source: trunk/DOC/TexFiles/Chapters/Chap_SBC.tex @ 994

% ================================================================
% Chapter Ñ Surface Boundary Condition (SBC) 
% ================================================================
\chapter{Surface Boundary Condition (SBC) }
\label{SBC}
\minitoc

\newpage
$\ $\newline    % force a new ligne
%---------------------------------------namsbc--------------------------------------------------
\namdisplay{namsbc}
%--------------------------------------------------------------------------------------------------------------
$\ $\newline    % force a new ligne

The ocean needs six fields as surface boundary condition:
\begin{itemize}
\item the two components of the surface ocean stress $\left( {\tau _u \;,\;\tau _v} \right)$
\item the incoming solar and non solar heat fluxes $\left( {Q_{ns} \;,\;Q_{sr} } \right)$
\item the surface freshwater budget $\left( {\text{EMP},\;\text{EMP}_S } \right)$
\end{itemize}

Four different ways to provide those six fields to the ocean are available which 
are controlled by namelist variables: an analytical formulation (\np{ln\_ana}=true), 
a flux formulation (\np{ln\_flx}=true), a bulk formulae formulation (CORE 
(\np{ln\_core}=true) or CLIO (\np{ln\_clio}=true) bulk formulae) and a coupled 
formulation (exchanges with a atmospheric model via the OASIS coupler) 
(\np{ln\_cpl}=true). The frequency at which the six fields have to be updated is
the  \np{nf\_sbc} namelist parameter. 
In addition, the resulting fields can be further modified using 
several namelist options. These options control the addition of a surface restoring 
term to observed SST and/or SSS (\np{ln\_ssr}=true), the modification of fluxes 
below ice-covered areas (using observed ice-cover or a sea-ice model) 
(\np{nn\_ice}=0,1, 2 or 3), the addition of river runoffs as surface freshwater 
fluxes (\np{ln\_rnf}=true), the addition of a freshwater flux adjustment in 
order to avoid a mean sea-level drift (\np{nn\_fwb}= 0, 1 or 2), and the 
transformation of the solar radiation (if provided as daily mean) into a diurnal 
cycle (\np{ln\_dm2dc}=true).

In this chapter, we first discuss where the surface boundary condition 
appears in the model equations. Then we present the four ways of providing 
the surface boundary condition. Finally, the different options that further modify 
the fluxes applied to the ocean are discussed.


% ================================================================
% Surface boundary condition for the ocean
% ================================================================
\section{Surface boundary condition for the ocean}
\label{SBC_general}


The surface ocean stress is the stress exerted by the wind and the sea-ice 
on the ocean. The two components of stress are assumed to be interpolated 
onto the ocean mesh, $i.e.$ resolved onto the model (\textbf{i},\textbf{j}) direction 
at $u$- and $v$-points They are applied as a surface boundary condition of the 
computation of the momentum vertical mixing trend (\mdl{dynzdf} module) :
\begin{equation} \label{Eq_sbc_dynzdf}
\left.{\left( {\frac{A^{vm} }{e_3 }\ \frac{\partial \textbf{U}_h}{\partial k}} \right)} \right|_{z=1}
    = \frac{1}{\rho _o} \binom{\tau _u}{\tau _v }
\end{equation}
where $(\tau _u ,\;\tau _v )=(utau,vtau)$ are the two components of the wind 
stress vector in the $(\textbf{i},\textbf{j})$ coordinate system.

