Version 9 (modified by gm, 11 years ago) (diff)

Last edited Timestamp?

Author : Matthieu Leclair & Gurvan Madec


Branch : DEV_r1837_MLF


Description

Introduce the modified Leap-Frog — Robert-Asselin filter (LF-RA) to fit the one presented in Leclair and Madec Ocean Modelling (2009). The scheme allows a exact conservation of the heat and salt contents when using variable volume thickness (key_vvl). The non-conservation of the standard LF-RA due to the time diffusion of the forcing through the filter. In the modified scheme the exact conservation is achieved by removing the forcing from the filter. Furthermore, the scheme allows to use a much smaller Asselin filter parameter (10-4 instead of 10-1) decreasing the damping effect of the LF-RA scheme, so that it is actually a quasi second order scheme.

The LF-RA flow chart of step is the one introduce in the trunk after the v3.1, to restore the key_vvl option. Its main characteristic is that the ssh is time-stepped first, followed immediately by the computation of the now vertical velocity (see figure below).

step flowchart for the modified LF-RA scheme
Step routine flow chart, form Leclair and Madec (OM 2009).

This update is part of the LOCEAN.8 task (Update of the ocean physics) due by June 25th 2010.

The 3 main modifications concern :


(1) The forcing terms. They are defined as a mean between time step n-½ and n+½

modules involved : sbc_oce.F90, sbcmod.F90, trasbc.F90, traqsr.F90, dynzdf….F90

step flowchart for the modified LF-RA scheme
Illustration of forcing integration methods. Old formulation (top) and new formulation (bottom).

At each time a forcing term appears in the 3 time evolution equations solved in NEMO/OPA (ssh, dynamics and tracer). The mean of kt+½ and kt+½ has to be used in order to remove the largest source of divergence of two consecutive time step. Therefore, the surface module (including the sea-ice!) must now provide both kt+½ and kt-½ forcing fields, and all the module involving a forcing term have to be modified. Note that TKE equation is solved with a two level time stepping scheme : no need of a before field for its forcing term (i.e. taum)


sbc_oce.F90 : add "before" forcing fields (denoted by a '_b' sufix)

All ocean forcing components are involved, i.e. utau_b, vtau_b, qns_b, qsr_b, emp_b,and emps_b


sbcmod.F90 : add the swap of surface fields and the read/write in the restart file.

Beginning of sbs routine, introduce the swap, but only for kt ≥ nit000+1. If no restart, the '_b' fields is known only at the end of the sbc calculation. Therefore we have choosen to regroup the setting of '_b' fields at nit000 at the end of sbc routine.

CAUTION : here the swap must be done at each kt, what ever the nn_fsbc value is. Otherwise the ocean forcing will be wrong.


trasbc.F90 : change in the heat and freshwater/salt fluxes

The thermohalin fluxes (qns, emp, emps) are now applied as the mean of 2 consecutive time-steps (kt+½ and kt-½). This involes the following changes : (1) incorporate the time mean of the forcing ; (2) put the IF-ELSE-ENDIF outside the DO-loop for vector optimisation ; (3) remove the key_zco optimisation (increase readability) as zco is less and less used ; (4) correct a bug in vvl case, where salt flux associated with freezing/melting were not taken into account.

CAUTION 1 : bug in the salt flux in key_vvl ==⇒ modif in limsbc_2.F90 (emps becomes a salt flux in vvl,limsbc, limsbc_2 and CICE interface must be modified)

CAUTION 2 : bug in with no solar light penetration (ln_traqsr=.false.) =⇒ modif in trasbc : qns = qns + qsr.


traqsr.F90 : applied the solar heat flux (qsr) as the mean of 2 consecutive time-steps (kt+½ and kt-½)

CAUTION 1 : the case where the light penetration is provided by the bio-model ( i.e. lk_qsr_bio = ln_qsr_bio =.true. is not yet treated. It probably requires changes in p4zopt.F90 and trcopt.F90. Not completely obvious since this depends on the TOP time-stepping strategy.


