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Changeset 12928 for NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_SBC.tex – NEMO

Ignore:
Timestamp:
2020-05-14T21:46:00+02:00 (4 years ago)
Author:
smueller
Message:

Synchronizing with /NEMO/trunk@12925 (ticket #2170)

Location:
NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser
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2 edited

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  • NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser

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  • NEMO/branches/2019/dev_r11078_OSMOSIS_IMMERSE_Nurser/doc/latex/NEMO/subfiles/chap_SBC.tex

    r12178 r12928  
    11\documentclass[../main/NEMO_manual]{subfiles} 
     2\usepackage{fontspec} 
     3\usepackage{fontawesome} 
    24 
    35\begin{document} 
     
    4547 
    4648\begin{itemize} 
    47 \item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk} with four possible bulk algorithms), 
     49\item a bulk formulation (\np[=.true.]{ln_blk}{ln\_blk}), featuring a selection of four bulk parameterization algorithms, 
    4850\item a flux formulation (\np[=.true.]{ln_flx}{ln\_flx}), 
    4951\item a coupled or mixed forced/coupled formulation (exchanges with a atmospheric model via the OASIS coupler), 
     
    504506\label{sec:SBC_flx} 
    505507 
     508% Laurent: DO NOT mix up ``bulk formulae'' (the classic equation) and the ``bulk 
     509% parameterization'' (i.e NCAR, COARE, ECMWF...) 
     510 
    506511\begin{listing} 
    507512  \nlst{namsbc_flx} 
     
    520525See \autoref{subsec:SBC_ssr} for its specification. 
    521526 
    522 %% ================================================================================================= 
     527 
     528 
     529 
     530 
     531 
     532 
     533%% ================================================================================================= 
     534\pagebreak 
     535\newpage 
    523536\section[Bulk formulation (\textit{sbcblk.F90})]{Bulk formulation (\protect\mdl{sbcblk})} 
    524537\label{sec:SBC_blk} 
     538 
     539% L. Brodeau, December 2019... % 
    525540 
    526541\begin{listing} 
     
