Changeset 9392 for branches/2017/dev_merge_2017/DOC/tex_sub/chap_TRA.tex
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r9389 r9392 57 57 58 58 The user has the option of extracting each tendency term on the RHS of the tracer 59 equation for output (\np{ln \_tra\_trd} or \np{ln\_tra\_mxl}~=~true), as described in Chap.~\ref{DIA}.59 equation for output (\np{ln_tra_trd} or \np{ln_tra_mxl}~=~true), as described in Chap.~\ref{DIA}. 60 60 61 61 $\ $\newline % force a new ligne … … 70 70 %------------------------------------------------------------------------------------------------------------- 71 71 72 When considered ($i.e.$ when \np{ln \_traadv\_NONE} is not set to \textit{true}),72 When considered ($i.e.$ when \np{ln_traadv_NONE} is not set to \textit{true}), 73 73 the advection tendency of a tracer is expressed in flux form, 74 74 $i.e.$ as the divergence of the advective fluxes. Its discrete expression is given by : … … 84 84 by using the following equality : $\nabla \cdot \left( \vect{U}\,T \right)=\vect{U} \cdot \nabla T$ 85 85 which results from the use of the continuity equation, $\partial _t e_3 + e_3\;\nabla \cdot \vect{U}=0$ 86 (which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, $i.e.$ \ np{ln\_linssh}=true).86 (which reduces to $\nabla \cdot \vect{U}=0$ in linear free surface, $i.e.$ \forcode{ln_linssh = .true.}). 87 87 Therefore it is of paramount importance to design the discrete analogue of the 88 88 advection tendency so that it is consistent with the continuity equation in order to … … 114 114 boundary condition depends on the type of sea surface chosen: 115 115 \begin{description} 116 \item [linear free surface:] (\ np{ln\_linssh}=true) the first level thickness is constant in time:116 \item [linear free surface:] (\forcode{ln_linssh = .true.}) the first level thickness is constant in time: 117 117 the vertical boundary condition is applied at the fixed surface $z=0$ 118 118 rather than on the moving surface $z=\eta$. There is a non-zero advective … … 120 120 $\left. {\tau _w } \right|_{k=1/2} =T_{k=1} $, $i.e.$ 121 121 the product of surface velocity (at $z=0$) by the first level tracer value. 122 \item [non-linear free surface:] (\ np{ln\_linssh}=false)122 \item [non-linear free surface:] (\forcode{ln_linssh = .false.}) 123 123 convergence/divergence in the first ocean level moves the free surface 124 124 up/down. There is no tracer advection through it so that the advective … … 174 174 % 2nd and 4th order centred schemes 175 175 % ------------------------------------------------------------------------------------------------------------- 176 \subsection [Centred schemes (CEN) (\protect\np{ln \_traadv\_cen})]177 {Centred schemes (CEN) (\protect\ np{ln\_traadv\_cen}=true)}176 \subsection [Centred schemes (CEN) (\protect\np{ln_traadv_cen})] 177 {Centred schemes (CEN) (\protect\forcode{ln_traadv_cen = .true.})} 178 178 \label{TRA_adv_cen} 179 179 180 180 % 2nd order centred scheme 181 181 182 The centred advection scheme (CEN) is used when \np{ln \_traadv\_cen}~=~\textit{true}.182 The centred advection scheme (CEN) is used when \np{ln_traadv_cen}~=~\textit{true}. 183 183 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) 184 and vertical direction by setting \np{nn \_cen\_h} and \np{nn\_cen\_v} to $2$ or $4$.184 and vertical direction by setting \np{nn_cen_h} and \np{nn_cen_v} to $2$ or $4$. 185 185 CEN implementation can be found in the \mdl{traadv\_cen} module. 186 186 … … 212 212 =\overline{ T - \frac{1}{6}\,\delta _i \left[ \delta_{i+1/2}[T] \,\right] }^{\,i+1/2} 213 213 \end{equation} 214 In the vertical direction (\np{nn \_cen\_v}=$4$), a $4^{th}$ COMPACT interpolation214 In the vertical direction (\np{nn_cen_v}=$4$), a $4^{th}$ COMPACT interpolation 215 215 has been prefered \citep{Demange_PhD2014}. 216 216 In the COMPACT scheme, both the field and its derivative are interpolated, … … 246 246 % FCT scheme 247 247 % ------------------------------------------------------------------------------------------------------------- 248 \subsection [Flux Corrected Transport schemes (FCT) (\protect\np{ln \_traadv\_fct})]249 {Flux Corrected Transport schemes (FCT) (\protect\ np{ln\_traadv\_fct}=true)}248 \subsection [Flux Corrected Transport schemes (FCT) (\protect\np{ln_traadv_fct})] 249 {Flux Corrected Transport schemes (FCT) (\protect\forcode{ln_traadv_fct = .true.})} 250 250 \label{TRA_adv_tvd} 251 251 252 The Flux Corrected Transport schemes (FCT) is used when \np{ln \_traadv\_fct}~=~\textit{true}.252 The Flux Corrected Transport schemes (FCT) is used when \np{ln_traadv_fct}~=~\textit{true}. 253 253 Its order ($2^{nd}$ or $4^{th}$) can be chosen independently on horizontal (iso-level) 254 and vertical direction by setting \np{nn \_fct\_h} and \np{nn\_fct\_v} to $2$ or $4$.254 and vertical direction by setting \np{nn_fct_h} and \np{nn_fct_v} to $2$ or $4$. 255 255 FCT implementation can be found in the \mdl{traadv\_fct} module. 256 256 … … 269 269 where $c_u$ is a flux limiter function taking values between 0 and 1. 270 270 The FCT order is the one of the centred scheme used ($i.e.$ it depends on the setting of 271 \np{nn \_fct\_h} and \np{nn\_fct\_v}.271 \np{nn_fct_h} and \np{nn_fct_v}. 