diff --git a/latex/NEMO/subfiles/chap_DYN.tex b/latex/NEMO/subfiles/chap_DYN.tex
index cc04666fdc480479ff209828a6c8e3d1ad1cab7b..b90ac9ddfac4212d71b1e9b4807c2729e30b6792 100644
--- a/latex/NEMO/subfiles/chap_DYN.tex
+++ b/latex/NEMO/subfiles/chap_DYN.tex
@@ -149,11 +149,11 @@ taking into account the change of the thickness of the levels:
   \right.
 \end{equation}
 
-In the case of a non-linear free surface (key{qco}), the top vertical velocity is $-\textit{emp}/\rho_w$,
+In the case of a non-linear free surface (\key{qco}), the top vertical velocity is $-\textit{emp}/\rho_w$,
 as changes in the divergence of the barotropic transport are absorbed into the change of the level thicknesses,
 re-orientated downward.
 \cmtgm{not sure of this...  to be modified with the change in emp setting}
-In the case of a linear free surface(key{linssh}), the time derivative in \autoref{eq:DYN_wzv} disappears.
+In the case of a linear free surface(\key{linssh}), the time derivative in \autoref{eq:DYN_wzv} disappears.
 The upper boundary condition applies at a fixed level $z=0$.
 The top vertical velocity is thus equal to the divergence of the barotropic transport
 (\ie\ the first term in the right-hand-side of \autoref{eq:DYN_spg_ssh}).
@@ -572,6 +572,10 @@ since HPG is a \emph{horizontal} pressure gradient, \ie\ computed along geopoten
 As a result, any tilt of the surface of the computational levels will require a specific treatment to
 compute the hydrostatic pressure gradient.
 
+In v5.0 partial cells are considered as penalized cells. A penalized cell has a solid fraction and 
+a liquid fraction, both are distributed homogeneouly across the cell. Therefore adjacent cells are not
+expected to live at distinct depth because of their content differences. 
+
 The hydrostatic pressure gradient term is evaluated either using a leapfrog scheme,
 \ie\ the density appearing in its expression is centred in time (\emph{now} $\rho$),
 or a RK3 scheme \ie\ the density appearing in its expression is forward in time (\emph{before} $\rho$),