All changes to reference manual for GEOMETRIC parameterisation (includes...

All changes to reference manual for GEOMETRIC parameterisation (includes updates to namelists submodule to point to previously committed changes to namelists)

latex/NEMO/main/bibliography.bib

@@ -972,6 +972,22 @@
   doi           = {10.5194/gmd-12-2255-2019}
 }
 
+@article{         ferreira.marshall.ea_JPO05,
+  title         = "Estimating eddy stresses by fitting dynamics to observations
+                  using a residual-mean ocean circulation model and its
+                  adjoint",
+  pages         = "1891--1910",
+  journal       = "Journal of Physical Oceanography",
+  volume        = "35",
+  number        = "10",
+  author        = "D. Ferreira and J. Marshall and P. Heimbach",
+  year          = "2005",
+  month         = "oct",
+  publisher     = "American Meteorological Society",
+  issn          = "1520-0485",
+  doi           = "10.1175/JPO2785.1"
+}
+
 @article{         flather_JPO94,
   title         = "A storm surge prediction model for the northern Bay of
                   Bengal with application to the cyclone disaster in April
@@ -2250,6 +2266,37 @@ DOI = {10.5194/gmd-15-1567-2022}
   doi           = "10.1029/1998jc900013"
 }
 
+@article{         mak.marshall.ea_GRL22,
+  title         = "Acute sensitivity of global ocean circulation and heat
+                  content to eddy energy dissipation timescale",
+  pages         = "e2021GL097259",
+  journal       = "Geophysical Research Letters",
+  volume        = "49",
+  number        = "8",
+  author        = "J. Mak and D. P. Marshall and G. Madec and J. R. Maddison",
+  year          = "2022",
+  month         = "apr",
+  publisher     = "American Geophysical Union (AGU)",
+  issn          = "0094-8276",
+  doi           = "10.1029/2021GL097259"
+}
+
+@article{         mak.avdis.ea_JAMES22,
+  title         = "On constraining the mesoscale eddy energy dissipation
+                  time-scale",
+  pages         = "e2022MS003223",
+  journal       = "Journal of Advances in Modeling Earth Systems",
+  volume        = "14",
+  number        = "11",
+  author        = "J. Mak and A. Avdis and T. W. David and H. S. Lee and Y. Na
+                  and Y. Wang and F. E. Yan",
+  year          = "2022",
+  month         = "nov",
+  publisher     = "American Geophysical Union (AGU)",
+  issn          = "1942-2466",
+  doi           = "10.1029/2022MS003223"
+}
+
 @article{         marchesiello.mcwilliams.ea_OM01,
   title         = "Open boundary conditions for long-term integration of
                   regional oceanic models",

latex/NEMO/subfiles/chap_LDF.tex

@@ -522,9 +522,53 @@ paramount importance.
 
 At the surface, lateral and bottom boundaries, the eddy induced velocity,
 and thus the advective eddy fluxes of heat and salt, are set to zero.
-The value of the eddy induced mixing coefficient and its space variation is controlled in a similar way as for lateral mixing coefficient described in the preceding subsection (\np{nn_aei_ijk_t}{nn\_aei\_ijk\_t}, \np{rn_Ue}{rn\_Ue}, \np{rn_Le}{rn\_Le} namelist parameters).
+The value of the eddy induced mixing coefficient and its space variation is controlled
+in a similar way as for lateral mixing coefficient described in the preceding subsection
+(\np{nn_aei_ijk_t}{nn\_aei\_ijk\_t}, \np{rn_Ue}{rn\_Ue}, \np{rn_Le}{rn\_Le} namelist
+parameters).
 \colorbox{yellow}{CASE \np{nn_aei_ijk_t}{nn\_aei\_ijk\_t} = 21 to be added}
 
+In the case of \np{nn_aei_ijk_t}{nn\_aei\_ijk\_t} = 32, the GEOMETRIC scaling for the
+eddy induced velocity coefficient from \citet{mak.marshall.ea_GRL22}
+\begin{equation}
+  \label{eq:ldf_eke_aeiv}
+    A^{eiv} = \alpha\frac{\hat{E}}{\int sN \; \Gamma(z) \; \mathrm{d}z} \Gamma(z),
+\end{equation}
+is used, where $\alpha$ (\np{rn_geom}{rn\_geom}) is a non-dimensional factor bounded in
+magnitude by 1, $\Gamma(z) = N^2 / N^2_{ref}$ (controlled by \np{rn_SFmin}{rn\_SFmin} and
+\np{rn_SFmax}{rn\_SFmax}, switch off by setting them equal to 1) is a vertical structure
+function based on \citet{ferreira.marshall.ea_JPO05}, and $s$ is the isopycnal slope
+($s^2 = r_{1w}^2 + r_{2w}^2$). The parameterized depth-integrated eddy energy $\hat{E}$
+is calculated from
+\begin{equation}
+  \label{eq:ldf_eke_ene}
+    \frac{\mathrm{d}\hat{E}}{\mathrm{d}t}
+    + \underbrace{\nabla_H \cdot \left( \left(\widetilde{u}^z - c\right) \hat{E} \right)}_\textnormal{advection}
+   = \underbrace{\int A^{eiv} s^2N^2\; \mathrm{d}z}_\textnormal{source}
+    - \underbrace{\lambda (\hat{E} - \hat{E}_0)}_\textnormal{dissipation} 
+    + \underbrace{\eta_E\nabla^2_H  \hat{E}}_\textnormal{diffusion},
+\end{equation}
+where $\nabla_H$ is the horiziontal gradient operator, $\tilde{u}^z$ is the
+depth-averaged velocity in the $1,2$ direction, $c$ is the long Rossby phase velocity
+pointing into the $i$ direction with speed $|c| = \pi^{-1}\int |N|\; \mathrm{d}z$
+via a WKB-type approximation, $\lambda$ (\np{rn_eke_dis}{rn\_eke\_dis}) is a linear
+dissipation time-scale in units of days (converted to per second in NEMO), $\hat{E}_0$
+(\np{rn_eke_min}{rn\_eke\_min}) is a stabilizer for oscillations in $\hat{E}$, and
+$\eta_E$ (\np{rn_eke_lap}{rn\_eke\_lap}) is a diffusion coefficient. Various options
+controlling the calculation of $A^{eiv}$ or $\hat{E}$ may be made through namelist
+parameters in \nam{ldf_eke}{ldf\_eke}.
+
+An option is provided to read in a bespoke spatially varying but constant in
+time $\lambda^{-1}$ in units of days (\np{rn_eke_dis}{rn\_eke\_dis} = -20). See
+\citet{mak.avdis.ea_JAMES22} and associated data repository for an estimate and some
+scripts to regenerate the estimates and/or sample this on various ORCA grids.
+
+\begin{listing}
+  \nlst{namldf_eke}
+  \caption{\forcode{&namldf_eke}}
+  \label{lst:namldf_eke}
+\end{listing}
+
 In case of setting \np[=.true.]{ln_traldf_triad}{ln\_traldf\_triad}, a skew form of the eddy induced advective fluxes is used, which is described in \autoref{apdx:TRIADS}.
 
 %% =================================================================================================

namelists @ 62d162f9

-Subproject commit 835213cd38ff66d60cf8c2b11a7665e7c4f68a75
+Subproject commit 62d162f9d27dfae37835d6f1a0e73690a65b84b0