Changeset 11043


Ignore:
Timestamp:
2019-05-23T15:51:08+02:00 (17 months ago)
Author:
nicolasmartin
Message:

Several fixes for the LaTeX compilation of the manuals

Location:
NEMO/trunk/doc
Files:
11 edited

Legend:

Unmodified
Added
Removed
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.sty

    r11022 r11043  
    66%% LaTeX packages 
    77%% ============================================================================== 
    8  
    98\usepackage{natbib}           %% bib 
    109\usepackage{caption}          %% caption 
     
    2423 
    2524%% Extensions in bundle package 
    26  
    2725\usepackage{amssymb, graphicx, makeidx, tabularx} 
    2826 
    29  
    3027%% Configuration 
    31  
    3228\captionsetup{margin=10pt, font={small}, labelsep=colon, labelfont={bf}} 
    33 \hypersetup{ 
    34    pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and NEMO System Team}, 
    35    colorlinks 
    36 } 
    3729\idxlayout{font=footnotesize, columns=3} 
    3830\renewcommand{\bibfont}{\footnotesize} 
     
    4234%% Styles 
    4335%% ============================================================================== 
    44  
    4536\pagestyle{fancy} 
    4637\bibliographystyle{../../NEMO/main/ametsoc} 
    4738 
    4839%% Additionnal fonts 
    49  
    5040\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} 
    5141 
    5242 
    5343%% Page layout 
    54  
    5544\fancyhf{} 
    5645\fancyhead[LE,RO]{\bfseries\thepage} 
     
    6554 
    6655%% Catcodes 
    67  
    6856\makeatletter 
    6957\def\LigneVerticale{\vrule height 5cm depth 2cm\hspace{0.1cm}\relax} 
  • NEMO/trunk/doc/latex/NEMO/main/NEMO_manual.tex

    r11013 r11043  
    1212%% Custom style (.sty) 
    1313\usepackage{../main/NEMO_manual} 
     14\hypersetup{ 
     15   pdftitle={NEMO ocean engine}, pdfauthor={Gurvan Madec, and NEMO System Team}, 
     16   colorlinks 
     17} 
    1418 
    1519%% Include references and index for single subfile compilation 
     
    4751% 
    4852%  }                                                        \\ 
    49 %                                                           \\ 
    5053  \textit{Issue 27, Notes du P\^{o}le de mod\'{e}lisation} \\ 
    5154  \textit{Institut Pierre-Simon Laplace (IPSL)}            \\ 
     
    5659\maketitle 
    5760\frontmatter 
    58  
    5961 
    6062%% ToC i.e. Table of Contents 
     
    123125\printindex 
    124126 
    125  
    126127\end{document} 
  • NEMO/trunk/doc/latex/SI3/main/SI3_manual.bib

    r11030 r11043  
    11 
    2 @Article{         assur_1958, 
    3   author        = {Assur, A}, 
    4   year          = {1958}, 
    5   month         = {01}, 
    6   pages         = {106-138}, 
    7   title         = {Composition of sea ice and its tensile strength}, 
    8   volume        = {598}, 
    9   journal       = {Arctic Sea Ice} 
     2@Article{     assur_1958, 
     3  author = {Assur, A}, 
     4  year      = {1958}, 
     5  month     = {01}, 
     6  pages     = {106-138}, 
     7  title     = {Composition of sea ice and its tensile strength}, 
     8  volume = {598}, 
     9  journal   = {Arctic Sea Ice} 
    1010} 
    1111 
     
    234234} 
    235235 
    236 @Article{     h_yland_2002, 
     236@Article{     hoyland_2002, 
    237237  author = {Høyland, Knut V.}, 
    238238  title     = {Consolidation of first-year sea ice ridges}, 
     
    308308} 
    309309 
    310 @Article{     lepp_ranta_1995, 
     310@Article{     lepparanta_1995, 
    311311  author = {Leppäranta, Matti and Lensu, Mikko and Kosloff, Pekka and 
    312312        Veitch, Brian}, 
     
    324324} 
    325325 
    326 @Article{     lepp_ranta_2011, 
     326@Article{     lepparanta_2011, 
    327327  author = {Leppäranta, Matti}, 
    328328  title     = {Drift ice material}, 
    329329  year      = 2011, 
    330330  pages     = {11–63}, 
    331   doi    = {10.1007/978-3-642-04683-4_2}, 
    332   url    = {http://dx.doi.org/10.1007/978-3-642-04683-4_2}, 
     331  doi    = {10.1007/978-3-642-04683-4\_2}, 
     332  url    = {http://dx.doi.org/10.1007/978-3-642-04683-4\_2}, 
    333333  isbn      = 9783642046834, 
    334334  journal   = {The Drift of Sea Ice}, 
     
    367367} 
    368368 
     369@Article{     massonnet_2018, 
     370  author = {Massonnet, F. and Barth\'el\'emy, A. and Worou, K. and 
     371        Fichefet, T. and Vancoppenolle, M. and Rousset, C.}, 
     372  title     = {Insights on the discretization of the ice thickness 
     373        distribution in large-scale sea ice models}, 
     374  journal   = {submitted}, 
     375  year      = {2018} 
     376} 
     377 
    369378@Article{     maykut_1971, 
    370379  author = {Maykut, Gary A. and Untersteiner, Norbert}, 
     
    383392} 
    384393 
     394@Article{     maykut_1973, 
     395  author = {Maykut, G. A. and Thorndike, A. S.}, 
     396  title     = {An approach to coupling the dynamics and thermodynamics of 
     397        Arctic sea ice}, 
     398  journal   = {AIDJEX Bulletin}, 
     399  year      = {1973}, 
     400  volume = {21}, 
     401  pages     = {23--29} 
     402} 
     403 
    385404@Article{     maykut_1986, 
    386405  author = {Maykut, Gary A.}, 
     
