--- manual/s_phys_pkgs/text/seaice.tex	2011/02/28 16:27:56	1.15
+++ manual/s_phys_pkgs/text/seaice.tex	2011/12/14 11:22:42	1.19
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.15 2011/02/28 16:27:56 mlosch Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_phys_pkgs/text/seaice.tex,v 1.19 2011/12/14 11:22:42 mlosch Exp $
 % $Name:  $
 
 %%EH3  Copied from "MITgcm/pkg/seaice/seaice_description.tex"
@@ -113,9 +113,9 @@
 \subsubsection{Run-time parameters
 \label{sec:pkg:seaice:runtime}}
 
-Run-time parameters are set in files 
-\code{data.pkg} (read in \code{packages\_readparms.F}),
-and \code{data.seaice} (read in \code{seaice\_readparms.F}).
+Run-time parameters (see Table~\ref{tab:pkg:seaice:runtimeparms}) are set
+in files \code{data.pkg} (read in \code{packages\_readparms.F}), and
+\code{data.seaice} (read in \code{seaice\_readparms.F}).
 
 \paragraph{Enabling the package}
 ~ \\
@@ -214,26 +214,39 @@
 to use the VP model as the default dynamic component of our ice
 model. To do this we extended the line successive over relaxation
 (LSOR) method of \citet{zhang97} for use in a parallel
-configuration.
+configuration. An EVP model and a free-drift implemtation can be
+selected with runtime flags.
 
-Note, that by default the seaice-package includes the orginial
+\paragraph{Compatibility with ice-thermodynamics package \code{thsice}\label{sec:pkg:seaice:thsice}}~\\
+%
+Note, that by default the \code{seaice}-package includes the orginial
 so-called zero-layer thermodynamics following \citet{hib80} with a
 snow cover as in \citet{zha98a}. The zero-layer thermodynamic model
 assumes that ice does not store heat and, therefore, tends to
 exaggerate the seasonal variability in ice thickness.  This
 exaggeration can be significantly reduced by using
-\citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic model
-that permits heat storage in ice.  Recently, the three-layer
-thermodynamic model has been reformulated by \citet{win00}.  The
-reformulation improves model physics by representing the brine content
-of the upper ice with a variable heat capacity.  It also improves
-model numerics and consumes less computer time and memory.  The Winton
-sea-ice thermodynamics have been ported to the MIT GCM; they currently
-reside under pkg/thsice. The package pkg/thsice is fully compatible
-with pkg/seaice and with pkg/exf. When turned on together with
-pkg/seaice, the zero-layer thermodynamics are replaced by the Winton
-thermodynamics.
+\citeauthor{sem76}'s~[\citeyear{sem76}] three-layer thermodynamic
+model that permits heat storage in ice. Recently, the three-layer thermodynamic model has been reformulated by
+\citet{win00}.  The reformulation improves model physics by
+representing the brine content of the upper ice with a variable heat
+capacity.  It also improves model numerics and consumes less computer
+time and memory. 
+
+The Winton sea-ice thermodynamics have been ported to the MIT GCM;
+they currently reside under \code{pkg/thsice}.  The package
+\code{thsice} is described in section~\ref{sec:pkg:thsice}; it is
+fully compatible with the packages \code{seaice} and \code{exf}. When
+turned on together with \code{seaice}, the zero-layer thermodynamics
+are replaced by the Winton thermodynamics. In order to use the
+\code{seaice}-package with the thermodynamics of \code{thsice},
+compile both packages and turn both package on in \code{data.pkg}; see
+an example in \code{global\_ocean.cs32x15/input.icedyn}. Note, that
+once \code{thsice} is turned on, the variables and diagnostics
+associated to the default thermodynamics are meaningless, and the
+diagnostics of \code{thsice} have to be used instead.
 
+\paragraph{Surface forcing\label{sec:pkg:seaice:surfaceforcing}}~\\
+%
 The sea ice model requires the following input fields: 10-m winds, 2-m
 air temperature and specific humidity, downward longwave and shortwave
 radiations, precipitation, evaporation, and river and glacier runoff.
@@ -244,8 +257,8 @@
 global: in ice-free regions bulk formulae are used to estimate oceanic
 forcing from the atmospheric fields.
 
