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revision 1.6 by mlosch, Fri Feb 29 16:47:45 2008 UTC revision 1.9 by mlosch, Wed Jun 4 13:33:45 2008 UTC
# Line 16  been modified and improved: Line 16  been modified and improved:
16    \citep{hunke97};    \citep{hunke97};
17  \item ice-ocean stress can be formulated as in \citet{hibler87};  \item ice-ocean stress can be formulated as in \citet{hibler87};
18  \item ice variables are advected by sophisticated advection schemes;  \item ice variables are advected by sophisticated advection schemes;
19  \item growth and melt parameterizaion have been refined and extended  \item growth and melt parameterization have been refined and extended
20    in order to allow for automatic differentiation of the code.    in order to allow for automatic differentiation of the code.
21  \end{itemize}  \end{itemize}
22  The model equations and their numerical realization are summarized  The model equations and their numerical realization are summarized
# Line 98  minor axis $e$ equal to $2$; they are gi Line 98  minor axis $e$ equal to $2$; they are gi
98      \left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right)      \left(\dot{\epsilon}_{11}^2+\dot{\epsilon}_{22}^2\right)
99      (1+e^{-2}) +  4e^{-2}\dot{\epsilon}_{12}^2 +      (1+e^{-2}) +  4e^{-2}\dot{\epsilon}_{12}^2 +
100      2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2})      2\dot{\epsilon}_{11}\dot{\epsilon}_{22} (1-e^{-2})
101    \right]^{-\frac{1}{2}}    \right]^{\frac{1}{2}}
102  \end{align*}  \end{align*}
103  The bulk viscosities are bounded above by imposing both a minimum  The bulk viscosities are bounded above by imposing both a minimum
104  $\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a  $\Delta_{\min}=10^{-11}\text{\,s}^{-1}$ (for numerical reasons) and a
# Line 147  timestep. According to the recommendatio Line 147  timestep. According to the recommendatio
147  EVP-model is stepped forward in time 120 times within the physical  EVP-model is stepped forward in time 120 times within the physical
148  ocean model time step (although this parameter is under debate), to  ocean model time step (although this parameter is under debate), to
149  allow for elastic waves to disappear.  Because the scheme does not  allow for elastic waves to disappear.  Because the scheme does not
150  require a matrix inversion it is fast in spite of the small timestep  require a matrix inversion it is fast in spite of the small internal
151    timestep and simple to implement on parallel computers
152  \citep{hunke97}. For completeness, we repeat the equations for the  \citep{hunke97}. For completeness, we repeat the equations for the
153  components of the stress tensor $\sigma_{1} =  components of the stress tensor $\sigma_{1} =
154  \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and  \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and
# Line 155  $\sigma_{12}$. Introducing the divergenc Line 156  $\sigma_{12}$. Introducing the divergenc
156  \dot{\epsilon}_{11}+\dot{\epsilon}_{22}$, and the horizontal tension  \dot{\epsilon}_{11}+\dot{\epsilon}_{22}$, and the horizontal tension
157  and shearing strain rates, $D_T =  and shearing strain rates, $D_T =
158  \dot{\epsilon}_{11}-\dot{\epsilon}_{22}$ and $D_S =  \dot{\epsilon}_{11}-\dot{\epsilon}_{22}$ and $D_S =
159  2\dot{\epsilon}_{12}$, respectively, and using the above abbreviations,  2\dot{\epsilon}_{12}$, respectively, and using the above
160  the equations can be written as:  abbreviations, the equations\refeq{evpequation} can be written as:
161  \begin{align}  \begin{align}
162    \label{eq:evpstresstensor1}    \label{eq:evpstresstensor1}
163    \frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} +    \frac{\partial\sigma_{1}}{\partial{t}} + \frac{\sigma_{1}}{2T} +
# Line 256  potentially very heterogeneous thickness Line 257  potentially very heterogeneous thickness
257  parameterize this sub-grid scale distribution for heat flux  parameterize this sub-grid scale distribution for heat flux
258  computations, the mean ice thickness $h$ is split into seven thickness  computations, the mean ice thickness $h$ is split into seven thickness
259  categories $H_{n}$ that are equally distributed between $2h$ and  categories $H_{n}$ that are equally distributed between $2h$ and
260  minimum imposed ice thickness of $5\text{\,cm}$ by $H_n=  a minimum imposed ice thickness of $5\text{\,cm}$ by $H_n=
261  \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each  \frac{2n-1}{7}\,h$ for $n\in[1,7]$. The heat fluxes computed for each
262  thickness category area averaged to give the total heat flux. \ml{[I  thickness category area averaged to give the total heat flux. \ml{[I
263    don't have citation for that, anyone?]}    don't have citation for that, anyone?]}
# Line 280  conserving parameterization of snowice f Line 281  conserving parameterization of snowice f
281  algorithm following Archimedes' principle) turns snow into ice until  algorithm following Archimedes' principle) turns snow into ice until
282  the ice surface is back at $z=0$ \citep{leppaeranta83}.  the ice surface is back at $z=0$ \citep{leppaeranta83}.
