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Changeset 14113 for NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex – NEMO

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Timestamp:
2020-12-04T20:15:58+01:00 (2 years ago)
Author:
nicolasmartin
Message:

#2414 Reintegration to the trunk, LaTeX manuals are compiling ;-)

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1 edited

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  • NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex

    r13916 r14113  
    11\documentclass[../main/NEMO_manual]{subfiles} 
    2 \usepackage{fontspec} 
    3 \usepackage{fontawesome} 
    42 
    53\begin{document} 
     
    526524See \autoref{subsec:SBC_ssr} for its specification. 
    527525 
    528  
    529  
    530  
    531  
    532  
    533  
    534 %% ================================================================================================= 
    535 \pagebreak 
    536 \newpage 
     526%% ================================================================================================= 
    537527\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})} 
    538528\label{sec:SBC_blk} 
     
    558548 
    559549Note: all the NEMO Fortran routines involved in the present section have been 
    560  initially developed (and are still developed in parallel) in 
    561  the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project 
    562 \citep{brodeau.barnier.ea_JPO17}. 
     550initially developed (and are still developed in parallel) in 
     551the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} open-source project 
     552\citep{brodeau.barnier.ea_JPO16}. 
    563553 
    564554%%% Bulk formulae are this: 
    565 \subsection{Bulk formulae}\label{subsec:SBC_blkform} 
    566 % 
     555\subsection{Bulk formulae} 
     556\label{subsec:SBC_blkform} 
     557 
    567558In NEMO, the set of equations that relate each component of the surface fluxes 
    568559to the near-surface atmosphere and sea surface states writes 
    569 % 
    570 \begin{subequations}\label{eq_bulk} 
     560 
     561\begin{subequations} 
     562  \label{eq:SBC_bulk} 
    571563  \label{eq:SBC_bulk_form} 
    572   \begin{eqnarray} 
    573     \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\ 
    574     Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\ 
    575     E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\ 
    576     Q_L           &=& -L_v \, E \\ 
    577     % 
    578     Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\ 
    579     Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4) 
    580   \end{eqnarray} 
     564  \begin{align} 
     565    \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\ 
     566    Q_H           &= \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\ 
     567    E             &= \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\ 
     568    Q_L           &= -L_v \, E \\ 
     569    Q_{sr}        &= (1 - a) Q_{sw\downarrow} \\ 
     570    Q_{ir}        &= \delta (Q_{lw\downarrow} -\sigma T_s^4) 
     571  \end{align} 
    581572\end{subequations} 
    582 % 
     573 
    583574with 
    584575   \[ \theta_z \simeq T_z+\gamma z \] 
    585576   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \] 
    586 % 
    587577from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \] 
    588 % 
    589578where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux, 
    590579$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave 
    591580flux. 
    592 % 
    593581$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave 
    594582and longwave radiative fluxes, respectively. 
    595 % 
    596583Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$ 
    597584implies a gain of the relevant quantity for the ocean, while a positive $E$ 
    598585implies a freshwater loss for the ocean. 
    599 % 
    600586$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer 
    601587coefficients for momentum, sensible heat, and moisture, respectively. 
    602 % 
    603588$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of 
    604589vaporization of water. 
    605 % 
    606590$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature, 
    607591and specific humidity of air at height $z$ above the sea surface, 
    608592respectively. $\gamma z$ is a temperature correction term which accounts for the 
    609593adiabatic lapse rate and approximates the potential temperature at height 
    610 $z$ \citep{josey.gulev.ea_2013}. 
    611 % 
     594$z$ \citep{josey.gulev.ea_OCC13}. 
    612595$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface 
    613 (possibly referenced to the surface current $\mathbf{u_0}$, 
    614 section \ref{s_res1}.\ref{ss_current}). 
    615 % 
     596(possibly referenced to the surface current $\mathbf{u_0}$).%, 
     597%\autoref{s_res1}.\autoref{ss_current}). %% Undefined references 
    616598The bulk scalar wind speed, namely $U_B$, is the scalar wind speed, 
    617599$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution. 
    618 % 
    619600$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\ 
    620 % 
    621601%$p_a$ is the mean sea-level pressure (SLP). 
    622 % 
    623602$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity 
    624603of air at temperature $T_s$; it includes a 2\% reduction to account for the 
    625 presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}. 
     604presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}. 
    626605Depending on the bulk parametrization used, $T_s$ can either be the temperature 
    627606at the air-sea interface (skin temperature, hereafter SSST) or at typically a 
    628607few tens of centimeters below the surface (bulk sea surface temperature, 
    629608hereafter SST). 
    630 % 
    631609The SSST differs from the SST due to the contributions of two effects of 
    632610opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL, 
    633 respectively, see section\,\ref{subsec:SBC_skin}). 
    634 % 
     611respectively, see \autoref{subsec:SBC_skin}). 
    635612Technically, when the ECMWF or COARE* bulk parametrizations are selected 
    636613(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}), 
     