-\paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}
-
+\paragraph{Dynamics\label{sec:pkg:seaice:dynamics}}~\\
+%
 \newcommand{\vek}[1]{\ensuremath{\vec{\mathbf{#1}}}}
 \newcommand{\vtau}{\vek{\mathbf{\tau}}}
 The momentum equation of the sea-ice model is
@@ -283,6 +296,8 @@
 densities; and $R_{air/ocean}$ are rotation matrices that act on the
 wind/current vectors.
 
+\paragraph{Viscous-Plastic (VP) Rheology and LSOR solver \label{sec:pkg:seaice:VPdynamics}}~\\
+%
 For an isotropic system the stress tensor $\sigma_{ij}$ ($i,j=1,2$) can
 be related to the ice strain rate and strength by a nonlinear
 viscous-plastic (VP) constitutive law \citep{hib79, zhang97}:
@@ -302,7 +317,7 @@
 The maximum ice pressure $P_{\max}$, a measure of ice strength, depends on
 both thickness $h$ and compactness (concentration) $c$:
 \begin{equation}
-  P_{\max} = P^{*}c\,h\,e^{[C^{*}\cdot(1-c)]},
+  P_{\max} = P^{*}c\,h\,\exp\{-C^{*}\cdot(1-c)\},
 \label{eq:icestrength}
 \end{equation}
 with the constants $P^{*}$ (run-time parameter \code{SEAICE\_strength}) and
@@ -334,19 +349,6 @@
 = 2\,\Delta\zeta$ \citep{hibler95} is used so that the stress state
 always lies on the elliptic yield curve by definition.
 
-In the so-called truncated ellipse method the shear viscosity $\eta$
-is capped to suppress any tensile stress \citep{hibler97, geiger98}:
-\begin{equation}
-  \label{eq:etatem}
-  \eta = \min\left(\frac{\zeta}{e^2},
-  \frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}
-  {\sqrt{(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})^2
-      +4\dot{\epsilon}_{12}^2}}\right).
-\end{equation}
-To enable this method, set \code{\#define SEAICE\_ALLOW\_TEM} in
-\code{SEAICE\_OPTIONS.h} and turn it on with
-\code{SEAICEuseTEM=.TRUE.} in \code{data.seaice}. 
-
 In the current implementation, the VP-model is integrated with the
 semi-implicit line successive over relaxation (LSOR)-solver of
 \citet{zhang97}, which allows for long time steps that, in our case,
@@ -356,6 +358,8 @@
 same length as in the ocean model where the Coriolis term is also
 treated explicitly.
 
+\paragraph{Elastic-Viscous-Plastic (EVP) Dynamics\label{sec:pkg:seaice:EVPdynamics}}~\\
+%
 \citet{hun97}'s introduced an elastic contribution to the strain
 rate in order to regularize Eq.~\ref{eq:vpequation} in such a way that
 the resulting elastic-viscous-plastic (EVP) and VP models are
@@ -373,11 +377,12 @@
 %used and compared the present sea-ice model study.
 The EVP-model uses an explicit time stepping scheme with a short
 timestep. According to the recommendation of \citet{hun97}, the
-EVP-model is stepped forward in time 120 times within the physical
-ocean model time step (although this parameter is under debate), to
-allow for elastic waves to disappear.  Because the scheme does not
-require a matrix inversion it is fast in spite of the small internal
-timestep and simple to implement on parallel computers
+EVP-model should be stepped forward in time 120 times
+($\code{SEAICE\_deltaTevp} = \code{SEAICIE\_deltaTdyn}/120$) within
+the physical ocean model time step (although this parameter is under
+debate), to allow for elastic waves to disappear.  Because the scheme
+does not require a matrix inversion it is fast in spite of the small
+internal timestep and simple to implement on parallel computers
 \citep{hun97}. For completeness, we repeat the equations for the
 components of the stress tensor $\sigma_{1} =
 \sigma_{11}+\sigma_{22}$, $\sigma_{2}= \sigma_{11}-\sigma_{22}$, and
@@ -398,11 +403,12 @@
   \frac{\partial\sigma_{12}}{\partial{t}} + \frac{\sigma_{12} e^{2}}{2T}
   &= \frac{P}{4T\Delta} D_S 
 \end{align}
-Here, the elastic parameter $E$ is redefined in terms of a damping timescale
-$T$ for elastic waves \[E=\frac{\zeta}{T}.\]
-$T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and
-the external (long) timestep $\Delta{t}$. \citet{hun97} recommend
-$E_{0} = \frac{1}{3}$ (which is the default value in the code).
+Here, the elastic parameter $E$ is redefined in terms of a damping
+timescale $T$ for elastic waves \[E=\frac{\zeta}{T}.\]
+$T=E_{0}\Delta{t}$ with the tunable parameter $E_0<1$ and the external
+(long) timestep $\Delta{t}$.  $E_{0} = \frac{1}{3}$ is the default
+value in the code and close to what \citet{hun97} and
+\citet{hun01} recommend.
 
