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**Author** : Gurvan Madec, Florian Lemarié, George Nurser, Christian Ethé

**ticket** : #1593

**Branch** : 2015/dev_r5721_CNRS9_NOC3_LDF

**WP2015 Action** : CNRS-9 and NOC-3

# Description

Development branch related to CNRS-9 and NOC-3 actions of 2015 work plan :

• simplify and improve the tracer advection and the lateral diffusion and dissipation in NEMO/OPA

• generalization of the use of surface scale factors (e1e2 at T, U, V, F points)

NB: This development consists in merging the current trunk with the last year work on that subject (see ticket #1260, and the associated branch 2014/dev_CNRS0_NOC1_LDF and wiki page 1260_CNRS0_NOC1_LDF.

*Simplification*:

(1) define bilaplacian operators on dynamics and tracers as re-entrant laplacian ;

(2) change the way the eddy diffusivity and viscosity are specified and controlled by the user ; add a new choice (read the coeff. in a file) ;

(3) generalize of the use of surface scale factors and their inverse ;

(4) add a optional read of surface scale factors in coordinate file in case of reduction of the scale factors in some straits (allows to suppress hard coded ORCA staff in domhgr.F90).

(5) suppress some CPP keys : key_ldfslp ; ley_ldftra_eiv ; key_traldf_ano ; key_traldf_c1d, _c2d, c3d ; key_dynldf_c1d, _c2d, c3d ; key_esopa (from traldf and traadv routines) ;

(6) remove Smagorinsky dependent eddy viscosity and diffusivity

*Improvements*:

(1) introduce Beckers et al. (2000) compact stencil in the cross-isoneutral direction in triads formalism ;

(2) introduce in both iso-neutral operator the Method of Stabilizing Correction (Lemarié et al. (2012) (it minimizes numerical errors, and allows the implementation of bilaplacian iso-neutral operator)** **;(3) implement bi-laplacian iso-neutral operators (Lemarié et al. (2012).

# Strategy

Three steps:

## I. Phasing of horizontal scale factors

==⇒>>

OKsee revision 5737+ minor correctionrevision 5737 (SETTE OK)

### (I.1) standardisation of the name

The chosen names of quantities derived from horizontal scale factors are:

- inverse of scale factors : r1_e1t, r1_e2t, r1_e1u, r1_e2u, r1_e1v, r1_e2v, r1_e1f, r1_e2f ;

- surfaces and their inverse: e1e2t, e1e2u , e1e2v, e1e2f and, r1_e1e2t , r1_e1e2u , r1_e1e2v, r1_e1e2f ;

- ratio (used in traldf…) : e2_e1u , e1_e2v(I.1) generalize of the use of surface scale factors ;

These quantities are defined in memory in dom_oce.F90, and set to their proper value in domhgr.F90

### (I.2) domhgr: add a optional read of surface scale factors

An optional read of surface scale factors at velocity points ( e1e2u and e1e2v) is needed in coordinate file. Indeed, in case of reduction of a scale factor (e1u or e2v) in a strait, the surface at u- and v-points must remain unchanged.

This allows to suppress the dom_vvl_orca_fix routine from dlmvvl.F90 module.

Note that this change modifies the model results, as it contains a better handling of reduced strait width (i.e. reduced face between 2 adjacent T-points, but unchanged U and V points volume).

The implementation performed here is a first step to the full simplification of domhgr.F90. We kept here the hard coded reduction of scale factor in some straits for some given ORCA configuration.

A last step (see IV) will be to suppress the hard coded reduction of some scale factor as it will be always given in the coordinates.nc file together with the e1e2u & e1e2v surfaces. ==⇒>> OK seerevision 5755

## II. Phasing of the advective/diffusive trends on tracers

### II.1 —** **LDF on tracers** (both TRA & TRC) - Diffusive trends**

===⇒>>> Bug in triad operator TO BE CHECKED

triad operator is neither restartable not repro in the branche (it was the case in v3.6 stable)

*operator*:

- laplacian operator: re-entrant laplacian for iso-level, standard iso-neutral, and triad iso-neutral operators ;

- bilaplacian operator: traldf_blp.F90 module: use of the re-entrant laplacian

- both standard and triad iso-neutral operators includes the Method of Stabilizing Correction (Lemarié et al. (2012) which allows bilaplacian along iso-neutral surfaces ;

- triad operator: introduce Beckers et al. (2000) compact stencil in the cross-isoneutral direction ; make the triad operator available in TOP

