diff --git a/latex/NEMO/subfiles/chap_DYN.tex b/latex/NEMO/subfiles/chap_DYN.tex
index 714769e6766c955158e3e740f9d23bfd81288161..cc70720a74ada721f5bf5490143cdf2320827b87 100644
--- a/latex/NEMO/subfiles/chap_DYN.tex
+++ b/latex/NEMO/subfiles/chap_DYN.tex
@@ -622,25 +622,6 @@ for $1<k<km$ (interior layer)
 Note that the $1/2$ factor in (\autoref{eq:DYN_hpg_zco_surf}) is adequate because of the definition of $e_{3w}$ as
 the vertical derivative of the scale factor at the surface level ($z=0$).
 
-%% =================================================================================================
-\subsection[Partial step $Z$-coordinate (\forcode{ln_dynhpg_zps})]{Partial step $Z$-coordinate (\protect\np{ln_dynhpg_zps}{ln\_dynhpg\_zps})}
-\label{subsec:DYN_hpg_zps}
-
-With partial bottom cells, tracers in horizontally adjacent cells generally live at different depths.
-Before taking horizontal gradients between these tracer points,
-a linear interpolation is used to approximate the deeper tracer as if
-it actually lived at the depth of the shallower tracer point.
-
-Apart from this modification,
-the horizontal hydrostatic pressure gradient evaluated in the $z$-coordinate with partial step is exactly as in
-the pure $z$-coordinate case.
-As explained in detail in section \autoref{sec:TRA_zpshde},
-the nonlinearity of pressure effects in the equation of state is such that
-it is better to interpolate temperature and salinity vertically before computing the density.
-Horizontal gradients of temperature and salinity are needed for the TRA modules,
-which is the reason why the horizontal gradients of density at the deepest model level are computed in
-module \mdl{zpsdhe} located in the TRA directory and described in \autoref{sec:TRA_zpshde}.
-
 %% =================================================================================================
 \subsection{$S$- and $Z$-$S$-coordinates}
 \label{subsec:DYN_hpg_sco}
@@ -846,7 +827,7 @@ a smaller time step than $\rdt$, the time step used for the three dimensional pr
 (\autoref{fig:DYN_spg_ts}).
 The size of the small time step, $\rdt_e$ (the external mode or barotropic time step) is provided through
 the \np{nn_e}{nn\_e} namelist parameter as: $\rdt_e = \rdt / nn\_e$.
-This parameter can be optionally defined automatically (\np[=.true.]{ln_bt_nn_auto}{ln\_bt\_nn\_auto}) considering that
+This parameter can be optionally defined automatically (\np[=.true.]{ln_bt_auto}{ln\_bt\_auto}) considering that
 the stability of the barotropic system is essentially controled by external waves propagation.
 Maximum Courant number is in that case time independent, and easily computed online from the input bathymetry.
 Therefore, $\rdt_e$ is adjusted so that the Maximum allowed Courant number is smaller than \np{rn_bt_cmax}{rn\_bt\_cmax}.
@@ -892,26 +873,26 @@ AB3-AM4 coefficients used in \NEMO\ follow the second-order accurate,
     The former are used to obtain time filtered quantities at $t+\rdt$ while
     the latter are used to obtain time averaged transports to advect tracers.
     a) Forward time integration:
-    \protect\np[=.true.]{ln_bt_fw}{ln\_bt\_fw},  \protect\np[=.true.]{ln_bt_av}{ln\_bt\_av}.
+    \protect\np[=1]{nn_bt_flt}{nn\_bt\_flt}.
     b) Centred time integration:
-    \protect\np[=.false.]{ln_bt_fw}{ln\_bt\_fw}, \protect\np[=.true.]{ln_bt_av}{ln\_bt\_av}.
+    \protect\np[=2]{nn_bt_flt}{nn\_bt\_flt}.
     c) Forward time integration with no time filtering (POM-like scheme):
-    \protect\np[=.true.]{ln_bt_fw}{ln\_bt\_fw},  \protect\np[=.false.]{ln_bt_av}{ln\_bt\_av}.}
+    \protect\np[=3]{nn_bt_flt}{nn\_bt\_flt}.}
   \label{fig:DYN_spg_ts}
 \end{figure}
 
-In the default case (\np[=.true.]{ln_bt_fw}{ln\_bt\_fw}),
+In the default case (\protect\np[=1]{nn_bt_flt}{nn\_bt\_flt}),
 the external mode is integrated between \textit{now} and \textit{after} baroclinic time-steps
 (\autoref{fig:DYN_spg_ts}a).
 To avoid aliasing of fast barotropic motions into three dimensional equations,
-time filtering is eventually applied on barotropic quantities (\np[=.true.]{ln_bt_av}{ln\_bt\_av}).
+time filtering is eventually applied on barotropic quantities.
 In that case, the integration is extended slightly beyond \textit{after} time step to
 provide time filtered quantities.
 These are used for the subsequent initialization of the barotropic mode in the following baroclinic step.
 Since external mode equations written at baroclinic time steps finally follow a forward time stepping scheme,
 asselin filtering is not applied to barotropic quantities.\\
 Alternatively, one can choose to integrate barotropic equations starting from \textit{before} time step
-(\np[=.false.]{ln_bt_fw}{ln\_bt\_fw}).
+(\protect\np[=2]{nn_bt_flt}{nn\_bt\_flt}).
 Although more computationaly expensive ( \np{nn_e}{nn\_e} additional iterations are indeed necessary),
 the baroclinic to barotropic forcing term given at \textit{now} time step become centred in
 the middle of the integration window.
@@ -934,7 +915,7 @@ obtain exact conservation.
 
 
 One can eventually choose to feedback instantaneous values by not using any time filter
-(\np[=.false.]{ln_bt_av}{ln\_bt\_av}).
+(\protect\np[=3]{nn_bt_flt}{nn\_bt\_flt}).
 In that case, external mode equations are continuous in time,
 \ie\ they are not re-initialized when starting a new sub-stepping sequence.
 This is the method used in the POM model for example, the stability being maintained by