    388407  year      = 1986, 
    389408  pages     = {395–463}, 
    390   doi    = {10.1007/978-1-4899-5352-0_6}, 
    391   url    = {http://dx.doi.org/10.1007/978-1-4899-5352-0_6}, 
     409  doi    = {10.1007/978-1-4899-5352-0\_6}, 
     410  url    = {http://dx.doi.org/10.1007/978-1-4899-5352-0\_6}, 
    392411  isbn      = 9781489953520, 
    393412  journal   = {The Geophysics of Sea Ice}, 
     
    546565} 
    547566 
     567@Book{        teos-10_2010, 
     568  title     = {{The international thermodynamic equation of seawater - 
     569        2010: Calculation and use of thermodynamic properties}}, 
     570  publisher = {UNESCO (English)}, 
     571  year      = {2010}, 
     572  author = {{IOC, SCOR and IAPSO}}, 
     573  series = {Intergovernmental Oceanographic Commission, Manuals and 
     574        Guides No. 56} 
     575} 
     576 
    548577@Article{     thorndike_1975, 
    549578  author = {Thorndike, A. S. and Rothrock, D. A. and Maykut, G. A. and 
     
    610639  year      = 1992, 
    611640  pages     = {113–138}, 
    612   doi    = {10.1007/978-94-011-2809-4_20}, 
    613   url    = {http://dx.doi.org/10.1007/978-94-011-2809-4_20}, 
     641  doi    = {10.1007/978-94-011-2809-4\_20}, 
     642  url    = {http://dx.doi.org/10.1007/978-94-011-2809-4\_20}, 
    614643  isbn      = 9789401128094, 
    615644  journal   = {Interactive Dynamics of Convection and Solidification}, 
  • NEMO/trunk/doc/latex/SI3/main/SI3_manual.tex

    r11030 r11043  
    1212%% Custom style (.sty) 
    1313\usepackage{../../NEMO/main/NEMO_manual} 
     14\hypersetup{ 
     15  pdftitle={SI³ – Sea Ice modelling Integrated Initiative – The NEMO Sea Ice engine}, 
     16  pdfauthor={NEMO Sea Ice Working Group}, 
     17  colorlinks 
     18} 
    1419 
    1520%% Include references and index for single subfile compilation 
  • NEMO/trunk/doc/latex/SI3/subfiles/chap_model_basics.tex

    r11031 r11043  
    2828 
    2929\subsection{Scales, thermodynamics and dynamics} 
    30 Because sea ice is much wider -- $\mathcal{O}$(100-1000 km) -- than thick -- $\mathcal{O}$(1 m) -- ice drift can be considered as purely horizontal: vertical motions around the hydrostatic equilibrium position are negligible. The same scaling argument justifies the assumption that heat exchanges are purely vertical\footnote{The latter assumption is probably less valid, because the horizontal scales of temperature variations are $\mathcal{O}$(10-100 m)}. It is on this basis that thermodynamics and dynamics are separated and rely upon different frameworks and sets of hypotheses: thermodynamics use the ice thickness distribution \citep{thorndike_1975} and the mushy-layer \citep{worster_1992} frameworks, whereas dynamics assume continuum mechanics \citep[e.g.,][]{lepp_ranta_2011}. Thermodynamics and dynamics interact by two means: first, advection impacts state variables; second, the horizontal momentum equation depends, among other things, on the ice state. 
     30Because sea ice is much wider -- $\mathcal{O}$(100-1000 km) -- than thick -- $\mathcal{O}$(1 m) -- ice drift can be considered as purely horizontal: vertical motions around the hydrostatic equilibrium position are negligible. The same scaling argument justifies the assumption that heat exchanges are purely vertical\footnote{The latter assumption is probably less valid, because the horizontal scales of temperature variations are $\mathcal{O}$(10-100 m)}. It is on this basis that thermodynamics and dynamics are separated and rely upon different frameworks and sets of hypotheses: thermodynamics use the ice thickness distribution \citep{thorndike_1975} and the mushy-layer \citep{worster_1992} frameworks, whereas dynamics assume continuum mechanics \citep[e.g.,][]{lepparanta_2011}. Thermodynamics and dynamics interact by two means: first, advection impacts state variables; second, the horizontal momentum equation depends, among other things, on the ice state. 
    3131 
    3232\subsection{Subgrid scale variations} 
     
    7070 & Description & Value & Units & Ref \\ \hline 
    7171$c_i$ (cpic) & Pure ice specific heat & 2067 & J/kg/K & ? \\ 
    72 $c_w$ (rcp) & Seawater specific heat & 3991 & J/kg/K & \cite{TEOS_2010} \\ 
     72$c_w$ (rcp) & Seawater specific heat & 3991 & J/kg/K & \cite{teos-10_2010} \\ 
    7373$L$ (lfus) & Latent heat of fusion (0$^\circ$C) & 334000 & J/kg/K & \cite{bitz_1999} \\ 
    7474$\rho_i$ (rhoic) & Sea ice density & 917 & kg/m$^3$ & \cite{bitz_1999} \\ 
     
    154154\subsection{Dynamic formulation} 
    155155 
    156 The formulation of ice dynamics is based on the continuum approach. The latter holds provided the drift ice particles are much larger than single ice floes, and much smaller than typical gradient scales. This compromise is rarely achieved in practice \citep{lepp_ranta_2011}. Yet the continuum approach generates a convenient momentum equation for the horizontal ice velocity vector $\mathbf{u}=(u,v)$, which can be solved with classical numerical methods (here, finite differences on the NEMO C-grid). The most important term in the momentum equation is internal stress. We follow the viscous-plastic (VP) rheological framework \citep{hibler_1979}, assuming that sea ice has no tensile strength but responds to compressive and shear deformations in a plastic way. In practice, the elastic-viscous-plastic (EVP) technique of  \citep{bouillon_2013} is used, more convient numerically than VP.  It is well accepted that the VP rheology and its relatives are the minimum complexity to get reasonable ice drift patterns \citep{kreyscher_2000}, but fail at generating the observed deformation patterns \citep{girard_2009}. This is a long-lasting problem: what is the ideal rheological model for sea ice and how it should be applied are still being debated \citep[see, e.g.][]{weiss_2013}.  
     156The formulation of ice dynamics is based on the continuum approach. The latter holds provided the drift ice particles are much larger than single ice floes, and much smaller than typical gradient scales. This compromise is rarely achieved in practice \citep{lepparanta_2011}. Yet the continuum approach generates a convenient momentum equation for the horizontal ice velocity vector $\mathbf{u}=(u,v)$, which can be solved with classical numerical methods (here, finite differences on the NEMO C-grid). The most important term in the momentum equation is internal stress. We follow the viscous-plastic (VP) rheological framework \citep{hibler_1979}, assuming that sea ice has no tensile strength but responds to compressive and shear deformations in a plastic way. In practice, the elastic-viscous-plastic (EVP) technique of  \citep{bouillon_2013} is used, more convient numerically than VP.  It is well accepted that the VP rheology and its relatives are the minimum complexity to get reasonable ice drift patterns \citep{kreyscher_2000}, but fail at generating the observed deformation patterns \citep{girard_2009}. This is a long-lasting problem: what is the ideal rheological model for sea ice and how it should be applied are still being debated \citep[see, e.g.][]{weiss_2013}.  
    157157 
    158158%------------------------------------------------------------------------------------------------------------------------- 
     