- change name: traldf_iso_grif.F90 becomes traldf_iso_triad.F90

- suppression of traadv_eiv.F90 ; traldf_bilap.F90 ; traldf_bilapg.F90 ;

- remove the possibility to compute the lateral diffusion from T-S anomalies (key_traldf_ano)

*lateral mixing coefficient*:

- new user interface (namelist) :

!---------------------------------------------------------------------------------- &namtra_ldf ! lateral diffusion scheme for tracers !---------------------------------------------------------------------------------- ! ! Operator type: ln_traldf_lap = .false. ! laplacian operator ln_traldf_blp = .false. ! bilaplacian operator ! ! Direction of action: ln_traldf_lev = .false. ! iso-level ln_traldf_hor = .false. ! horizontal (geopotential) ln_traldf_iso = .true. ! iso-neutral ln_traldf_triad = .false. ! iso-neutral using Griffies triads ! ! ! iso-neutral options: ln_traldf_msc = .true. ! Method of Stabilizing Correction (both operators) rn_slpmax = 0.01 ! slope limit (both operators) ln_triad_iso = .false. ! pure horizontal mixing in ML (triad only) rn_sw_triad = 1 ! =1 switching triad ; =0 all 4 triads used (triad only) ln_botmix_triad = .false. ! lateral mixing on bottom (triad only) ! ! ! Coefficients: nn_aht_ijk_t = 21 ! space/time variation of eddy coef ! ! =-20 (=-30) read in eddy_diffusivity_2D.nc (..._3D.nc) file ! ! = 0 constant ! ! = 10 F(k) =ldf_c1d ! ! = 20 F(i,j) =ldf_c2d ! ! = 21 F(i,j,t) =Treguier et al. JPO 1997 formulation ! ! = 30 F(i,j,k) =ldf_c2d + ldf_c1d ! ! = 31 F(i,j,k,t)=F(local velocity) rn_aht_0 = 2000. ! lateral eddy diffusivity (lap. operator) [m2/s] rn_bht_0 = 1.e+12 ! lateral eddy diffusivity (bilap. operator) [m4/s] / !---------------------------------------------------------------------------------- &namtra_ldfeiv ! eddy induced velocity param. !---------------------------------------------------------------------------------- ln_ldfeiv =.true. ! use eddy induced velocity parameterization ln_ldfeiv_dia =.true. ! diagnose eiv stream function and velocities rn_aeiv_0 = 2000. ! eddy induced velocity coefficient [m2/s] nn_aei_ijk_t = 21 ! space/time variation of the eiv coeficient ! ! =-20 (=-30) read in eddy_induced_velocity_2D.nc (..._3D.nc) file ! ! = 0 constant ! ! = 10 F(k) =ldf_c1d ! ! = 20 F(i,j) =ldf_c2d ! ! = 21 F(i,j,t) =Treguier et al. JPO 1997 formulation ! ! = 30 F(i,j,k) =ldf_c2d + ldf_c1d /

- default value of the namelist: *no operator chosen*: lln_traldf_lap=traldf_blp=0 No lateral diffusion applied on tracers.

- bi-laplacian eddy coefficient defined as SQRT(bhm)

- ah and bh coefficients defined only at u- and v-points.

- redesign the management of eddy induced velocity and its associated diagnostics. In particular ldfeiv.F90 and ldfeiv_substitute.h90 has been suppressed (ldf_eiv routine is now included in ldftra.F90)

- redesign of space variation of the eddy diffusivity: suppression of: ldftra_substitute.h90 ; ldftra_c1d.h90 , ldftra_c2d.h90 and ldftra_c3d.h90 (replaced by ldfc1d_c2d.F90, a module share with ldftra.F90) ; ldftra_oce.F90 (now included in ldftra.F90)

- remove ldftra_smag.F90 (suppression of smagorinski option) **=⇒>> TO BE re-add in the new framework by someone…**- suppression of cpp keys : key_ldfslp ;

*key_traldf_c1d ; key_traldf_c2d ; key_traldf_c3d ;*key_diaeiv ; key_traldf_eiv ; key_traldf_eiv ; key_traldf_ano

- suppression of key_esopa in traldf.F90

- zpshde.F90 correct an issue with position of optional argument in zps_hde_isf routine

- change in all standard namelist_cfg and 1_namelist_cfg

*passive tracers*

- all changes in the management of diffusive coefficients and operator has been taken into account in TOP

- change in all standard namelist_top_cfg

**Pending issues** :

- verify diaptr.F90 : not sure it is OK

- add the max grid size in the coordinate file and use it to compute grid dependent diffusivity. This will solve an issue with regional and AGRIF configurations

- test all 6 operators.

