Changeset 11422 for NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_DYN.tex

Timestamp:

2019-08-08T15:40:47+02:00 (5 years ago)

Author:

jchanut

Message:

#1791, merge with trunk

Location:

NEMO/branches/2019/fix_vvl_ticket1791/doc

Files:

• . (modified) (1 prop)
• latex (modified) (1 prop)
• latex/NEMO (modified) (1 prop)
• latex/NEMO/subfiles/chap_DYN.tex (modified) (58 diffs)

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures

NEMO/branches/2019/fix_vvl_ticket1791/doc/latex/NEMO/subfiles/chap_DYN.tex

@@ -65 +65 @@
 %           Horizontal divergence and relative vorticity
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Horizontal divergence and relative vorticity (\protect\mdl{divcur})}
+\subsection[Horizontal divergence and relative vorticity (\textit{divcur.F90})]
+{Horizontal divergence and relative vorticity (\protect\mdl{divcur})}
 \label{subsec:DYN_divcur}
 
@@ -101 +102 @@
 %           Sea Surface Height evolution
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})}
+\subsection[Horizontal divergence and relative vorticity (\textit{sshwzv.F90})]
+{Horizontal divergence and relative vorticity (\protect\mdl{sshwzv})}
 \label{subsec:DYN_sshwzv}
 
@@ -127 +129 @@
 Replacing $T$ by the number $1$ in the tracer equation and summing over the water column must lead to
 the sea surface height equation otherwise tracer content will not be conserved
-\citep{Griffies_al_MWR01, Leclair_Madec_OM09}.
+\citep{griffies.pacanowski.ea_MWR01, leclair.madec_OM09}.
 
 The vertical velocity is computed by an upward integration of the horizontal divergence starting at the bottom,
@@ -181 +183 @@
 %        Vorticity term 
 % -------------------------------------------------------------------------------------------------------------
-\subsection{Vorticity term (\protect\mdl{dynvor})}
+\subsection[Vorticity term (\textit{dynvor.F90})]
+{Vorticity term (\protect\mdl{dynvor})}
 \label{subsec:DYN_vor}
 %------------------------------------------nam_dynvor----------------------------------------------------
@@ -203 +206 @@
 %                 enstrophy conserving scheme
 %-------------------------------------------------------------
-\subsubsection{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})}
+\subsubsection[Enstrophy conserving scheme (\forcode{ln_dynvor_ens = .true.})]
+{Enstrophy conserving scheme (\protect\np{ln\_dynvor\_ens}\forcode{ = .true.})}
 \label{subsec:DYN_vor_ens}
 
@@ -226 +230 @@
 %                 energy conserving scheme
 %-------------------------------------------------------------
-\subsubsection{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})}
+\subsubsection[Energy conserving scheme (\forcode{ln_dynvor_ene = .true.})]
+{Energy conserving scheme (\protect\np{ln\_dynvor\_ene}\forcode{ = .true.})}
 \label{subsec:DYN_vor_ene}
 
@@ -246 +251 @@
 %                 mix energy/enstrophy conserving scheme
 %-------------------------------------------------------------
-\subsubsection{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.}) }
+\subsubsection[Mixed energy/enstrophy conserving scheme (\forcode{ln_dynvor_mix = .true.})]
+{Mixed energy/enstrophy conserving scheme (\protect\np{ln\_dynvor\_mix}\forcode{ = .true.})}
 \label{subsec:DYN_vor_mix}
 
@@ -271 +277 @@
 %                 energy and enstrophy conserving scheme
 %-------------------------------------------------------------
-\subsubsection{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.}) }
+\subsubsection[Energy and enstrophy conserving scheme (\forcode{ln_dynvor_een = .true.})]
+{Energy and enstrophy conserving scheme (\protect\np{ln\_dynvor\_een}\forcode{ = .true.})}
 \label{subsec:DYN_vor_een}
 
@@ -287 +294 @@
 Nevertheless, this technique strongly distort the phase and group velocity of Rossby waves....}
 