The surface heat flux is decomposed into two parts, a non solar and a solar heat 
flux, $Q_{ns}$ and $Q_{sr}$, respectively. The former is the non penetrative part 
of the heat flux ($i.e.$ the sum of sensible, latent and long wave heat fluxes). 
It is applied as a surface boundary condition trend of the first level temperature 
time evolution equation (\mdl{trasbc} module). 
\begin{equation} \label{Eq_sbc_trasbc_q}
\frac{\partial T}{\partial t}\equiv \cdots \;+\;\left. {\frac{Q_{ns} }{\rho 
_o \;C_p \;e_{3T} }} \right|_{k=1} \quad
\end{equation}
$Q_{sr}$ is the penetrative part of the heat flux. It is applied as a 3D 
trends of the temperature equation (\mdl{traqsr} module) when \np{ln\_traqsr}=True.

\begin{equation} \label{Eq_sbc_traqsr}
\frac{\partial T}{\partial t}\equiv \cdots \;+\frac{Q_{sr} }{\rho _o C_p 
\,e_{3T} }\delta _k \left[ {I_w } \right]
\end{equation}
where $I_w$ is a non-dimensional function that describes the way the light 
penetrates inside the water column. It is generally a sum of decreasing 
exponentials (see \S\ref{TRA_qsr}).

The surface freshwater budget is provided by fields: EMP and EMP$_S$ which 
may or may not be identical. Indeed, a surface freshwater flux has two effects: 
it changes the volume of the ocean and it changes the surface concentration of 
salt (and other tracers). Therefore it appears in the sea surface height as a volume 
flux, EMP (\textit{dynspg\_xxx} modules), and in the salinity time evolution equations 
as a concentration/dilution effect, 
EMP$_{S}$ (\mdl{trasbc} module). 
\begin{equation} \label{Eq_trasbc_emp}
\begin{aligned}
&\frac{\partial \eta }{\partial t}\equiv \cdots \;+\;\text{EMP}\quad  \\ 
\\
 &\frac{\partial S}{\partial t}\equiv \cdots \;+\left. {\frac{\text{EMP}_S \;S}{e_{3T} }} \right|_{k=1} \\ 
 \end{aligned}
\end{equation} 

In the real ocean, EMP$=$EMP$_S$ and the ocean salt content is conserved, 
but it exist several numerical reasons why this equality should be broken. 
For example:

When rigid-lid assumption is made, the ocean volume becomes constant and 
thus, EMP$=$0, not EMP$_{S }$.

When the ocean is coupled to a sea-ice model, the water exchanged between ice and 
ocean is slightly salty (mean sea-ice salinity is $\sim $\textit{4 psu}). In this case, 
EMP$_{S}$ take into account both concentration/dilution effect associated with 
freezing/melting and the salt flux between ice and ocean, while EMP is 
only the volume flux. In addition, in the current version of \NEMO, the 
sea-ice is assumed to be above the ocean. Freezing/melting does not change 
the ocean volume (not impact on EMP) but it modifies the SSS.
%gm  \colorbox{yellow}{(see {\S} on LIM sea-ice model)}.

Note that SST can also be modified by a freshwater flux. Precipitation (in 
particular solid precipitation) may have a temperature significantly different from 
the SST. Due to the lack of information about the temperature of 
precipitation, we assume it is equal to the SST. Therefore, no 
concentration/dilution term appears in the temperature equation. It has to 
be emphasised that this absence does not mean that there is no heat flux 
associated with precipitation! Precipitation can change the ocean volume and thus the
ocean heat content. It is therefore associated with a heat flux (not yet  
diagnosed in the model) \citep{Roullet2000}).

%\colorbox{yellow}{Miss: }
%
%A extensive description of all namsbc namelist (parameter that have to be 
%created!)
%
%Especially the \np{nf\_sbc}, the \mdl{sbc\_oce} module (fluxes + mean sst sss ssu 
%ssv) i.e. information required by flux computation or sea-ice
%
%\mdl{sbc\_oce} containt the definition in memory of the 7 fields (6+runoff), add 
%a word on runoff: included in surface bc or add as lateral obc{\ldots}.
%
%Sbcmod manage the ``providing'' (fourniture) to the ocean the 7 fields
%
%Fluxes update only each nf{\_}sbc time step (namsbc) explain relation 
%between nf{\_}sbc and nf{\_}ice, do we define nf{\_}blk??? ? only one 
%nf{\_}sbc
%
%Explain here all the namlist namsbc variable{\ldots}.
%
%\colorbox{yellow}{End Miss }

The ocean model provides the surface currents, temperature and salinity 
averaged over \np{nf\_sbc} time-step (\ref{Tab_ssm}).The computation of the 
mean is done in \mdl{sbcmod} module.