    530545\end{listing} 
    531546 
    532 In the bulk formulation, the surface boundary condition fields are computed with bulk formulae using atmospheric fields 
    533 and ocean (and sea-ice) variables averaged over \np{nn_fsbc}{nn\_fsbc} time-step. 
    534  
    535 The atmospheric fields used depend on the bulk formulae used. 
    536 In forced mode, when a sea-ice model is used, a specific bulk formulation is used. 
    537 Therefore, different bulk formulae are used for the turbulent fluxes computation 
    538 over the ocean and over sea-ice surface. 
    539 For the ocean, four bulk formulations are available thanks to the \href{https://brodeau.github.io/aerobulk/}{Aerobulk} package (\citet{brodeau.barnier.ea_JPO16}): 
    540 the NCAR (formerly named CORE), COARE 3.0, COARE 3.5 and ECMWF bulk formulae. 
    541 The choice is made by setting to true one of the following namelist variable: 
    542  \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0},  \np{ln_COARE_3p5}{ln\_COARE\_3p5} and  \np{ln_ECMWF}{ln\_ECMWF}. 
    543 For sea-ice, three possibilities can be selected: 
    544 a constant transfer coefficient (1.4e-3; default value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 
     547If the bulk formulation is selected (\np[=.true.]{ln_blk}{ln\_blk}), the air-sea 
     548fluxes associated with surface boundary conditions are estimated by means of the 
     549traditional \emph{bulk formulae}. As input, bulk formulae rely on a prescribed 
     550near-surface atmosphere state (typically extracted from a weather reanalysis) 
     551and the prognostic sea (-ice) surface state averaged over \np{nn_fsbc}{nn\_fsbc} 
     552time-step(s). 
     553 
     554% Turbulent air-sea fluxes are computed using the sea surface properties and 
     555% atmospheric SSVs at height $z$ above the sea surface, with the traditional 
     556% aerodynamic bulk formulae: 
     557 
     558Note: all the NEMO Fortran routines involved in the present section have been 
     559 initially developed (and are still developed in parallel) in 
     560 the \href{https://brodeau.github.io/aerobulk/}{\texttt{AeroBulk}} open-source project 
     561\citep{brodeau.barnier.ea_JPO17}. 
     562 
     563%%% Bulk formulae are this: 
     564\subsection{Bulk formulae}\label{subsec:SBC_blkform} 
     565% 
     566In NEMO, the set of equations that relate each component of the surface fluxes 
     567to the near-surface atmosphere and sea surface states writes 
     568% 
     569\begin{subequations}\label{eq_bulk} 
     570  \label{eq:SBC_bulk_form} 
     571  \begin{eqnarray} 
     572    \mathbf{\tau} &=& \rho~ C_D ~ \mathbf{U}_z  ~ U_B \\ 
     573    Q_H           &=& \rho~C_H~C_P~\big[ \theta_z - T_s \big] ~ U_B \\ 
     574    E             &=& \rho~C_E    ~\big[    q_s   - q_z \big] ~ U_B \\ 
     575    Q_L           &=& -L_v \, E \\ 
     576    % 
     577    Q_{sr}        &=& (1 - a) Q_{sw\downarrow} \\ 
     578    Q_{ir}        &=& \delta (Q_{lw\downarrow} -\sigma T_s^4) 
     579  \end{eqnarray} 
     580\end{subequations} 
     581% 
     582with 
     583   \[ \theta_z \simeq T_z+\gamma z \] 
     584   \[  q_s \simeq 0.98\,q_{sat}(T_s,p_a ) \] 
     585% 
     586from which, the the non-solar heat flux is \[ Q_{ns} = Q_L + Q_H + Q_{ir} \] 
     587% 
     588where $\mathbf{\tau}$ is the wind stress vector, $Q_H$ the sensible heat flux, 
     589$E$ the evaporation, $Q_L$ the latent heat flux, and $Q_{ir}$ the net longwave 
     590flux. 
     591% 
     592$Q_{sw\downarrow}$ and $Q_{lw\downarrow}$ are the surface downwelling shortwave 
     593and longwave radiative fluxes, respectively. 
     594% 
     595Note: a positive sign for $\mathbf{\tau}$, $Q_H$, $Q_L$, $Q_{sr}$ or $Q_{ir}$ 
     596implies a gain of the relevant quantity for the ocean, while a positive $E$ 
     597implies a freshwater loss for the ocean. 
     598% 
     599$\rho$ is the density of air. $C_D$, $C_H$ and $C_E$ are the bulk transfer 
     600coefficients for momentum, sensible heat, and moisture, respectively. 
     601% 
     602$C_P$ is the heat capacity of moist air, and $L_v$ is the latent heat of 
     603vaporization of water. 
     604% 
     605$\theta_z$, $T_z$ and $q_z$ are the potential temperature, absolute temperature, 
     606and specific humidity of air at height $z$ above the sea surface, 
     607respectively. $\gamma z$ is a temperature correction term which accounts for the 
     608adiabatic lapse rate and approximates the potential temperature at height 
     609$z$ \citep{josey.gulev.ea_2013}. 
     610% 
     611$\mathbf{U}_z$ is the wind speed vector at height $z$ above the sea surface 
     612(possibly referenced to the surface current $\mathbf{u_0}$, 
     613section \ref{s_res1}.\ref{ss_current}). 
     614% 
     615The bulk scalar wind speed, namely $U_B$, is the scalar wind speed, 
     616$|\mathbf{U}_z|$, with the potential inclusion of a gustiness contribution. 
     617% 
     618$a$ and $\delta$ are the albedo and emissivity of the sea surface, respectively.\\ 
     619% 
     620%$p_a$ is the mean sea-level pressure (SLP). 
     621% 
     622$T_s$ is the sea surface temperature. $q_s$ is the saturation specific humidity 
     623of air at temperature $T_s$; it includes a 2\% reduction to account for the 
     624presence of salt in seawater \citep{sverdrup.johnson.ea_1942,kraus.businger_QJRMS96}. 
     625Depending on the bulk parametrization used, $T_s$ can either be the temperature 
     626at the air-sea interface (skin temperature, hereafter SSST) or at typically a 
     627few tens of centimeters below the surface (bulk sea surface temperature, 
     628hereafter SST). 
     629% 
     630The SSST differs from the SST due to the contributions of two effects of 
     631opposite sign, the \emph{cool skin} and \emph{warm layer} (hereafter CS and WL, 
     632respectively, see section\,\ref{subsec:SBC_skin}). 
     633% 
     634Technically, when the ECMWF or COARE* bulk parametrizations are selected 
     635(\np[=.true.]{ln_ECMWF}{ln\_ECMWF} or \np[=.true.]{ln_COARE*}{ln\_COARE\*}), 
     636$T_s$ is the SSST, as opposed to the NCAR bulk parametrization 
     637(\np[=.true.]{ln_NCAR}{ln\_NCAR}) for which $T_s$ is the bulk SST (\ie~temperature 
     638at first T-point level). 
     639 
     640For more details on all these aspects the reader is invited to refer 
     641to \citet{brodeau.barnier.ea_JPO17}. 
     642 
     643 
     644 
     645\subsection{Bulk parametrizations}\label{subsec:SBC_blk_ocean} 
     646%%%\label{subsec:SBC_param} 
     647 
     648Accuracy of the estimate of surface turbulent fluxes by means of bulk formulae 
     649strongly relies on that of the bulk transfer coefficients: $C_D$, $C_H$ and 
     650$C_E$. They are estimated with what we refer to as a \emph{bulk 
     651parametrization} algorithm. When relevant, these algorithms also perform the 
     652height adjustment of humidity and temperature to the wind reference measurement 
     653height (from \np{rn_zqt}{rn\_zqt} to \np{rn_zu}{rn\_zu}). 
     654 
     655 
     656 
     657For the open ocean, four bulk parametrization algorithms are available in NEMO: 