-A very nice solution to the problem of double averaging was proposed by \citet{Arakawa_Hsu_MWR90}.
+A very nice solution to the problem of double averaging was proposed by \citet{arakawa.hsu_MWR90}.
 The idea is to get rid of the double averaging by considering triad combinations of vorticity.
 It is noteworthy that this solution is conceptually quite similar to the one proposed by
-\citep{Griffies_al_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}).
-
-The \citet{Arakawa_Hsu_MWR90} vorticity advection scheme for a single layer is modified 
-for spherical coordinates as described by \citet{Arakawa_Lamb_MWR81} to obtain the EEN scheme. 
+\citep{griffies.gnanadesikan.ea_JPO98} for the discretization of the iso-neutral diffusion operator (see \autoref{apdx:C}).
+
+The \citet{arakawa.hsu_MWR90} vorticity advection scheme for a single layer is modified 
+for spherical coordinates as described by \citet{arakawa.lamb_MWR81} to obtain the EEN scheme. 
 First consider the discrete expression of the potential vorticity, $q$, defined at an $f$-point: 
 \[
@@ -309 +316 @@
 \begin{figure}[!ht]
   \begin{center}
-    \includegraphics[width=0.70\textwidth]{Fig_DYN_een_triad}
+    \includegraphics[width=\textwidth]{Fig_DYN_een_triad}
     \caption{
       \protect\label{fig:DYN_een_triad}
@@ -327 +334 @@
 (with a systematic reduction of $e_{3f}$ when a model level intercept the bathymetry)
 that tends to reinforce the topostrophy of the flow
-(\ie the tendency of the flow to follow the isobaths) \citep{Penduff_al_OS07}. 
+(\ie the tendency of the flow to follow the isobaths) \citep{penduff.le-sommer.ea_OS07}. 
 
 Next, the vorticity triads, $ {^i_j}\mathbb{Q}^{i_p}_{j_p}$ can be defined at a $T$-point as
@@ -356 +363 @@
 (\ie $\chi$=$0$) (see \autoref{subsec:C_vorEEN}). 
 Applied to a realistic ocean configuration, it has been shown that it leads to a significant reduction of
-the noise in the vertical velocity field \citep{Le_Sommer_al_OM09}.
+the noise in the vertical velocity field \citep{le-sommer.penduff.ea_OM09}.
 Furthermore, used in combination with a partial steps representation of bottom topography,
 it improves the interaction between current and topography,
-leading to a larger topostrophy of the flow \citep{Barnier_al_OD06, Penduff_al_OS07}. 
+leading to a larger topostrophy of the flow \citep{barnier.madec.ea_OD06, penduff.le-sommer.ea_OS07}. 
 
 %--------------------------------------------------------------------------------------------------------------
 %           Kinetic Energy Gradient term
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Kinetic energy gradient term (\protect\mdl{dynkeg})}
+\subsection[Kinetic energy gradient term (\textit{dynkeg.F90})]
+{Kinetic energy gradient term (\protect\mdl{dynkeg})}
 \label{subsec:DYN_keg}
 
@@ -384 +392 @@
 %           Vertical advection term
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Vertical advection term (\protect\mdl{dynzad}) }
+\subsection[Vertical advection term (\textit{dynzad.F90})]
+{Vertical advection term (\protect\mdl{dynzad})}
 \label{subsec:DYN_zad}
 
@@ -403 +412 @@
 When \np{ln\_dynzad\_zts}\forcode{ = .true.},
 a split-explicit time stepping with 5 sub-timesteps is used on the vertical advection term.
-This option can be useful when the value of the timestep is limited by vertical advection \citep{Lemarie_OM2015}. 
+This option can be useful when the value of the timestep is limited by vertical advection \citep{lemarie.debreu.ea_OM15}. 
 Note that in this case,
 a similar split-explicit time stepping should be used on vertical advection of tracer to ensure a better stability,
@@ -430 +439 @@
 %           Coriolis plus curvature metric terms
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Coriolis plus curvature metric terms (\protect\mdl{dynvor}) }
+\subsection[Coriolis plus curvature metric terms (\textit{dynvor.F90})]
+{Coriolis plus curvature metric terms (\protect\mdl{dynvor})}
 \label{subsec:DYN_cor_flux}
 