%-------------------------------------------------TABLE---------------------------------------------------
\begin{table}[tb]  \label{Tab_ssm}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Variable description             & Model variable  & Units  & point \\  \hline
i-component of the surface current  & ssu\_m & $m.s^{-1}$   & U \\   \hline
j-component of the surface current  & ssv\_m & $m.s^{-1}$   & V \\   \hline
Sea surface temperature          & sst\_m & \r{}$K$      & T \\   \hline
Sea surface salinty              & sss\_m & $psu$        & T \\   \hline
\end{tabular}
\caption{Ocean variables provided by the ocean to the surface module (SBC). 
The variable are averaged over nf{\_}sbc time step, $i.e.$ the frequency of 
computation of surface fluxes.}
\end{center}
\end{table}
%--------------------------------------------------------------------------------------------------------------



%\colorbox{yellow}{Penser a} mettre dans le restant l'info nf{\_}sbc ET nf{\_}sbc*rdt de sorte de reinitialiser la moyenne si on change la frequence ou le pdt


% ================================================================
% Analytical formulation (sbcana module) 
% ================================================================
\section  [Analytical formulation (\textit{sbcana}) ]
      {Analytical formulation (\mdl{sbcana} module) }
\label{SBC_ana}

%---------------------------------------namsbc_ana--------------------------------------------------
\namdisplay{namsbc_ana}
%--------------------------------------------------------------------------------------------------------------


The analytical formulation of the surface boundary condition is the default scheme.
In this case, all the six fluxes needed by the ocean are assumed to 
be uniform in space. They take constant values given in the namelist 
namsbc{\_}ana by the variables \np{rn\_utau0}, \np{rn\_vtau0}, \np{rn\_qns0}, 
\np{rn\_qsr0}, and \np{rn\_emp0} (EMP$=$EMP$_S$). The runoff is set to zero. 
In addition, the wind is allowed to reach its nominal value within a given number 
of time steps (\np{nn\_tau000}).

If a user wants to apply a different analytical forcing, the \mdl{sbcana} 
module can be modified to use another scheme. As an example, 
the \mdl{sbc\_ana\_gyre} routine provides the analytical forcing for the 
GYRE configuration (see GYRE configuration manual, in preparation).


% ================================================================
% Flux formulation 
% ================================================================
\section  [Flux formulation (\textit{sbcflx}) ]
      {Flux formulation (\mdl{sbcflx} module) }
\label{SBC_flx}
%------------------------------------------namsbc_flx----------------------------------------------------
\namdisplay{namsbc_flx} 
%-------------------------------------------------------------------------------------------------------------

In the flux formulation (\np{ln\_flx}=true), the surface boundary 
condition fields are directly read from input files. The user has to define 
in the namelist namsbc{\_}flx the name of the file, the name of the variable 
read in the file, the time frequency at which it is given (in hours), and a logical 
setting whether a time interpolation to the model time step is required 
for this field). (fld\_i namelist structure).

\textbf{Caution}: when the frequency is set to --12, the data are monthly 
values. These are assumed to be climatological values, so time interpolation 
between December the 15$^{th}$ and January the 15$^{th}$ is done using 
records 12 and 1

When higher frequency is set and time interpolation is demanded, the model 
will try to read the last (first) record of previous (next) year in a file 
having the same name but a suffix {\_}prev{\_}year ({\_}next{\_}year) being 
added (e.g. "{\_}1989"). These files must only contain a single record. If they don't exist, 
the model assumes that the last record of the previous year is equal to the first 
record of the current year, and similarly, that the first record of the 
next year is equal to the last record of the current year. This will cause 
the forcing to remain constant over the first and last half fld\_frequ hours.

