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

Timestamp:

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

Author:

nicolasmartin

Message:

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

File:

• NEMO/trunk/doc/latex/NEMO/subfiles/chap_SBC.tex (modified) (25 diffs)

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

@@ -1 +1 @@
 \documentclass[../main/NEMO_manual]{subfiles}
-\usepackage{fontspec}
-\usepackage{fontawesome}
 
 \begin{document}
@@ -526 +524 @@
 See \autoref{subsec:SBC_ssr} for its specification.
 
-
-
-
-
-
-
-%% =================================================================================================
-\pagebreak
-\newpage
+%% =================================================================================================
 \section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})}
 \label{sec:SBC_blk}
@@ -558 +548 @@
 
 Note: all the NEMO Fortran routines involved in the present section have been
- initially developed (and are still developed in parallel) in
- the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project
-\citep{brodeau.barnier.ea_JPO17}.
+initially developed (and are still developed in parallel) in
+the \href{https://brodeau.github.io/aerobulk}{\texttt{AeroBulk}} open-source project
+\citep{brodeau.barnier.ea_JPO16}.
 
 %%% Bulk formulae are this:
-\subsection{Bulk formulae}\label{subsec:SBC_blkform}
-%
+\subsection{Bulk formulae}
+\label{subsec:SBC_blkform}
+
 In NEMO, the set of equations that relate each component of the surface fluxes
 to the near-surface atmosphere and sea surface states writes
-%
-\begin{subequations}\label{eq_bulk}
+
+\begin{subequations}
+  \label{eq:SBC_bulk}
   \label{eq:SBC_bulk_form}
-  \begin{eqnarray}
-    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
-    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
-    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
-    Q_L           &=& -L_v \, E \\
-    %
-    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\
-    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4)
-  \end{eqnarray}
+  \begin{align}
+    \mathbf{\tau} &= \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\
+    Q_H           &= \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\
+    E             &= \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\
+    Q_L           &= -L_v \, E \\
+    Q_{sr}        &= (1 - a) Q_{sw\downarrow} \\
+    Q_{ir}        &= \delta (Q_{lw\downarrow} -\sigma T_s^4)
+  \end{align}
 \end{subequations}
-%
+
 with
    \[ \theta_z \simeq T_z+\gamma z \]
    \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \]
-%
 from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \]
-%
 where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux,
 $E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave
 flux.
-%
 $Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave
 and longwave radiative fluxes, respectively.
-%
 Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$
 implies a gain of the relevant quantity for the ocean, while a positive $E$
 implies a freshwater loss for the ocean.
-%
 $\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer
 coefficients for momentum, sensible heat, and moisture, respectively.
-%
 $C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of
 vaporization of water.
-%
 $\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature,
 and specific humidity of air at height $z$ above the sea surface,
 respectively. $\gamma z$ is a temperature correction term which accounts for the
 adiabatic lapse rate and approximates the potential temperature at height
-$z$ \citep{josey.gulev.ea_2013}.
-%
+$z$ \citep{josey.gulev.ea_OCC13}.
 $\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface
-(possibly referenced to the surface current $\mathbf{u_0}$,
-section \ref{s_res1}.\ref{ss_current}).
-%
+(possibly referenced to the surface current $\mathbf{u_0}$).%,
+%\autoref{s_res1}.\autoref{ss_current}). %% Undefined references
 The bulk scalar wind speed, namely $U_B$, is the scalar wind speed,
 $|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution.
-%
 $a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\
-%
 %$p_a$ is the mean sea-level pressure (SLP).
-%
 $T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity
 of air at temperature $T_s$; it includes a 2\% reduction to account for the
-presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}.
+presence of salt in seawater \citep{sverdrup.johnson.ea_bk42,kraus.businger_QJRMS96}.
 Depending on the bulk parametrization used, $T_s$ can either be the temperature
 at the air-sea interface (skin temperature, hereafter SSST) or at typically a
 few tens of centimeters below the surface (bulk sea surface temperature,
 hereafter SST).
-%
 The SSST differs from the SST due to the contributions of two effects of
 opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL,
-respectively, see section\,\ref{subsec:SBC_skin}).
-%
+respectively, see \autoref{subsec:SBC_skin}).
 Technically, when the ECMWF or COARE* bulk parametrizations are selected
 (\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}),
@@ -640 +617 @@
 