@@ -451 +461 @@
 %           Flux form Advection term
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Flux form advection term (\protect\mdl{dynadv}) }
+\subsection[Flux form advection term (\textit{dynadv.F90})]
+{Flux form advection term (\protect\mdl{dynadv})}
 \label{subsec:DYN_adv_flux}
 
@@ -475 +486 @@
 a $2^{nd}$ order centered finite difference scheme, CEN2,
 or a $3^{rd}$ order upstream biased scheme, UBS.
-The latter is described in \citet{Shchepetkin_McWilliams_OM05}.
+The latter is described in \citet{shchepetkin.mcwilliams_OM05}.
 The schemes are selected using the namelist logicals \np{ln\_dynadv\_cen2} and \np{ln\_dynadv\_ubs}. 
 In flux form, the schemes differ by the choice of a space and time interpolation to define the value of
@@ -484 +495 @@
 %                 2nd order centred scheme
 %-------------------------------------------------------------
-\subsubsection{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})}
+\subsubsection[CEN2: $2^{nd}$ order centred scheme (\forcode{ln_dynadv_cen2 = .true.})]
+{CEN2: $2^{nd}$ order centred scheme (\protect\np{ln\_dynadv\_cen2}\forcode{ = .true.})}
 \label{subsec:DYN_adv_cen2}
 
@@ -507 +519 @@
 %                 UBS scheme
 %-------------------------------------------------------------
-\subsubsection{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})}
+\subsubsection[UBS: Upstream Biased Scheme (\forcode{ln_dynadv_ubs = .true.})]
+{UBS: Upstream Biased Scheme (\protect\np{ln\_dynadv\_ubs}\forcode{ = .true.})}
 \label{subsec:DYN_adv_ubs}
 
@@ -523 +536 @@
 where $u"_{i+1/2} =\delta_{i+1/2} \left[ {\delta_i \left[ u \right]} \right]$.
 This results in a dissipatively dominant (\ie hyper-diffusive) truncation error
-\citep{Shchepetkin_McWilliams_OM05}.
-The overall performance of the advection scheme is similar to that reported in \citet{Farrow1995}.
+\citep{shchepetkin.mcwilliams_OM05}.
+The overall performance of the advection scheme is similar to that reported in \citet{farrow.stevens_JPO95}.
 It is a relatively good compromise between accuracy and smoothness.
 It is not a \emph{positive} scheme, meaning that false extrema are permitted.
@@ -542 +555 @@
 while the second term, which is the diffusion part of the scheme,
 is evaluated using the \textit{before} velocity (forward in time).
-This is discussed by \citet{Webb_al_JAOT98} in the context of the Quick advection scheme.
+This is discussed by \citet{webb.de-cuevas.ea_JAOT98} in the context of the Quick advection scheme.
 
 Note that the UBS and QUICK (Quadratic Upstream Interpolation for Convective Kinematics) schemes only differ by
 one coefficient.
-Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{Webb_al_JAOT98}.
+Replacing $1/6$ by $1/8$ in (\autoref{eq:dynadv_ubs}) leads to the QUICK advection scheme \citep{webb.de-cuevas.ea_JAOT98}.
 This option is not available through a namelist parameter, since the $1/6$ coefficient is hard coded.
 Nevertheless it is quite easy to make the substitution in the \mdl{dynadv\_ubs} module and obtain a QUICK scheme.
@@ -560 +573 @@
 %           Hydrostatic pressure gradient term
 % ================================================================
-\section{Hydrostatic pressure gradient (\protect\mdl{dynhpg})}
+\section[Hydrostatic pressure gradient (\textit{dynhpg.F90})]
+{Hydrostatic pressure gradient (\protect\mdl{dynhpg})}
 \label{sec:DYN_hpg}
 %------------------------------------------nam_dynhpg---------------------------------------------------
@@ -582 +596 @@
 %           z-coordinate with full step
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})}
+\subsection[Full step $Z$-coordinate (\forcode{ln_dynhpg_zco = .true.})]
+{Full step $Z$-coordinate (\protect\np{ln\_dynhpg\_zco}\forcode{ = .true.})}
 \label{subsec:DYN_hpg_zco}
 
