[MITgcm-support] Heat budget in MITGCM
Jean-Michel Campin
jmc at ocean.mit.edu
Mon Nov 24 15:51:42 EST 2014
Hi Abhisek,
> Following your suggestions, I think I am now able to close the heat budget
> for the subsurface levels.
This is good news.
> I have attached two figures (one for subsurface at 20 m depth and another
> for surface).
Could you clarify what is represented on these 2 figs: it is for a
single grid point (but where ?) or the horizontal mean ?
Regarding the surface forcing, which diagnostics are you using:
surForcT ? TFLUX ? or oceQnet and TRELAX ?
If you are using TFLUX (which contains the vertically integrated SW heating)
for the surface budget, you may want to remove oceQsw and then
add back tend_Qsw(k=1) (as you wrote below).
Cheers,
Jean-Michel
On Fri, Nov 21, 2014 at 07:13:31PM +0530, Abhisek Chakraborty wrote:
> Dear Jean-Michel,
>
> To close the surface heat budget, I followed your suggestion:
>
> 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))
>
> Also, the shortwave tendency terms is computed as:
>
> tend_Qsw = oceQsw/(rhoConst*Cp)/(drF(k)*hFacC(I,j,k))
> * ( swfrac(k) - swfrac(k+1) )
> where for surface, k=1
>
> But in this way, the surface tendency term is becoming one order higher in
> magnitude than other terms (advection, diffusion, surface correction. Pls.
> see the figure in my earlier mail).
>
> So, please guide me how to close the budget at surface.
>
> regards,
> 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 Thu, Nov 20, 2014 at 6:59 PM, Abhisek Chakraborty <abhisek.sac at gmail.com>
> wrote:
>
> > Hi Jean-Michel,
> >
> > Sorry for delayed reply.
> >
> > Following your suggestions, I think I am now able to close the heat budget
> > for the subsurface levels.
> >
> > However, in spite of my different attempts I am not able to close the
> > budget at surface where I am finding the surface correction term (as
> > specified in your mail) along with other advection-diffusion terms are too
> > small to balance the shortwave heating term.
> >
> > I have attached two figures (one for subsurface at 20 m depth and another
> > for surface).
> >
> > Pls. let me know if I am missing something.
> >
> > 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 Wed, Nov 19, 2014 at 1:19 AM, Jean-Michel Campin <jmc at ocean.mit.edu>
> > wrote:
> >
> >> 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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