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% \usepackage{amssymb} |
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% \begin{document} |
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% |
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%%%--------------------------------------%%% |
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\def\deg{$^o$} |
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\section{Bulk Formula Package} |
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author: Stephanie Dutkiewicz\\ |
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\noindent |
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Instead of forcing the model with heat and fresh water flux data, |
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this package calculates these fluxes using the changing sea surface |
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temperature. We need to read in some atmospheric data: |
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{\bf air temperature, air humidity, down shortwave radiation, |
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down longwave radiation, precipitation, wind speed}. |
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The current setup also reads in {\bf wind stress}, but this |
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can be changed so that the stresses are calculated from the |
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wind speed. |
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The current setup requires that there is the thermodynamic-seaice package |
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({\it pkg/thsice}, also refered below as seaice) |
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is also used. It would be useful though to have it also |
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setup to run with some very simple parametrization of the sea ice. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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The heat and fresh water fluxes are calculated in {\it bulkf\_forcing.F} |
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called from {\it forward\_step.F}. These fluxes are used over open water, |
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fluxes over seaice are recalculated in the sea-ice package. |
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Before the call to {\it bulkf\_forcing.F} we call |
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{\it bulkf\_fields\_load.F} to find the current atmospheric conditions. |
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The only other changes to the model code come from the initializing |
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and writing diagnostics of these fluxes. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf \underline{subroutine BULKF\_FIELDS\_LOAD}} |
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\noindent |
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Here we find the atmospheric data needed for the bulk formula |
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calculations. These are read in at periodic intervals and |
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values are interpolated to the current time. The data file names |
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come from {\bf data.blk}. The values that can be read in are: |
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air temperature, air humidity, precipitation, |
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down solar radiation, down long |
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wave radiation, zonal and meridional wind speeds, total wind |
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speed, net heat flux, net freshwater forcing, cloud cover, |
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snow fall, zonal and meridional wind stresses, and SST and SSS |
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used for relaxation terms. |
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Not all these files are necessary or used. For instance cloud |
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cover and snow fall are not used in the current bulk formula |
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calculation. If total wind speed is not supplied, wind speed |
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is calculate from the zonal and meridional components. If |
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wind stresses are not read in, then the stresses are calculated |
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from the wind speed. Net heat flux and net freshwater can be |
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read in and used over open ocean instead of the bulk formula |
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calculations (but over seaice the bulkf formula is always |
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used). This is "hardwired" into {\it bulkf\_forcing} and |
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the "ch" in the variable names suggests that this is "cheating". |
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SST and SSS need to be read in if there is any relaxation used. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf \underline{subroutine BULKF\_FORCING}} |
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\noindent |
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In {\it bulkf\_forcing.F}, we calculate heat and fresh water |
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fluxes (and wind stress, if necessary) for each grid cell. |
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First we determine if the grid cell is open water or seaice |
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and this information is carried by {\bf iceornot}. There is |
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a provision here for a different designation if there is |
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snow cover (but currently this does not make any difference). |
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We then call {\it bulkf\_formula\_lanl.F} which provides |
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values for: up long wave radiation, latent and sensible heat |
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fluxes, the derivative of these three with respect to surface |
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temperature, wind stress, evaporation. |
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Net long wave radiation is calculated from the combination |
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of the down long wave read in and the up long wave calculated. |
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We then find the albedo of the surface - with a call to |
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{\it sfc\_albedo} if there is sea-ice (see the seaice package |
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for information on the subroutine). If the grid cell is open |
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ocean the albedo is set as 0.1. Note that this is a parameter |
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that can be used to tune the results. The net short wave |
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radiation is then the down shortwave radiation minus the |
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amount reflected. |
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If the wind stress needed to be calculated in {\it bulkf\_formula\_lanl.F}, |
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it was calculated to grid cell center points, so in {\it bulkf\_forcing.F} |