@@ -627 +642 @@
 %           z-coordinate with partial step
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})}
+\subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps = .true.})]
+{Partial step $Z$-coordinate (\protect\np{ln\_dynhpg\_zps}\forcode{ = .true.})}
 \label{subsec:DYN_hpg_zps}
 
@@ -652 +668 @@
 
 Pressure gradient formulations in an $s$-coordinate have been the subject of a vast number of papers
-(\eg, \citet{Song1998, Shchepetkin_McWilliams_OM05}). 
+(\eg, \citet{song_MWR98, shchepetkin.mcwilliams_OM05}). 
 A number of different pressure gradient options are coded but the ROMS-like,
 density Jacobian with cubic polynomial method is currently disabled whilst known bugs are under investigation.
 
-$\bullet$ Traditional coding (see for example \citet{Madec_al_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.})
+$\bullet$ Traditional coding (see for example \citet{madec.delecluse.ea_JPO96}: (\np{ln\_dynhpg\_sco}\forcode{ = .true.})
 \begin{equation}
   \label{eq:dynhpg_sco}
@@ -679 +695 @@
 $\bullet$ Pressure Jacobian scheme (prj) (a research paper in preparation) (\np{ln\_dynhpg\_prj}\forcode{ = .true.})
 
-$\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{Shchepetkin_McWilliams_OM05} 
+$\bullet$ Density Jacobian with cubic polynomial scheme (DJC) \citep{shchepetkin.mcwilliams_OM05} 
 (\np{ln\_dynhpg\_djc}\forcode{ = .true.}) (currently disabled; under development)
 
 Note that expression \autoref{eq:dynhpg_sco} is commonly used when the variable volume formulation is activated
 (\key{vvl}) because in that case, even with a flat bottom,
-the coordinate surfaces are not horizontal but follow the free surface \citep{Levier2007}.
+the coordinate surfaces are not horizontal but follow the free surface \citep{levier.treguier.ea_rpt07}.
 The pressure jacobian scheme (\np{ln\_dynhpg\_prj}\forcode{ = .true.}) is available as
 an improved option to \np{ln\_dynhpg\_sco}\forcode{ = .true.} when \key{vvl} is active.
@@ -704 +720 @@
 corresponds to the water replaced by the ice shelf.
 This top pressure is constant over time.
-A detailed description of this method is described in \citet{Losch2008}.\\
+A detailed description of this method is described in \citet{losch_JGR08}.\\
 
 The pressure gradient due to ocean load is computed using the expression \autoref{eq:dynhpg_sco} described in
@@ -712 +728 @@
 %           Time-scheme
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .true./.false.})}
+\subsection[Time-scheme (\forcode{ln_dynhpg_imp = .{true,false}.})]
+{Time-scheme (\protect\np{ln\_dynhpg\_imp}\forcode{ = .\{true,false\}}.)}
 \label{subsec:DYN_hpg_imp}
 