    640617 
    641618For more details on all these aspects the reader is invited to refer 
    642 to \citet{brodeau.barnier.ea_JPO17}. 
    643  
    644  
    645  
    646 \subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean} 
     619to \citet{brodeau.barnier.ea_JPO16}. 
     620 
     621\subsection{Bulk parametrizations} 
     622\label{subsec:SBC_blk_ocean} 
    647623%%%\label{subsec:SBC_param} 
    648624 
     
    654630height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}). 
    655631 
    656  
    657  
    658632For the open ocean, four bulk parametrization algorithms are available in NEMO: 
     633 
    659634\begin{itemize} 
    660 \item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09} 
     635\item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09} 
    661636\item COARE 3.0 \citep{fairall.bradley.ea_JC03} 
    662637\item COARE 3.6 \citep{edson.jampana.ea_JPO13} 
     
    664639\end{itemize} 
    665640 
    666  
    667641With respect to version 3, the principal advances in version 3.6 of the COARE 
    668642bulk parametrization are built around improvements in the representation of the 
    669643effects of waves on 
    670 fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes 
     644fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes 
    671645improved relationships of surface roughness, and whitecap fraction on wave 
    672646parameters. It is therefore recommended to chose version 3.6 over 3. 
    673647 
    674  
    675  
    676  
    677 \subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin} 
    678 %\subsection[Cool-skin and warm-layer parameterizations 
    679 %(\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})} 
    680 %\label{subsec:SBC_skin} 
    681 % 
     648\subsection{Cool-skin and warm-layer parametrizations} 
     649%\subsection[Cool-skin and warm-layer parameterizations (\forcode{ln_skin_cs} \& \forcode{ln_skin_wl})]{Cool-skin and warm-layer parameterizations (\protect\np{ln_skin_cs}{ln\_skin\_cs} \& \np{ln_skin_wl}{ln\_skin\_wl})} 
     650\label{subsec:SBC_skin} 
     651 
    682652As opposed to the NCAR bulk parametrization, more advanced bulk 
    683653parametrizations such as COARE3.x and ECMWF are meant to be used with the skin 
    684654temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at 
    685 the first T-point level, see section\,\ref{subsec:SBC_blkform}). 
    686 % 
     655the first T-point level, see \autoref{subsec:SBC_blkform}). 
     656 
    687657As such, the relevant cool-skin and warm-layer parametrization must be 
    688658activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs} 
     
    693663 
    694664For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same 
    695 basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based 
     665basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based 
    696666on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE 
    6976673.6. 
     
    704674equation for the thickness of the warm-layer, while it is considered as constant 
    705675in the ECWMF algorithm. 
    706  
    707676 
    708677\subsection{Appropriate use of each bulk parametrization} 
     
    714683temperature is the bulk SST. Hence the following namelist parameters must be 
    715684set: 
    716 % 
    717 \begin{verbatim} 
     685 
     686\begin{forlines} 
    718687  ... 
    719688  ln_NCAR    = .true. 
     
    726695  ... 
    727696  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg] 
    728 \end{verbatim} 
    729  
     697\end{forlines} 
    730698 
    731699\subsubsection{ECMWF} 
    732 % 
     700 
    733701With an atmospheric forcing based on a reanalysis of the ECMWF, such as the 
    734702Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to 
     
    737705humidity are provided at the 2\,m height, and given that the humidity is 
    738706distributed as the dew-point temperature, the namelist must be tuned as follows: 
    739 % 
    740 \begin{verbatim} 
     707 
     708\begin{forlines} 
    741709  ... 
    742710  ln_ECMWF   = .true. 
     