    296296$C$ (rn\_crhg) & ice strength concentration param. & 20 & - & \citep{hibler_1979} \\ 
    297297$H^*$ (rn\_hstar) & maximum ridged ice thickness param. & 25 & m & \citep{lipscomb_2007} \\ 
    298 $p$ (rn\_por\_rdg) & porosity of new ridges & 0.3 & - & \citep{lepp_ranta_1995} \\ 
     298$p$ (rn\_por\_rdg) & porosity of new ridges & 0.3 & - & \citep{lepparanta_1995} \\ 
    299299$amax$ (rn\_amax) & maximum ice concentration & 0.999 & - & -\\ 
    300300$h_0$ (rn\_hnewice) & thickness of newly formed ice & 0.1 & m & - \\ 
     
    313313Transport connects the horizontal velocity fields and the rest of the ice properties. LIM assumes that the ice properties in the different thickness categories are transported at the same velocity. The scheme of \cite{prather_1986}, based on the conservation of 0, 1$^{st}$ and 2$^{nd}$ order moments in $x-$ and $y-$directions,  is used, with some numerical diffusion if desired. Whereas this scheme is accurate, nearly conservative, it is also quite expensive since, for each advected field, five moments need to be advected, which proves CPU consuming, in particular when multiple categories are used. Other solutions are currently explored. 
    314314 
    315 The dissipation of energy associated with plastic failure under convergence and shear is accomplished by rafting (overriding of two ice plates) and ridging (breaking of an ice plate and subsequent piling of the broken ice blocks into pressure ridges). Thin ice preferentially rafts whereas thick ice preferentially ridges \citep{tuhkuri_2002}. Because observations of these processes are limited, their representation in LIM is rather heuristic. The amount of ice that rafts/ridges depends on the strain rate tensor invariants (shear and divergence) as in \citep{flato_1995}, while the ice categories involved are determined by a participation function favouring thin ice \citep{lipscomb_2007}. The thickness of ice being deformed ($h'$) determines whether ice rafts ($h'<$ 0.75 m) or ridges ($h'>$ 0.75 m), following \cite{haapala_2000}. The deformed ice thickness is $2h'$ after rafting, and is distributed between $2h'$ and $2 \sqrt{H^*h'}$ after ridging, where $H^* = 25$ m \citep{lipscomb_2007}. Newly ridged ice is highly porous, effectively trapping seawater. To represent this, a prescribed volume fraction (30\%) of newly ridged ice \citep{lepp_ranta_1995} incorporates mass, salt and heat are extracted from the ocean. Hence, in contrast with other models, the net thermodynamic ice production during convergence is not zero in LIM, since mass is added to sea ice during ridging. Consequently, simulated new ridges have high temperature and salinity as observed \citep{h_yland_2002}. A fraction of snow (50 \%) falls into the ocean during deformation. 
     315The dissipation of energy associated with plastic failure under convergence and shear is accomplished by rafting (overriding of two ice plates) and ridging (breaking of an ice plate and subsequent piling of the broken ice blocks into pressure ridges). Thin ice preferentially rafts whereas thick ice preferentially ridges \citep{tuhkuri_2002}. Because observations of these processes are limited, their representation in LIM is rather heuristic. The amount of ice that rafts/ridges depends on the strain rate tensor invariants (shear and divergence) as in \citep{flato_1995}, while the ice categories involved are determined by a participation function favouring thin ice \citep{lipscomb_2007}. The thickness of ice being deformed ($h'$) determines whether ice rafts ($h'<$ 0.75 m) or ridges ($h'>$ 0.75 m), following \cite{haapala_2000}. The deformed ice thickness is $2h'$ after rafting, and is distributed between $2h'$ and $2 \sqrt{H^*h'}$ after ridging, where $H^* = 25$ m \citep{lipscomb_2007}. Newly ridged ice is highly porous, effectively trapping seawater. To represent this, a prescribed volume fraction (30\%) of newly ridged ice \citep{lepparanta_1995} incorporates mass, salt and heat are extracted from the ocean. Hence, in contrast with other models, the net thermodynamic ice production during convergence is not zero in LIM, since mass is added to sea ice during ridging. Consequently, simulated new ridges have high temperature and salinity as observed \citep{hoyland_2002}. A fraction of snow (50 \%) falls into the ocean during deformation. 
    316316 
    317317\section{Ice thermodynamics} 
  • NEMO/trunk/doc/latex/SI3/subfiles/chap_ridging_rafting.tex

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    7070\textbf{Rafting} is the piling of two ice sheets on top of each other. Rafting doubles the participating ice thickness and is a volume-conserving process. \cite{babko_2002} concluded that rafting plays a significant role during initial ice growth in fall, therefore we included it into the model.  
    7171 
    72 \textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepp_ranta_1995,h_yland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}. 
     72\textbf{Ridging} is the piling of a series of broken ice blocks into pressure ridges. Ridging redistributes participating ice on a various range of thicknesses. Ridging does not conserve ice volume, as pressure ridges are porous. Therefore, the volume of ridged ice is larger than the volume of new ice being ridged. In the model, newly ridged is has a prescribed porosity $p=30\%$ (\textit{ridge\_por} in \textit{namelist\_ice}), following observations \citep{lepparanta_1995,hoyland_2002}. The importance of ridging is now since the early works of \citep{thorndike_1975}. 
    7373 
    7474The deformation modes are formulated using \textbf{participation} and \textbf{transfer} functions with specific contributions from ridging and rafting: 
     