 To use the EVP solver, make sure that both \code{SEAICE\_CGRID} and
 \code{SEAICE\_ALLOW\_EVP} are defined in \code{SEAICE\_OPTIONS.h}
@@ -417,6 +423,23 @@
 $E_{0}\Delta{t}=\mbox{forcing time scale}$, or directly
 \code{SEAICE\_evpTauRelax} ($T$) to the forcing time scale.
 
+\paragraph{Truncated ellipse method (TEM) for yield curve \label{sec:pkg:seaice:TEM}}~\\
+%
+In the so-called truncated ellipse method the shear viscosity $\eta$
+is capped to suppress any tensile stress \citep{hibler97, geiger98}:
+\begin{equation}
+  \label{eq:etatem}
+  \eta = \min\left(\frac{\zeta}{e^2},
+  \frac{\frac{P}{2}-\zeta(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})}
+  {\sqrt{(\dot{\epsilon}_{11}+\dot{\epsilon}_{22})^2
+      +4\dot{\epsilon}_{12}^2}}\right).
+\end{equation}
+To enable this method, set \code{\#define SEAICE\_ALLOW\_TEM} in
+\code{SEAICE\_OPTIONS.h} and turn it on with
+\code{SEAICEuseTEM} in \code{data.seaice}. 
+
+\paragraph{Ice-Ocean stress \label{sec:pkg:seaice:iceoceanstress}}~\\
+%
 Moving sea ice exerts a stress on the ocean which is the opposite of
 the stress $\vtau_{ocean}$ in Eq.~\ref{eq:momseaice}. This stess is
 applied directly to the surface layer of the ocean model. An
@@ -446,7 +469,8 @@
 % $P$ at vorticity points.
 
 \paragraph{Finite-volume discretization of the stress tensor
-  divergence\label{sec:pkg:seaice:discretization}}
+  divergence\label{sec:pkg:seaice:discretization}}~\\
+%
 On an Arakawa C~grid, ice thickness and concentration and thus ice
 strength $P$ and bulk and shear viscosities $\zeta$ and $\eta$ are
 naturally defined a C-points in the center of the grid
@@ -607,8 +631,8 @@
 analogy to $(\epsilon_{12})^Z=0$ on boundaries, we set
 $\sigma_{21}^{Z}=0$, or equivalently $\eta_{i,j}^{Z}=0$, on boundaries.
 
-\paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}
-
+\paragraph{Thermodynamics\label{sec:pkg:seaice:thermodynamics}}~\\
+%
 In its original formulation the sea ice model \citep{menemenlis05}
 uses simple thermodynamics following the appendix of
 \citet{sem76}. This formulation does not allow storage of heat,
@@ -662,6 +686,8 @@
 \code{SEAICE\_ALLOW\_FLOODING} and turned on with run-time parameter
 \code{SEAICEuseFlooding=.true.}.
 
+\paragraph{Advection of thermodynamic variables\label{sec:pkg:seaice:advection}}~\\
+%
 Effective ice thickness (ice volume per unit area,
 $c\cdot{h}$), concentration $c$ and effective snow thickness
 ($c\cdot{h}_{s}$) are advected by ice velocities:
@@ -681,14 +707,11 @@
 (negative thickness or concentration). These schemes conserve volume
 and horizontal area and are unconditionally stable, so that we can set
 $D_{X}=0$. Run-timeflags: \code{SEAICEadvScheme} (default=2, is the
-historic 2nd-order, centered difference scheme), \code{DIFF1}
+historic 2nd-order, centered difference scheme), \code{DIFF1} =
+$D_{X}/\Delta{x}$
 (default=0.004).
 