     658\begin{itemize} 
     659\item NCAR, formerly known as CORE, \citep{large.yeager_rpt04,large.yeager_CD09} 
     660\item COARE 3.0 \citep{fairall.bradley.ea_JC03} 
     661\item COARE 3.6 \citep{edson.jampana.ea_JPO13} 
     662\item ECMWF (IFS documentation, cy45) 
     663\end{itemize} 
     664 
     665 
     666With respect to version 3, the principal advances in version 3.6 of the COARE 
     667bulk parametrization are built around improvements in the representation of the 
     668effects of waves on 
     669fluxes \citep{edson.jampana.ea_JPO13,brodeau.barnier.ea_JPO17}. This includes 
     670improved relationships of surface roughness, and whitecap fraction on wave 
     671parameters. It is therefore recommended to chose version 3.6 over 3. 
     672 
     673 
     674 
     675 
     676\subsection{Cool-skin and warm-layer parametrizations}\label{subsec:SBC_skin} 
     677%\subsection[Cool-skin and warm-layer parameterizations 
     678%(\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})} 
     679%\label{subsec:SBC_skin} 
     680% 
     681As opposed to the NCAR bulk parametrization, more advanced bulk 
     682parametrizations such as COARE3.x and ECMWF are meant to be used with the skin 
     683temperature $T_s$ rather than the bulk SST (which, in NEMO is the temperature at 
     684the first T-point level, see section\,\ref{subsec:SBC_blkform}). 
     685% 
     686As such, the relevant cool-skin and warm-layer parametrization must be 
     687activated through \np[=T]{ln_skin_cs}{ln\_skin\_cs} 
     688and \np[=T]{ln_skin_wl}{ln\_skin\_wl} to use COARE3.x or ECMWF in a consistent 
     689way. 
     690 
     691\texttt{\#LB: ADD BLBLA ABOUT THE TWO CS/WL PARAMETRIZATIONS (ECMWF and COARE) !!!} 
     692 
     693For the cool-skin scheme parametrization COARE and ECMWF algorithms share the same 
     694basis: \citet{fairall.bradley.ea_JGR96}. With some minor updates based 
     695on \citet{zeng.beljaars_GRL05} for ECMWF, and \citet{fairall.ea_19} for COARE 
     6963.6. 
     697 
     698For the warm-layer scheme, ECMWF is based on \citet{zeng.beljaars_GRL05} with a 
     699recent update from \citet{takaya.bidlot.ea_JGR10} (consideration of the 
     700turbulence input from Langmuir circulation). 
     701 
     702Importantly, COARE warm-layer scheme \citep{fairall.ea_19} includes a prognostic 
     703equation for the thickness of the warm-layer, while it is considered as constant 
     704in the ECWMF algorithm. 
     705 
     706 
     707\subsection{Appropriate use of each bulk parametrization} 
     708 
     709\subsubsection{NCAR} 
     710 
     711NCAR bulk parametrizations (formerly known as CORE) is meant to be used with the 
     712CORE II atmospheric forcing \citep{large.yeager_CD09}. The expected sea surface 
     713temperature is the bulk SST. Hence the following namelist parameters must be 
     714set: 
     715% 
     716\begin{verbatim} 
     717  ... 
     718  ln_NCAR    = .true. 
     719  ... 
     720  rn_zqt     = 10.     ! Air temperature & humidity reference height (m) 
     721  rn_zu      = 10.     ! Wind vector reference height (m) 
     722  ... 
     723  ln_skin_cs = .false. ! use the cool-skin parameterization 
     724  ln_skin_wl = .false. ! use the warm-layer parameterization 
     725  ... 
     726  ln_humi_sph = .true. ! humidity "sn_humi" is specific humidity  [kg/kg] 
     727\end{verbatim} 
     728 
     729 
     730\subsubsection{ECMWF} 
     731% 
     732With an atmospheric forcing based on a reanalysis of the ECMWF, such as the 
     733Drakkar Forcing Set \citep{brodeau.barnier.ea_OM10}, we strongly recommend to 
     734use the ECMWF bulk parametrizations with the cool-skin and warm-layer 
     735parametrizations activated. In ECMWF reanalyzes, since air temperature and 
     736humidity are provided at the 2\,m height, and given that the humidity is 
     737distributed as the dew-point temperature, the namelist must be tuned as follows: 
     738% 
     739\begin{verbatim} 
     740  ... 
     741  ln_ECMWF   = .true. 
     742  ...      
     743  rn_zqt     =  2.     ! Air temperature & humidity reference height (m) 
     744  rn_zu      = 10.     ! Wind vector reference height (m) 
     745  ... 
     746  ln_skin_cs = .true. ! use the cool-skin parameterization 
     747  ln_skin_wl = .true. ! use the warm-layer parameterization 
     748  ... 
     749  ln_humi_dpt = .true. !  humidity "sn_humi" is dew-point temperature [K] 
     750  ... 
     751\end{verbatim} 
     752% 
     753Note: when \np{ln_ECMWF}{ln\_ECMWF} is selected, the selection 
     754of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly 
     755triggers the use of the ECMWF cool-skin and warm-layer parametrizations, 
     756respectively (found in \textit{sbcblk\_skin\_ecmwf.F90}). 
     757 
     758 
     759\subsubsection{COARE 3.x} 
     760% 
     761Since the ECMWF parametrization is largely based on the COARE* parametrization, 
     762the two algorithms are very similar in terms of structure and closure 
     763approach. As such, the namelist tuning for COARE 3.x is identical to that of 
     764ECMWF: 
     765% 
     766\begin{verbatim} 
     767  ... 
     768  ln_COARE3p6 = .true. 
     769  ...      
     770  ln_skin_cs = .true. ! use the cool-skin parameterization 
     771  ln_skin_wl = .true. ! use the warm-layer parameterization 
     772  ... 
     773\end{verbatim} 
     774 
     775Note: when \np[=T]{ln_COARE3p0}{ln\_COARE3p0} is selected, the selection 
     776of \np{ln_skin_cs}{ln\_skin\_cs} and \np{ln_skin_wl}{ln\_skin\_wl} implicitly 
     777triggers the use of the COARE cool-skin and warm-layer parametrizations, 
     778respectively (found in \textit{sbcblk\_skin\_coare.F90}). 
     779 
     780 
     781%lulu 
     782 
     783 
     784 
     785% In a typical bulk algorithm, the BTCs under neutral stability conditions are 
     786% defined using \emph{in-situ} flux measurements while their dependence on the 
     787% stability is accounted through the \emph{Monin-Obukhov Similarity Theory} and 
     788% the \emph{flux-profile} relationships \citep[\eg{}][]{Paulson_1970}. BTCs are 
     789% functions of the wind speed and the near-surface stability of the atmospheric 
     790% surface layer (hereafter ASL), and hence, depend on $U_B$, $T_s$, $T_z$, $q_s$ 
     791% and $q_z$. 
     792 
     793 
     794 
     795\subsection{Prescribed near-surface atmospheric state} 
     796 
     797The atmospheric fields used depend on the bulk formulae used.  In forced mode, 
     798when a sea-ice model is used, a specific bulk formulation is used.  Therefore, 
     799different bulk formulae are used for the turbulent fluxes computation over the 
     800ocean and over sea-ice surface. 
     801% 
     802 
     803%The choice is made by setting to true one of the following namelist 
     804%variable: \np{ln_NCAR}{ln\_NCAR}, \np{ln_COARE_3p0}{ln\_COARE\_3p0}, \np{ln_COARE_3p6}{ln\_COARE\_3p6} 
     805%and \np{ln_ECMWF}{ln\_ECMWF}.  
    545806 
    546807Common options are defined through the \nam{sbc_blk}{sbc\_blk} namelist variables. 
     
