[MITgcm-support] Heat budget in MITGCM
Abhisek Chakraborty
abhisek.sac at gmail.com
Tue Nov 25 12:16:31 EST 2014
Dear Jean-Michel,
The figures (posted in my earlier mail) represents the various terms
required for closing the heat budget at surface as well as at a depth of
20m (sub-surface) at a particular location (90E12N). All the terms are
daily time series at that location (no horizontal mean).
For the surface level, I am using the TFLUX diagnostics. From your mail
what I understand is that
tend_heat_surf = tend_advection +
tend_diffusion +
tend_kpp +
(TFLUX-oceQsw)/(rhoConst*Cp*DRF(1)*hFacC(i,j,1))
+
tend_Qsw -
(WTHMASS(i,j,1) -
TsurfCor)/(DRF(1)*hFacC(i,j,1))
where
tend_Qsw = oceQsw/(rhoConst*Cp)/(DRF(1)*hFacC(i,j,1))*(swfrac(1)-swfrac(2))
and
TsurfCor = SUM( WTHMASS(i,j,1)*RAC(i,j) ) / globalArea
and "swfrac" is already defined in our earlier communications.
Am I correct?
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 25, 2014 at 2:21 AM, Jean-Michel Campin <jmc at ocean.mit.edu>
wrote:
> 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
> > >> > > > >>
> > >> > > > >> --
> > >> > > > >>
> > >> > > > >>
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