dynzdf_exp.F90 : applied the stress (utau, vtau) as the mean of 2 consecutive time-steps (kt+½ and kt-½)


dynzdf_imp.F90 : applied the stress (utau, vtau) as the mean of 2 consecutive time-steps (kt+½ and kt-½)


sshwzv.F90 : applied the freshwater flux (emp) as the mean of 2 consecutive time-steps (kt+½ and kt-½)


(2) The Asselin filter remove the forcing from the filter (tranxt and sshwzv)

CAUTION : the sign of the correction applied to the asselin filter has to be checked.


tranxt.F90 : remove the forcing term from the Asselin filter

after the application of the classical Asselin filter, the part applied to the forcing term is removed :

at jk=1 : - atfp * rdt * ( qns_b - qns ) on temperature (vvl case)

at jk=1 : - atfp * rdt * ( emps_b - emps ) on salinity (vvl case)

if lk_vvl=F, the part applied to the concentration dilution term has also to be removed.

Solar penetration part :

CAUTION 1 : the case where the light penetration is provided by the bio-model ( i.e. lk_qsr_bio = ln_qsr_bio =.true. is not yet treated. It probably requires changes in p4zopt.F90 and trcopt.F90. Not completely obvious since this depends on the TOP time-stepping strategy.


sshwzv.F90 : a additional term appears in the filter (the last part of the RHS) :

sshn = ssha + atfp * ( sshb -2 sshn + ssha ) - atfp * rdt * ( emp_b - emp ) / rau0


N.B. : We choose not to remove the momentum forcing from the Asselin time filter. Therefore dynnxt.F90 is not changed.


(3) The semi-implicit hpg.

In tranxt.F90, for the semi-implicit hydrostatic pressure gradient, the coefficients are changed in order to take into account the Asselin filter parameter

time mean T and S for the semi implicit hpg computation was (ta+2*tn + tb) / 4 . It is now replaced by

rbcp*ta+(2-rbcp)*tn+rbcp*tb

with rbcp=(1+atfp)*(1+atfp*atfp) / 4, and atfp is the Asselin filter parameter.

The change extend further the stability limit of the time stepping scheme when ln_dynhpg_imp = T


N.B. : Three key elements of the LF-RA scheme have already been implemented in former version of NEMO (v3.0 and v3.1). As a remainder, there are:

Forcing evaluation : the momentum and tracers forcing are evaluated at kt+½, no-more at kt. This is done in the fldread routine since v3.0

Flow chart : general structure has changed for key_vvl (variable volume or equivalently non-linear free surface) (v3.1). In particular the ssh equation is solved first together followed immediately by the computation of the now vertical velocity, so that wn is available to solve the tracer and the dynamics equations.

The enhanced vertical diffusion (evd) is no more a source of small divergence of two consecutive time step as the static instability is now tested on both before and now fields. See ticket #401.


Pending issues

  • correct the bug in limsbc, limsbc_2 and CICE interface (nned help from Met Office for the later)
  • Do we need to remove the stress component from the filter in dynnxt?
  • in vvl case : thickness weighted tracer in the time mean, do we need to compute and use a time mean thickness in the hpg computation?
  • The associated changes in TOP are still unclear. A priori, in PISCES p4zopt.F90 should be modified. Nevertheless, the TOP time stepping strategy seems to be a forward in time scheme. If yes, then the evaluation of the forcing at kt+½ is an improvement (if not to say a bug fix!). If not, action is required…
  • Check the consistency with the change planned in the emps field (switch to fsalt, a true salt flux).
  • modification required in limsbc, limsbc_2 and CICE interface : conversion of emps into a salt flux (new name 'fsalt' ?)
  • the modifications in trasbc will interfere with the new runoff scheme (see 2009WP/2009Stream3#Substream3.2:fromNEMOteamshort-term)

Testing

Testing could consider (where appropriate) other configurations in addition to NVTK].

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