- In field_def.xml add a comment to say where is the routine calling the corresponding iom_put

- in the documentation, add a change in the DOCTOR norm: np_ is now a prefix used for PARAMETER

### II.2 — Advective trends (TRA/traadv….)

==⇒>>

OKsee revision 5770 & 5771 ==⇒> SETTE OK with revision 5774 & 5775

- traadv_muscl2.F90 removed

- traadv_muscl.F90 renamed traadv_mus.F90

- traadv_cen2.F90 replaced by traadv_cen which provides 2nd and 4th order centered scheme on both horizontal and vertical directions.

- name TVD has been changed to the more commonly used FCT (Flux Correction Transport)

- FCT offers now 2nd and 4th order centered scheme on both horizontal and vertical directions.

- UBS offers now in option either a 2nd order FCT or a 4th order COMPACT scheme in the vertical direction

- NB in case of 4th order in the vertical, CEN, UBS and FCT use a compact 4th order scheme

- key_esopa removed from traadv.F90

- Surface boundary condition in ISF case has been added in all cases (except 4th order COMPACT scheme which currently don't work with ISF)

!----------------------------------------------------------------------- &namtra_adv ! advection scheme for tracer !----------------------------------------------------------------------- ln_traadv_cen = .false. ! 2nd order centered scheme nn_cen_h = 4 ! =2/4, horizontal 2nd order CEN / 4th order CEN nn_cen_v = 4 ! =2/4, vertical 2nd order CEN / 4th order COMPACT ln_traadv_fct = .false. ! FCT scheme nn_fct_h = 2 ! =2/4, horizontal 2nd / 4th order nn_fct_v = 2 ! =2/4, vertical 2nd / COMPACT 4th order nn_fct_zts = 0 ! > 1 , 2nd order FCT scheme with vertical sub-timestepping ! ! (number of sub-timestep = nn_fct_zts) ln_traadv_mus = .false. ! MUSCL scheme ln_mus_ups = .false. ! use upstream scheme near river mouths ln_traadv_ubs = .false. ! UBS scheme nn_ubs_v = 2 ! =2 , vertical 2nd order FCT ln_traadv_qck = .false. ! QUICKEST scheme /

**Unresolved issues/improvement** on TRAADV:

- QCK: cross terms are missing. alternate direction should be added….

- Bug in FCT with sub-time-stepping and key_vvl. The change in e3 should be taken into account in the sub-timesteps.

- traadv_mus.F90 some rather simple optimization can be added…

- traadv_qck.F90 : possibility to add a 4th order COMPACT scheme on the vertical.

- 4th order COMPACT doesn't work with ISF the routine have to be modified

### II.3 — Miscellaneous

- Atmospheric pressure forcing: change to a systematic call of sbc_apr in step.F90 (with or without BDY) and remove its call from sbcmod
- remove key_vectopt_loop from all the code except in vectopt_loop_substitute.h90 (it is an obsolescent feature only adapted to vector computers)
- remove all "!CDIR " lines = NEC vector compiler instructions

## III. Phasing of momentum trends

### III.1 — LDF on dynamics - viscous trends

*operator*:

- laplacian operator: re-entrant laplacian for iso-level operators (routine dyn_ldf_lap found in dynldf_lap_blp);

- bilaplacian operator: dynldf_blp.F90 module: use of the re-entrant iso-level laplacian (routine dyn_ldf_blp found in dynldf_lap_blp.F90)

- suppression of dynnept.F90 to finalize the suppression of Neptune effect param. ;

- suppression of dynldf_lap.F90 and dynldf_bilap.F90 replaced by dynldf_lap_blp.F90 (which contains dyn_ldf_lap & dyn_ldf_blp routines) ; dynldf_bilapg.F90 (remove old and approximative rotated bi-laplacian on momentum)

- rotb and rotn arrays suppressed (even from the restart file) NB: the viscous operator now uses the full before velocity field (i.e. including the asselin filter)

- hdivb array is suppressed. hdivn and hdivb are removed from restart

- associate with rotn and rotb suppression comes the suppression of no-slip accurate option (key_noslip_accurate is removed)

- divcur.F90 becomes divhor.F90 and only computes the horizontal divergence

*lateral mixing coefficient*:

- new user interface (namelist) :