-There is considerable doubt about the reliability of a ``zero-layer''
-thermodynamic model --- \citet{semtner84} found significant errors in
-phase (one month lead) and amplitude ($\approx$50\%\,overestimate) in
-such models --- so that today many sea ice models employ more complex
-thermodynamics. The MITgcm sea ice model provides the option to use
+The MITgcm sea ice model provides the option to use
 the thermodynamics model of \citet{win00}, which in turn is based on
 the 3-layer model of \citet{sem76} and which treats brine content by
 means of enthalpy conservation; the corresponding package
@@ -700,21 +723,19 @@
 The internal sea ice temperature is inferred from ice enthalpy.  To
 avoid unphysical (negative) values for ice thickness and
 concentration, a positive 2nd-order advection scheme with a SuperBee
-flux limiter \citep{roe:85} is used in this study to advect all
-sea-ice-related quantities of the \citet{win00} thermodynamic model.
-Because of the non-linearity of the advection scheme, care must be
-taken in advecting these quantities: when simply using ice velocity to
-advect enthalpy, the total energy (i.e., the volume integral of
-enthalpy) is not conserved. Alternatively, one can advect the energy
-content (i.e., product of ice-volume and enthalpy) but then false
-enthalpy extrema can occur, which then leads to unrealistic ice
-temperature.  In the currently implemented solution, the sea-ice mass
-flux is used to advect the enthalpy in order to ensure conservation of
-enthalpy and to prevent false enthalpy extrema. %
-In order to use the \code{seaice}-package with the more sophisticated
-thermodynamics of \code{thsice}, compile both packages and turn both
-package on in \code{data.pkg}; see an example in
-\code{global\_ocean.cs32x15/input.icedyn}.
+flux limiter \citep{roe:85} should be used to advect all
+sea-ice-related quantities of the \citet{win00} thermodynamic model
+(runtime flag \code{thSIceAdvScheme=77} and
+\code{thSIce\_diffK}=$D_{X}$=0 in \code{data.ice}, defaults are 0).  Because of the
+non-linearity of the advection scheme, care must be taken in advecting
+these quantities: when simply using ice velocity to advect enthalpy,
+the total energy (i.e., the volume integral of enthalpy) is not
+conserved. Alternatively, one can advect the energy content (i.e.,
+product of ice-volume and enthalpy) but then false enthalpy extrema
+can occur, which then leads to unrealistic ice temperature.  In the
+currently implemented solution, the sea-ice mass flux is used to
+advect the enthalpy in order to ensure conservation of enthalpy and to
+prevent false enthalpy extrema. %
 
 %----------------------------------------------------------------------
 
@@ -780,58 +801,7 @@
 Available output fields are summarized in 
 Table \ref{tab:pkg:seaice:diagnostics}.
 
