| 167 |
\end{array} |
\end{array} |
| 168 |
\right) |
\right) |
| 169 |
\end{equation} |
\end{equation} |
| 170 |
which differs from the variable laplacian diffusion tensor by only |
which differs from the variable Laplacian diffusion tensor by only |
| 171 |
two non-zero elements in the $z$-row. |
two non-zero elements in the $z$-row. |
| 172 |
|
|
| 173 |
\fbox{ \begin{minipage}{4.75in} |
\fbox{ \begin{minipage}{4.75in} |
| 218 |
Experience with the GFDL model showed that the GM scheme has to be |
Experience with the GFDL model showed that the GM scheme has to be |
| 219 |
matched to the convective parameterization. This was originally |
matched to the convective parameterization. This was originally |
| 220 |
expressed in connection with the introduction of the KPP boundary |
expressed in connection with the introduction of the KPP boundary |
| 221 |
layer scheme (Large et al., 97) but infact, as subsequent experience |
layer scheme (Large et al., 97) but in fact, as subsequent experience |
| 222 |
with the MIT model has found, is necessary for any convective |
with the MIT model has found, is necessary for any convective |
| 223 |
parameterization. |
parameterization. |
| 224 |
|
|
| 261 |
such regions can be either infinite, very large with a sign reversal |
such regions can be either infinite, very large with a sign reversal |
| 262 |
or simply very large. From a numerical point of view, large slopes |
or simply very large. From a numerical point of view, large slopes |
| 263 |
lead to large variations in the tensor elements (implying large bolus |
lead to large variations in the tensor elements (implying large bolus |
| 264 |
flow) and can be numerically unstable. This was first reognized by |
flow) and can be numerically unstable. This was first recognized by |
| 265 |
Cox, 1987, who implemented ``slope clipping'' in the isopycnal mixing |
Cox, 1987, who implemented ``slope clipping'' in the isopycnal mixing |
| 266 |
tensor. Here, the slope magnitude is simply restricted by an upper |
tensor. Here, the slope magnitude is simply restricted by an upper |
| 267 |
limit: |
limit: |
| 296 |
diffusion). The classic result of dramatically reduced mixed layers is |
diffusion). The classic result of dramatically reduced mixed layers is |
| 297 |
evident. Indeed, the deep convection sites to just one or two points |
evident. Indeed, the deep convection sites to just one or two points |
| 298 |
each and are much shallower than we might prefer. This, it turns out, |
each and are much shallower than we might prefer. This, it turns out, |
| 299 |
is due to the over zealous restratification due to the bolus transport |
is due to the over zealous re-stratification due to the bolus transport |
| 300 |
parameterization. Limiting the slopes also breaks the adiabatic nature |
parameterization. Limiting the slopes also breaks the adiabatic nature |
| 301 |
of the GM/Redi parameterization, re-introducing diabatic fluxes in |
of the GM/Redi parameterization, re-introducing diabatic fluxes in |
| 302 |
regions where the limiting is in effect. |
regions where the limiting is in effect. |
| 362 |
|
|
| 363 |
|
|
| 364 |
\begin{figure} |
\begin{figure} |
| 365 |
|
\begin{center} |
| 366 |
%\includegraphics{mixedlayer-cox.eps} |
%\includegraphics{mixedlayer-cox.eps} |
| 367 |
%\includegraphics{mixedlayer-diff.eps} |
%\includegraphics{mixedlayer-diff.eps} |
| 368 |
|
Figure missing. |
| 369 |
|
\end{center} |
| 370 |
\caption{Mixed layer depth using GM parameterization with a) Cox slope |
\caption{Mixed layer depth using GM parameterization with a) Cox slope |
| 371 |
clipping and for comparison b) using horizontal constant diffusion.} |
clipping and for comparison b) using horizontal constant diffusion.} |
| 372 |
\ref{fig-mixedlayer} |
\label{fig-mixedlayer} |
| 373 |
\end{figure} |
\end{figure} |
| 374 |
|
|
| 375 |
|
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