[MITgcm-support] Heat budget in MITGCM
Jean-Michel Campin
jmc at ocean.mit.edu
Tue Nov 18 14:49:34 EST 2014
Hi Abhisek,
This budget looks better. Just few remarks (see below).
On Tue, Nov 18, 2014 at 11:20:46PM +0530, Abhisek Chakraborty wrote:
> Dear Jean-Michel,
>
> Thanks for your prompt suggestion.
>
>
> (1) the advection term for k>1 will be
>
> - [ (ADVx_TH(i+1,j,k) – ADVx_TH(I,j,k))/CV +
>
> (ADVy_TH(I,j+1,k) – ADVy_TH(I,j,k))/CV +
>
> (ADVr_TH(I,j,k+1) – ADVr_TH(I,j,k))/CV ]
The vertical advective & diffusive transport/flux are (I think)
positive in the direction of the vertical coordinate, i.e.,
when using z-coords, positive upward. So you will have to reverse
(or add a minus sign) in front of:
(ADVr_TH(I,j,k+1) – ADVr_TH(I,j,k))/CV
>
> Where CV=Ac * del RF * Hc = RAC(I,j) * (RF(K+1)-RF(K)) * hFacC(I,j,k)
>
> ( http://mitgcm.org/public/r2_manual/latest/online_documents/node73.html)
>
>
>
> And similarly the diffusion and KPP terms. Correct?
>
>
> (2) The source term (shortwave) for k>1 will be the following
>
> depth=RF(k)
>
> swfrac=0.62*exp(depth/0.6) + (1.0-0.62) * exp(depth/20)
>
> if(depth < -200.0) swfrac=0.0
>
> source term = (oceQsw/(rhoConst*Cp)) * swfrac * hFacC(I,j,k)
>
> Is this correct for k>1 ?
This does not look right:
from depth=RF(k) , we compute swfrac(k) as above
from depth=RF(k+1), we compute swfrac(k+1) as above except that
at the bottom (deepest level of this column) swfrac(k+1)=0.
and the tendency contribution from shortwave heating should be something like:
tend_Qsw = oceQsw/(rhoConst*Cp)/(drF(k)*hFacC(I,j,k))
* ( swfrac(k) - swfrac(k+1) )
>
> (3) I am using the tendency as TOTTTEND/86400. Is it correct?
yes, providing you are using linear free-surface.
>
> (4) I am using linFSConserveTr=TRUE. Yet I have to use
> WTHMASS(i,j,1)*RAC(i,j) to correct the heat budget at the surface?
Yes, but since you are using linFSConserveTr=TRUE., the global mean
value of WTHMASS has to be removed in the budget (like it is in the model):
TsurfCor = SUM( WTHMASS(i,j,1)*RAC(i,j) ) / globalArea
and finally:
tend_T = (...) - ( WTHMASS(i,j,1) - TsurfCor )/(drF(1)*hFacC(i,j,1))
Cheers,
Jean-Michel
>
> Thanking in advance,
>
> Abhisek
>
>
>
> *--------------------------------------------------------------------------------ABHISEK
> CHAKRABORTY*
>
> *Scientist - "SD"Oceanic Sciences Division (*
> *AOSG/EPSA)*
>
> *Space Applications Centre*
>
> *Indian Space Research Organization*
>
> *Ahmedabad - 380 015*
>
> *Gujarat, INDIA*
> *Contact: +91-79-2691-6054 (O), +91-79-2686-1929(R)*
>
> On Tue, Nov 18, 2014 at 10:42 PM, Jean-Michel Campin <jmc at ocean.mit.edu>
> wrote:
>
> > Hi Abhisek,
> >
> > I would recommand to concentrate first on any level except the surface
> > (k=1),
> > and try to close the budget ; then, once you get a clean closed budget
> > for levels at depth, you can revisit the surface level problem.
> >
> > at depth (k>1):
> > the way you estimate the tendency is not what is done in the model,
> > see e.g.:
> > http://mitgcm.org/public/r2_manual/latest/online_documents/node73.html
> >
> > The diagnostics for the KPP non-local term is like a vertical flux
> > (added to fVerT), so it can be treated (for budget purpose) the same way
> > as DIFrI_TH.
> >
> > at the surface, you can search the mitgcm-support archive and find some
> > information there, e.g.:
> > http://mitgcm.org/pipermail/mitgcm-support/2014-April/009093.html
> > but it's likely that you would need additional diagnostics output,i
> > e.g. WTHMASS & WSLTMASS at k=1.
> >
> > Cheers,
> > Jean-Michel
> >
> > On Tue, Nov 18, 2014 at 09:49:34PM +0530, Abhisek Chakraborty wrote:
> > > Many thanks Ryan, Dimitris, John and Gael for your suggestions.
> > >
> > >
> > > I am not much familiar with MATLAB, so for me it was too much difficult
> > to
> > > understand the code shared by Gael, though I tried to look into it.