@@ -722 +739 @@
 the physical phenomenon that controls the time-step is internal gravity waves (IGWs).
 A semi-implicit scheme for doubling the stability limit associated with IGWs can be used
-\citep{Brown_Campana_MWR78, Maltrud1998}.
+\citep{brown.campana_MWR78, maltrud.smith.ea_JGR98}.
 It involves the evaluation of the hydrostatic pressure gradient as
 an average over the three time levels $t-\rdt$, $t$, and $t+\rdt$
@@ -773 +790 @@
 % Surface Pressure Gradient
 % ================================================================
-\section{Surface pressure gradient (\protect\mdl{dynspg})}
+\section[Surface pressure gradient (\textit{dynspg.F90})]
+{Surface pressure gradient (\protect\mdl{dynspg})}
 \label{sec:DYN_spg}
 %-----------------------------------------nam_dynspg----------------------------------------------------
@@ -790 +808 @@
 which imposes a very small time step when an explicit time stepping is used.
 Two methods are proposed to allow a longer time step for the three-dimensional equations: 
-the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt}), 
+the filtered free surface, which is a modification of the continuous equations (see \autoref{eq:PE_flt?}), 
 and the split-explicit free surface described below.
 The extra term introduced in the filtered method is calculated implicitly, 
@@ -811 +829 @@
 % Explicit free surface formulation
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Explicit free surface (\protect\key{dynspg\_exp})}
+\subsection[Explicit free surface (\texttt{\textbf{key\_dynspg\_exp}})]
+{Explicit free surface (\protect\key{dynspg\_exp})}
 \label{subsec:DYN_spg_exp}
 
@@ -837 +856 @@
 % Split-explict free surface formulation
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Split-explicit free surface (\protect\key{dynspg\_ts})}
+\subsection[Split-explicit free surface (\texttt{\textbf{key\_dynspg\_ts}})]
+{Split-explicit free surface (\protect\key{dynspg\_ts})}
 \label{subsec:DYN_spg_ts}
 %------------------------------------------namsplit-----------------------------------------------------------
@@ -845 +865 @@
 
 The split-explicit free surface formulation used in \NEMO (\key{dynspg\_ts} defined),
-also called the time-splitting formulation, follows the one proposed by \citet{Shchepetkin_McWilliams_OM05}.
+also called the time-splitting formulation, follows the one proposed by \citet{shchepetkin.mcwilliams_OM05}.
 The general idea is to solve the free surface equation and the associated barotropic velocity equations with
 a smaller time step than $\rdt$, the time step used for the three dimensional prognostic variables
@@ -862 +882 @@
 \begin{equation}
   \label{eq:BT_dyn}
-  \frac{\partial {\rm \overline{{\bf U}}_h} }{\partial t}=
-  -f\;{\rm {\bf k}}\times {\rm \overline{{\bf U}}_h}
-  -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \rm {\overline{{\bf U}}_h} + \rm {\overline{\bf G}}
+  \frac{\partial {\mathrm \overline{{\mathbf U}}_h} }{\partial t}=
+  -f\;{\mathrm {\mathbf k}}\times {\mathrm \overline{{\mathbf U}}_h}
+  -g\nabla _h \eta -\frac{c_b^{\textbf U}}{H+\eta} \mathrm {\overline{{\mathbf U}}_h} + \mathrm {\overline{\mathbf G}}
 \end{equation}
 \[
   % \label{eq:BT_ssh}
-  \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\rm{\bf \overline{U}}}_h \,} \right]+P-E
+  \frac{\partial \eta }{\partial t}=-\nabla \cdot \left[ {\left( {H+\eta } \right) \; {\mathrm{\mathbf \overline{U}}}_h \,} \right]+P-E
 \]
 % \end{subequations}
-where $\rm {\overline{\bf G}}$ is a forcing term held constant, containing coupling term between modes,
+where $\mathrm {\overline{\mathbf G}}$ is a forcing term held constant, containing coupling term between modes,
 surface atmospheric forcing as well as slowly varying barotropic terms not explicitly computed to gain efficiency.
 The third term on the right hand side of \autoref{eq:BT_dyn} represents the bottom stress
 (see section \autoref{sec:ZDF_bfr}), explicitly accounted for at each barotropic iteration.
 Temporal discretization of the system above follows a three-time step Generalized Forward Backward algorithm
-detailed in \citet{Shchepetkin_McWilliams_OM05}.
+detailed in \citet{shchepetkin.mcwilliams_OM05}.
 AB3-AM4 coefficients used in \NEMO follow the second-order accurate,
-"multi-purpose" stability compromise as defined in \citet{Shchepetkin_McWilliams_Bk08}
+"multi-purpose" stability compromise as defined in \citet{shchepetkin.mcwilliams_ibk09}
 (see their figure 12, lower left). 
 
