... face^21.1

This is the the longitude of the grid point within .

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... substituted^21.2

The grid distances must also be replaced accordingly.

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... component^21.3

Subscript n=1 denotes the temperature and n=2 denotes the salinity. n>2 is for passive tracers

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... changes^21.4

The only change is whether a time step length is $\Delta\tau$ or $2\Delta\tau$

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... opened^21.5

This can be eliminated by recalculating the pointers differently on the time step after the Euler backward step. However, the calculation gets tricky and has complications.

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... subroutine mom^22.1

Contained in file mom.F.

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... module tmngr^22.2

Contained in file tmngr.F.

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... required^22.3

Assuming these diagnostics have been enabled by their options at compile time.

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... one^22.4

Requiring three rows in the memory window.

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...-2)latitudes^22.5

Requiring jmt rows in the memory window.

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... Subroutine loadmw^22.6

Contained in file loadmw.F.

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... necessary^22.7

It is necessary for all but the first group of latitudes. If the memory window is opened all the way (when jmw=jmt), then no movement is necessary.

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... velocities^22.8

After each group of internal mode velocities are solved within a time step, they are written back to disk. The external mode is unknown until all rows have been solved and subroutine barotropic solves for the external mode. The only way to get the total velocity on disk is to read all rows back into memory after the external mode has been solved. This is why the external mode is added at the beginning of each time step for time levels $\tau$ and $\tau-1$.

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...^22.9

Contained within file adv_vel.F.

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... implementations^22.10

This was the motivation for exploring grid construction by method 2 as detailed in Section 16.2.3

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... construction^22.11

The old construction method 1 is enabled by option centered_t. Refer to Chapter 16 for a description of grid design.

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... T-cells^22.12

This cell face is also the top face of the first land T-cell below the ocean bottom.

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... Subroutine isopyc^22.13

Contained in file isopyc.F.

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... Subroutine vmixc^22.14

Contained in file vmixc.F.

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... coefficient^22.15

This is effectively done by adding diffusive fluxes from the basic scheme to the isoneutral flux across the bottom face of the T cell.

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... Subroutine hmixc^22.16

Contained in file hmixc.F.

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... coefficients^22.17

This is effectively done by adding diffusive fluxes from the basic scheme to the isoneutral flux across the northern and eastern face of the T cell.

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... Subroutine setvbc^22.18

Contained in file setvbc.F.

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... zero^22.19

Zero to within roundoff. Note that unlike adv_vbt_i,kb,j, adv_vbu_i,kb,j can be non-zero if there is a bottom slope.

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... terms^22.20

These could have been added directly to the advective fluxes computed previously. For now they are kept separately for diagnostic reasons.

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... Subroutine baroclinic^22.21

Contained in file baroclinic.F.

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... for^22.22

Indeed, lack of knowledge about these barotropic surface pressure gradients is the very reason the internal mode velocities are being solved for.

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...zt^22.23

This is the depth of the grid point within the first T cell and U cell.

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... rate^22.24

The 43082.0 sec is arrived at assuming approximately $86400*(1-\frac{1}{366}) = 86164$seconds in one sidereal day. The 366 is used to account for a 1 day co-rotation.

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... (1992)^22.25

The surface boundary condition smf_i,j,n should be at $\tau+1$ but that value isn't known. Instead, the $\tau$ value is used. In MOM 1, The Richardson number in ppmix.F was calculated at tau-1 in the implicit case. It should be at $\tau+1$ but that is unknown. In MOM, the Richardson number can easily be changed to $\tau$. The effect of this on the solution should be small but has not been explored.

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... velocities^22.26

Velocities with incorrect vertical means due to the missing unknown surface pressure.

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... 1987)^22.27

Although the paper explored the affect on SST primarily through Ekman divergence, there may also be an impact on evaporative flux in certain regions where the ocean surface velocities are large.

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... Subroutine barotropic^22.28

Contained in file tropic.F.

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... subroutine diago^22.29

Contained in file diago.F.

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