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we regrid to {\bf u} and {\bf v} points. We let the model know |
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if it has read in stresses or calculated stresses by the switch |
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{\bf readwindstress} which is can be set in data.blk, and defaults |
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to {\bf .TRUE.}. |
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We then calculate {\bf Qnet} and {\bf EmPmR} that will be used |
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as the fluxes over the open ocean. There is a provision for |
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using runoff. If we are "cheating" and using observed fluxes |
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over the open ocean, then there is a provision here to |
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use read in {\bf Qnet} and {\bf EmPmR}. |
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The final call is to calculate averages of the terms found |
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in this subroutine. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{ subroutine BULKF\_FORMULA\_LANL}}} |
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\noindent |
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This is the main program of the package where the |
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heat fluxes and freshwater fluxes over ice and |
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open water are calculated. Note that this subroutine |
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is also called from the seaice package during the |
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iterations to find the ice surface temperature. |
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Latent heat ($L$) used in this subroutine |
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depends on the state of the surface: vaporization for |
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open water, fusion and vaporization for ice surfaces. |
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Air temperature is converted from Celsius to Kelvin. |
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If there is no wind speed ($u_s$) given, then the wind speed |
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is calculated from the zonal and meridional components. |
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We calculate the virtual temperature: |
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\[ |
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T_o = T_{air} (1+\gamma q_{air}) |
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\] |
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where $T_{air}$ is the air temperature at $h_T$, $q_{air}$ is |
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humidity at $h_q$ and $\gamma$ is a constant. |
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The saturated vapor pressure is calculate (QQ ref): |
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\[ |
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q_{sat} = \frac{a}{p_o} e^{L (b-\frac{c}{T_{srf}})} |
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\] |
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where $a,b,c$ are constants, $T_{srf}$ is surface temperature |
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and $p_o$ is the surface pressure. |
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The two values crucial for the bulk formula calculations are |
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the difference between air at sea surface and sea surface temperature: |
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\[ |
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\Delta T = T_{air} - T_{srf} +\alpha h_T |
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\] |
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where $\alpha$ is adiabatic lapse rate and $h_T$ is the height |
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where the air temperature was taken; and the difference |
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between the air humidity and the saturated humidity |
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\[ |
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\Delta q = q_{air} - q_{sat}. |
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\] |
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We then calculate the turbulent exchange coefficients |
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following Bryan et al (1996) and the numerical scheme |
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of Hunke and Lipscombe (1998). |
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We estimate initial values for the exchange coefficients, $c_u$, |
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$c_T$ and $c_q$ as |
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\[ |
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\frac{\kappa}{ln(z_{ref}/z_{rou})} |
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\] |
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where $\kappa$ is the Von Karman constant, $z_{ref}$ is a |
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reference height and $z_{rou}$ is a roughness length scale |
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which could be a function of type of surface, but is here set |
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as a constant. Turbulent scales are: |
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\begin{eqnarray} |
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u^* & = & c_u u_s \nonumber\\ |
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T^* & = & c_T \Delta T \nonumber\\ |
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q^* & = & c_q \Delta q \nonumber |
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\end{eqnarray} |
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We find the "integrated flux profile" for momentum and stability |
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if there are stable QQ conditions ($\Upsilon>0$) : |
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\[ |
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\psi_m = \psi_s = -5 \Upsilon |
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\] |
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and for unstable QQ conditions ($\Upsilon<0$): |
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\begin{eqnarray} |
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\psi_m & = & 2 ln(0.5(1+\chi)) + ln(0.5(1+\chi^2)) - 2 \tan^{-1} \chi + \pi/2 |
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\nonumber \\ |
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\psi_s & = & 2 ln(0.5(1+\chi^2)) \nonumber |
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\end{eqnarray} |
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where |
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\[ |
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\Upsilon = \frac{\kappa g z_{ref}}{u^{*2}} (\frac{T^*}{T_o} + |
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\frac{q^*}{1/\gamma + q_a}) |
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\] |
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and $\chi=(1-16\Upsilon)^{1/2}$. |
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The coefficients are updated through 5 iterations as: |
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\begin{eqnarray} |
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c_u & = & \frac {\hat{c_u}}{1+\hat{c_u}(\lambda - \psi_m)/\kappa} \nonumber \\ |
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c_T & = & \frac {\hat{c_T}}{1+\hat{c_T}(\lambda - \psi_s)/\kappa} \nonumber \\ |