    750718  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K] 
    751719  ... 
    752 \end{verbatim} 
    753 % 
     720\end{forlines} 
     721 
    754722Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection 
    755723of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly 
     
    757725respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}). 
    758726 
    759  
    760727\subsubsection{COARE 3.x} 
    761 % 
     728 
    762729Since the ECMWF parametrization is largely based on the COARE* parametrization, 
    763730the two algorithms are very similar in terms of structure and closure 
    764731approach. As such, the namelist tuning for COARE 3.x is identical to that of 
    765732ECMWF: 
    766 % 
    767 \begin{verbatim} 
     733 
     734\begin{forlines} 
    768735  ... 
    769736  ln_COARE3p6 = .true. 
     
    772739  ln_skin_wl = .true. ! use the warm-layer parameterization 
    773740  ... 
    774 \end{verbatim} 
     741\end{forlines} 
    775742 
    776743Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection 
     
    779746respectively (found in \textit{sbcblk\_skin\_coare.F90}). 
    780747 
    781  
    782748%lulu 
    783  
    784  
    785749 
    786750% In a typical bulk algorithm, the BTCs under neutral stability conditions are 
     
    792756% and $q_z$. 
    793757 
    794  
    795  
    796758\subsection{Prescribed near-surface atmospheric state} 
    797759 
     
    800762different bulk formulae are used for the turbulent fluxes computation over the 
    801763ocean and over sea-ice surface. 
    802 % 
    803764 
    804765%The choice is made by setting to true one of the following namelist 
     
    862823the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 
    863824 
    864  
    865825\subsubsection{Air humidity} 
    866826 
     
    868828[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist 
    869829parameters)... 
    870  
    871  
    872 ~\\ 
    873  
    874  
    875  
    876  
    877  
    878  
    879  
    880  
    881  
    882830 
    883831%% ================================================================================================= 
     
    889837%their neutral transfer coefficients relationships with neutral wind. 
    890838%\begin{itemize} 
    891 %\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}. 
     839%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}. 
    892840%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 
    893841%  They use an inertial dissipative method to compute the turbulent transfer coefficients 
    894842%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 
    895 %  This \citet{large.yeager_rpt04} dataset is available through 
     843%  This \citet{large.yeager_trpt04} dataset is available through 
    896844%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 
    897845%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 
     
    908856\label{subsec:SBC_blk_ice} 
    909857 
    910  
    911858\texttt{\#out\_of\_place:} 
    912859 For sea-ice, three possibilities can be selected: 
    913860a constant transfer coefficient (1.4e-3; default 
    914 value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 
     861value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 
    915862and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 
    916863\texttt{\#out\_of\_place.} 
    917864 
    918  
    919  
    920  
    921865Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways: 
    922866 
    923867\begin{itemize} 
    924 \item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}): 
     868\item Constant value (\forcode{Cd_ice=1.4e-3}): 
    925869  default constant value used for momentum and heat neutral transfer coefficients 
    926 \item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}): 
     870\item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}): 
    927871  This scheme adds a dependency on edges at leads, melt ponds and flows 
    928872  of the constant neutral air-ice drag. After some approximations, 
     
    12601204  \begin{description} 
    12611205  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and 
    1262     the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 
     1206    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_trpt06}. 
    12631207  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation 
    12641208    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 
     
    13321276The fw addition due to the ice shelf melting is, at each relevant depth level, added to 
    13331277the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}. 
    1334 See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\ 
     1278See \autoref{sec:SBC_rnf} for all the details about the divergence correction. 
    13351279 
    13361280\begin{figure}[!t] 
     
    15031447Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided, 
    15041448the drag coefficient is computed according to the stable/unstable conditions of the 
    1505 air-sea interface following \citet{large.yeager_rpt04}. 
     1449air-sea interface following \citet{large.yeager_trpt04}. 
    15061450 
    15071451%% ================================================================================================= 
     
    16141558 
    16151559The surface stress felt by the ocean is the atmospheric stress minus the net stress going 
    1616 into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not 
     1560into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not 
    16171561available for forcing the mean circulation, while in the opposite case of a decaying sea 
    16181562state, more momentum is available for forcing the ocean. 
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