272 272 There exist many ways to define $c_u$, each corresponding to a different 273 273 FCT scheme. The one chosen in \NEMO is described in \citet{Zalesak_JCP79}. … … 277 277 A comparison of FCT-2 with MUSCL and a MPDATA scheme can be found in \citet{Levy_al_GRL01}. 278 278 279 An additional option has been added controlled by \np{nn \_fct\_zts}. By setting this integer to279 An additional option has been added controlled by \np{nn_fct_zts}. By setting this integer to 280 280 a value larger than zero, a $2^{nd}$ order FCT scheme is used on both horizontal and vertical direction, 281 281 but on the latter, a split-explicit time stepping is used, with a number of sub-timestep equals 282 to \np{nn \_fct\_zts}. This option can be useful when the size of the timestep is limited282 to \np{nn_fct_zts}. This option can be useful when the size of the timestep is limited 283 283 by vertical advection \citep{Lemarie_OM2015}. Note that in this case, a similar split-explicit 284 284 time stepping should be used on vertical advection of momentum to insure a better stability … … 293 293 % MUSCL scheme 294 294 % ------------------------------------------------------------------------------------------------------------- 295 \subsection[MUSCL scheme (\protect\np{ln \_traadv\_mus})]296 {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\protect\ np{ln\_traadv\_mus}=T)}295 \subsection[MUSCL scheme (\protect\np{ln_traadv_mus})] 296 {Monotone Upstream Scheme for Conservative Laws (MUSCL) (\protect\forcode{ln_traadv_mus = .true.})} 297 297 \label{TRA_adv_mus} 298 298 299 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln \_traadv\_mus}~=~\textit{true}.299 The Monotone Upstream Scheme for Conservative Laws (MUSCL) is used when \np{ln_traadv_mus}~=~\textit{true}. 300 300 MUSCL implementation can be found in the \mdl{traadv\_mus} module. 301 301 … … 321 321 the \textit{positive} character of the scheme. 322 322 In addition, fluxes round a grid-point where a runoff is applied can optionally be 323 computed using upstream fluxes (\np{ln \_mus\_ups}~=~\textit{true}).323 computed using upstream fluxes (\np{ln_mus_ups}~=~\textit{true}). 324 324 325 325 % ------------------------------------------------------------------------------------------------------------- 326 326 % UBS scheme 327 327 % ------------------------------------------------------------------------------------------------------------- 328 \subsection [Upstream-Biased Scheme (UBS) (\protect\np{ln \_traadv\_ubs})]329 {Upstream-Biased Scheme (UBS) (\protect\ np{ln\_traadv\_ubs}=true)}328 \subsection [Upstream-Biased Scheme (UBS) (\protect\np{ln_traadv_ubs})] 329 {Upstream-Biased Scheme (UBS) (\protect\forcode{ln_traadv_ubs = .true.})} 330 330 \label{TRA_adv_ubs} 331 331 332 The Upstream-Biased Scheme (UBS) is used when \np{ln \_traadv\_ubs}~=~\textit{true}.332 The Upstream-Biased Scheme (UBS) is used when \np{ln_traadv_ubs}~=~\textit{true}. 333 333 UBS implementation can be found in the \mdl{traadv\_mus} module. 334 334 … … 358 358 where the control of artificial diapycnal fluxes is of paramount importance \citep{Shchepetkin_McWilliams_OM05, Demange_PhD2014}. 359 359 Therefore the vertical flux is evaluated using either a $2^nd$ order FCT scheme 360 or a $4^th$ order COMPACT scheme (\ np{nn\_cen\_v}=2or 4).360 or a $4^th$ order COMPACT scheme (\forcode{nn_cen_v = 2} or 4). 361 361 362 362 For stability reasons (see \S\ref{STP}), … … 401 401 % QCK scheme 402 402 % ------------------------------------------------------------------------------------------------------------- 403 \subsection [QUICKEST scheme (QCK) (\protect\np{ln \_traadv\_qck})]404 {QUICKEST scheme (QCK) (\protect\ np{ln\_traadv\_qck}=true)}403 \subsection [QUICKEST scheme (QCK) (\protect\np{ln_traadv_qck})] 404 {QUICKEST scheme (QCK) (\protect\forcode{ln_traadv_qck = .true.})} 405 405 \label{TRA_adv_qck} 406 406 407 407 The Quadratic Upstream Interpolation for Convective Kinematics with 408 408 Estimated Streaming Terms (QUICKEST) scheme proposed by \citet{Leonard1979} 409 is used when \np{ln \_traadv\_qck}~=~\textit{true}.409 is used when \np{ln_traadv_qck}~=~\textit{true}. 410 410 QUICKEST implementation can be found in the \mdl{traadv\_qck} module. 411 411 … … 449 449 except for the pure vertical component that appears when a rotation tensor is used. 450 450 This latter component is solved implicitly together with the vertical diffusion term (see \S\ref{STP}). 451 When \np{ln \_traldf\_msc}~=~\textit{true}, a Method of Stabilizing Correction is used in which451 When \np{ln_traldf_msc}~=~\textit{true}, a Method of Stabilizing Correction is used in which 452 452 the pure vertical component is split into an explicit and an implicit part \citep{Lemarie_OM2012}. 