    553814    Variable description                 & Model variable & Units              & point \\ 
    554815    \hline 
    555     i-component of the 10m air velocity  & utau           & $m.s^{-1}$         & T     \\ 
     816    i-component of the 10m air velocity  & wndi           & $m.s^{-1}$         & T     \\ 
    556817    \hline 
    557     j-component of the 10m air velocity  & vtau           & $m.s^{-1}$         & T     \\ 
     818    j-component of the 10m air velocity  & wndj           & $m.s^{-1}$         & T     \\ 
    558819    \hline 
    559     10m air temperature                  & tair           & \r{}$K$            & T     \\ 
     820    10m air temperature                  & tair           & $K$               & T     \\ 
    560821    \hline 
    561     Specific humidity                    & humi           & \%                 & T     \\ 
     822    Specific humidity                    & humi           & $-$               & T     \\ 
     823    Relative humidity                    & ~              & $\%$              & T     \\ 
     824    Dew-point temperature                & ~              & $K$               & T     \\     
    562825    \hline 
    563     Incoming long wave radiation         & qlw            & $W.m^{-2}$         & T     \\ 
     826    Downwelling longwave radiation       & qlw            & $W.m^{-2}$         & T     \\ 
    564827    \hline 
    565     Incoming short wave radiation        & qsr            & $W.m^{-2}$         & T     \\ 
     828    Downwelling shortwave radiation      & qsr            & $W.m^{-2}$         & T     \\ 
    566829    \hline 
    567830    Total precipitation (liquid + solid) & precip         & $Kg.m^{-2}.s^{-1}$ & T     \\ 
     
