/[MITgcm]/manual/s_phys_pkgs/text/thsice.tex

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+revision 1.9 by jmc,
Thu Dec  1 20:11:45 2011 UTC
 Line 34 
 a variable specific heat resulting from
  the lower layer has a fixed heat capacity. A zero heat capacity snow
  layer lies above the ice. Heat fluxes at the top and bottom
  surfaces are used to calculate the change in ice and snow layer
  thickness. Grid cells of the ocean model are
  either fully covered in ice or are open water. There is
  a provision to parametrize ice fraction (and leads) in this package.
  Modifications are discussed in small font following the
 Line 59 
 ocean model surface layer of water:
  \[
    {\bf frzmlt} = (T_f - SST) \frac{c_{sw} \rho_{sw} \Delta z}{\Delta t}
  \]
  where $c_{sw}$ is seawater heat capacity,
  $\rho_{sw}$ is the seawater density, $\Delta z$
  is the ocean model upper layer thickness and $\Delta t$ is the model (tracer)
  timestep. The freezing temperature, $T_f=\mu S$ is a function of the
 Line 72 
 salinity.
 ) If there is ice present in the grid cell
     we call the main ice model routine {\it ice\_therm.F} (see below).
     Output from this routine gives net heat and freshwater flux
     affecting the top of the ocean.
  Subroutine {\it ice\_forcing.F} uses these values to find the
  sea surface tendencies
  in grid cells. When there is ice present,
  the surface stress tendencies are
  set to zero; the ice model is purely thermodynamic and the
  effect of ice motion on the sea-surface is not examined.
 Line 96 
 open water and seaice; if {\bf compact}
  {\bf {\underline{ subroutine ICE\_FREEZE}}}
  This routine is called from {\it thermodynamics.F}
  after the new temperature calculation, {\it calc\_gt.F},
  but before {\it calc\_gs.F}.
  In {\it ice\_freeze.F}, any ocean upper layer grid cell
  with no ice cover, but with temperature below freezing,
 Line 106 
 the water column that have a temperature
  freezing. In this routine, any water below the surface
  that is below freezing is set to $T_f$.
  A call to
  {\it ice\_start.F} is made if {\bf frzmlt} $>0$,
  and salinity tendancy is updated for brine release.
  \noindent
 Line 126 
 the sea surface is brought into this rou
  The enthalpy of the 2 layers of any new ice is calculated as:
  \begin{eqnarray}
  q_1 & = & -c_{i}*T_f + L_i \nonumber \\
- q_2 & = & -c_{f}T_{mlt}+ c_{i}(T_{mlt}-T{f}) + L_i(1-\frac{T_{mlt}}{T_f}
+ q_2 & = & -c_{f}T_{mlt}+ c_{i}(T_{mlt}-T{f}) + L_i(1-\frac{T_{mlt}}{T_f})
- \nonumber \\
+ \nonumber
  \end{eqnarray}
  where  $c_f$ is specific heat of liquid fresh water, $c_i$ is the
  specific heat of fresh ice, $L_i$ is latent heat of freezing,
  $\rho_i$ is density of ice and
  $T_{mlt}$ is melting temperature of ice with salinity of 1.
  The height of a new layer of ice is
 Line 148 
 new ice is formed over open water; the f
  must have a height of {\bf himin0}; this determines the ice
  fraction {\bf compact}. If there is already ice in the grid cell,
  the new ice must have the same height and the new ice fraction
  is
  \[
  i_f=(1-\hat{i_f}) \frac{h_{i new}}{h_i}
  \]
  where $\hat{i_f}$ is ice fraction from previous timestep
  and $h_i$ is current ice height. Snow is redistributed
  over the new ice fraction. The ice fraction is
  not allowed to become larger than {\bf iceMaskmax} and
  if the ice height is above {\bf hihig} then freezing energy
 Line 169 
 under orginal ice due to freezing water.
  \noindent
  The main subroutine of this package is {\it ice\_therm.F} where the
  ice temperatures are calculated and the changes in ice and snow
  thicknesses are determined. Output provides the net heat and fresh
  water fluxes that force the top layer of the ocean model.
  If the current ice height is less than {\bf himin} then
 Line 181 
 the ice model calculation.
  We follow the procedure
  of Winton (1999) -- see equations 3 to 21 -- to calculate
  the surface and internal ice temperatures.
  The surface temperature is found from the balance of the
  flux at the surface $F_s$, the shortwave heat flux absorbed by the ice,
  {\bf fswint}, and
  the upward conduction of heat through the snow and/or ice, $F_u$.