453 453 … … 456 456 % ------------------------------------------------------------------------------------------------------------- 457 457 \subsection [Type of operator (\protect\np{ln\_traldf\{\_NONE, \_lap, \_blp\}})] 458 {Type of operator (\protect\np{ln \_traldf\_NONE}, \protect\np{ln\_traldf\_lap}, or \protect\np{ln\_traldf\_blp} = true) }458 {Type of operator (\protect\np{ln_traldf_NONE}, \protect\np{ln_traldf_lap}, or \protect\np{ln_traldf_blp} = true) } 459 459 \label{TRA_ldf_op} 460 460 461 461 Three operator options are proposed and, one and only one of them must be selected: 462 462 \begin{description} 463 \item [\np{ln \_traldf\_NONE}] = true : no operator selected, the lateral diffusive tendency will not be463 \item [\np{ln_traldf_NONE}] = true : no operator selected, the lateral diffusive tendency will not be 464 464 applied to the tracer equation. This option can be used when the selected advection scheme 465 465 is diffusive enough (MUSCL scheme for example). 466 \item [ \np{ln \_traldf\_lap}] = true : a laplacian operator is selected. This harmonic operator466 \item [ \np{ln_traldf_lap}] = true : a laplacian operator is selected. This harmonic operator 467 467 takes the following expression: $\mathpzc{L}(T)=\nabla \cdot A_{ht}\;\nabla T $, 468 468 where the gradient operates along the selected direction (see \S\ref{TRA_ldf_dir}), 469 469 and $A_{ht}$ is the eddy diffusivity coefficient expressed in $m^2/s$ (see Chap.~\ref{LDF}). 470 \item [\np{ln \_traldf\_blp}] = true : a bilaplacian operator is selected. This biharmonic operator470 \item [\np{ln_traldf_blp}] = true : a bilaplacian operator is selected. This biharmonic operator 471 471 takes the following expression: 472 472 $\mathpzc{B}=- \mathpzc{L}\left(\mathpzc{L}(T) \right) = -\nabla \cdot b\nabla \left( {\nabla \cdot b\nabla T} \right)$ … … 489 489 % ------------------------------------------------------------------------------------------------------------- 490 490 \subsection [Direction of action (\protect\np{ln\_traldf\{\_lev, \_hor, \_iso, \_triad\}})] 491 {Direction of action (\protect\np{ln \_traldf\_lev}, \textit{...\_hor}, \textit{...\_iso}, or \textit{...\_triad} = true) }491 {Direction of action (\protect\np{ln_traldf_lev}, \textit{...\_hor}, \textit{...\_iso}, or \textit{...\_triad} = true) } 492 492 \label{TRA_ldf_dir} 493 493 494 494 The choice of a direction of action determines the form of operator used. 495 495 The operator is a simple (re-entrant) laplacian acting in the (\textbf{i},\textbf{j}) plane 496 when iso-level option is used (\np{ln \_traldf\_lev}~=~\textit{true})496 when iso-level option is used (\np{ln_traldf_lev}~=~\textit{true}) 497 497 or when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{z}-coordinate 498 (\np{ln \_traldf\_hor} and \np{ln\_zco} equal \textit{true}).498 (\np{ln_traldf_hor} and \np{ln_zco} equal \textit{true}). 499 499 The associated code can be found in the \mdl{traldf\_lap\_blp} module. 500 500 The operator is a rotated (re-entrant) laplacian when the direction along which it acts 501 501 does not coincide with the iso-level surfaces, 502 that is when standard or triad iso-neutral option is used (\np{ln \_traldf\_iso} or503 \np{ln \_traldf\_triad} equals \textit{true}, see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.),502 that is when standard or triad iso-neutral option is used (\np{ln_traldf_iso} or 503 \np{ln_traldf_triad} equals \textit{true}, see \mdl{traldf\_iso} or \mdl{traldf\_triad} module, resp.), 504 504 or when a horizontal ($i.e.$ geopotential) operator is demanded in \textit{s}-coordinate 505 (\np{ln \_traldf\_hor} and \np{ln\_sco} equal \textit{true})505 (\np{ln_traldf_hor} and \np{ln_sco} equal \textit{true}) 506 506 \footnote{In this case, the standard iso-neutral operator will be automatically selected}. 507 507 In that case, a rotation is applied to the gradient(s) that appears in the operator … … 515 515 % iso-level operator 516 516 % ------------------------------------------------------------------------------------------------------------- 517 \subsection [Iso-level (bi-)laplacian operator ( \protect\np{ln \_traldf\_iso})]518 {Iso-level (bi-)laplacian operator ( \protect\np{ln \_traldf\_iso}) }517 \subsection [Iso-level (bi-)laplacian operator ( \protect\np{ln_traldf_iso})] 518 {Iso-level (bi-)laplacian operator ( \protect\np{ln_traldf_iso}) } 519 519 \label{TRA_ldf_lev} 520 520 … … 534 534 It is a \emph{horizontal} operator ($i.e.$ acting along geopotential surfaces) in the $z$-coordinate 535 535 with or without partial steps, but is simply an iso-level operator in the $s$-coordinate. 536 It is thus used when, in addition to \np{ln \_traldf\_lap} or \np{ln\_traldf\_blp}~=~\textit{true},537 we have \np{ln \_traldf\_lev}~=~\textit{true} or \np{ln\_traldf\_hor}~=~\np{ln\_zco}~=~\textit{true}.536 It is thus used when, in addition to \np{ln_traldf_lap} or \np{ln_traldf_blp}~=~\textit{true}, 537 we have \np{ln_traldf_lev}~=~\textit{true} or \np{ln_traldf_hor}~=~\np{ln_zco}~=~\textit{true}. 538 538 In both cases, it significantly contributes to diapycnal mixing. 539 539 It is therefore never recommended, even when using it in the bilaplacian case. 540 540 541 Note that in the partial step $z$-coordinate (\ np{ln\_zps}=true), tracers in horizontally541 Note that in the partial step $z$-coordinate (\forcode{ln_zps = .true.}), tracers in horizontally 542 542 adjacent cells are located at different depths in the vicinity of the bottom. 543 543 In this case, horizontal derivatives in (\ref{Eq_tra_ldf_lap}) at the bottom level … … 584 584 ($z$- or $s$-surfaces) and the surface along which the diffusion operator 585 585 acts ($i.e.