> > >
> > >
> > > As a matter of fact is that I am using is the ECCO1 version (1 deg
> > global,
> > > 50 levels, excluding poles; i=1:360; j=1:160; k=1:50) of MITGCM with
> > linear
> > > free surface and linFSConserveTR=True. The diagnostic parameters are
> > > written in every day with diagnostic timephase=0. Model parameterizations
> > > are KPP and GM-Redi.
> > >
> > >
> > > I’d like to analyze the heat budget at a particular location, say,
> > (i,j,k).
> > > So, from the suggestions by Ryan, Dimitris and looking into the Gael’s
> > > code, I am trying the following:
> > >
> > >
> > > !!Cell volumes (center difference)
> > >
> > > Cvx = (RAC(i+1,j) - RAC(i-1,j)) * RF(k) * hFacC(i,j,k)
> > >
> > > Cvy = (RAC(i,j+1) - RAC(i,j-1)) * RF(k) * hFacC(i,j,k)
> > >
> > > Cvz = RAC(i,j) * (RF(k+1) – RF(k)) * hFacC(i,j,k)
> > >
> > >
> > >
> > > !!Divergence of advection & diffusion by center difference
> > >
> > >
> > > if (k>1) then
> > >
> > > adc_dif_vert_k = (ADVr_TH(i,j,k+1) – ADVr_TH(I,j,k-1))/cvz +
> > >
> > > (DIFrE_TH(I,j,k+1) –
> > DIFrE_TH(I,j,k-1))/cvz +
> > >
> > > (DIFrI_TH(I,j,k+1) – DIFrI_TH(I,j,k-1))/cvz
> > >
> > > else
> > >
> > > adc_dif_vert_k = 0.0
> > >
> > > endif
> > >
> > >
> > >
> > > adc_dif_hori_k = (ADVx_TH(i+1,j,k) – ADVx_TH(i-1,j,k))/cvx +
> > >
> > > (ADVy_TH(i,j+1,k) – ADVy_TH(i,j-1,k))/cvy +
> > >
> > > (DIFxE_TH(i+1,j,k) – DIFxE_TH(i-1,j,k))/cvx +
> > >
> > > (DIFyE_TH(i,j+1,k) – DIFyE_TH(i,j-1,k))/cvy
> > >
> > >
> > > !!To account for the shortwave heating
> > >
> > > depth=RF(k)
> > >
> > > swfrac=0.62*exp(depth/0.6) + (1.0-0.62) * exp(depth/20)
> > >
> > > if(depth < -200.0) then
> > >
> > > swfrac=0.0
> > >
> > > endif
> > >
> > > if (k=1)then
> > >
> > > swfrac=1.0
> > >
> > > endif
> > >
> > >
> > > !!Finally balance
> > >
> > >
> > > TOTTTEND/86400.0 = - adc_dif_vert_k - adc_dif_hori_k +
> > > (oceQsw/(rhoConst*Cp)) * swfrac * hFacC(I,j,k) + KPPg_TH(i,j,k)
> > >
> > >
> > > Please let me know whether I am doing properly or not.
> > >
> > >
> > >
> > > Thanking in advance,
> > >
> > > Abhisek
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > *--------------------------------------------------------------------------------ABHISEK
> > > CHAKRABORTY*
> > >
> > > *Scientist - "SD"Oceanic Sciences Division (*
> > > *AOSG/EPSA)*
> > >
> > > *Space Applications Centre*
> > >
> > > *Indian Space Research Organization*
> > >
> > > *Ahmedabad - 380 015*
> > >
> > > *Gujarat, INDIA*
> > > *Contact: +91-79-2691-6054 (O), +91-79-2686-1929(R)*
> > >
> > > On Tue, Nov 18, 2014 at 5:06 AM, gael forget <gforget at mit.edu> wrote:
> > >
> > > > Hi Abhisek, et al,
> > > >
> > > > the following matlab code may provide some guidance :
> > > >
> > > >
> > http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/gael/matlab_class/gcmfaces_diags/diags_set_D.m
> > > >
> > > > It does not cover every possible combination of model options
> > > > (e.g., no kpp or thsice) of course, but treats a few. In that code,
> > > > it is assumed that
> > > > 1) the setting for the diagnostics package was according to
> > > >
> > > >
> > http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/gael/verification/global_oce_llc90/input/data.diagnostics
> > > > which includes vertical integration. The relevant diagnostics
> > > > for budget are those with filename like 'diags/budg2d_snap_set1',
> > > > 2) tendencies have been pre-computed by differencing between
> > > > consecutive (monthly) snap shots — so that ETAN
> > > > really means dETAN/dt in this context, and similarly for
> > > > THETA, SALT, etc. The other variable names used in
> > > > diags_set_D.m
> > > > <
> > http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/gael/matlab_class/gcmfaces_diags/diags_set_D.m>
> > match
> > > > those used in pkg/diagnostics
> > > >
> > > > I should also mention that diags_set_D.m
> > > > <
> > http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/gael/matlab_class/gcmfaces_diags/diags_set_D.m>
> > is
> > > > part of a
> > > > broader framework (gcmfaces) which is documented in
> > > >
> > > >
> > http://mitgcm.org/viewvc/*checkout*/MITgcm/MITgcm_contrib/gael/matlab_class/gcmfaces.pd
> > > > <
> > http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/gael/matlab_class/gcmfaces.pd
> > >
> > > > f
> > > > … although I am afraid this documentation is also
> > > > lacking wrt the budget diagnostic codes.