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c_q & = & c'_T |
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\end{eqnarray} |
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where $\lambda =ln(h_T/z_{ref})$. |
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We can then find the bulk formula heat fluxes: |
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\vspace{.2cm} |
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\noindent |
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Sensible heat flux: |
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\[ |
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Q_s=\rho_{air} c_{p_{air}} u_s c_u c_T \Delta T |
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\] |
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\vspace{.2cm} |
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\noindent |
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Latent heat flux: |
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\[ |
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Q_l=\rho_{air} L u_s c_u c_q \Delta q |
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\] |
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\vspace{.2cm} |
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\noindent |
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Up long wave radiation |
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\[ |
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Q_{lw}^{up}=\epsilon \sigma T_{srf}^4 |
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\] |
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where $\epsilon$ is emissivity (which can be different for |
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open ocean, ice and snow), $\sigma$ is Stefan-Boltzman constant. |
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We calculate the derivatives of the three above functions |
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with respect to surface temperature |
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\begin{eqnarray} |
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\frac{dQ_s}{d_T} & = & \rho_{air} c_{p_{air}} u_s c_u c_T \nonumber \\ |
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\frac{dQ_l}{d_T} & = & \frac{\rho_{air} L^2 u_s c_u c_q c}{T_{srf}^2} \nonumber \\ |
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\frac{dQ_{]lw}^{up}}{d_T} & = & 4 \epsilon \sigma t_{srf}^3 \nonumber |
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\end{eqnarray} |
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And total derivative $\frac{dQ_o}{dT}= \frac{dQ_s}{dT} + |
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\frac{dQ_l}{dT} + \frac{dQ_{lw}^{up}}{dT}$. |
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If we do not read in the wind stress, it is calculated here. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{Initializing subroutines}}} |
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\noindent |
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{\it bulkf\_init.F}: |
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Set bulkf variables to zero. |
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\noindent |
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{\it bulkf\_readparms.F}: |
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Reads {\bf data.blk} |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{Diagnostic subroutines}}} |
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\noindent |
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{\it bulkf\_ave.F}: |
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Keeps track of means of the bulkf variables |
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\noindent |
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{\it bulkf\_diags.F}: |
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Finds averages and writes out diagnostics |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{Common Blocks}}} |
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\noindent |
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{\it BULKF.h}: BULKF Variables, data file names, and logicals |
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{\bf readwindstress} and {\bf readsurface} |
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\noindent |
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{\it BULKF\_DIAGS.h}: matrices for diagnostics: averages of fields |
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from {\it bulkf\_diags.F} |
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\noindent |
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{\it BULKF\_ICE\_CONSTANTS.h}: |
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all the parameters need by the ice model and in the bulkf formula |
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calculations. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{Input file DATA.ICE}}} |
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\noindent |
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We read in the file names of atmospheric data used in |
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the bulk formula calculations. Here we can also set |
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the logicals: {\bf readwindstress} if we read in the |
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wind stress rather than calculate it from the wind |
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speed; and {\bf readsurface} to read in the surface |
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temperature and salinity if these will be used as |
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part of a relaxing term. |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{Important Notes}}} |
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\noindent |
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{\bf 1)} heat fluxes have different signs in the ocean and ice |
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models. |
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\noindent |
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{\bf 2)} {\bf StartIceModel} must be changed in {\bf data.ice}: |
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1 (if starting from no ice), 0 (if using pickup.ic file). |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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\vspace{1cm} |
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\noindent |
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{\bf {\underline{References}}} |
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\vspace{.2cm} |
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\noindent |
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Bryan F.O., B.G Kauffman, W.G. Large, P.R. Gent, 1996: |
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The NCAR CSM flux coupler. Technical note TN-425+STR, |
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NCAR. |
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\vspace{.2cm} |
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\noindent |
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Hunke, E.C and W.H. Lipscomb, circa 2001: CICE: the Los Alamos |
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Sea Ice Model Documentation and Software User's Manual. |
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LACC-98-16v.2.\\ |
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(note: this documentation is no longer available as CICE has progressed |
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to a very different version 3) |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% \end{document} |
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