@@ -884 +904 @@
 \begin{figure}[!t]
   \begin{center}
-    \includegraphics[width=0.7\textwidth]{Fig_DYN_dynspg_ts}
+    \includegraphics[width=\textwidth]{Fig_DYN_dynspg_ts}
     \caption{
       \protect\label{fig:DYN_dynspg_ts}
@@ -936 +956 @@
 and time splitting not compatible.
 Advective barotropic velocities are obtained by using a secondary set of filtering weights,
-uniquely defined from the filter coefficients used for the time averaging (\citet{Shchepetkin_McWilliams_OM05}).
+uniquely defined from the filter coefficients used for the time averaging (\citet{shchepetkin.mcwilliams_OM05}).
 Consistency between the time averaged continuity equation and the time stepping of tracers is here the key to
 obtain exact conservation.
@@ -953 +973 @@
 external gravity waves in idealized or weakly non-linear cases.
 Although the damping is lower than for the filtered free surface,
-it is still significant as shown by \citet{Levier2007} in the case of an analytical barotropic Kelvin wave.
+it is still significant as shown by \citet{levier.treguier.ea_rpt07} in the case of an analytical barotropic Kelvin wave.
 
 %>>>>>===============
@@ -1051 +1071 @@
 the leap-frog splitting mode in equation \autoref{eq:DYN_spg_ts_ssh}.
 We have tried various forms of such filtering,
-with the following method discussed in \cite{Griffies_al_MWR01} chosen due to
+with the following method discussed in \cite{griffies.pacanowski.ea_MWR01} chosen due to
 its stability and reasonably good maintenance of tracer conservation properties (see ??).
 
@@ -1081 +1101 @@
 % Filtered free surface formulation
 %--------------------------------------------------------------------------------------------------------------
-\subsection{Filtered free surface (\protect\key{dynspg\_flt})}
+\subsection[Filtered free surface (\texttt{\textbf{key\_dynspg\_flt}})]
+{Filtered free surface (\protect\key{dynspg\_flt})}
 \label{subsec:DYN_spg_fltp}
 
-The filtered formulation follows the \citet{Roullet_Madec_JGR00} implementation. 
+The filtered formulation follows the \citet{roullet.madec_JGR00} implementation. 
 The extra term introduced in the equations (see \autoref{subsec:PE_free_surface}) is solved implicitly. 
 The elliptic solvers available in the code are documented in \autoref{chap:MISC}.
@@ -1092 +1113 @@
   \[
     % \label{eq:spg_flt}
-    \frac{\partial {\rm {\bf U}}_h }{\partial t}= {\rm {\bf M}}
+    \frac{\partial {\mathrm {\mathbf U}}_h }{\partial t}= {\mathrm {\mathbf M}}
     - g \nabla \left( \tilde{\rho} \ \eta \right)
     - g \ T_c \nabla \left( \widetilde{\rho} \ \partial_t \eta \right)
@@ -1098 +1119 @@
   where $T_c$, is a parameter with dimensions of time which characterizes the force,
   $\widetilde{\rho} = \rho / \rho_o$ is the dimensionless density,
-  and $\rm {\bf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,
+  and $\mathrm {\mathbf M}$ represents the collected contributions of the Coriolis, hydrostatic pressure gradient,
   non-linear and viscous terms in \autoref{eq:PE_dyn}.
 }   %end gmcomment
@@ -1109 +1130 @@
 % Lateral diffusion term
 % ================================================================
-\section{Lateral diffusion term and operators (\protect\mdl{dynldf})}
+\section[Lateral diffusion term and operators (\textit{dynldf.F90})]
+{Lateral diffusion term and operators (\protect\mdl{dynldf})}
 \label{sec:DYN_ldf}
 %------------------------------------------nam_dynldf----------------------------------------------------
@@ -1143 +1165 @@
 
