| 674 |
diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$. |
diffusive terms for quantities $X=(c\cdot{h}), c, (c\cdot{h}_{s})$. |
| 675 |
% |
% |
| 676 |
From the various advection scheme that are available in the MITgcm, we |
From the various advection scheme that are available in the MITgcm, we |
| 677 |
choose flux-limited schemes \citep[multidimensional 2nd and 3rd-order |
recommend flux-limited schemes \citep[multidimensional 2nd and |
| 678 |
advection scheme with flux limiter][]{roe:85, hundsdorfer94} to |
3rd-order advection scheme with flux limiter][]{roe:85, hundsdorfer94} |
| 679 |
preserve sharp gradients and edges that are typical of sea ice |
to preserve sharp gradients and edges that are typical of sea ice |
| 680 |
distributions and to rule out unphysical over- and undershoots |
distributions and to rule out unphysical over- and undershoots |
| 681 |
(negative thickness or concentration). These scheme conserve volume |
(negative thickness or concentration). These schemes conserve volume |
| 682 |
and horizontal area and are unconditionally stable, so that we can set |
and horizontal area and are unconditionally stable, so that we can set |
| 683 |
$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2), |
$D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the |
| 684 |
\code{DIFF1} (default=0.004). |
historic 2nd-order, centered difference scheme), \code{DIFF1} |
| 685 |
|
(default=0.004). |
| 686 |
|
|
| 687 |
There is considerable doubt about the reliability of a ``zero-layer'' |
There is considerable doubt about the reliability of a ``zero-layer'' |
| 688 |
thermodynamic model --- \citet{semtner84} found significant errors in |
thermodynamic model --- \citet{semtner84} found significant errors in |
| 689 |
phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in |
phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in |
| 690 |
such models --- so that today many sea ice models employ more complex |
such models --- so that today many sea ice models employ more complex |
| 691 |
thermodynamics. The MITgcm sea ice model provides the option to use |
thermodynamics. The MITgcm sea ice model provides the option to use |
| 692 |
the thermodynamics model of \citet{win00}, which in turn is based |
the thermodynamics model of \citet{win00}, which in turn is based on |
| 693 |
on the 3-layer model of \citet{sem76} and which treats brine |
the 3-layer model of \citet{sem76} and which treats brine content by |
| 694 |
content by means of enthalpy conservation. This scheme requires |
means of enthalpy conservation; the corresponding package |
| 695 |
additional state variables, namely the enthalpy of the two ice layers |
\code{thsice} is described in section~\ref{sec:pkg:thsice}. This |
| 696 |
(instead of effective ice salinity), to be advected by ice velocities. |
scheme requires additional state variables, namely the enthalpy of the |
| 697 |
|
two ice layers (instead of effective ice salinity), to be advected by |
| 698 |
|
ice velocities. |
| 699 |
% |
% |
| 700 |
The internal sea ice temperature is inferred from ice enthalpy. To |
The internal sea ice temperature is inferred from ice enthalpy. To |
| 701 |
avoid unphysical (negative) values for ice thickness and |
avoid unphysical (negative) values for ice thickness and |
| 702 |
concentration, a positive 2nd-order advection scheme with a SuperBee |
concentration, a positive 2nd-order advection scheme with a SuperBee |
| 703 |
flux limiter \citep{roe:85} is used in this study to advect all |
flux limiter \citep{roe:85} is used in this study to advect all |
| 704 |
sea-ice-related quantities of the \citet{win00} thermodynamic |
sea-ice-related quantities of the \citet{win00} thermodynamic model. |
| 705 |
model. Because of the non-linearity of the advection scheme, care |
Because of the non-linearity of the advection scheme, care must be |
| 706 |
must be taken in advecting these quantities: when simply using ice |
taken in advecting these quantities: when simply using ice velocity to |
| 707 |
velocity to advect enthalpy, the total energy (i.e., the volume |
advect enthalpy, the total energy (i.e., the volume integral of |
| 708 |
integral of enthalpy) is not conserved. Alternatively, one can advect |
enthalpy) is not conserved. Alternatively, one can advect the energy |
| 709 |
the energy content (i.e., product of ice-volume and enthalpy) but then |
content (i.e., product of ice-volume and enthalpy) but then false |
| 710 |
false enthalpy extrema can occur, which then leads to unrealistic ice |
enthalpy extrema can occur, which then leads to unrealistic ice |
| 711 |
temperature. In the currently implemented solution, the sea-ice mass |
temperature. In the currently implemented solution, the sea-ice mass |
| 712 |
flux is used to advect the enthalpy in order to ensure conservation of |
flux is used to advect the enthalpy in order to ensure conservation of |
| 713 |
enthalpy and to prevent false enthalpy extrema. |
enthalpy and to prevent false enthalpy extrema. % |
| 714 |
|
In order to use the \code{seaice}-package with the more sophisticated |
| 715 |
|
thermodynamics of \code{thsice}, compile both packages and turn both |
| 716 |
|
package on in \code{data.pkg}; see an example in |
| 717 |
|
\code{global\_ocean.cs32x15/input.icedyn}. |
| 718 |
|
|
| 719 |
%---------------------------------------------------------------------- |
%---------------------------------------------------------------------- |
| 720 |
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