    115115\label{eq:nri} 
    116116\end{equation} 
    117 The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepp_ranta_1995,h_yland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice. 
     117The redistributor $\gamma(h',h)$ specifies how area of thickness $h'$ is redistributed on area of thickness $h$. We follow \citep{hibler_1980} who constructed a rule, based on observations, that forces all ice participating in ridging with thickness $h'$ to be linearly distributed between ice that is between $2h'$ and $2\sqrt{H^*h'}$ thick, where $H^\star=100$ m (\textit{Hstar} in \textit{namelist\_ice}). This in turn determines how to construct the ice volume redistribution function $\Psi^v$. Volumes equal to participating area times thickness are removed from thin ice. They are redistributed following Hibler's rule. The factor $(1+p)$ accounts for initial ridge porosity $p$ (\textit{ridge\_por} in \textit{namelist\_ice}, defined as the fractional volume of seawater initially included into ridges. In many previous models, the initial ridge porosity has been assumed to be 0, which is not the case in reality since newly formed ridges are porous, as indicated by in-situ observations \citep{lepparanta_1995,hoyland_2002}. In other words, LIM3 creates a higher volume of ridged ice with the same participating ice. 
    118118 
    119119For the numerical computation of the integrals, we have to compute several temporary values: 
     
    152152\section{Mechanical redistribution for other global ice variables} 
    153153 
    154 The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{h_yland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean. 
     154The other global ice state variables redistribution functions $\Psi^X$ are computed based on $\Psi^g$ for the ice age content and on $\Psi^{v^i}$ for the remainder (ice enthalpy and salt content, snow volume and enthalpy). The general principles behind this derivation are described in Appendix A of \cite{bitz_2001}. A fraction $f_s=0.5$ (\textit{fsnowrdg} and \textit{fsnowrft} in \textit{namelist\_ice}) of the snow volume and enthalpy is assumed to be lost during ridging and rafting and transferred to the ocean. The contribution of the seawater trapped into the porous ridges is included in the computation of the redistribution of ice enthalpy and salt content (i.e., $\Psi^{e^i}$ and $\Psi^{M^s}$). During this computation, seawater is supposed to be in thermal equilibrium with the surrounding ice blocks. Ridged ice desalination induces an implicit decrease in internal brine volume, and heat supply to the ocean, which accounts for ridge consolidation as described by \cite{hoyland_2002}. The inclusion of seawater in ridges does not imply any net change in ocean salinity. The energy used to cool down the seawater trapped in porous ridges until the seawater freezing point is rejected into the ocean. 
    155155 
    156156\end{document} 
  • NEMO/trunk/doc/latex/SI3/subfiles/introduction.tex

    r11031 r11043  
    1515 
    1616% Limitations & scope 
    17 %There are limitations to the applicability of models such as SI$^3$. The continuum approach is not invalid for grid cell size above at least 1 km, below which sea ice particles may include just a few floes, which is not sufficient \citep{lepp_ranta_2011}. Second, one must remember that our current knowledge of sea ice is not as complete as for the ocean: there are no fundamental equations such as Navier Stokes equations for sea ice. Besides, important features and processes span widely different scales, such as brine inclusions (1 $\mu$m-1 mm) \citep{perovich_1996}, horizontal thickness variations (1 m-100 km) \citep{percival_2008}, deformation and fracturing (10 m-1000 km) \citep{marsan_2004}. These impose complicated and often subjective subgrid-scale treatments. All in all, there is more empirism in sea ice models than in ocean models.  
     17%There are limitations to the applicability of models such as SI$^3$. The continuum approach is not invalid for grid cell size above at least 1 km, below which sea ice particles may include just a few floes, which is not sufficient \citep{lepparanta_2011}. Second, one must remember that our current knowledge of sea ice is not as complete as for the ocean: there are no fundamental equations such as Navier Stokes equations for sea ice. Besides, important features and processes span widely different scales, such as brine inclusions (1 $\mu$m-1 mm) \citep{perovich_1996}, horizontal thickness variations (1 m-100 km) \citep{percival_2008}, deformation and fracturing (10 m-1000 km) \citep{marsan_2004}. These impose complicated and often subjective subgrid-scale treatments. All in all, there is more empirism in sea ice models than in ocean models.  
    1818 
    1919In order to handle all the subsequent required subjective choices, we applied the following guidelines or principles: 
  • NEMO/trunk/doc/latex/TOP/main/TOP_manual.bib

    r11037 r11043  
    8787        CFC-113, CCl4, SF6 and N2O (NCEI Accession 0164584)}, 
    8888  year      = 2017, 
    89   doi    = {10.3334/cdiac/otg.cfc_atm_hist_2015}, 
     89  doi    = {10.3334/cdiac/otg.cfc\_atm\_hist\_2015}, 
    9090  url    = {https://accession.nodc.noaa.gov/0164584}, 
    9191  publisher = {NOAA National Centers for Environmental Information} 
     
    349349  number = {3–4}, 
    350350  issn      = {0033-8222}, 
    351   doi    = {10.2458/azu_js_rc.55.16402}, 
    352   url    = {http://dx.doi.org/10.2458/azu_js_rc.55.16402}, 
     351  doi    = {10.2458/azu\_js\_rc.55.16402}, 
     352  url    = {http://dx.doi.org/10.2458/azu\_js\_rc.55.16402}, 
    353353  journal   = {Radiocarbon}, 
    354354  publisher = {Cambridge University Press (CUP)} 
     
    422422        Béranger, K. and Schneider, A. and Beuvier, J. and Somot, 
    423423        S.}, 
    424   title     = {Simulated anthropogenic CO&lt;sub&gt;2&lt;/sub&gt; storage 
     424  title     = {Simulated anthropogenic CO$_{2}$ storage 
    425425        and acidification of the Mediterranean Sea}, 
    426426  year      = 2015, 
     