  We linearize $F_s$ about the surface temperature, $\hat{T_s}$,
  at the previous timestep (where \mbox{}$\hat{ }$ indicates the value at
  the  previous timestep):
  \[
  F_s (T_s) = F_s(\hat{T_s}) + \frac{\partial F_s(\hat{T_s)}}{\partial T_s}
  (T_s-\hat{T_s})
  \]
  where,
  \[
  F_s  =  F_{sensible}+F_{latent}+F_{longwave}^{down}+F_{longwave}^{up}+ (1-
  \alpha) F_{shortwave}
 Line 203 
 and
   \frac{d F_s}{dT} = \frac{d F_{sensible}}{dT} + \frac{d F_{latent}}{dT}
  +\frac{d F_{longwave}^{up}}{dT}.
  \]
  $F_s$ and $\frac{d F_s}{dT}$ are currently calculated from the {\bf BULKF}
  package described separately, but could also be provided by an atmospheric
  model. The surface albedo is calculated from the ice height and/or
  surface temperature (see below, {\it srf\_albedo.F}) and the
  shortwave flux absorbed in the ice is
  \[
  {\bf fswint} = (1-e^{\kappa_i h_i})(1-\alpha) F_{shortwave}
 Line 257 
 E_{bot} &= & (\frac{4K_i(T_2-T_f)}{h_i}-
  \end{eqnarray}
  where $F_b$ is the heat flux at the ice bottom due to the sea surface
  temperature variations from freezing.
  If $T_{sst}$ is above freezing, $F_b=c_{sw} \rho_{sw}
  \gamma (T_{sst}-T_f)u^{*}$, $\gamma$ is the heat transfer coefficient
  and $u^{*}=QQ$ is frictional velocity between ice
  and water. If $T_{sst}$ is below freezing,
  $F_b=(T_f - T_{sst})c_f \rho_f \Delta z /\Delta t$ and set $T_{sst}$
  to $T_f$. We also
 Line 268 
 and set those layers to $T_f$.
  If $E_{top}>0$ we melt snow from the surface, if all the snow is melted
  and there is energy left, we melt the ice. If the ice is all gone
  and there is still energy left, we apply the left over energy to
  heating the ocean model upper layer (See Winton, 1999, equations 27-29).
  Similarly if $E_{bot}>0$ we melt ice from the bottom. If all the ice
  is melted, the snow is melted (with energy from the ocean model upper layer
 Line 286 
 q_2 = \frac{ \hat{h_i}/2 \hat{q_2} + \De
  If there is a ice layer and the overlying air temperature is
  below 0$^o$C then any precipitation, $P$ joins the snow layer:
  \[
  \Delta h_s  = -P \frac{\rho_f}{\rho_s} \Delta t,
  \]
  $\rho_f$ and $\rho_s$ are the fresh water and snow densities.
  Any evaporation, similarly, removes snow or ice from the surface.
 Line 342 
 the surface albedo. There are two calcul
  \[ \alpha = f_s \alpha_s + (1-f_s) (\alpha_{i_{min}}
           + (\alpha_{i_{max}}- \alpha_{i_{min}}) (1-e^{-h_i/h_{\alpha}}))
  \]
  where $f_s$ is 1 if there is snow, 0 if not; the snow albedo,
  $\alpha_s$ has two values
  depending on whether $T_s<0$ or not; $\alpha_{i_{min}}$ and
  $\alpha_{i_{max}}$ are ice albedos for thin melting ice, and
  thick bare ice respectively, and $h_{\alpha}$ is a scale
  height.
 Line 430 
 Finds averages and writes out diagnostic
  {\bf {\underline{Common Blocks}}}
  \noindent
  {\it ICE.h}: Ice Varibles, also
  {\bf relaxlat} and {\bf startIceModel}
  \noindent
 Line 438 
 Finds averages and writes out diagnostic
  from {\it ice\_diags.F}
  \noindent
  {\it BULKF\_ICE\_CONSTANTS.h} (in {\bf BULKF} package):
  all the parameters need by the ice model
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 Line 485 
 models.
  \begin{verbatim}
  ------------------------------------------------------------------------
  <-Name->|Levs|<-parsing code->|<--  Units   -->|<- Tile (max=80c)
  ------------------------------------------------------------------------
  SI_Fract|  1 |SM P    M1      |0-1             |Sea-Ice fraction  [0-1]
  SI_Thick|  1 |SM PC197M1      |m               |Sea-Ice thickness (area weighted average)
 Line 511 
 SIsOcMxL|  1 |SM P    M1      |psu
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  \vspace{1cm}
  \noindent
  {\bf {\underline{References}}}
  \noindent

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