> > > >
> > > > Cheers,
> > > > Gael
> > > >
> > > > On Nov 17, 2014, at 5:53 PM, Dimitris Menemenlis <
> > dmenemenlis at gmail.com>
> > > > wrote:
> > > >
> > > > … and you probably already know this, but not clear from your email:
> > > > shortwave is not dumped in surface level only, but rather is
> > distributed
> > > > with exponentially
> > > > decaying profile in top 200-m, with subtle modifications if this
> > heating
> > > > is occurring within
> > > > the KPP mixing layer depth.
> > > >
> > > > On Nov 17, 2014, at 2:44 PM, Ryan Abernathey <
> > ryan.abernathey at gmail.com>
> > > > wrote:
> > > >
> > > > Abhisek,
> > > >
> > > > This is a very common question that unfortunately is not documented
> > very
> > > > well. A couple of suggestions...
> > > >
> > > > For the transport terms, (ADV* and DF*), keep in mind that these are
> > FLUX
> > > > terms, defined on the cell boundaries. In order to calculate a heat
> > budget,
> > > > you need to calculate the DIVERGENCE of those fluxes.
> > > > http://mitgcm.org/public/r2_manual/latest/online_documents/node71.html
> > > > Maybe this is obvious, but your email did not make it clear whether you
> > > > were doing this or not.
> > > >
> > > > Likewise, TFLUX is the downward flux at the surface, in W/m^2. In
> > order to
> > > > convert to temperature units, you need to divide by
> > > > HeatCapacity_Cp*rUnit2mass. For z coordinates, rUnit2mass is equal
> > > > to rhoConst.
> > > >
> > > > There are some subtleties regarding tracer budgets under different free
> > > > surface treatments. Maybe someone else on the list understands this
> > issue
> > > > better and is willing to explain. Anyway, those should be second-order
> > > > effects.
> > > >
> > > > Good luck with your analysis.
> > > >
> > > > -Ryan
> > > >
> > > >
> > > > On Sat, Nov 15, 2014 at 2:29 AM, Abhisek Chakraborty <
> > > > abhisek.sac at gmail.com> wrote:
> > > >
> > > >> Dear Users,
> > > >>
> > > >> I am trying to analyze heat budget in MITGCM. From the diagnostic
> > > >> outputs I have the following terms
> > > >>
> > > >> TOTTTEND , ADVr_TH, ADVx_TH, ADVy_TH, DFrE_TH, DFxE_TH, DFyE_TH,
> > > >> DFrI_TH, KPPg_TH, TFLUX (i.e. all terms corresponding to tendency,
> > > >> advection, diffusion, KPP and total heat flux).
> > > >>
> > > >> Apart from these, I have other usual outputs like THETA, SALT etc.
> > > >>
> > > >> The tendency term is in degC/day, the other terms are in degC*m^3/s
> > > >> and TFLUX is in W/m^2. Thus I have converted the tendency term into
> > > >> degC/s by dividing by 86400.0 and the advection-diffusion terms are
> > > >> divided by cell volume (=RAC*RF*HFACC).
> > > >>
> > > >> I am using "linFSconserveTr=True".
> > > >>
> > > >> For the surface layer I have to consider TFLUX (watt/m^2), but how to
> > > >> convert it into degC/s unit?
> > > >>
> > > >> For subsurface levels, I am trying to equate tendency term with
> > > >> (advection + diffusion + KPP term). But there is a mismatch.
> > > >>
> > > >> Can somebody please guide me how to achieve the exact heat budget for
> > > >> both surface and subsurface levels ?
> > > >>
> > > >> Thanking in advance,
> > > >> Abhisek
> > > >>
> > > >> --
> > > >>
> > > >>
> > > >> *ABHISEK CHAKRABORTY*
> > > >>
> > > >> *Scientist - "SD"Oceanic Sciences Division (*AOSG/EPSA)*
> > > >>
> > > >> *Space Applications Centre*
> > > >>
> > > >> *Indian Space Research Organization*
> > > >>
> > > >> *Ahmedabad - 380 015*
> > > >>
> > > >> *Gujarat, INDIA*
> > > >> *Contact: +91-79-2691-6054 (O), +91-79-2686-1929(R)*
> > > >>
> > > >
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