    448448  pages     = {1869–1887}, 
    449449  issn      = {1945-5755}, 
    450   doi    = {10.2458/azu_js_rc.55.16947}, 
    451   url    = {http://dx.doi.org/10.2458/azu_js_rc.55.16947}, 
     450  doi    = {10.2458/azu\_js\_rc.55.16947}, 
     451  url    = {http://dx.doi.org/10.2458/azu\_js\_rc.55.16947}, 
    452452  journal   = {Radiocarbon}, 
    453453  publisher = {Cambridge University Press (CUP)} 
     
    495495} 
    496496 
    497 @Article{     toggweiler_1989, 
     497@Article{     toggweiler_1989a, 
    498498  author = {Toggweiler, J. R. and Dixon, K. and Bryan, K.}, 
    499499  title     = {Simulations of radiocarbon in a coarse-resolution world 
     
    510510} 
    511511 
    512 @Article{     toggweiler_1989, 
     512@Article{     toggweiler_1989b, 
    513513  author = {Toggweiler, J. R. and Dixon, K. and Bryan, K.}, 
    514514  title     = {Simulations of radiocarbon in a coarse-resolution world 
     
    615615  doi    = {10.1016/j.tree.2012.10.021}, 
    616616  url    = {http://dx.doi.org/10.1016/j.tree.2012.10.021}, 
    617   journal   = {Trends in Ecology & Evolution}, 
    618   publisher = {Elsevier BV} 
    619 } 
     617  journal   = {Trends in Ecology \& Evolution}, 
     618  publisher = {Elsevier BV} 
     619} 
  • NEMO/trunk/doc/latex/TOP/main/TOP_manual.tex

    r11019 r11043  
    1212%% Custom style (.sty) 
    1313\usepackage{../../NEMO/main/NEMO_manual} 
     14\hypersetup{ 
     15  pdftitle={TOP – Tracers in Ocean Paradigm – The NEMO Tracers engine}, 
     16  pdfauthor={NEMO TOP Working Group}, 
     17  colorlinks 
     18} 
    1419 
    1520%% Include references and index for single subfile compilation 
  • NEMO/trunk/doc/latex/TOP/subfiles/model_description.tex

    r11032 r11043  
    2626\end{equation} 
    2727 
    28 where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{Madec_Bk2008}  
     28where expressions of $D^{lC}$ and $D^{vC}$ depend on the choice for the lateral and vertical subgrid scale parameterizations, see equations 5.10 and 5.11 in \citep{nemo_manual}  
    2929 
    3030{S(C)} , the first term on the right hand side of \ref{Eq_tracer}; is the SMS - Source Minus Sink - inherent to the tracer.  In the case of biological tracer such as phytoplankton, {S(C)} is the balance between phytoplankton growth and its decay through mortality and grazing. In the case of a tracer comprising carbon,  {S(C)} accounts for gas exchange, river discharge, flux to the sediments, gravitational sinking and other biological processes. In the case of a radioactive tracer, {S(C)} is simply loss due to radioactive decay. 
     
    6161        \item \textbf{AGE}     :    Water age tracking 
    6262        \item \textbf{MY\_TRC}  :   Template for creation of new modules and external BGC models coupling 
    63         \item \textbf{PISCES}    :   Built in BGC model. See \citep{Aumont_al_2015} for a throughout description. 
     63        \item \textbf{PISCES}    :   Built in BGC model. See \citep{aumont_2015} for a throughout description. 
    6464\end{itemize} 
    6565%  ---------------------------------------------------------- 
     
    7373\nlst{namtrc_adv} 
    7474%------------------------------------------------------------------------------------------------------------- 
    75 The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{Madec_Bk2008}. The choice of an advection scheme  can be selected independently and  can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by  setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics. 
     75The advection schemes used for the passive tracers are the same than the ones for $T$ and $S$ and described in section 5.1 of \citep{nemo_manual}. The choice of an advection scheme  can be selected independently and  can differ from the ones used for active tracers. This choice is made in the \textit{namtrc\_adv} namelist, by  setting to \textit{true} one and only one of the logicals \textit{ln\_trcadv\_xxx}, the same way of what is done for dynamics. 
    7676cen2, MUSCL2, and UBS are not \textit{positive} schemes meaning that negative values can appear in an initially strictly positive tracer field which is advected, implying that false extrema are permitted. Their use is not recommended on passive tracers 
    7777 
     
    8080\nlst{namtrc_ldf} 
    8181%------------------------------------------------------------------------------------------------------------- 
    82 In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{Madec_Bk2008}.  
     82In NEMO v4.0, the passive tracer diffusion has necessarily the same form as the active tracer diffusion, meaning that the numerical scheme must be the same. However the passive tracer mixing coefficient can be chosen as a multiple of the active ones by changing the value of \textit{rn\_ldf\_multi} in namelist \textit{namtrc\_ldf}. The choice of numerical scheme is then set  in the \ngn{namtra\_ldf} namelist for the dynamic described in section 5.2 of \citep{nemo_manual}.  
    8383 
    8484 
     
    145145 
    146146 
    147  This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{Danabasoglu_al_2014}. 
     147 This implementation was first used in the CORE-II intercomparison runs described e.g.\ in \citet{danabasoglu_2014}. 
    148148 
    149149\subsection{Inert carbons tracer} 
     
    178178Measuring the dissolved concentrations of the gases -- as well as the mixing ratios between them -- shows circulation pathways within the ocean as well as water mass ages (i.e. the time since last contact with the 
    179179atmosphere). This feature of the gases has made them valuable across a wide range of oceanographic problems. One use lies in ocean modelling, where they can be used to evaluate the realism of the circulation and  
    180 ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{Dutay_al_2002,Palmieri_2015}). \\ 
     180ventilation of models, key for understanding the behaviour of wider modelled marine biogeochemistry (e.g. \citep{dutay_2002,palmieri_2015}). \\ 
    181181 
    182182Modelling these gases (henceforth CFCs) in NEMO is done within the passive tracer transport module, TOP, using the conservation state equation \ref{Eq_tracer} 
     
    187187stable within the ocean, we assume that there are no sinks (i.e. no loss processes) within the ocean interior.  
    188188Consequently, the sinks-minus-sources term for CFCs consists only of their air-sea fluxes, $F_{cfc}$, as 
    189 described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{Orr_al_2017}: 
     189described in the Ocean Model Inter-comparison Project (OMIP) protocol \citep{orr_2017}: 
    190190 
    191191% Because CFCs being stable in the ocean, we consider that there is no CFCs sink. 
     