$ horizontal or iso-neutral surfaces). It is thus used when, 586 in addition to \np{ln \_traldf\_lap}= true, we have \np{ln\_traldf\_iso}=true,587 or both \ np{ln\_traldf\_hor}=true and \np{ln\_zco}=true. The way these586 in addition to \np{ln_traldf_lap}= true, we have \forcode{ln_traldf_iso = .true.}, 587 or both \forcode{ln_traldf_hor = .true.} and \forcode{ln_zco = .true.}. The way these 588 588 slopes are evaluated is given in \S\ref{LDF_slp}. At the surface, bottom 589 589 and lateral boundaries, the turbulent fluxes of heat and salt are set to zero … … 603 603 background horizontal diffusion \citep{Guilyardi_al_CD01}. 604 604 605 Note that in the partial step $z$-coordinate (\ np{ln\_zps}=true), the horizontal derivatives605 Note that in the partial step $z$-coordinate (\forcode{ln_zps = .true.}), the horizontal derivatives 606 606 at the bottom level in \eqref{Eq_tra_ldf_iso} require a specific treatment. 607 607 They are calculated in module zpshde, described in \S\ref{TRA_zpshde}. … … 609 609 %&& Triad rotated (bi-)laplacian operator 610 610 %&& ------------------------------------------- 611 \subsubsection [Triad rotated (bi-)laplacian operator (\protect\np{ln \_traldf\_triad})]612 {Triad rotated (bi-)laplacian operator (\protect\np{ln \_traldf\_triad})}611 \subsubsection [Triad rotated (bi-)laplacian operator (\protect\np{ln_traldf_triad})] 612 {Triad rotated (bi-)laplacian operator (\protect\np{ln_traldf_triad})} 613 613 \label{TRA_ldf_triad} 614 614 615 If the Griffies triad scheme is employed (\ np{ln\_traldf\_triad}=true; see App.\ref{sec:triad})615 If the Griffies triad scheme is employed (\forcode{ln_traldf_triad = .true.} ; see App.\ref{sec:triad}) 616 616 617 617 An alternative scheme developed by \cite{Griffies_al_JPO98} which ensures tracer variance decreases 618 is also available in \NEMO (\ np{ln\_traldf\_grif}=true). A complete description of618 is also available in \NEMO (\forcode{ln_traldf_grif = .true.}). A complete description of 619 619 the algorithm is given in App.\ref{sec:triad}. 620 620 … … 635 635 \label{TRA_ldf_options} 636 636 637 \np{ln \_traldf\_msc} = Method of Stabilizing Correction (both operators)638 639 \np{rn \_slpmax} = slope limit (both operators)640 641 \np{ln \_triad\_iso} = pure horizontal mixing in ML (triad only)642 643 \np{rn \_sw\_triad} =1 switching triad ; =0 all 4 triads used (triad only)644 645 \np{ln \_botmix\_triad} = lateral mixing on bottom (triad only)637 \np{ln_traldf_msc} = Method of Stabilizing Correction (both operators) 638 639 \np{rn_slpmax} = slope limit (both operators) 640 641 \np{ln_triad_iso} = pure horizontal mixing in ML (triad only) 642 643 \np{rn_sw_triad} =1 switching triad ; =0 all 4 triads used (triad only) 644 645 \np{ln_botmix_triad} = lateral mixing on bottom (triad only) 646 646 647 647 % ================================================================ … … 685 685 The large eddy coefficient found in the mixed layer together with high 686 686 vertical resolution implies that in the case of explicit time stepping 687 (\ np{ln\_zdfexp}=true) there would be too restrictive a constraint on687 (\forcode{ln_zdfexp = .true.}) there would be too restrictive a constraint on 688 688 the time step. Therefore, the default implicit time stepping is preferred 689 689 for the vertical diffusion since it overcomes the stability constraint. 690 A forward time differencing scheme (\ np{ln\_zdfexp}=true) using a time691 splitting technique (\np{nn \_zdfexp} $> 1$) is provided as an alternative.692 Namelist variables \np{ln \_zdfexp} and \np{nn\_zdfexp} apply to both690 A forward time differencing scheme (\forcode{ln_zdfexp = .true.}) using a time 691 splitting technique (\np{nn_zdfexp} $> 1$) is provided as an alternative. 692 Namelist variables \np{ln_zdfexp} and \np{nn_zdfexp} apply to both 693 693 tracers and dynamics. 694 694 … … 750 750 divergence of odd and even time step (see \S\ref{STP}). 751 751 752 In the linear free surface case (\np{ln \_linssh}~=~\textit{true}),752 In the linear free surface case (\np{ln_linssh}~=~\textit{true}), 753 753 an additional term has to be added on both temperature and salinity. 754 754 On temperature, this term remove the heat content associated with mass exchange … … 781 781 782 782 Options are defined through the \ngn{namtra\_qsr} namelist variables. 783 When the penetrative solar radiation option is used (\ np{ln\_flxqsr}=true),783 When the penetrative solar radiation option is used (\forcode{ln_flxqsr = .true.}), 784 784 the solar radiation penetrates the top few tens of meters of the ocean. If it is not used 785 (\ np{ln\_flxqsr}=false) all the heat flux is absorbed in the first ocean level.785 (\forcode{ln_flxqsr = .false.}) all the heat flux is absorbed in the first ocean level. 786 786 Thus, in the former case a term is added to the time evolution equation of 787 787 temperature \eqref{Eq_PE_tra_T} and the surface boundary condition is … … 805 805 wavelengths contribute to heating the upper few tens of centimetres. The fraction of $Q_{sr}$ 806 806 that resides in these almost non-penetrative wavebands, $R$, is $\sim 58\%$ (specified 807 through namelist parameter \np{rn \_abs}). It is assumed to penetrate the ocean807 through namelist parameter \np{rn_abs}). It is assumed to penetrate the ocean 808 808 with a decreasing exponential profile, with an e-folding depth scale, $\xi_0$, 809 of a few tens of centimetres (typically $\xi_0=0.35~m$ set as \np{rn \_si0} in the namtra\_qsr namelist).809 of a few tens of centimetres (typically $\xi_0=0.35~m$ set as \np{rn_si0} in the namtra\_qsr namelist). 