... Subroutine checks^22.30

contained in file checks.F

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... computed^23.1

It is no longer required to construct density coefficients before executing the model.

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... dataset^25.1

This dataset may be purchased from the Marine Geology and Geophysics Division of the National Geophysical Data Center and is not included in the MOM DATABASE.

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... levels^26.1

Increasing the number of vertical levels does allow interior flows to be better resolved.

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... coefficient^26.2

The formulation is for constant A_m. Variable A_m requires additional terms.

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... understand^27.1

If any researcher understands what is being done then please contact me. (rcp@gfdl.gov)

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... coefficients^27.2

Strips for the vorticity do not include coastal ocean cells because of the island integrals.

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... condition^28.1

Note that solar shortwave data is not supplied with MOM and so must be supplied by the researcher.

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... script run_sponge^28.2

Note that this script can only be run after script run_ic which prepares temperature and salinity data for all latitude rows.

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... topography^29.1

This instability has been associated with problems in various versions of the GFDL coupled model in the Drake Passage region. For example, a traditional time step analysis indicates that the ocean component of the 4-degree/R15 GFDL coupled model should work fine with a 6 hour barotropic time step. However, it is unable to run with time steps much larger than 2 hours. The consensus is that the Killworth instability is the dominant factor determining the time step in this rigid lid model (Keith Dixon and Ron Stouffer, personal communication).

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... Changes^29.2

Worked out by Charles Goldberg.

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... Jacobian^29.3

The Jacobian is given as $J(A,B)= \frac{1}{a^2\cos\phi}(\frac{\partial A}{\partial\lambda}\frac{\partial ... ...rtial\phi} - \frac{\partial B}{\partial\lambda}\frac{\partial A}{\partial\phi})$.

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... factor^29.4

 acor = zero implies that the Coriolis term is handled explicitly. Otherwise, $0.5 \leq acor < 1.0$implies implicit handling of the Coriolis term. This is useful for coarse models with global domains where the time step is limited by the inertial period 1/f.

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... approach^29.5

This approach was first worked out by Charles Goldberg (personal communication) using algebraic manipulations. The derivation given here is in terms of finite difference operators.

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... caution^29.6

This filtering induces spurious vertical velocities because each latitude if filtered independently and the strips are of varying length due to topography.

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... solutions^29.7

To within roundoff.

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... coefficient^29.8

Only the first brackets are being done here. The implicit Coriolis terms stand no chance of being symmetric.

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... result^29.9

Note that remote island perimeter cells neither appear in the equation centered at $\alpha$, nor do they contain references to cell $\alpha$ in their (up to) nine terms.

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... SIMD^29.10

Single Instruction stream-Multiple Data streams

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... topography^29.11

The bottom velocity cell generally does not sit on the ocean bottom, and so can support a vertical velocity due to sloping topography. Details of how MOM handles this velocity are given in Webb (1995) and Section 22.3.3.

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... steps.^29.12

Tests conducted at the Southampton Oceanography Center indicate a need to perform a time average over barotropic time steps, even when using equal tracer and baroclinic time steps, to suppress an instability associated with aliased barotropic Rossby waves near the equator (David Webb, personal communication).

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... MOM 1^30.1

Because of the difference in meaning between the MOM 1 tolerance crit and the MOM tolerance tolrsf, care must be taken to assure that both are converging to the same tolerance when doing these tests.

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... eliminates^30.2

To within roundoff.

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... matrix^30.3

However, in these cases, the elliptic equations for the prognostic surface pressure p^s are, of course, different than those given above for the prognostic stream function $\Psi$.

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... bucket^30.4

We have come to call these loops ``Amtrack Normal Form,'' because the indentation of the DO loops and the long executable statement in the middle resemble the ``Amtrack'' logo. Properly ordered, these nested loops vectorize very well on a Cray YMP.

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... symmetric^30.5

Refer to Section 29.2.5.

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... order^31.1

The idea of a psuedo fourth order technique was taken from the GFDL SKYHI stratospheric GCM.

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... undershoots^31.2

Experimentation with the limitation process can be useful: The combination of two-dimensional limiting in the horizontal and one-dimensional limiting in the vertical is likely to generate less implicit diffusion than the implemented scheme.

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... ratios^31.3

Where $\epsilon$ is a small value O(10^-25) to avoid division by zero.

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... version^33.1

It was in MOM 2.0 version 2.0 (beta).

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... reason^33.2

If a simple four point average is used, cases arise where values of rit are generated near the bottom which are much lower than any surrounding riu in the area. This is an artificial result which can lead to a situation with high vertical diffusion amidst low vertical viscosity. Martin Schmidt (personal communication) has observed the vertical density profile being unrealically eroded away in shallow regions when zero values of riu are used in the average.

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... number^34.1

Recall that the Prandtl number is the ratio of the viscosity to diffusivity.

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... terms^35.1

This point was emphasized by Bob Hallberg, 1997.

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... interaction^36.1

Which is missing or at best poorly represented in numerical models at any resolution.

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... flow^36.2

This is referred to as the Neptune effect because when Greg Holloway described coastal currents that persistantly flow againgst both wind forcing and pressure gradient, the response was that it must be due to King Neptune. Who else?

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