Ignore:
Timestamp:
2019-05-23T15:51:08+02:00 (22 months ago)
Author:
nicolasmartin
Message:

Several fixes for the LaTeX compilation of the manuals

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NEMO/trunk/doc/latex/SI3
Files:
5 edited

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  • 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

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    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: 
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