283    
284  Effective ich thickness (ice volume per unit area,  Effective ice thickness (ice volume per unit area,
285  $c\cdot{h}$), concentration $c$ and effective snow thickness  $c\cdot{h}$), concentration $c$ and effective snow thickness
286  ($c\cdot{h}_{s}$) are advected by ice velocities:  ($c\cdot{h}_{s}$) are advected by ice velocities:
287  \begin{equation}  \begin{equation}
# Line 317  the two ice layers and the thickness of Line 318  the two ice layers and the thickness of
318    flux limiter \citep{roe85}.}    flux limiter \citep{roe85}.}
319    
320    
321  \subsection{C-grid}  %\subsection{C-grid}
322  \begin{itemize}  %\begin{itemize}
323  \item no-slip vs. free-slip for both lsr and evp;  %\item no-slip vs. free-slip for both lsr and evp;
324    "diagnostics" to look at and use for comparison  %  "diagnostics" to look at and use for comparison
325    \begin{itemize}  %  \begin{itemize}
326    \item ice transport through Fram Strait/Denmark Strait/Davis  %  \item ice transport through Fram Strait/Denmark Strait/Davis
327      Strait/Bering strait (these are general)  %    Strait/Bering strait (these are general)
328    \item ice transport through narrow passages, e.g.\ Nares-Strait  %  \item ice transport through narrow passages, e.g.\ Nares-Strait
329    \end{itemize}  %  \end{itemize}
330  \item compare different advection schemes (if lsr turns out to be more  %\item compare different advection schemes (if lsr turns out to be more
331    effective, then with lsr otherwise I prefer evp), eg.  %  effective, then with lsr otherwise I prefer evp), eg.
332    \begin{itemize}  %  \begin{itemize}
333    \item default 2nd-order with diff1=0.002  %  \item default 2nd-order with diff1=0.002
334    \item 1st-order upwind with diff1=0.  %  \item 1st-order upwind with diff1=0.
335    \item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me)  %  \item DST3FL (SEAICEadvScheme=33 with diff1=0., should work, works for me)
336    \item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.)  %  \item 2nd-order wit flux limiter (SEAICEadvScheme=77 with diff1=0.)
337    \end{itemize}  %  \end{itemize}
338    That should be enough. Here, total ice mass and location of ice edge  %  That should be enough. Here, total ice mass and location of ice edge
339    is interesting. However, this comparison can be done in an idealized  %  is interesting. However, this comparison can be done in an idealized
340    domain, may not require full Arctic Domain?  %  domain, may not require full Arctic Domain?
341  \item  %\item
342  Do a little study on the parameters of LSR and EVP  %Do a little study on the parameters of LSR and EVP
343  \begin{enumerate}  %\begin{enumerate}
344  \item convergence of LSR, how many iterations do you need to get a  %\item convergence of LSR, how many iterations do you need to get a
345    true elliptic yield curve  %  true elliptic yield curve
346  \item vary deltaTevp and the relaxation parameter for EVP and see when  %\item vary deltaTevp and the relaxation parameter for EVP and see when
347    the EVP solution breaks down (relative to the forcing time scale).  %  the EVP solution breaks down (relative to the forcing time scale).
348    For this, it is essential that the evp solver gives use "stripeless"  %  For this, it is essential that the evp solver gives use "stripeless"
349    solutions, that is your dtevp = 1sec solutions/or 10sec solutions  %  solutions, that is your dtevp = 1sec solutions/or 10sec solutions
350    with SEAICE\_evpDampC = 615.  %  with SEAICE\_evpDampC = 615.
351  \end{enumerate}  %\end{enumerate}
352    
353  \end{itemize}  %\end{itemize}
354    
355  %%% Local Variables:  %%% Local Variables:
356  %%% mode: latex  %%% mode: latex
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