gamma(C) \,+ \, S$ (5.15)

also includes a source term $ S$. This term represents interior sources of $ C$ such as would arise due to direct injection. The velocity term, $ U$, is the sum of the model Eulerian circulation and an eddy-induced velocity, the latter parameterized according to Gent/McWilliams ([16,17]). The convection function, $ \Gamma$, mixes $ C$ vertically wherever the fluid is locally statically unstable.

The out-gassing time scale, $ \mu$, in eqn. (5.15) is set so that $ 1/\mu \sim 1 \ \mathrm{year} $ for the surface ocean and $ \mu=0$ elsewhere. With this value, eqn. (5.15) is valid as a prognostic equation for small perturbations in oceanic carbon concentrations. This configuration provides a powerful tool for examining the impact of large-scale ocean circulation on $ CO_2 $ out-gassing due to interior injections. As source we choose a constant in time injection of $ S = 1 \,\, {\rm mol / s}$.


5.3.1.2 Model configuration

The model configuration employed has a constant $ 4^\circ \times 4^\circ$ resolution horizontal grid and realistic geography and bathymetry. Twenty vertical layers are used with vertical spacing ranging from 50 m near the surface to 815 m at depth. Driven to steady-state by climatological wind-stress, heat and fresh-water forcing the model reproduces well known large-scale features of the ocean general circulation.


5.3.1.3 Out-gassing cost function

To quantify and understand out-gassing due to injections of $ C$ in eqn. (5.15), we define a cost function $ {\cal J} $ that measures the total amount of tracer out-gassed at each timestep:

$\displaystyle {\cal J}(t=T)=\int_{t=0}^{t=T}\int_{A} \mu C \, dA \, dt$ (5.16)

Equation(5.16) integrates the out-gassing term, $ \mu C$, from (5.15) over the entire ocean surface area, $ A $, and accumulates it up to time $ T$. Physically, $ {\cal J} $ can be thought of as representing the amount of $ CO_2 $ that our model predicts would be out-gassed following an injection at rate $ S$. The sensitivity of $ {\cal J} $ to the spatial location of $ S$, $ \frac{\partial {\cal J}}{\partial S}$, can be used to identify regions from which circulation would cause $ CO_2 $ to rapidly out-gas following injection and regions in which $ CO_2 $ injections would remain effectively sequestered within the ocean.

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Next: 5.3.2 Code configuration Up: 5.3 Sensitivity of Air-Sea Previous: 5.3 Sensitivity of Air-Sea   Contents
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