    584847 
    585848\np{cn_dir}{cn\_dir} is the directory of location of bulk files 
    586 \np{ln_taudif}{ln\_taudif} is the flag to specify if we use Hight Frequency (HF) tau information (.true.) or not (.false.) 
     849%\np{ln_taudif}{ln\_taudif} is the flag to specify if we use High Frequency (HF) tau information (.true.) or not (.false.) 
    587850\np{rn_zqt}{rn\_zqt}: is the height of humidity and temperature measurements (m) 
    588851\np{rn_zu}{rn\_zu}: is the height of wind measurements (m) 
     
    595858Its range must be between zero and one, and it is recommended to set it to 0 at low-resolution (ORCA2 configuration). 
    596859 
    597 As for the flux formulation, information about the input data required by the model is provided in 
     860As for the flux parametrization, information about the input data required by the model is provided in 
    598861the namsbc\_blk namelist (see \autoref{subsec:SBC_fldread}). 
    599862 
    600 %% ================================================================================================= 
    601 \subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare.F90, sbcblk\_algo\_coare3p5.F90, sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare}, \mdl{sbcblk\_algo\_coare3p5}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})} 
    602 \label{subsec:SBC_blk_ocean} 
    603  
    604 Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean. 
    605 COARE 3.0, COARE 3.5 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently 
    606 their neutral transfer coefficients relationships with neutral wind. 
    607 \begin{itemize} 
    608 \item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}. 
    609   They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 
    610   They use an inertial dissipative method to compute the turbulent transfer coefficients 
    611   (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 
    612   This \citet{large.yeager_rpt04} dataset is available through 
    613   the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 
    614   Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 
    615   This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 
    616 \item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details 
    617 \item COARE 3.5 (\np[=.true.]{ln_COARE_3p5}{ln\_COARE\_3p5}): See \citet{edson.jampana.ea_JPO13} for more details 
    618 \item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9221}{IFS (Cy31)} implementation and documentation. 
    619   Surface roughness lengths needed for the Obukhov length are computed following \citet{beljaars_QJRMS95}. 
    620 \end{itemize} 
     863 
     864\subsubsection{Air humidity} 
     865 
     866Air humidity can be provided as three different parameters: specific humidity 
     867[kg/kg], relative humidity [\%], or dew-point temperature [K] (LINK to namelist 
     868parameters)... 
     869 
     870 
     871~\\ 
     872 
     873 
     874 
     875 
     876 
     877 
     878 
     879 
     880 
     881 
     882%% ================================================================================================= 
     883%\subsection[Ocean-Atmosphere Bulk formulae (\textit{sbcblk\_algo\_coare3p0.F90, sbcblk\_algo\_coare3p6.F90, %sbcblk\_algo\_ecmwf.F90, sbcblk\_algo\_ncar.F90})]{Ocean-Atmosphere Bulk formulae (\mdl{sbcblk\_algo\_coare3p0}, %\mdl{sbcblk\_algo\_coare3p6}, \mdl{sbcblk\_algo\_ecmwf}, \mdl{sbcblk\_algo\_ncar})} 
     884%\label{subsec:SBC_blk_ocean} 
     885 
     886%Four different bulk algorithms are available to compute surface turbulent momentum and heat fluxes over the ocean. 
     887%COARE 3.0, COARE 3.6 and ECMWF schemes mainly differ by their roughness lenghts computation and consequently 
     888%their neutral transfer coefficients relationships with neutral wind. 
     889%\begin{itemize} 
     890%\item NCAR (\np[=.true.]{ln_NCAR}{ln\_NCAR}): The NCAR bulk formulae have been developed by \citet{large.yeager_rpt04}. 
     891%  They have been designed to handle the NCAR forcing, a mixture of NCEP reanalysis and satellite data. 
     892%  They use an inertial dissipative method to compute the turbulent transfer coefficients 
     893%  (momentum, sensible heat and evaporation) from the 10m wind speed, air temperature and specific humidity. 
     894%  This \citet{large.yeager_rpt04} dataset is available through 
     895%  the \href{http://nomads.gfdl.noaa.gov/nomads/forms/mom4/NCAR.html}{GFDL web site}. 
     896%  Note that substituting ERA40 to NCEP reanalysis fields does not require changes in the bulk formulea themself. 
     897%  This is the so-called DRAKKAR Forcing Set (DFS) \citep{brodeau.barnier.ea_OM10}. 
     898%\item COARE 3.0 (\np[=.true.]{ln_COARE_3p0}{ln\_COARE\_3p0}): See \citet{fairall.bradley.ea_JC03} for more details 
     899%\item COARE 3.6 (\np[=.true.]{ln_COARE_3p6}{ln\_COARE\_3p6}): See \citet{edson.jampana.ea_JPO13} for more details 
     900%\item ECMWF (\np[=.true.]{ln_ECMWF}{ln\_ECMWF}): Based on \href{https://www.ecmwf.int/node/9204}{IFS (Cy40r1)} %implementation and documentation. 
     901%  Surface roughness lengths needed for the Obukhov length are computed 
     902%  following \citet{beljaars_QJRMS95}. 
     903%\end{itemize} 
    621904 
    622905%% ================================================================================================= 
    623906\subsection{Ice-Atmosphere Bulk formulae} 
    624907\label{subsec:SBC_blk_ice} 
     908 
     909 
     910\texttt{\#out\_of\_place:} 
     911 For sea-ice, three possibilities can be selected: 
     912a constant transfer coefficient (1.4e-3; default 
     913value), \citet{lupkes.gryanik.ea_JGR12} (\np{ln_Cd_L12}{ln\_Cd\_L12}), 
     914and \citet{lupkes.gryanik_JGR15} (\np{ln_Cd_L15}{ln\_Cd\_L15}) parameterizations 
     915\texttt{\#out\_of\_place.} 
     916 
     917 
     918 
    625919 
    626920Surface turbulent fluxes between sea-ice and the atmosphere can be computed in three different ways: 
     