Note that in general, a flux formulation is used in associated with a 
restoring term to observed SST and/or SSS. See \S\ref{SBC_ssr} for its 
specification.


% ================================================================
% Bulk formulation
% ================================================================
\section  [Bulk formulation (\textit{sbcblk\_core} or \textit{sbcblk\_clio}) ]
      {Bulk formulation \small{(\mdl{sbcblk\_core} or \mdl{sbcblk\_clio} module)} }
\label{SBC_blk}

In the bulk formulation, the surface boundary condition fields are computed 
using bulk formulae and atmospheric fields and ocean (and ice) variables. 

The atmospheric fields used depend on the bulk formulae used. Two bulk formulations 
are available : the CORE and CLIO bulk formulea. The choice is made by setting to true
one of the following namelist variable : \np{ln\_core} and \np{ln\_clio}.

Note : in forced mode, when a sea-ice model is used, a bulk formulation have to be used. 
Therefore the two bulk formulea provided include the computation of the fluxes over both 
an ocean and an ice surface. 

% -------------------------------------------------------------------------------------------------------------
%        CORE Bulk formulea
% -------------------------------------------------------------------------------------------------------------
\subsection    [CORE Bulk formulea (\np{ln\_core}=true)]
            {CORE Bulk formulea (\np{ln\_core}=true, \mdl{sbcblk\_core})}
\label{SBC_blk_core}
%------------------------------------------namsbc_core----------------------------------------------------
\namdisplay{namsbc_core} 
%-------------------------------------------------------------------------------------------------------------

The CORE bulk formulae have been developed by \citet{LargeYeager2004}. 
They have been designed to handle the CORE forcing, a mixture of NCEP 
reanalysis and satellite data. They use an inertial dissipative method to compute 
the turbulent transfer coefficients (momentum, sensible heat and evaporation) 
from the 10 metre wind speed, air temperature and specific humidity.

Note that substituting ERA40 to NCEP reanalysis fields 
does not require changes in the bulk formulea themself. 

The required 8 input fields are:

%--------------------------------------------------TABLE--------------------------------------------------
\begin{table}[htbp]   \label{Tab_CORE}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Variable desciption              & Model variable  & Units   & point \\    \hline
i-component of the 10m air velocity & utau      & $m.s^{-1}$         & T  \\  \hline
j-component of the 10m air velocity & vtau      & $m.s^{-1}$         & T  \\  \hline
10m air temperature              & tair      & \r{}$K$            & T   \\ \hline
Specific humidity             & humi      & \%              & T \\      \hline
Incoming long wave radiation     & qlw    & $W.m^{-2}$         & T \\      \hline
Incoming short wave radiation    & qsr    & $W.m^{-2}$         & T \\      \hline
Total precipitation (liquid + solid)   & precip & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
Solid precipitation              & snow      & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
\end{tabular}
\end{center}
\end{table}
%--------------------------------------------------------------------------------------------------------------

Note that the air velocity is provided at a tracer ocean point, not at a velocity ocean point ($u$- and $v$-points). It is simpler and faster (less fields to be read), but it is not the recommended method when the ocean grid
size is the same or larger than the one of the input atmospheric fields.

% -------------------------------------------------------------------------------------------------------------
%        CLIO Bulk formulea
% -------------------------------------------------------------------------------------------------------------
\subsection    [CLIO Bulk formulea (\np{ln\_clio}=true)]
            {CLIO Bulk formulea (\np{ln\_clio}=true, \mdl{sbcblk\_clio})}
\label{SBC_blk_clio}
%------------------------------------------namsbc_clio----------------------------------------------------
\namdisplay{namsbc_clio} 
%-------------------------------------------------------------------------------------------------------------

The CLIO bulk formulae were developed several years ago for the 
Louvain-la-neuve coupled ice-ocean model (CLIO, \cite{Goosse_al_JGR99}). 
They are simpler bulk formulae. They assume the stress to be known and 
compute the radiative fluxes from a climatological cloud cover. 