 % ================================================================
-\subsection[Iso-level laplacian (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})]
-            {Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})}
+\subsection[Iso-level laplacian (\forcode{ln_dynldf_lap = .true.})]
+{Iso-level laplacian operator (\protect\np{ln\_dynldf\_lap}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_lap}
 
@@ -1152 +1174 @@
   \left\{
     \begin{aligned}
-      D_u^{l{\rm {\bf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}
+      D_u^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{1u} }\delta_{i+1/2} \left[ {A_T^{lm}
           \;\chi } \right]-\frac{1}{e_{2u} {\kern 1pt}e_{3u} }\delta_j \left[ 
         {A_f^{lm} \;e_{3f} \zeta } \right] \\ \\
-      D_v^{l{\rm {\bf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}
+      D_v^{l{\mathrm {\mathbf U}}} =\frac{1}{e_{2v} }\delta_{j+1/2} \left[ {A_T^{lm}
           \;\chi } \right]+\frac{1}{e_{1v} {\kern 1pt}e_{3v} }\delta_i \left[ 
         {A_f^{lm} \;e_{3f} \zeta } \right]
@@ -1169 +1191 @@
 %           Rotated laplacian operator
 %--------------------------------------------------------------------------------------------------------------
-\subsection[Rotated laplacian (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})]
-            {Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})}
+\subsection[Rotated laplacian (\forcode{ln_dynldf_iso = .true.})]
+{Rotated laplacian operator (\protect\np{ln\_dynldf\_iso}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_iso}
 
@@ -1228 +1250 @@
 %           Iso-level bilaplacian operator
 %--------------------------------------------------------------------------------------------------------------
-\subsection[Iso-level bilaplacian (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})]
-            {Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})}
+\subsection[Iso-level bilaplacian (\forcode{ln_dynldf_bilap = .true.})]
+{Iso-level bilaplacian operator (\protect\np{ln\_dynldf\_bilap}\forcode{ = .true.})}
 \label{subsec:DYN_ldf_bilap}
 
@@ -1243 +1265 @@
 %           Vertical diffusion term
 % ================================================================
-\section{Vertical diffusion term (\protect\mdl{dynzdf})}
+\section[Vertical diffusion term (\textit{dynzdf.F90})]
+{Vertical diffusion term (\protect\mdl{dynzdf})}
 \label{sec:DYN_zdf}
 %----------------------------------------------namzdf------------------------------------------------------
@@ -1326 +1349 @@
 There are two main options for wetting and drying code (wd):
 (a) an iterative limiter (il) and (b) a directional limiter (dl).
-The directional limiter is based on the scheme developed by \cite{WarnerEtal13} for RO
+The directional limiter is based on the scheme developed by \cite{warner.defne.ea_CG13} for RO
 MS
-which was in turn based on ideas developed for POM by \cite{Oey06}. The iterative
+which was in turn based on ideas developed for POM by \cite{oey_OM06}. The iterative
 limiter is a new scheme.  The iterative limiter is activated by setting $\mathrm{ln\_wd\_il} = \mathrm{.true.}$
 and $\mathrm{ln\_wd\_dl} = \mathrm{.false.}$. The directional limiter is activated
@@ -1372 +1395 @@
 %   Iterative limiters
 %-----------------------------------------------------------------------------------------
-\subsection   [Directional limiter (\textit{wet\_dry})]
-         {Directional limiter (\mdl{wet\_dry})}
+\subsection[Directional limiter (\textit{wet\_dry.F90})]
+{Directional limiter (\mdl{wet\_dry})}
 \label{subsec:DYN_wd_directional_limiter}
 The principal idea of the directional limiter is that
@@ -1400 +1423 @@
 