    8801174%ENDIF 
    8811175 
    882 %\gmcomment{  word doc of runoffs: 
    883 %In the current \NEMO\ setup river runoff is added to emp fluxes, these are then applied at just the sea surface as a volume change (in the variable volume case this is a literal volume change, and in the linear free surface case the free surface is moved) and a salt flux due to the concentration/dilution effect.  There is also an option to increase vertical mixing near river mouths; this gives the effect of having a 3d river.  All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and at the same temperature as the sea surface. 
    884 %Our aim was to code the option to specify the temperature and salinity of river runoff, (as well as the amount), along with the depth that the river water will affect.  This would make it possible to model low salinity outflow, such as the Baltic, and would allow the ocean temperature to be affected by river runoff. 
    885  
    886 %The depth option makes it possible to have the river water affecting just the surface layer, throughout depth, or some specified point in between. 
    887  
    888 %To do this we need to treat evaporation/precipitation fluxes and river runoff differently in the tra_sbc module.  We decided to separate them throughout the code, so that the variable emp represented solely evaporation minus precipitation fluxes, and a new 2d variable rnf was added which represents the volume flux of river runoff (in kg/m2s to remain consistent with emp).  This meant many uses of emp and emps needed to be changed, a list of all modules which use emp or emps and the changes made are below: 
     1176\cmtgm{  word doc of runoffs: 
     1177In the current \NEMO\ setup river runoff is added to emp fluxes, 
     1178these are then applied at just the sea surface as a volume change (in the variable volume case 
     1179this is a literal volume change, and in the linear free surface case the free surface is moved) 
     1180and a salt flux due to the concentration/dilution effect. 
     1181There is also an option to increase vertical mixing near river mouths; 
     1182this gives the effect of having a 3d river. 
     1183All river runoff and emp fluxes are assumed to be fresh water (zero salinity) and 
     1184at the same temperature as the sea surface. 
     1185Our aim was to code the option to specify the temperature and salinity of river runoff, 
     1186(as well as the amount), along with the depth that the river water will affect. 
     1187This would make it possible to model low salinity outflow, such as the Baltic, 
     1188and would allow the ocean temperature to be affected by river runoff. 
     1189 
     1190The depth option makes it possible to have the river water affecting just the surface layer, 
     1191throughout depth, or some specified point in between. 
     1192 
     1193To do this we need to treat evaporation/precipitation fluxes and river runoff differently in 
     1194the \mdl{tra_sbc} module. 
     1195We decided to separate them throughout the code, 
     1196so that the variable emp represented solely evaporation minus precipitation fluxes, 
     1197and a new 2d variable rnf was added which represents the volume flux of river runoff 
     1198(in $kg/m^2s$ to remain consistent with $emp$). 
     1199This meant many uses of emp and emps needed to be changed, 
     1200a list of all modules which use $emp$ or $emps$ and the changes made are below:} 
    8891201 
    8901202%% ================================================================================================= 
     