    213213Where $Sol$ is the gas solubility in mol~m$^{-3}$~pptv$^{-1}$, as defined in Equation \ref{equ_Sol_CFC};  
    214214and $P_{cfc}$ is the atmosphere concentration of the CFC (in parts per trillion by volume, pptv). 
    215 This latter concentration is provided to the model by the historical time-series of \citet{Bullister_2015}. 
     215This latter concentration is provided to the model by the historical time-series of \citet{bullister_2017}. 
    216216This includes bulk atmospheric concentrations of the CFCs for both hemispheres -- this is necessary because of  
    217217the geographical asymmetry in the production and release of CFCs to the atmosphere.  
     
    220220 
    221221The piston velocity $K_{w}$ is a function of 10~m wind speed (in m~s$^{-1}$) and sea surface temperature,  
    222 $T$ (in $^{\circ}$C), and is calculated here following \citet{Wanninkhof_1992}: 
     222$T$ (in $^{\circ}$C), and is calculated here following \citet{wanninkhof_1992}: 
    223223 
    224224\begin{eqnarray} 
     
    229229Where $X_{conv}$ = $\frac{0.01}{3600}$, a conversion factor that changes the piston velocity  
    230230from cm~h$^{-1}$ to m~s$^{-1}$;  
    231 $a$ is a constant re-estimated by \citet{Wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$); 
     231$a$ is a constant re-estimated by \citet{wanninkhof_2014} to 0.251 (in $\frac{cm~h^{-1}}{(m~s^{-1})^{2}}$); 
    232232and $u$ is the 10~m wind speed in m~s$^{-1}$ from either an atmosphere model or reanalysis atmospheric forcing. 
    233 $Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{Wanninkhof_2014} (see Table \ref{tab_Sc}). 
     233$Sc$ is the Schmidt number, and is calculated as follow, using coefficients from \citet{wanninkhof_2014} (see Table \ref{tab_Sc}). 
    234234 
    235235\begin{eqnarray} 
     
    240240The solubility, $Sol$, used in Equation \ref{equ_C_sat} is calculated in mol~l$^{-1}$~atm$^{-1}$,  
    241241and is specific for each gas.  
    242 It has been experimentally estimated by \citet{Warner_Weiss_1985} as a function of temperature  
     242It has been experimentally estimated by \citet{warner_1985} as a function of temperature  
    243243and salinity: 
    244244 
     
    363363where $\Rq_{\textrm{ref}}$ is a reference ratio. For the purpose of ocean ventilation studies $\Rq_{\textrm{ref}}$ is set to one. 
    364364 
    365 Here we adopt the approach of \cite{Fiadeiro_1982} and \cite{Toggweiler_al_1989a,Toggweiler_al_1989b} in which  the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$. 
    366 This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{Toggweiler_al_1989a,Mouchet_2013}. While in terms of 
    367 oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{Naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements. 
    368  
    369 This simplified approach also neglects the effects of fractionation (e.g.,  air-sea exchange) and of biological processes. Previous studies by \cite{Bacastow_MaierReimer_1990} and \cite{Joos_al_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not. 
    370 Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{Stuiver_Polach_1977} the model results are directly comparable to observations.  
     365Here we adopt the approach of \cite{fiadeiro_1982} and \cite{toggweiler_1989a,toggweiler_1989b} in which  the ratio $\Rq$ is transported rather than the individual concentrations C and $\cq$. 
     366This approach calls for a strong assumption, i.e., that of a homogeneous and constant dissolved inorganic carbon (DIC) field \citep{toggweiler_1989a,mouchet_2013}. While in terms of 
     367oceanic $\Dcq$, it yields similar results to approaches involving carbonate chemistry, it underestimates the bomb radiocarbon inventory because it assumes a constant air-sea $\cd$ disequilibrium (Mouchet, 2013). Yet, field reconstructions of the ocean bomb $\cq$ inventory are also biased low \citep{naegler_2009} since they assume that the anthropogenic perturbation did not affect ocean DIC since the pre-bomb epoch. For these reasons, bomb $\cq$ inventories obtained with the present method are directly comparable to reconstructions based on field measurements. 
     368 
     369This simplified approach also neglects the effects of fractionation (e.g.,  air-sea exchange) and of biological processes. Previous studies by \cite{bacastow_1990} and \cite{joos_1997} resulted in nearly identical $\Dcq$ distributions among experiments considering biology or not. 
     370Since observed $\Rq$ ratios are corrected for the isotopic fractionation when converted to the standard $\Dcq$ notation \citep{stuiver_1977} the model results are directly comparable to observations.  
    371371 
    372372Therefore the simplified approach is justified for the purpose of assessing the circulation and ventilation of OGCMs. 
     