 For more details on all these aspects the reader is invited to refer
-to \citet{brodeau.barnier.ea_JPO17}.
-
-
-
-\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean}
+to \citet{brodeau.barnier.ea_JPO16}.
+
+\subsection{Bulk parametrizations}
+\label{subsec:SBC_blk_ocean}
 %%%\label{subsec:SBC_param}
 
@@ -654 +630 @@
 height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}).
 
-
-
 For the open ocean, four bulk parametrization algorithms are available in NEMO:
+
 \begin{itemize}
-\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09}
+\item NCAR, formerly known as CORE, \citep{large.yeager_trpt04,large.yeager_CD09}
 \item COARE 3.0 \citep{fairall.bradley.ea_JC03}
 \item COARE 3.6 \citep{edson.jampana.ea_JPO13}
@@ -664 +639 @@
 \end{itemize}
 
-
 With respect to version 3, the principal advances in version 3.6 of the COARE
 bulk parametrization are built around improvements in the representation of the
 effects of waves on
-fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes
+fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO16}. This includes
 improved relationships of surface roughness, and whitecap fraction on wave
 parameters. It is therefore recommended to chose version 3.6 over 3.
 
-
-
-
-\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin}
-%\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})}
-%\label{subsec:SBC_skin}
-%
+\subsection{Cool-skin and warm-layer parametrizations}
+%\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})}
+\label{subsec:SBC_skin}
+
 As opposed to the NCAR bulk parametrization, more advanced bulk
 parametrizations such as COARE3.x and ECMWF are meant to be used with the skin
 temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at
-the first T-point level, see section\,\ref{subsec:SBC_blkform}).
-%
+the first T-point level, see \autoref{subsec:SBC_blkform}).
+
 As such, the relevant cool-skin and warm-layer parametrization must be
 activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs}
@@ -693 +663 @@
 
 For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same
-basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based
+basis: \citet{fairall.bradley.ea_JGRO96}. With some minor updates based
 on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE
 3.6.
@@ -704 +674 @@
 equation for the thickness of the warm-layer, while it is considered as constant
 in the ECWMF algorithm.
-
 
 \subsection{Appropriate use of each bulk parametrization}
@@ -714 +683 @@
 temperature is the bulk SST. Hence the following namelist parameters must be
 set:
-%
-\begin{verbatim}
+
+\begin{forlines}
   ...
   ln_NCAR    = .true.
@@ -726 +695 @@
   ...
   ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg]
-\end{verbatim}
-
+\end{forlines}
 
 \subsubsection{ECMWF}
-%
+
 With an atmospheric forcing based on a reanalysis of the ECMWF, such as the
 Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to
@@ -737 +705 @@
 humidity are provided at the 2\,m height, and given that the humidity is
 distributed as the dew-point temperature, the namelist must be tuned as follows:
-%
-\begin{verbatim}
+
+\begin{forlines}
   ...
   ln_ECMWF   = .true.
@@ -750 +718 @@
   ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K]
   ...
-\end{verbatim}
-%
+\end{forlines}
+
 Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection
 of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly
@@ -757 +725 @@
 respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}).
 
-
 \subsubsection{COARE 3.x}
-%
+
 Since the ECMWF parametrization is largely based on the COARE* parametrization,
 the two algorithms are very similar in terms of structure and closure
 approach. As such, the namelist tuning for COARE 3.x is identical to that of
 ECMWF:
-%
-\begin{verbatim}
+
+\begin{forlines}
   ...
   ln_COARE3p6 = .true.
@@ -772 +739 @@
   ln_skin_wl = .true. ! use the warm-layer parameterization
   ...
-\end{verbatim}
+\end{forlines}
 
 Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection
@@ -779 +746 @@
 respectively (found in \textit{sbcblk\_skin\_coare.F90}).
 