-\begin{table}[!ht]
-\centering
-\label{tab:pkg:seaice:diagnostics}
-{\footnotesize
-\begin{verbatim}
----------+----+----+----------------+-----------------
- <-Name->|Levs|grid|<--  Units   -->|<- Tile (max=80c)
----------+----+----+----------------+-----------------
- SIarea  |  1 |SM  |m^2/m^2         |SEAICE fractional ice-covered area [0 to 1]
- SIheff  |  1 |SM  |m               |SEAICE effective ice thickness
- SIuice  |  1 |UU  |m/s             |SEAICE zonal ice velocity, >0 from West to East
- SIvice  |  1 |VV  |m/s             |SEAICE merid. ice velocity, >0 from South to North
- SIhsnow |  1 |SM  |m               |SEAICE snow thickness
- SIhsalt |  1 |SM  |g/m^2           |SEAICE effective salinity
- SIatmFW |  1 |SM  |kg/m^2/s        |Net freshwater flux from the atmosphere (+=down)
- SIuwind |  1 |SM  |m/s             |SEAICE zonal 10-m wind speed, >0 increases uVel
- SIvwind |  1 |SM  |m/s             |SEAICE meridional 10-m wind speed, >0 increases uVel
- SIfu    |  1 |UU  |N/m^2           |SEAICE zonal surface wind stress, >0 increases uVel
- SIfv    |  1 |VV  |N/m^2           |SEAICE merid. surface wind stress, >0 increases vVel
- SIempmr |  1 |SM  |kg/m^2/s        |SEAICE upward freshwater flux, > 0 increases salt
- SIqnet  |  1 |SM  |W/m^2           |SEAICE upward heatflux, turb+rad, >0 decreases theta
- SIqsw   |  1 |SM  |W/m^2           |SEAICE upward shortwave radiat., >0 decreases theta
- SIpress |  1 |SM  |m^2/s^2         |SEAICE strength (with upper and lower limit)
- SIzeta  |  1 |SM  |m^2/s           |SEAICE nonlinear bulk viscosity
- SIeta   |  1 |SM  |m^2/s           |SEAICE nonlinear shear viscosity
- SIsigI  |  1 |SM  |no units        |SEAICE normalized principle stress, component one
- SIsigII |  1 |SM  |no units        |SEAICE normalized principle stress, component two
- SIthdgrh|  1 |SM  |m/s             |SEAICE thermodynamic growth rate of effective ice thickness
- SIsnwice|  1 |SM  |m/s             |SEAICE ice formation rate due to flooding
- SIuheff |  1 |UU  |m^2/s           |Zonal Transport of effective ice thickness
- SIvheff |  1 |VV  |m^2/s           |Meridional Transport of effective ice thickness
- ADVxHEFF|  1 |UU  |m.m^2/s         |Zonal      Advective Flux of eff ice thickn
- ADVyHEFF|  1 |VV  |m.m^2/s         |Meridional Advective Flux of eff ice thickn
- DFxEHEFF|  1 |UU  |m.m^2/s         |Zonal      Diffusive Flux of eff ice thickn
- DFyEHEFF|  1 |VV  |m.m^2/s         |Meridional Diffusive Flux of eff ice thickn
- ADVxAREA|  1 |UU  |m^2/m^2.m^2/s   |Zonal      Advective Flux of fract area
- ADVyAREA|  1 |VV  |m^2/m^2.m^2/s   |Meridional Advective Flux of fract area
- DFxEAREA|  1 |UU  |m^2/m^2.m^2/s   |Zonal      Diffusive Flux of fract area
- DFyEAREA|  1 |VV  |m^2/m^2.m^2/s   |Meridional Diffusive Flux of fract area
- ADVxSNOW|  1 |UU  |m.m^2/s         |Zonal      Advective Flux of eff snow thickn
- ADVySNOW|  1 |VV  |m.m^2/s         |Meridional Advective Flux of eff snow thickn
- DFxESNOW|  1 |UU  |m.m^2/s         |Zonal      Diffusive Flux of eff snow thickn
- DFyESNOW|  1 |VV  |m.m^2/s         |Meridional Diffusive Flux of eff snow thickn
- ADVxSSLT|  1 |UU  |psu.m^2/s       |Zonal      Advective Flux of seaice salinity
- ADVySSLT|  1 |VV  |psu.m^2/s       |Meridional Advective Flux of seaice salinity
- DFxESSLT|  1 |UU  |psu.m^2/s       |Zonal      Diffusive Flux of seaice salinity
- DFyESSLT|  1 |VV  |psu.m^2/s       |Meridional Diffusive Flux of seaice salinity
-\end{verbatim}
-}
-\caption{Available diagnostics of the seaice-package}
-\end{table}
-
+\input{s_phys_pkgs/text/seaice_diags.tex}
 
 %\subsubsection{Package Reference}
 
@@ -839,7 +809,13 @@
 \label{sec:pkg:seaice:experiments}
 
 \begin{itemize}
-\item{Labrador Sea experiment in lab\_sea verification directory. }
+\item{Labrador Sea experiment in \code{lab\_sea} verification directory. }
+\item \code{seaice\_obcs}, based on \code{lab\_sea}
+\item \code{offline\_exf\_seaice/input.seaicetd}, based on \code{lab\_sea}
+\item \code{global\_ocean.cs32x15/input.icedyn} and
+  \code{global\_ocean.cs32x15/input.seaice}, global
+  cubed-sphere-experiment with combinations of \code{seaice} and
+  \code{thsice}
 \end{itemize}
 
 
