--- manual/s_phys_pkgs/text/thsice.tex 2006/06/28 15:35:09 1.8 +++ manual/s_phys_pkgs/text/thsice.tex 2011/12/01 20:11:45 1.9 @@ -34,7 +34,7 @@ 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 +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 @@ -59,7 +59,7 @@ \[ {\bf frzmlt} = (T_f - SST) \frac{c_{sw} \rho_{sw} \Delta z}{\Delta t} \] -where $c_{sw}$ is seawater heat capacity, +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 @@ -72,12 +72,12 @@ 2) 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 + 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 +Subroutine {\it ice\_forcing.F} uses these values to find the sea surface tendencies -in grid cells. When there is ice present, +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. @@ -96,7 +96,7 @@ {\bf {\underline{ subroutine ICE\_FREEZE}}} This routine is called from {\it thermodynamics.F} -after the new temperature calculation, {\it calc\_gt.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, @@ -106,7 +106,7 @@ 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} $>0$, +{\it ice\_start.F} is made if {\bf frzmlt} $>0$, and salinity tendancy is updated for brine release. \noindent @@ -126,11 +126,11 @@ 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} -\nonumber \\ +q_2 & = & -c_{f}T_{mlt}+ c_{i}(T_{mlt}-T{f}) + L_i(1-\frac{T_{mlt}}{T_f}) +\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, +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 @@ -148,12 +148,12 @@ 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 +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 +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 @@ -169,7 +169,7 @@ \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 +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 @@ -181,19 +181,19 @@ We follow the procedure of Winton (1999) -- see equations 3 to 21 -- to calculate -the surface and internal ice temperatures. +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, +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, $\hat{T_s}$, +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, +where, \[ F_s = F_{sensible}+F_{latent}+F_{longwave}^{down}+F_{longwave}^{up}+ (1- \alpha) F_{shortwave} @@ -203,10 +203,10 @@ \frac{d F_s}{dT} = \frac{d F_{sensible}}{dT} + \frac{d F_{latent}}{dT} +\frac{d F_{longwave}^{up}}{dT}. \] -$F_s$ and $\frac{d F_s}{dT}$ are currently calculated from the {\bf BULKF} +$F_s$ 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 +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} @@ -257,9 +257,9 @@ \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} +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 $u^{*}=QQ$ 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 @@ -268,7 +268,7 @@ 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 +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 @@ -286,7 +286,7 @@ If there is a ice layer and the overlying air temperature is below 0$^o$C then any precipitation, $P$ joins the snow layer: \[ -\Delta h_s = -P \frac{\rho_f}{\rho_s} \Delta t, +\Delta h_s = -P \frac{\rho_f}{\rho_s} \Delta t, \] $\rho_f$ and $\rho_s$ are the fresh water and snow densities. Any evaporation, similarly, removes snow or ice from the surface. @@ -342,9 +342,9 @@ \[ \alpha = f_s \alpha_s + (1-f_s) (\alpha_{i_{min}} + (\alpha_{i_{max}}- \alpha_{i_{min}}) (1-e^{-h_i/h_{\alpha}})) \] -where $f_s$ is 1 if there is snow, 0 if not; the snow albedo, +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 +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. @@ -430,7 +430,7 @@ {\bf {\underline{Common Blocks}}} \noindent -{\it ICE.h}: Ice Varibles, also +{\it ICE.h}: Ice Varibles, also {\bf relaxlat} and {\bf startIceModel} \noindent @@ -438,7 +438,7 @@ from {\it ice\_diags.F} \noindent -{\it BULKF\_ICE\_CONSTANTS.h} (in {\bf BULKF} package): +{\it BULKF\_ICE\_CONSTANTS.h} (in {\bf BULKF} package): all the parameters need by the ice model %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -485,7 +485,7 @@ \begin{verbatim} ------------------------------------------------------------------------ -<-Name->|Levs|<-parsing code->|<-- Units -->|<- Tile (max=80c) +<-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) @@ -511,7 +511,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vspace{1cm} -\noindent +\noindent {\bf {\underline{References}}} \noindent