The required 7 input fields are:

%--------------------------------------------------TABLE--------------------------------------------------
\begin{table}[htbp]   \label{Tab_CLIO}
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Variable desciption           & Model variable  & Units           & point \\  \hline
i-component of the ocean stress     & utau         & $N.m^{-2}$         & U \\   \hline
j-component of the ocean stress     & vtau         & $N.m^{-2}$         & V \\   \hline
Wind speed module             & vatm         & $m.s^{-1}$         & T \\   \hline
10m air temperature              & tair         & \r{}$K$            & T \\   \hline
Specific humidity                & humi         & \%              & T \\   \hline
Cloud cover                   &           & \%              & T \\   \hline
Total precipitation (liquid + solid)   & precip    & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
Solid precipitation              & snow         & $Kg.m^{-2}.s^{-1}$ & T \\   \hline
\end{tabular}
\end{center}
\end{table}
%--------------------------------------------------------------------------------------------------------------

As for the flux formulation, information about the input data required by the 
model is provided in the namsbc\_blk\_core or namsbc\_blk\_clio 
namelist (via the structure fld\_i). The first and last record assumption is also made 
(see \S\ref{SBC_flx})

% ================================================================
% Coupled formulation
% ================================================================
\section  [Coupled formulation (\textit{sbccpl}) ]
      {Coupled formulation (\mdl{sbccpl} module)}
\label{SBC_cpl}
%------------------------------------------namsbc_cpl----------------------------------------------------
\namdisplay{namsbc_cpl} 
%-------------------------------------------------------------------------------------------------------------

In the coupled formulation of the surface boundary condition, the fluxes are 
provided by the OASIS coupler at each \np{nf\_cpl} time-step, while sea and ice 
surface temperature, ocean and ice albedo, and ocean currents are sent to 
the atmospheric component.

The generalised coupled interface is under development. It should be available
in summer 2008. It will include the ocean interface for most of the European 
atmospheric GCM (ARPEGE, ECHAM, ECMWF, HadAM, LMDz).


% ================================================================
% Miscellanea options
% ================================================================
\section{Miscellaneous options}
\label{SBC_misc}

% -------------------------------------------------------------------------------------------------------------
%        Surface restoring to observed SST and/or SSS
% -------------------------------------------------------------------------------------------------------------
\subsection    [Surface restoring to observed SST and/or SSS (\textit{sbcssr})]
         {Surface restoring to observed SST and/or SSS (\mdl{sbcssr})}
\label{SBC_ssr}
%------------------------------------------namsbc_ssr----------------------------------------------------
\namdisplay{namsbc_ssr} 
%-------------------------------------------------------------------------------------------------------------

In forced mode using a flux formulation (default option or \key{flx} defined), a 
feedback term \emph{must} be added to the surface heat flux $Q_{ns}^o$:
\begin{equation} \label{Eq_sbc_dmp_q}
Q_{ns} = Q_{ns}^o + \frac{dQ}{dT} \left( \left. T \right|_{k=1} - SST_{Obs} \right)
\end{equation}
where SST is a sea surface temperature field (observed or climatological), $T$ is 
the model surface layer temperature and $\frac{dQ}{dT}$ is a negative feedback 
coefficient usually taken equal to $-40~W/m^2/K$. For a $50~m$ 
mixed-layer depth, this value corresponds to a relaxation time scale of two months. 
This term ensures that if $T$ perfectly matches the supplied SST, then $Q$ is 
equal to $Q_o$. 