    378378where $\lambda$ is the radiocarbon decay rate, ${\mathbf{u}}$ the 3-D velocity field, and $\mathbf{K}$ the diffusivity tensor. 
    379379 
    380 At the air-sea interface a Robin boundary condition \citep{Haine_2006} is applied to \eqref{eq:quick}, i.e., the flux 
     380At the air-sea interface a Robin boundary condition \citep{haine_2006} is applied to \eqref{eq:quick}, i.e., the flux 
    381381through the interface is proportional to the difference in the ratios between 
    382382the ocean and the atmosphere 
     
    391391 
    392392 
    393 The $\cd$ transfer velocity is based on the empirical formulation of \cite{Wanninkhof_1992} with chemical enhancement \citep{Wanninkhof_Knox_1996,Wanninkhof_2014}. The original formulation is modified to account for the reduction of the  air-sea exchange rate in the presence of sea ice. Hence 
     393The $\cd$ transfer velocity is based on the empirical formulation of \cite{wanninkhof_1992} with chemical enhancement \citep{wanninkhof_1996,wanninkhof_2014}. The original formulation is modified to account for the reduction of the  air-sea exchange rate in the presence of sea ice. Hence 
    394394\begin{equation} 
    395395\kappa_\cd=\left( K_W\,\mathrm{w}^2 + b  \right)\, (1-f_\mathrm{ice})\,\sqrt{660/Sc}, \label{eq:wanc14} 
     
    397397with $\mathrm{w}$ the wind magnitude, $f_\mathrm{ice}$ the fractional ice cover, and $Sc$ the Schmidt number. 
    398398$K_W$ in \eqref{eq:wanc14} is an empirical coefficient with dimension of an inverse velocity. 
    399 The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{Wanninkhof_1992} 
     399The chemical enhancement term $b$ is represented as a function of temperature $T$ \citep{wanninkhof_1992} 
    400400\begin{equation} 
    401401b=2.5 ( 0.5246 + 0.016256 T+ 0.00049946  * T^2 ). \label{eq:wanchem} 
     
    413413\label{sec:param} 
    414414 % 
    415 The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{Stuiver_Polach_1977}, which corresponds to a half-life of 5730 yr.\\[1pt] 
    416 % 
    417 The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{Wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{Weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt] 
     415The radiocarbon decay rate (\CODE{rlam14}; in \texttt{trcnam\_c14} module) is set to $\lambda=(1/8267)$ yr$^{-1}$ \citep{stuiver_1977}, which corresponds to a half-life of 5730 yr.\\[1pt] 
     416% 
     417The Schmidt number $Sc$, Eq. \eqref{eq:wanc14}, is calculated with the help of the formulation of \cite{wanninkhof_2014}. The $\cd$ solubility $K_0$ in \eqref{eq:Rspeed} is taken from \cite{weiss_1974}. $K_0$ and $Sc$ are computed with the OGCM temperature and salinity fields (\texttt{trcsms\_c14} module).\\[1pt] 
    418418% 
    419419The following parameters intervening in the air-sea exchange rate are set in \texttt{namelist\_c14}: 
    420420\begin{itemize} 
    421 \item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{Toggweiler_al_1989a,Orr_al_2001,Butzin_al_2005}. 
    422 % 
    423 \item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{Toggweiler_al_1989a,Wanninkhof_1992,Naegler_2009,Wanninkhof_2014}. 
    424 It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{Naegler_2009}. 
     421\item The reference DIC concentration $\overline{\Ct}$ (\CODE{xdicsur}) intervening in \eqref{eq:Rspeed} is classically set to 2 mol m$^{-3}$ \citep{toggweiler_1989a,orr_2001,butzin_2005}. 
     422% 
     423\item The value of the empirical coefficient $K_W$ (\CODE{xkwind}) in \eqref{eq:wanc14} depends on the wind field and on the model upper ocean mixing rate \citep{toggweiler_1989a,wanninkhof_1992,naegler_2009,wanninkhof_2014}. 
     424It should be adjusted so that the globally averaged $\cd$ piston velocity is $\kappa_\cd = 16.5\pm 3.2$ cm/h \citep{naegler_2009}. 
    425425%The sensitivity to this parametrization is discussed in section \ref{sec:result}. 
    426426% 
     
    440440\CODE{kc14typ}=0 
    441441 
    442 Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand  \cite[typical for deep-ocean, Fig 6 in][]{Key_al_2004}. 
    443  
    444 Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{Orr_al_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}). 
     442Unless otherwise specified in \texttt{namelist\_c14}, the atmospheric $\Rq_a$ (\CODE{rc14at}) is set to one, the atmospheric $\cd$ (\CODE{pco2at}) to 280 ppm, and the ocean $\Rq$ is initialized with \CODE{rc14init=0.85}, i.e., $\Dcq=$-150\textperthousand  \cite[typical for deep-ocean, Fig 6 in][]{key_2004}. 
     443 
     444Equilibrium experiment should last until 98\% of the ocean volume exhibit a drift of less than 0.001\textperthousand/year \citep{orr_2000}; this is usually achieved after few kyr (Fig. \ref{fig:drift}). 
    445445% 
    446446\begin{figure}[!h] 
     
    469469 
    470470The model  is integrated from a given initial date following the observed records provided from 1765 AD on ( Fig. \ref{fig:bomb}). 
    471 The file \texttt{atmc14.dat}  \cite[][\& I. Levin, personal comm.]{Enting_al_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S,    20S-20N \&    20N-90N. 
    472 Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{Orr_al_2000}. 
     471The file \texttt{atmc14.dat}  \cite[][\& I. Levin, personal comm.]{enting_1994} provides atmospheric $\Dcq$ for three latitudinal bands: 90S-20S,    20S-20N \&    20N-90N. 
     472Atmospheric $\cd$ in the file \texttt{splco2.dat} is obtained from a spline fit through ice core data and direct atmospheric measurements \cite[][\& J. Orr, personal comm.]{orr_2000}. 
    473473Dates in these forcing files are expressed as yr AD. 
    474474 
     
    496496Atmospheric $\Rq_a$ and $\cd$ are prescribed from forcing files. The ocean $\Rq$ is initialized with the value attributed to \CODE{rc14init} in \texttt{namelist\_c14}. 
    497497 
    498 The file \texttt{intcal13.14c} \citep{Reimer_al_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}. 
    499 The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on  the high resolution record from EPICA Dome C \citep{Monnin_al_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP  \citep{Ahn_Brook_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP.  
     498The file \texttt{intcal13.14c} \citep{reimer_2013} contains atmospheric $\Dcq$ from 0 to 50 kyr cal BP\footnote{cal BP: number of years before 1950 AD}. 
     499The $\cd$ forcing is provided in file \texttt{ByrdEdcCO2.txt}. The content of this file is based on  the high resolution record from EPICA Dome C \citep{monnin_2004} for the Holocene and the Transition, and on Byrd Ice Core CO2 Data for 20--90 kyr BP  \citep{ahn_2008}. These atmospheric values are reproduced in Fig. \ref{fig:paleo}. Dates in these files are expressed as yr BP.  
    500500 
    501501To ensure that the atmospheric forcing is applied properly as well as that output files contain consistent dates and inventories the experiment should be set up carefully. 
     