    9081220  Two different bulk formulae are available: 
    9091221 
    910    \begin{description} 
    911    \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and 
    912      the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 
    913    \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation 
    914      (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 
    915      A complete description is available in \citet{jenkins_JGR91}. 
    916    \end{description} 
    917  
    918      Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}. 
    919      Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}. 
    920      The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m. 
    921      Then, the fluxes are spread over the same thickness (ie over one or several cells). 
    922      If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature. 
    923      This can lead to super-cool temperature in the top cell under melting condition. 
    924      If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\ 
    925  
    926      Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice. 
    927      There are 3 different ways to compute the exchange coeficient: 
    928    \begin{description} 
    929         \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}. 
    930      \begin{gather*} 
     1222  \begin{description} 
     1223  \item [{\np[=1]{nn_isfblk}{nn\_isfblk}}]: The melt rate is based on a balance between the upward ocean heat flux and 
     1224    the latent heat flux at the ice shelf base. A complete description is available in \citet{hunter_rpt06}. 
     1225  \item [{\np[=2]{nn_isfblk}{nn\_isfblk}}]: The melt rate and the heat flux are based on a 3 equations formulation 
     1226    (a heat flux budget at the ice base, a salt flux budget at the ice base and a linearised freezing point temperature equation). 
     1227    A complete description is available in \citet{jenkins_JGR91}. 
     1228  \end{description} 
     1229 
     1230  Temperature and salinity used to compute the melt are the average temperature in the top boundary layer \citet{losch_JGR08}. 
     1231  Its thickness is defined by \np{rn_hisf_tbl}{rn\_hisf\_tbl}. 
     1232  The fluxes and friction velocity are computed using the mean temperature, salinity and velocity in the the first \np{rn_hisf_tbl}{rn\_hisf\_tbl} m. 
     1233  Then, the fluxes are spread over the same thickness (ie over one or several cells). 
     1234  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} larger than top $e_{3}t$, there is no more feedback between the freezing point at the interface and the the top cell temperature. 
     1235  This can lead to super-cool temperature in the top cell under melting condition. 
     1236  If \np{rn_hisf_tbl}{rn\_hisf\_tbl} smaller than top $e_{3}t$, the top boundary layer thickness is set to the top cell thickness.\\ 
     1237 
     1238  Each melt bulk formula depends on a exchange coeficient ($\Gamma^{T,S}$) between the ocean and the ice. 
     1239  There are 3 different ways to compute the exchange coeficient: 
     1240  \begin{description} 
     1241  \item [{\np[=0]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are constant and defined by \np{rn_gammas0}{rn\_gammas0} and \np{rn_gammat0}{rn\_gammat0}. 
     1242    \begin{gather*} 
    9311243       % \label{eq:SBC_isf_gamma_iso} 
    932        \gamma^{T} = rn\_gammat0 \\ 
    933        \gamma^{S} = rn\_gammas0 
    934      \end{gather*} 
    935      This is the recommended formulation for ISOMIP. 
    936    \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as 
    937      \begin{gather*} 
    938        \gamma^{T} = rn\_gammat0 \times u_{*} \\ 
    939        \gamma^{S} = rn\_gammas0 \times u_{*} 
    940      \end{gather*} 
    941      where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters). 
    942      See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 
    943    \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as: 
    944 \[ 
    945 \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}} 
    946 \] 
    947      where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters), 
    948      $\Gamma_{Turb}$ the contribution of the ocean stability and 
    949      $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 
    950      See \citet{holland.jenkins_JPO99} for all the details on this formulation. 
    951      This formulation has not been extensively tested in \NEMO\ (not recommended). 
    952    \end{description} 
    953   \item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented. 
    954    The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 
    955    The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 
    956    (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 
    957    (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}). 
    958    The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file. 
    959   \item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented. 
    960    The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between 
    961    the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and 
    962    the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}). 
    963    The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 
    964   \item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed). 
    965    However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}). 
    966    The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 
    967    As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl})\\ 
     1244      \gamma^{T} = rn\_gammat0 \\ 
     1245      \gamma^{S} = rn\_gammas0 
     1246    \end{gather*} 
     1247    This is the recommended formulation for ISOMIP. 
     1248  \item [{\np[=1]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity dependent and defined as 
     1249    \begin{gather*} 
     1250      \gamma^{T} = rn\_gammat0 \times u_{*} \\ 
     1251      \gamma^{S} = rn\_gammas0 \times u_{*} 
     1252    \end{gather*} 
     1253    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters). 
     1254    See \citet{jenkins.nicholls.ea_JPO10} for all the details on this formulation. It is the recommended formulation for realistic application. 
     1255  \item [{\np[=2]{nn_gammablk}{nn\_gammablk}}]: The salt and heat exchange coefficients are velocity and stability dependent and defined as: 
     1256    \[ 
     1257      \gamma^{T,S} = \frac{u_{*}}{\Gamma_{Turb} + \Gamma^{T,S}_{Mole}} 
     1258    \] 
     1259    where $u_{*}$ is the friction velocity in the top boundary layer (ie first \np{rn_hisf_tbl}{rn\_hisf\_tbl} meters), 
     1260    $\Gamma_{Turb}$ the contribution of the ocean stability and 
     1261    $\Gamma^{T,S}_{Mole}$ the contribution of the molecular diffusion. 
     1262    See \citet{holland.jenkins_JPO99} for all the details on this formulation. 
     1263    This formulation has not been extensively tested in \NEMO\ (not recommended). 
     1264  \end{description} 
     1265\item [{\np[=2]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented. 
     1266  The fwf and heat flux are computed using the \citet{beckmann.goosse_OM03} parameterisation of isf melting. 
     1267  The fluxes are distributed along the ice shelf edge between the depth of the average grounding line (GL) 
     1268  (\np{sn_depmax_isf}{sn\_depmax\_isf}) and the base of the ice shelf along the calving front 
     1269  (\np{sn_depmin_isf}{sn\_depmin\_isf}) as in (\np[=3]{nn_isf}{nn\_isf}). 
     1270  The effective melting length (\np{sn_Leff_isf}{sn\_Leff\_isf}) is read from a file. 
     1271\item [{\np[=3]{nn_isf}{nn\_isf}}]: The ice shelf cavity is not represented. 
     1272  The fwf (\np{sn_rnfisf}{sn\_rnfisf}) is prescribed and distributed along the ice shelf edge between 
     1273  the depth of the average grounding line (GL) (\np{sn_depmax_isf}{sn\_depmax\_isf}) and 
     1274  the base of the ice shelf along the calving front (\np{sn_depmin_isf}{sn\_depmin\_isf}). 
     1275  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 
     1276\item [{\np[=4]{nn_isf}{nn\_isf}}]: The ice shelf cavity is opened (\np[=.true.]{ln_isfcav}{ln\_isfcav} needed). 
     1277  However, the fwf is not computed but specified from file \np{sn_fwfisf}{sn\_fwfisf}). 
     1278  The heat flux ($Q_h$) is computed as $Q_h = fwf \times L_f$. 
     1279  As in \np[=1]{nn_isf}{nn\_isf}, the fluxes are spread over the top boundary layer thickness (\np{rn_hisf_tbl}{rn\_hisf\_tbl}) 
    9681280\end{description} 
    9691281 
     