In the fresh water budget, a feedback term can also be added. Converted into an 
equivalent freshwater flux, it takes the following expression :

\begin{equation} \label{Eq_sbc_dmp_emp}
EMP = EMP_o + \gamma_s^{-1} e_{3t}  \frac{  \left(\left.S\right|_{k=1}-SSS_{Obs}\right)}
                                             {\left.S\right|_{k=1}}
\end{equation}

where EMP$_{o }$ is a net surface fresh water flux (observed, climatological or an
atmospheric model product), \textit{SSS}$_{Obs}$ is a sea surface salinity (usually a time 
interpolation of the monthly mean Polar Hydrographic Climatology \citep{Steele2001}), 
$\left.S\right|_{k=1}$ is the model surface layer salinity and $\gamma_s$ is a negative 
feedback coefficient which is provided as a namelist parameter. Unlike heat flux, there is no 
physical justification for the feedback term in \ref{Eq_sbc_dmp_emp} as the atmosphere 
does not care about ocean surface salinity \citep{Madec1997}. The SSS restoring 
term should be viewed as a flux correction on freshwater fluxes to reduce the 
uncertainties we have on the observed freshwater budget.

% -------------------------------------------------------------------------------------------------------------
%        Handling of ice-covered area
% -------------------------------------------------------------------------------------------------------------
\subsection{Handling of ice-covered area}
\label{SBC_ice-cover}

The presence at the sea surface of an ice covered area modifies all the fluxes 
transmitted to the ocean. There are several way to handle sea-ice in the system depending on the value of the \np{nn{\_}ice} namelist parameter.  
\begin{description}
\item[nn{\_}ice = 0]  there will never be sea-ice in the computational domain. This is a typical namelist value used for tropical ocean domain. The surface fluxes are simply specified for an ice-free ocean. No specific things are done for sea-ice.
\item[nn{\_}ice = 1]  sea-ice can exist in the computational domain, but no sea-ice model is used. An observed ice covered area is read in a file. Below this area, the SST is restored to the freezing point and the heat fluxes are set to $-4~W/m^2$ ($-2~W/m^2$) in the northern (southern) hemisphere. The associated modification of the freshwater fluxes are done in such a way that the change in buoyancy fluxes remains zero. This prevents deep convection to occur when trying to reach the freezing point (and so ice covered area condition) while the SSS is too large. This manner of managing sea-ice area, just by using si IF case, is usually referred as the \textit{ice-if} model. It can be found in the \mdl{sbcice{\_}if} module.
\item[nn{\_}ice = 2 or more]  A full sea ice model is used. This model computes the ice-ocean fluxes, that are combined with the air-sea fluxes using the ice fraction of each model cell to provide the surface ocean fluxes. Note that the activation of a sea-ice model is is done by defining a CPP key (\key{lim2} or \key{lim3}). The activation automatically ovewrite the read value of nn{\_}ice to its appropriate value ($i.e.$ $2$ for LIM-2 and $3$ for LIM-3).
\end{description}

% {Description of Ice-ocean interface to be added here or in LIM 2 and 3 doc ?}

% -------------------------------------------------------------------------------------------------------------
%        Addition of river runoffs
% -------------------------------------------------------------------------------------------------------------
\subsection   [Addition of river runoffs (\textit{sbcrnf})]
         {Addition of river runoffs (\mdl{sbcrnf})}
\label{SBC_rnf}
%------------------------------------------namsbc_rnf----------------------------------------------------
\namdisplay{namsbc_rnf} 
%-------------------------------------------------------------------------------------------------------------

It is convenient to introduce the river runoff in the model as a surface 
fresh water flux. 

\colorbox{yellow}{Nevertheless, Pb of vertical resolution and increase of Kz in vicinity of }

\colorbox{yellow}{river mouths{\ldots}}

Control of the mean sea level

% -------------------------------------------------------------------------------------------------------------
%        Freshwater budget control 
% -------------------------------------------------------------------------------------------------------------
\subsection   [Freshwater budget control (\textit{sbcfwb})]
         {Freshwater budget control (\mdl{sbcfwb})}
\label{SBC_fwb}

To be written later...

\gmcomment{The descrition of the technique used to control the freshwater budget has to be added here}