810 810 For shorter wavelengths (400-700~nm), the ocean is more transparent, and solar energy 811 811 propagates to larger depths where it contributes to 812 812 local heating. 813 813 The way this second part of the solar energy penetrates into the ocean depends on 814 which formulation is chosen. In the simple 2-waveband light penetration scheme (\ np{ln\_qsr\_2bd}=true)814 which formulation is chosen. In the simple 2-waveband light penetration scheme (\forcode{ln_qsr_2bd = .true.}) 815 815 a chlorophyll-independent monochromatic formulation is chosen for the shorter wavelengths, 816 816 leading to the following expression \citep{Paulson1977}: … … 819 819 \end{equation} 820 820 where $\xi_1$ is the second extinction length scale associated with the shorter wavelengths. 821 It is usually chosen to be 23~m by setting the \np{rn \_si0} namelist parameter.821 It is usually chosen to be 23~m by setting the \np{rn_si0} namelist parameter. 822 822 The set of default values ($\xi_0$, $\xi_1$, $R$) corresponds to a Type I water in 823 823 Jerlov's (1968) classification (oligotrophic waters). … … 839 839 computational efficiency. The 2-bands formulation does not reproduce the full model very well. 840 840 841 The RGB formulation is used when \ np{ln\_qsr\_rgb}=true. The RGB attenuation coefficients841 The RGB formulation is used when \forcode{ln_qsr_rgb = .true.}. The RGB attenuation coefficients 842 842 ($i.e.$ the inverses of the extinction length scales) are tabulated over 61 nonuniform 843 843 chlorophyll classes ranging from 0.01 to 10 g.Chl/L (see the routine \rou{trc\_oce\_rgb} 844 844 in \mdl{trc\_oce} module). Four types of chlorophyll can be chosen in the RGB formulation: 845 845 \begin{description} 846 \item[\ np{nn\_chdta}=0]846 \item[\forcode{nn_chdta = 0}] 847 847 a constant 0.05 g.Chl/L value everywhere ; 848 \item[\ np{nn\_chdta}=1]848 \item[\forcode{nn_chdta = 1}] 849 849 an observed time varying chlorophyll deduced from satellite surface ocean color measurement 850 850 spread uniformly in the vertical direction ; 851 \item[\ np{nn\_chdta}=2]851 \item[\forcode{nn_chdta = 2}] 852 852 same as previous case except that a vertical profile of chlorophyl is used. 853 853 Following \cite{Morel_Berthon_LO89}, the profile is computed from the local surface chlorophyll value ; 854 \item[\ np{ln\_qsr\_bio}=true]854 \item[\forcode{ln_qsr_bio = .true.}] 855 855 simulated time varying chlorophyll by TOP biogeochemical model. 856 856 In this case, the RGB formulation is used to calculate both the phytoplankton … … 913 913 Options are defined through the \ngn{namtra\_bbc} namelist variables. 914 914 The presence of geothermal heating is controlled by setting the namelist 915 parameter \np{ln \_trabbc} to true. Then, when \np{nn\_geoflx} is set to 1,915 parameter \np{ln_trabbc} to true. Then, when \np{nn_geoflx} is set to 1, 916 916 a constant geothermal heating is introduced whose value is given by the 917 \np{nn \_geoflx\_cst}, which is also a namelist parameter.918 When \np{nn \_geoflx} is set to 2, a spatially varying geothermal heat flux is917 \np{nn_geoflx_cst}, which is also a namelist parameter. 918 When \np{nn_geoflx} is set to 2, a spatially varying geothermal heat flux is 919 919 introduced which is provided in the \ifile{geothermal\_heating} NetCDF file 920 920 (Fig.\ref{Fig_geothermal}) \citep{Emile-Geay_Madec_OS09}. … … 959 959 % Diffusive BBL 960 960 % ------------------------------------------------------------------------------------------------------------- 961 \subsection{Diffusive Bottom Boundary layer (\protect\ np{nn\_bbl\_ldf}=1)}961 \subsection{Diffusive Bottom Boundary layer (\protect\forcode{nn_bbl_ldf = 1})} 962 962 \label{TRA_bbl_diff} 963 963 964 When applying sigma-diffusion (\key{trabbl} defined and \np{nn \_bbl\_ldf} set to 1),964 When applying sigma-diffusion (\key{trabbl} defined and \np{nn_bbl_ldf} set to 1), 965 965 the diffusive flux between two adjacent cells at the ocean floor is given by 966 966 \begin{equation} \label{Eq_tra_bbl_diff} … … 978 978 \end{equation} 979 979 where $A_{bbl}$ is the BBL diffusivity coefficient, given by the namelist 980 parameter \np{rn \_ahtbbl} and usually set to a value much larger980 parameter \np{rn_ahtbbl} and usually set to a value much larger 981 981 than the one used for lateral mixing in the open ocean. The constraint in \eqref{Eq_tra_bbl_coef} 982 982 implies that sigma-like diffusion only occurs when the density above the sea floor, at the top of … … 994 994 % Advective BBL 995 995 % ------------------------------------------------------------------------------------------------------------- 996 \subsection {Advective Bottom Boundary Layer (\protect\np{nn \_bbl\_adv}= 1 or 2)}996 \subsection {Advective Bottom Boundary Layer (\protect\np{nn_bbl_adv}= 1 or 2)} 997 997 \label{TRA_bbl_adv} 998 998 … … 1022 1022 %%%gmcomment : this section has to be really written 1023 1023 1024 When applying an advective BBL (\np{nn \_bbl\_adv} = 1 or 2), an overturning1024 When applying an advective BBL (\np{nn_bbl_adv} = 1 or 2), an overturning 1025 1025 circulation is added which connects two adjacent bottom grid-points only if dense 1026 1026 water overlies less dense water on the slope. The density difference causes dense 1027 1027 water to move down the slope. 