    539539The radiocarbon age is computed as  $(-1/\lambda) \ln{ \left( \Rq \right)}$, with zero age corresponding to $\Rq=1$.  
    540540 
    541 The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{Stuiver_Polach_1977} 
     541The reservoir age is the age difference between the ocean uppermost layer and the atmosphere. It is usually reported as conventional radiocarbon age; i.e., computed by means of the Libby radiocarbon mean life \cite[8033 yr;][]{stuiver_1977} 
    542542\begin{align} 
    543543{^{14}\tau_\mathrm{c}}= -8033 \; \ln \left(1 + \frac{\Dcq}{10^3}\right), \label{eq:convage} 
     
    549549N_A \Rq_\mathrm{oxa} \overline{\Ct} \left( \int_\Omega \Rq d\Omega \right) /10^{26}, \label{eq:inv} 
    550550\end{equation} 
    551 where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{Stuiver_Polach_1977}, and $\Omega$ is the ocean volume.  Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}. 
     551where $N_A$ is the Avogadro's number ($N_A=6.022\times10^{23}$ at/mol), $\Rq_\mathrm{oxa}$ is the oxalic acid radiocarbon standard \cite[$\Rq_\mathrm{oxa}=1.176\times10^{-12}$;][]{stuiver_1977}, and $\Omega$ is the ocean volume.  Bomb $\cq$ inventories are traditionally reported in units of $10^{26}$ atoms, hence the denominator in \eqref{eq:inv}. 
    552552 
    553553All transformations from second to year, and inversely, are performed with the help of the physical constant \CODE{rsiyea} the sideral year length expressed in seconds\footnote{The variable (\CODE{nyear\_len}) which reports the length in days of the previous/current/future year (see \textrm{oce\_trc.F90}) is not a constant. }. 
     
    564564Two versions of PISCES are available in NEMO v4.0 : 
    565565 
    566 PISCES-v2, by setting in namelist\_pisces\_ref  \np{ln\_p4z} to true,  can be seen as one of the many Monod models \citep{Monod_1942}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments  (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and  mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.  
    567  
    568 PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{Aumont_al_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus,  iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted  by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{Sterner_2002,Woods_Wilson_2013,Meunier_al_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{Takahashi_al_1985} and the -O/C ratio is set to 1.34 \citep{Kortzinger_al_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled. 
    569  
    570 There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{Honjo_1996,Armstrong_al_2002}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM. 
     566PISCES-v2, by setting in namelist\_pisces\_ref  \np{ln\_p4z} to true,  can be seen as one of the many Monod models \citep{monod_1958}. It assumes a constant Redfield ratio and phytoplankton growth depends on the external concentration in nutrients. There are twenty-four prognostic variables (tracers) including two phytoplankton compartments  (diatoms and nanophytoplankton), two zooplankton size-classes (microzooplankton and  mesozooplankton) and a description of the carbonate chemistry. Formulations in PISCES-v2 are based on a mixed Monod/Quota formalism: On one hand, stoichiometry of C/N/P is fixed and growth rate of phytoplankton is limited by the external availability in N, P and Si. On the other hand, the iron and silicium quotas are variable and growth rate of phytoplankton is limited by the internal availability in Fe. Various parameterizations can be activated in PISCES-v2, setting for instance the complexity of iron chemistry or the description of particulate organic materials.  
     567 
     568PISCES-QUOTA has been built on the PISCES-v2 model described in \citet{aumont_2015}. PISCES-QUOTA has thirty-nine prognostic compartments. Phytoplankton growth can be controlled by five modeled limiting nutrients: Nitrate and Ammonium, Phosphate, Silicate and Iron. Five living compartments are represented: Three phytoplankton size classes/groups corresponding to picophytoplankton, nanophytoplankton and diatoms, and two zooplankton size classes which are microzooplankton and mesozooplankton. For phytoplankton, the prognostic variables are the carbon, nitrogen, phosphorus,  iron, chlorophyll and silicon biomasses (the latter only for diatoms). This means that the N/C, P/C, Fe/C and Chl/C ratios of both phytoplankton groups as well as the Si/C ratio of diatoms are prognostically predicted  by the model. Zooplankton are assumed to be strictly homeostatic \citep[e.g.,][]{sterner_2003,woods_2013,meunier_2014}. As a consequence, the C/N/P/Fe ratios of these groups are maintained constant and are not allowed to vary. In PISCES, the Redfield ratios C/N/P are set to 122/16/1 \citep{takahashi_1985} and the -O/C ratio is set to 1.34 \citep{kortzinger_2001}. No silicified zooplankton is assumed. The bacterial pool is not yet explicitly modeled. 
     569 
     570There are three non-living compartments: Semi-labile dissolved organic matter, small sinking particles, and large sinking particles. As a consequence of the variable stoichiometric ratios of phytoplankton and of the stoichiometric regulation of zooplankton, elemental ratios in organic matter cannot be supposed constant anymore as that was the case in PISCES-v2. Indeed, the nitrogen, phosphorus, iron, silicon and calcite pools of the particles are now all explicitly modeled. The sinking speed of the particles is not altered by their content in calcite and biogenic silicate (''The ballast effect'', \citep{honjo_1996,armstrong_2001}). The latter particles are assumed to sink at the same speed as the large organic matter particles. All the non-living compartments experience aggregation due to turbulence and differential settling as well as Brownian coagulation for DOM. 
    571571 
    572572  
  • NEMO/trunk/doc/manual_build.sh

    r11033 r11043  
    4545   printf "\t  The export should be available at root\n" 
    4646   printf "\t  If not check LaTeX log in ./latex/$model/main/${model}_manual.log\n" 
     47   echo 
    4748done 
    4849 
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