!----------------------------------------------------------------------- &namdyn_ldf ! lateral diffusion on momentum !----------------------------------------------------------------------- ! ! Type of the operator : ! ! no diffusion: set ln_dynldf_lap=..._blp=F ln_dynldf_lap = .false. ! laplacian operator ln_dynldf_blp = .false. ! bilaplacian operator ! ! Direction of action : ln_dynldf_lev = .false. ! iso-level ln_dynldf_hor = .false. ! horizontal (geopotential) ln_dynldf_iso = .false. ! iso-neutral ! ! Coefficient nn_ahm_ijk_t = 0 ! space/time variation of eddy coef ! ! =-30 read in eddy_viscosity_3D.nc file ! ! =-20 read in eddy_viscosity_3D.nc file ! ! = 0 constant ! ! = 10 F(k)=c1d ! ! = 20 F(i,j)=F(grid spacing)=c2d ! ! = 30 F(i,j,k)=c2d*c1d ! ! = 31 F(i,j,k)=F(grid spacing and local velocity) rn_ahm_0 = 40000. ! horizontal laplacian eddy viscosity [m2/s] rn_ahm_b = 0. ! background eddy viscosity for ldf_iso [m2/s] rn_bhm_0 = 1.e+12 ! horizontal bilaplacian eddy viscosity [m4/s] ! ! Caution in 20 and 30 cases the coefficient have to be given for a 1 degree grid (~111km) /

- default value of the namelist: *no operator chosen*: ln_dynldf_lap=dyndf_blp=0 =⇒>> No lateral diffusion applied on momentum

- create the 2D and 3D ahmt and ahmf file for ORCA_R2 **==⇒>> TO BE DONE for ORCA_R1** . nn_ahm_ijk_t must be set to -20 or -30 for ORCA2 and ORCA1 (read in a file)

- both laplacian and bi-laplacian coef. are always 3D arrays defined at T- and F- points. Bi-laplacian eddy coefficient defined as SQRT(bhm) ** ===⇒>> TO BE DONE explore the possibility of u- and v-points**

- redesign of space variation of the eddy viscosity: suppression of: ldfdyn_substitute.h90 ; ldfdyn_c1d.h90 , ldfdyn_c2d.h90 and ldfdyn_c3d.h90 (replaced by ldfc1d_c2d.F90, a module share with ldftra.F90) ; ldfdyn_oce.F90 (now included in ldfdyn.F90)

- remove ldfdyn_smag.F90 (suppression of smagorinsky option) **=⇒>> TO BE re-add in the new framework by someone…**

- suppression of key_esopa in dynldf.F90

- suppression of key_dynldf_c1d, key_dynldf_c2d, key_dynldf_c3d

- change in all standard namelist_cfg and 1_namelist_cfg

- Namelist default values : NO operator ; NO direction ==⇒>> No lateral mixing applied on momentum ==⇒>> must be specified in all CONFIG

### III.2 —** **ADV on dynamics** - advective trends**

*dynvor.F90 (impact also dynspg_ts.F90)*

- remove key_esopa

- remove dyn_vor_mix : now successive call of den_vor_ene (Coriolis) and din_vor_ens (relative voricity)

- replace rotn by its calculation everywhere in dynvor.F90

- remove the use of fmask from standard vorticity calculation in dynvor.F90 but add a namelist parameter (ln_dynvor_msk) to multiply by fmask the vorticity term

- add an namelist option to mask or not the vorticity (including Coriolis) **CAUTION** : the mask option does not work: set to FALSE by default with comment DO NOT set it to TRUE (see ** 5827** )

- change ln_dynvor_een_old into nn_een_e3f = 0/1

namdyn_vor becomes:

!----------------------------------------------------------------------- &namdyn_vor ! option of physics/algorithm (not control by CPP keys) !----------------------------------------------------------------------- ln_dynvor_ene = .false. ! enstrophy conserving scheme ln_dynvor_ens = .false. ! energy conserving scheme ln_dynvor_mix = .false. ! mixed scheme ln_dynvor_een = .true. ! energy & enstrophy scheme nn_een_e3f = 1 ! e3f = masked averaging of e3t divided by 4 (=0) or by the sum of mask (=1) ln_dynvor_msk = .false. ! vorticity multiplied by fmask (=T) or not (=F) (all vorticity schemes) /