1028 1028 1029 \np{nn \_bbl\_adv} = 1 : the downslope velocity is chosen to be the Eulerian1029 \np{nn_bbl_adv} = 1 : the downslope velocity is chosen to be the Eulerian 1030 1030 ocean velocity just above the topographic step (see black arrow in Fig.\ref{Fig_bbl}) 1031 1031 \citep{Beckmann_Doscher1997}. It is a \textit{conditional advection}, that is, advection … … 1034 1034 greater depth ($i.e.$ $\vect{U} \cdot \nabla H>0$). 1035 1035 1036 \np{nn \_bbl\_adv} = 2 : the downslope velocity is chosen to be proportional to $\Delta \rho$,1036 \np{nn_bbl_adv} = 2 : the downslope velocity is chosen to be proportional to $\Delta \rho$, 1037 1037 the density difference between the higher cell and lower cell densities \citep{Campin_Goosse_Tel99}. 1038 1038 The advection is allowed only if dense water overlies less dense water on the slope ($i.e.$ … … 1044 1044 \end{equation} 1045 1045 where $\gamma$, expressed in seconds, is the coefficient of proportionality 1046 provided as \np{rn \_gambbl}, a namelist parameter, and \textit{kup} and \textit{kdwn}1046 provided as \np{rn_gambbl}, a namelist parameter, and \textit{kup} and \textit{kdwn} 1047 1047 are the vertical index of the higher and lower cells, respectively. 1048 1048 The parameter $\gamma$ should take a different value for each bathymetric … … 1101 1101 are given temperature and salinity fields (usually a climatology). 1102 1102 Options are defined through the \ngn{namtra\_dmp} namelist variables. 1103 The restoring term is added when the namelist parameter \np{ln \_tradmp} is set to true.1104 It also requires that both \np{ln \_tsd\_init} and \np{ln\_tsd\_tradmp} are set to true1105 in \textit{namtsd} namelist as well as \np{sn \_tem} and \np{sn\_sal} structures are1103 The restoring term is added when the namelist parameter \np{ln_tradmp} is set to true. 1104 It also requires that both \np{ln_tsd_init} and \np{ln_tsd_tradmp} are set to true 1105 in \textit{namtsd} namelist as well as \np{sn_tem} and \np{sn_sal} structures are 1106 1106 correctly set ($i.e.$ that $T_o$ and $S_o$ are provided in input files and read 1107 1107 using \mdl{fldread}, see \S\ref{SBC_fldread}). 1108 The restoring coefficient $\gamma$ is a three-dimensional array read in during the \rou{tra\_dmp\_init} routine. The file name is specified by the namelist variable \np{cn \_resto}. The DMP\_TOOLS tool is provided to allow users to generate the netcdf file.1108 The restoring coefficient $\gamma$ is a three-dimensional array read in during the \rou{tra\_dmp\_init} routine. The file name is specified by the namelist variable \np{cn_resto}. The DMP\_TOOLS tool is provided to allow users to generate the netcdf file. 1109 1109 1110 1110 The two main cases in which \eqref{Eq_tra_dmp} is used are \textit{(a)} … … 1128 1128 by stabilising the water column too much. 1129 1129 1130 The namelist parameter \np{nn \_zdmp} sets whether the damping should be applied in the whole water column or only below the mixed layer (defined either on a density or $S_o$ criterion). It is common to set the damping to zero in the mixed layer as the adjustment time scale is short here \citep{Madec_al_JPO96}.1131 1132 \subsection[DMP\_TOOLS]{Generating resto.ncusing DMP\_TOOLS}1130 The namelist parameter \np{nn_zdmp} sets whether the damping should be applied in the whole water column or only below the mixed layer (defined either on a density or $S_o$ criterion). It is common to set the damping to zero in the mixed layer as the adjustment time scale is short here \citep{Madec_al_JPO96}. 1131 1132 \subsection[DMP\_TOOLS]{Generating \ifile{resto} using DMP\_TOOLS} 1133 1133 1134 1134 DMP\_TOOLS can be used to generate a netcdf file containing the restoration coefficient $\gamma$. 1135 1135 Note that in order to maintain bit comparison with previous NEMO versions DMP\_TOOLS must be compiled 1136 and run on the same machine as the NEMO model. A mesh\_mask.ncfile for the model configuration is required as an input.1137 This can be generated by carrying out a short model run with the namelist parameter \np{nn \_msh} set to 1.1138 The namelist parameter \np{ln \_tradmp} will also need to be set to .false. for this to work.1136 and run on the same machine as the NEMO model. A \ifile{mesh\_mask} file for the model configuration is required as an input. 1137 This can be generated by carrying out a short model run with the namelist parameter \np{nn_msh} set to 1. 1138 The namelist parameter \np{ln_tradmp} will also need to be set to .false. for this to work. 1139 1139 The \nl{nam\_dmp\_create} namelist in the DMP\_TOOLS directory is used to specify options for the restoration coefficient. 