[MITgcm-support] advective fluxes and transports

[Baylor Fox-Kemper]

Hi Dimitris (and Paola),
   A bit more:
1) UVELTH is just the correlation between U and T.
2) UTHMASS is the correlation between U and T, weighted by 'mass', or  
HFac, which gives free-surface corrections.
3) ADVx_TH is the 'effect of advection'.  It includes flux-limiting  
and diffusion from the numerical scheme.

So,
1) for statistics, UVELTH is probably best, because other  
complexities are just messing things up.
2) for transports that are 'advective', i.e., no explicit or overt  
implicit diffusive fluxes UTHMASS is good.
3) for closing budgets, or for diagnosing the full effect of the  
advection operator (which is, when flux-limiting, partly 'diffusive'  
in nature) use ADVx_TH.  You will not, for example, be able to easily  
account for all the terms leading to dT/dt at a given gridcell unless  
you use ADVx_TH.

If you really want to get fancy, you could save all three and see  
what the differences are... This allows you to break things down  
into, e.g., Stokes drift at the surface due to free surface effects  
(UVELTH vs UTHMASS), or how much of ADVx_TH is 'diffusive' versus  
'advective'.
    -Baylor

P.S. Keep in mind that second-order centered is not totally without  
'diffusive' discretization errors, just that no effort is made to  
exploit the diffusive errors to our advantage.  The discretization  
errors in second order centered appear as a hyperdiffusion: \nabla^4  
T.  Fourth-order centered is less 'diffusive', with discretization  
errors appearing only at \nabla^6 T.

Upwinding and flux-limiting exploit the fact that errors can be  
steered toward monotonicity and stability by messing around with  
diffusive errors at the cost of lower order accuracy. So, for  
example, first order upwinding can be thought of as adding an  
automatic \nabla^2 T diffusion to a second-ordered centered scheme.   
Third-order upwinding can be thought of as adding an automatic  
\nabla^4 T hyperdiffusion to a fourth-order centered scheme, etc.   
But, the amount of diffusivity added is dependent on velocity, e.g.,  
the "effective kappa" added is proportional gridscale*|U| in the  
first-order upwind versus second-order centered.  Thus, it is hard to  
diagnose after the fact.  Comparing ADVx and UTHMASS allows one to  
quickly do so.

On Feb 13, 2007, at 2:44 PM, Dimitris Menemenlis wrote:

> Baylor, for computation of transports, which diagnostic should one  
> use: ADVx_TH, UTHMASS, or UVELTH?  To date I have been using  
> UTHMASS but from your description below it sounds like it would be  
> more accurate to use ADVx_TH ?  D.
>
>
>> Hi Paola, UVELTH is just the correlation of the U and theta  
>> fields, with
>> temperature appropriate interpolated.  ADVx_TH is the advective  
>> flux, which
>> can include things like the variable grid box size with nonlinear  
>> free
>> surface, shaved cells, etc, as well as the flux-limiting  
>> corrections.  UVELTH
>> will be equivalent to ADVx_TH only with centered 2nd-order  
>> advection and
>> simple vertical discretization/boundary conditions. Cheers, -Baylor
>
>
> -- 
> Dimitris Menemenlis <menemenlis at jpl.nasa.gov>
> Jet Propulsion Lab, California Institute of Technology
> MS 300-323, 4800 Oak Grove Dr, Pasadena CA 91109-8099
> tel: 818-354-1656;  fax: 818-393-6720
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