-
 %lulu
-
-
 
 % In a typical bulk algorithm, the BTCs under neutral stability conditions are
@@ -792 +756 @@
 % and $q_z$.
 
-
-
 \subsection{Prescribed near-surface atmospheric state}
 
@@ -800 +762 @@
 different bulk formulae are used for the turbulent fluxes computation over the
 ocean and over sea-ice surface.
-%
 
 %The choice is made by setting to true one of the following namelist
@@ -862 +823 @@
 the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}).
 
-
 \subsubsection{Air humidity}
 
@@ -868 +828 @@
 [kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist
 parameters)...
-
-
-~\\
-
-
-
-
-
-
-
-
-
 
 %% =================================================================================================
@@ -889 +837 @@
 %their neutral transfer coefficients relationships with neutral wind.
 %\begin{itemize}
-%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}.
+%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_trpt04}.
 %  They have been designed to handle the NCAR 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 10m wind speed, air temperature and specific humidity.
-%  This \citet{large.yeager_rpt04} dataset is available through
+%  This \citet{large.yeager_trpt04} dataset is available through
 %  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}.
 %  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself.
@@ -908 +856 @@
 \label{subsec:SBC_blk_ice}
 
-
 \texttt{\#out\_of\_place:}
  For sea-ice, three possibilities can be selected:
 a constant transfer coefficient (1.4e-3; default
-value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
+value), \citet{lupkes.gryanik.ea_JGRA12} (\np{ln_Cd_L12}{ln\_Cd\_L12}),
 and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations
 \texttt{\#out\_of\_place.}
 
-
-
-
 Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways:
 
 \begin{itemize}
-\item Constant value (\np[ Cd_ice=1.4e-3 ]{constant value}{constant\ value}):
+\item Constant value (\forcode{Cd_ice=1.4e-3}):
   default constant value used for momentum and heat neutral transfer coefficients
-\item \citet{lupkes.gryanik.ea_JGR12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
+\item \citet{lupkes.gryanik.ea_JGRA12} (\np[=.true.]{ln_Cd_L12}{ln\_Cd\_L12}):
   This scheme adds a dependency on edges at leads, melt ponds and flows
   of the constant neutral air-ice drag. After some approximations,
@@ -1260 +1204 @@
   \begin{description}
   \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and
-    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}.
+    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_trpt06}.
   \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation
     (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation).
@@ -1332 +1276 @@
 The fw addition due to the ice shelf melting is, at each relevant depth level, added to
 the horizontal divergence (\textit{hdivn}) in the subroutine \rou{sbc\_isf\_div}, called from \mdl{divhor}.
-See the runoff section \autoref{sec:SBC_rnf} for all the details about the divergence correction.\\
+See \autoref{sec:SBC_rnf} for all the details about the divergence correction.
 
 \begin{figure}[!t]
@@ -1503 +1447 @@
 Then using the routine \rou{sbcblk\_algo\_ncar} and starting from the neutral drag coefficent provided,
 the drag coefficient is computed according to the stable/unstable conditions of the
-air-sea interface following \citet{large.yeager_rpt04}.
+air-sea interface following \citet{large.yeager_trpt04}.
 
 %% =================================================================================================
@@ -1614 +1558 @@
 
 The surface stress felt by the ocean is the atmospheric stress minus the net stress going
-into the waves \citep{janssen.breivik.ea_rpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
+into the waves \citep{janssen.breivik.ea_trpt13}. Therefore, when waves are growing, momentum and energy is spent and is not
 available for forcing the mean circulation, while in the opposite case of a decaying sea
 state, more momentum is available for forcing the ocean.