1140 1140 … … 1143 1143 %------------------------------------------------------------------------------------------------------- 1144 1144 1145 \np{cp \_cfg}, \np{cp\_cpz}, \np{jp\_cfg} and \np{jperio} specify the model configuration being used and should be the same as specified in \nl{namcfg}. The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to provide boundary conditions to a zoom configuration. In the case of the arctic or antarctic zoom configurations this includes some specific treatment. Otherwise damping is applied to the 6 grid points along the ocean boundaries. The open boundaries are specified by the variables \np{lzoom\_n}, \np{lzoom\_e}, \np{lzoom\_s}, \np{lzoom\_w} in the \nl{nam\_zoom\_dmp} name list.1145 \np{cp_cfg}, \np{cp_cpz}, \np{jp_cfg} and \np{jperio} specify the model configuration being used and should be the same as specified in \nl{namcfg}. The variable \nl{lzoom} is used to specify that the damping is being used as in case \textit{a} above to provide boundary conditions to a zoom configuration. In the case of the arctic or antarctic zoom configurations this includes some specific treatment. Otherwise damping is applied to the 6 grid points along the ocean boundaries. The open boundaries are specified by the variables \np{lzoom_n}, \np{lzoom_e}, \np{lzoom_s}, \np{lzoom_w} in the \nl{nam\_zoom\_dmp} name list. 1146 1146 1147 1147 The remaining switch namelist variables determine the spatial variation of the restoration coefficient in non-zoom configurations. 1148 \np{ln \_full\_field} specifies that newtonian damping should be applied to the whole model domain.1149 \np{ln \_med\_red\_seas} specifies grid specific restoration coefficients in the Mediterranean Sea1148 \np{ln_full_field} specifies that newtonian damping should be applied to the whole model domain. 1149 \np{ln_med_red_seas} specifies grid specific restoration coefficients in the Mediterranean Sea 1150 1150 for the ORCA4, ORCA2 and ORCA05 configurations. 1151 If \np{ln \_old\_31\_lev\_code} is set then the depth variation of the coeffients will be specified as1151 If \np{ln_old_31_lev_code} is set then the depth variation of the coeffients will be specified as 1152 1152 a function of the model number. This option is included to allow backwards compatability of the ORCA2 reference 1153 1153 configurations with previous model versions. 1154 \np{ln \_coast} specifies that the restoration coefficient should be reduced near to coastlines.1155 This option only has an effect if \np{ln \_full\_field} is true.1156 \np{ln \_zero\_top\_layer} specifies that the restoration coefficient should be zero in the surface layer.1157 Finally \np{ln \_custom} specifies that the custom module will be called.1154 \np{ln_coast} specifies that the restoration coefficient should be reduced near to coastlines. 1155 This option only has an effect if \np{ln_full_field} is true. 1156 \np{ln_zero_top_layer} specifies that the restoration coefficient should be zero in the surface layer. 1157 Finally \np{ln_custom} specifies that the custom module will be called. 1158 1158 This module is contained in the file custom.F90 and can be edited by users. For example damping could be applied in a specific region. 1159 1159 1160 The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn \_hdmp}.1160 The restoration coefficient can be set to zero in equatorial regions by specifying a positive value of \np{nn_hdmp}. 1161 1161 Equatorward of this latitude the restoration coefficient will be zero with a smooth transition to 1162 1162 the full values of a 10\deg latitud band. 1163 1163 This is often used because of the short adjustment time scale in the equatorial region 1164 1164 \citep{Reverdin1991, Fujio1991, Marti_PhD92}. The time scale associated with the damping depends on the depth as a 1165 hyperbolic tangent, with \np{rn \_surf} as surface value, \np{rn\_bot} as bottom value and a transition depth of \np{rn\_dep}.1165 hyperbolic tangent, with \np{rn_surf} as surface value, \np{rn_bot} as bottom value and a transition depth of \np{rn_dep}. 1166 1166 1167 1167 % ================================================================ … … 1191 1191 the subscript $f$ denotes filtered values, $\gamma$ is the Asselin coefficient, 1192 1192 and $S$ is the total forcing applied on $T$ ($i.e.$ fluxes plus content in mass exchanges). 1193 $\gamma$ is initialized as \np{rn \_atfp} (\textbf{namelist} parameter).1194 Its default value is \np{rn \_atfp}=$10^{-3}$. Note that the forcing correction term in the filter1193 $\gamma$ is initialized as \np{rn_atfp} (\textbf{namelist} parameter). 1194 Its default value is \np{rn_atfp}=$10^{-3}$. Note that the forcing correction term in the filter 1195 1195 is not applied in linear free surface (\jp{lk\_vvl}=false) (see \S\ref{TRA_sbc}. 1196 1196 Not also that in constant volume case, the time stepping is performed on $T$, … … 1217 1217 % Equation of State 1218 1218 % ------------------------------------------------------------------------------------------------------------- 1219 \subsection{Equation Of Seawater (\protect\np{nn \_eos} = -1, 0, or 1)}1219 \subsection{Equation Of Seawater (\protect\np{nn_eos} = -1, 0, or 1)} 1220 1220 \label{TRA_eos} 1221 1221 … … 1248 1248 density in the World Ocean varies by no more than 2$\%$ from that value \citep{Gill1982}. 