*dynadv.F90*- remove key_esopa

- introduce parameter in the SELECT CASE

namlist_ref and all CONFIG namelists updated

### III.3 Miscellaneous

- key_esopa has been remove from the whole NEMO code
**DONE**see rev. 5778 - remove key_noslip_accurate from dom_oce.F90 and domsk.F90.
**DONE**see rev. 5829 - remove duplicate print of "W A R N I N G" and "E R R O R" in ctl_nam routine
**DONE**see rev. 5829 - remove ll_is_orca and its associated use in domvvl.F90 (no used anymore)
**DONE**see rev 5829 - remove ttrdmp & strdmp arrays (not used anymore)
**DONE see rev**.**5830** - remove the remaining use of ua,va as workspace (changes in trazdf_imp.F90, zdfevd.F90, zdftmx.F90 and oce_trc.F90)
**DONE**see rev. 5831

## IV. Pending issues : need to be solved before v3.7 release

**•** Update the documentation.

**•** ensure the restartability & reproducibility for triad operator.

**• ** specification of eddy viscosity/diffusivity coefficients in case of grid-size dependency.

Issue: define the grid-size dependency in such a way that does not require the Equator being inside the domain.

Solution: **- add** a scalar in the coordinate file which is equal to the grid-size at the equator even if Equator is not in the domain and use this scalar to compute the grid-size dependency of the coefficients.

In addition:

- **add** in NEMOGCM/TOOLS directory a program that read a coordinates.nc file apply a reduction of scale factors in some straits, and create the associated extended coordinates file (coordinates_e1e2u_v.nc)

- **create** the extended coordinates files form ORCA 2°, 1°, and 0.5°. ==⇒>> Done for ORCA 2° and 1°, **½° and ¼° missing…**-

**explore**the possibility of defining ahm coef. at u- and v-points. This will improve the velocity dependent case.

**• **specification of lateral friction at the coast.

Issue: the different values of fmask at the coast have been removed so that this lateral boundary condition doesn't affect the advective term (** double check that** !). fmask is still used for laplacian and bilaplacian viscosities. Nevertheless, the magnitude of lateral friction depends on the magnitude of ahm (bhm, reap.). It seems better to define this magnitude

Solution:

## V. Pending issues : to be solved in 2016 ?

**(V.1)** Add a proper coding of Smagorinsky eddy viscosity and diffusivity…

**(V.2)** It should be possible to remove hdivn … think about that

Next Step :

Starting from this branch, another branch is created (**given the name here**) which will contain the following item (random order):

- remove all remaining hard coded parts specific to a configuration (especially ORCA2)

- ZDF simplification: introduce a vertical physics manager that allows to save MPP communications. remove avmu, avmv. remove all key_zdfxxx

- create trptra.F90 which compute the effective velocity for both TRC and TRA

- vertical scale factors defined systematically in vvl case (no more domzgr_substitute.h90)

- remove most of the remaining CPP keys (key_trabbl, key_zdf…)

….

**To be CHECKED** (not necessary associated with this branch)

- find
*!!gm*everywhere in the fortran code, and try to solve the issues raised ! - check that task_i use ssmask, i.e. that it takes into account the under ice shelf seas.
- CRS : the new arrays derived from horizontal scale factors MUST be added in CRS.
- Bug in diawri.F90 when NOT using key_iomput (OK =⇒> see ticket #1596)

- Idea for finalization of domhgr.F90 :
**add**2 modules (from domhgr.F90), domhgr_read.F90 and domhgr_ana.F90, which contains:

- domhgr_read.F90: the CASE jphgr_msh=0 of domhgr.F90 (i.e. read the coordinates file)

- domhgr_ana.F90: the CASE jphgr_msh=5 of domhgr.F90 (i.e. the GYRE analytical definition of the coordinates)**add**in NEMOGCM/TOOLS a directory containing 3 domhgr_ana.F90 modules associated with (1) a geographical mesh on the sphere with regular (in degree) grid-spacing (jphgr_msh=1) ; (2) f- or beta-plane with regular grid-spacing (jphgr_msh=2 or 3)) ; (3) geographical mesh on the sphere, isotropic MERCATOR type (jphgr_msh=4)**remove**from the namelist_ref/namdom all variable related to the horizontal mesh, and add a flag, ln_mesh_read, =T read the coordinates.nc file ; =F analytical mesh (by default GYRE mesh). - sbcisf.F90 : use of hard coded staff associated with EOS (in situ temperature and co …)
- sbcwave.F90 : lot of modifications has been done, but I'm still uncomfortable with the calculation of stokes drift velocities….

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