 
-\cite{WarnerEtal13} state that in their scheme the velocity masks at the cell faces for the baroclinic
+\cite{warner.defne.ea_CG13} state that in their scheme the velocity masks at the cell faces for the baroclinic
 timesteps are set to 0 or 1 depending on whether the average of the masks over the barotropic sub-steps is respectively less than
 or greater than 0.5. That scheme does not conserve tracers in integrations started from constant tracer
@@ -1412 +1435 @@
 %-----------------------------------------------------------------------------------------
 
-\subsection   [Iterative limiter (\textit{wet\_dry})]
-         {Iterative limiter (\mdl{wet\_dry})}
+\subsection[Iterative limiter (\textit{wet\_dry.F90})]
+{Iterative limiter (\mdl{wet\_dry})}
 \label{subsec:DYN_wd_iterative_limiter}
 
-\subsubsection [Iterative flux limiter (\textit{wet\_dry})]
-         {Iterative flux limiter (\mdl{wet\_dry})}
+\subsubsection[Iterative flux limiter (\textit{wet\_dry.F90})]
+{Iterative flux limiter (\mdl{wet\_dry})}
 \label{subsubsec:DYN_wd_il_spg_limiter}
 
@@ -1494 +1517 @@
 \end{equation}
 
-Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\it [Q: Why is
+Note a small tolerance ($\mathrm{rn\_wdmin2}$) has been introduced here {\itshape [Q: Why is
 this necessary/desirable?]}. Substituting from (\ref{dyn_wd_continuity_coef}) gives an
 expression for the coefficient needed to multiply the outward flux at this cell in order
@@ -1522 +1545 @@
 %      Surface pressure gradients
 %----------------------------------------------------------------------------------------
-\subsubsection   [Modification of surface pressure gradients (\textit{dynhpg})]
-         {Modification of surface pressure gradients (\mdl{dynhpg})}
+\subsubsection[Modification of surface pressure gradients (\textit{dynhpg.F90})]
+{Modification of surface pressure gradients (\mdl{dynhpg})}
 \label{subsubsec:DYN_wd_il_spg}
 
@@ -1541 +1564 @@
 %>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
 \begin{figure}[!ht] \begin{center}
-\includegraphics[width=0.8\textwidth]{Fig_WAD_dynhpg}
+\includegraphics[width=\textwidth]{Fig_WAD_dynhpg}
 \caption{ \label{Fig_WAD_dynhpg}
 Illustrations of the three possible combinations of the logical variables controlling the
@@ -1588 +1611 @@
 conditions.
 
-\subsubsection   [Additional considerations (\textit{usrdef\_zgr})]
-         {Additional considerations (\mdl{usrdef\_zgr})}
+\subsubsection[Additional considerations (\textit{usrdef\_zgr.F90})]
+{Additional considerations (\mdl{usrdef\_zgr})}
 \label{subsubsec:WAD_additional}
 
@@ -1603 +1626 @@
 %      The WAD test cases
 %----------------------------------------------------------------------------------------
-\subsection   [The WAD test cases (\textit{usrdef\_zgr})]
-         {The WAD test cases (\mdl{usrdef\_zgr})}
+\subsection[The WAD test cases (\textit{usrdef\_zgr.F90})]
+{The WAD test cases (\mdl{usrdef\_zgr})}
 \label{WAD_test_cases}
 
@@ -1614 +1637 @@
 % Time evolution term 
 % ================================================================
-\section{Time evolution term (\protect\mdl{dynnxt})}
+\section[Time evolution term (\textit{dynnxt.F90})]
+{Time evolution term (\protect\mdl{dynnxt})}
 \label{sec:DYN_nxt}
 

@@ -1 @@
-*.aux
-*.bbl
-*.blg
-*.dvi
-*.fdb*
-*.fls
-*.idx
-*.ilg
-*.ind
-*.log
-*.maf
-*.mtc*
-*.out
-*.pdf
-*.toc
-_minted-*
+figures