1249 1249 1250 Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn \_eos}1250 Options are defined through the \ngn{nameos} namelist variables, and in particular \np{nn_eos} 1251 1251 which controls the EOS used (=-1 for TEOS10 ; =0 for EOS-80 ; =1 for S-EOS). 1252 1252 \begin{description} 1253 1253 1254 \item[\np{nn \_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used.1254 \item[\np{nn_eos}$=-1$] the polyTEOS10-bsq equation of seawater \citep{Roquet_OM2015} is used. 1255 1255 The accuracy of this approximation is comparable to the TEOS-10 rational function approximation, 1256 1256 but it is optimized for a boussinesq fluid and the polynomial expressions have simpler … … 1268 1268 $\Theta$ and $S_A$. In particular, the initial state deined by the user have to be given as 1269 1269 \textit{Conservative} Temperature and \textit{Absolute} Salinity. 1270 In addition, setting \np{ln \_useCT} to \textit{true} convert the Conservative SST to potential SST1270 In addition, setting \np{ln_useCT} to \textit{true} convert the Conservative SST to potential SST 1271 1271 prior to either computing the air-sea and ice-sea fluxes (forced mode) 1272 1272 or sending the SST field to the atmosphere (coupled mode). 1273 1273 1274 \item[\np{nn \_eos}$=0$] the polyEOS80-bsq equation of seawater is used.1274 \item[\np{nn_eos}$=0$] the polyEOS80-bsq equation of seawater is used. 1275 1275 It takes the same polynomial form as the polyTEOS10, but the coefficients have been optimized 1276 1276 to accurately fit EOS80 (Roquet, personal comm.). The state variables used in both the EOS80 … … 1283 1283 value, the TEOS10 value. 1284 1284 1285 \item[\np{nn \_eos}$=1$] a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen,1285 \item[\np{nn_eos}$=1$] a simplified EOS (S-EOS) inspired by \citet{Vallis06} is chosen, 1286 1286 the coefficients of which has been optimized to fit the behavior of TEOS10 (Roquet, personal comm.) 1287 1287 (see also \citet{Roquet_JPO2015}). It provides a simplistic linear representation of both … … 1315 1315 \hline 1316 1316 coeff. & computer name & S-EOS & description \\ \hline 1317 $a_0$ & \np{rn \_a0} & 1.6550 $10^{-1}$ & linear thermal expansion coeff. \\ \hline1318 $b_0$ & \np{rn \_b0} & 7.6554 $10^{-1}$ & linear haline expansion coeff. \\ \hline1319 $\lambda_1$ & \np{rn \_lambda1}& 5.9520 $10^{-2}$ & cabbeling coeff. in $T^2$ \\ \hline1320 $\lambda_2$ & \np{rn \_lambda2}& 5.4914 $10^{-4}$ & cabbeling coeff. in $S^2$ \\ \hline1321 $\nu$ & \np{rn \_nu} & 2.4341 $10^{-3}$ & cabbeling coeff. in $T \, S$ \\ \hline1322 $\mu_1$ & \np{rn \_mu1} & 1.4970 $10^{-4}$ & thermobaric coeff. in T \\ \hline1323 $\mu_2$ & \np{rn \_mu2} & 1.1090 $10^{-5}$ & thermobaric coeff. in S \\ \hline1317 $a_0$ & \np{rn_a0} & 1.6550 $10^{-1}$ & linear thermal expansion coeff. \\ \hline 1318 $b_0$ & \np{rn_b0} & 7.6554 $10^{-1}$ & linear haline expansion coeff. \\ \hline 1319 $\lambda_1$ & \np{rn_lambda1}& 5.9520 $10^{-2}$ & cabbeling coeff. in $T^2$ \\ \hline 1320 $\lambda_2$ & \np{rn_lambda2}& 5.4914 $10^{-4}$ & cabbeling coeff. in $S^2$ \\ \hline 1321 $\nu$ & \np{rn_nu} & 2.4341 $10^{-3}$ & cabbeling coeff. in $T \, S$ \\ \hline 1322 $\mu_1$ & \np{rn_mu1} & 1.4970 $10^{-4}$ & thermobaric coeff. in T \\ \hline 1323 $\mu_2$ & \np{rn_mu2} & 1.1090 $10^{-5}$ & thermobaric coeff. in S \\ \hline 1324 1324 \end{tabular} 1325 1325 \caption{ \protect\label{Tab_SEOS} … … 1333 1333 % Brunt-V\"{a}is\"{a}l\"{a} Frequency 1334 1334 % ------------------------------------------------------------------------------------------------------------- 1335 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\protect\np{nn \_eos} = 0, 1 or 2)}1335 \subsection{Brunt-V\"{a}is\"{a}l\"{a} Frequency (\protect\np{nn_eos} = 0, 1 or 2)} 1336 1336 \label{TRA_bn2} 1337 1337 … … 1395 1395 I've changed "derivative" to "difference" and "mean" to "average"} 1396 1396 1397 With partial cells (\ np{ln\_zps}=true) at bottom and top (\np{ln\_isfcav}=true), in general,1397 With partial cells (\forcode{ln_zps = .true.}) at bottom and top (\forcode{ln_isfcav = .true.}), in general, 1398 1398 tracers in horizontally adjacent cells live at different depths. 1399 1399 Horizontal gradients of tracers are needed for horizontal diffusion (\mdl{traldf} module) 1400 1400 and the hydrostatic pressure gradient calculations (\mdl{dynhpg} module). 1401 The partial cell properties at the top (\ np{ln\_isfcav}=true) are computed in the same way as for the bottom.1401 The partial cell properties at the top (\forcode{ln_isfcav = .true.}) are computed in the same way as for the bottom. 1402 1402 So, only the bottom interpolation is explained below. 1403 1403 … … 1413 1413 \caption{ \protect\label{Fig_Partial_step_scheme} 1414 1414 Discretisation of the horizontal difference and average of tracers in the $z$-partial 1415 step coordinate (\protect\ np{ln\_zps}=true) in the case $( e3w_k^{i+1} - e3w_k^i )>0$.1415 step coordinate (\protect\forcode{ln_zps = .true.}) in the case $( e3w_k^{i+1} - e3w_k^i )>0$. 1416 1416 A linear interpolation is used to estimate $\widetilde{T}_k^{i+1}$, the tracer value 1417 1417 at the depth of the shallower tracer point of the two adjacent bottom $T$-points.
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