[MITgcm-devel] smoothing package for dimensional controls

[Matthew Mazloff]

HI Gael:

This:

> Modified Files:
> 	ctrl_map_ini_gen.F ctrl_get_gen.F
> Log Message:
> - introducing ALLOW_SMOOTH_CTRL2D/3D that apply
>  a simple smoother to control vector adjustments
> - this is for the case when IFNDEF ALLOW_SMOOTH_CORREL2D/3D

is perfect!  Thanks so much for cleaning this up -- this is exactly  
what I needed.  I'll remove the stuff I added asap.

I would, however, like to still output the effective controls if you  
don't mind.  So I propose

#elif (defined (ALLOW_SMOOTH_CTRL2D))
       call smooth2D(xx_gen1,genmask,1,mythid)
#endif

becomes

#elif (defined (ALLOW_SMOOTH_CTRL2D))
       call smooth2D(xx_gen1,genmask,1,mythid)
       write(fnamegeneric(1:80),'(2a,i10.10)')
      & xx_gen_file(1:ilgen),'.effective.',optimcycle
       call mdswritefield(fnamegeneric,ctrlprec,.FALSE.,'RL',
      & 1, xx_gen1, gencount0, optimcycle, mythid)
#endif

Is this ok?  Or would you propose I name it differently or even,  
perhaps, use a diagnostic or debug level flag?

Thanks
Matt




On May 18, 2011, at 7:39 PM, Matthew Mazloff wrote:

> Hi Gael,
>
> OK, I simply took it outside of ALLOW_SMOOTH_CORREL until I can  
> think of a better way to do it
>
> I switched the CPP flag to NONDIMENSIONALIZE_CONTROL and have this  
> flag only nondim the controls (for later use in smoothing package).
>
> An issue is the I left smooth_correl2Dw.F the way it was and use it  
> to non-dim 2d ctrls.  Ideally smooth_correl2Dw would be reverted and  
> a separate function from package ctrl would be used to non- 
> dimensionalize...
>
> Is what I have done ok for now?
>
> Thanks
> Matt
>
>
>
>
>
>
>
>
> On May 18, 2011, at 6:29 PM, Gael Forget wrote:
>
>> Hi Matt,
>>
>>> I don't agree that the important smoothing correlation operator of  
>>> Weaver and Courtier 2001 requires non-dim controls.  Just let S be  
>>> a diagonal identity matrix instead of the diagonal uncertainty and  
>>> all is ok...the important part, that the correlation matrix B is  
>>> represented by a diagonal matrix times a smoother (B^(0.5) = A  
>>> L^(0.5) W^(-0.5) ) remains...or am I missing something...
>> I agree with your thought exp. The l.h.s. factor S is the one that  
>> sets the
>> error variance of the dimensional dx. You can set it to one, sure.
>>
>> But I was questioning what you did on the r.h.s. as part of  
>> B^(0.5), rather than
>> what is done on its l.h.s. of it. Now I am unsure (I would need to  
>> redo the
>> maths) but my recollection was that one cannot mess with the r.h.s.  
>> if one
>> wants to ensure that the error variance of dx be the one spec. by  
>> S^2.
>> May be I am mistaken though.
>>
>> Gael
>>
>>> Regardless, I can move the ALLOW_DIMENSIONAL_CONTROL stuff outside  
>>> of ALLOW_SMOOTH_CORREL...but would it be ok to leave the  
>>> smooth_correl2Dw.F the way it is....or do you object to that?  Or  
>>> am I missing a better way to do this...
>>>
>>> Sorry for causing trouble -- and perhaps missing something key --  
>>> I can call you if you want to discuss the best way to implement this
>>>
>>> Thanks
>>> Matt
>>>
>>>
>>> On May 18, 2011, at 5:17 PM, Gael Forget wrote:
>>>
>>>>
>>>> Hi Matt,
>>>>
>>>> I guess I was not fast enough to object, but I am not excited by  
>>>> what you did.
>>>>
>>>> To smooth dimensional controls I would much prefer you added  
>>>> calls to
>>>> smooth_diff2d / 3d.F outside of the ifdef ALLOW_SMOOTH_CORREL3D/2D.
>>>>
>>>> To make my reasons more clear I shall summarize the difference  
>>>> between the
>>>> smoothing and correlation components of pkg/smooth. I reckon I  
>>>> should have
>>>> documented this stuff in MITgcm-manual already, so I tried to  
>>>> write the
>>>> following as a draft for the MITgcm-manual.
>>>>
>>>> ---
>>>>
>>>> The very smoothing boils down to a call to smooth_diff3d / 2d.F
>>>> which can of course happen outside of ALLOW_SMOOTH_CORREL3D/2D.
>>>> The smoothing is done by time integrating diffusion equation with  
>>>> diffusion coeffs
>>>> matching a smoothing spatial scale (typically specified through  
>>>> data.smooth).
>>>>
>>>> The covariance construct of Weaver and Courtier 2001 (se their Eq. 
>>>> 52&15)
>>>> is more elaborate than that. In matrix form, it reads as
>>>>    dx = S B^(0.5) du
>>>> where dx is the dimensional control vector adjustment,
>>>> du is the nondimensional one, S is the diagonal uncertainty
>>>> matrix (i.e. the scaling factor), and B is the correlation matrix
>>>>    B^(0.5) = A L^(0.5) W^(-0.5)
>>>> where W is the diagonal matrix of grid cell volumes, L is the  
>>>> smoother,
>>>> and A is the diagonal normalization matrix. A must be computed
>>>> so that B=B^(T.5) B^(0.5) has ones on the diagonal. Hence
>>>> B does qualify as a correlation matrix, and B^(T.5) S^(2) B^(0.5)  
>>>> does
>>>> qualify as a covariance matrix. This is what is done within ifdef
>>>> ALLOW_SMOOTH_CORREL3D / 2D (assuming I did not put bugs or typos).
>>>>
>>>> ---
>>>>
>>>> So, coming back to your checkin, Matt,  I would rather not have  
>>>> CPP brackets
>>>> within ALLOW_SMOOTH_CORREL3D / 2D that would break this defining  
>>>> property of B.
>>>> Such as adding S^(-1) on the r.h.s. of B^(0.5) …
>>>>
>>>> Outside of ALLOW_SMOOTH_CORREL3D / 2D such self-consistency does  
>>>> not
>>>> matter much, and there is a number of preconditioner options  
>>>> (combinations of
>>>> ALLOW_NONDIMENSIONAL_CONTROL_IO, CTRL_PACK_PRECISE,
>>>> CTRL_DELZNORM, CTRL_SMOOTH, etc?).
>>>>
>>>> My guess is that adding some smooth_diffXd.F to that mix would  
>>>> fit your usage. Would it?
>>>>
>>>> Cheers,
>>>> Gael
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> <ATT00001.txt>
>>>
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