    9861298\begin{figure}[!t] 
    9871299  \centering 
    988   \includegraphics[width=0.66\textwidth]{Fig_SBC_isf} 
     1300  \includegraphics[width=0.66\textwidth]{SBC_isf} 
    9891301  \caption[Ice shelf location and fresh water flux definition]{ 
    9901302    Illustration of the location where the fwf is injected and 
     
    13071619\begin{figure}[!t] 
    13081620  \centering 
    1309   \includegraphics[width=0.66\textwidth]{Fig_SBC_diurnal} 
     1621  \includegraphics[width=0.66\textwidth]{SBC_diurnal} 
    13101622  \caption[Reconstruction of the diurnal cycle variation of short wave flux]{ 
    13111623    Example of reconstruction of the diurnal cycle variation of short wave flux from 
     
    13411653\begin{figure}[!t] 
    13421654  \centering 
    1343   \includegraphics[width=0.66\textwidth]{Fig_SBC_dcy} 
     1655  \includegraphics[width=0.66\textwidth]{SBC_dcy} 
    13441656  \caption[Reconstruction of the diurnal cycle variation of short wave flux on an ORCA2 grid]{ 
    13451657    Example of reconstruction of the diurnal cycle variation of short wave flux from 
     
    15211833% in ocean-ice models. 
    15221834 
    1523 \onlyinsubfile{\input{../../global/epilogue}} 
     1835\subinc{\input{../../global/epilogue}} 
    15241836 
    15251837\end{document} 
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