[MITgcm-devel] smoothing package for dimensional controls

Fri May 20 01:31:20 EDT 2011

Hi Matt,
> #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?
Sure. I don't have a strong preference for the name. May be 'smooth' rather than 'effective'.  Up to you.

Cheers,
Gael


> 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>
>>>> 
>>>> _______________________________________________
>>>> MITgcm-devel mailing list
>>>> MITgcm-devel at mitgcm.org
>>>> http://mitgcm.org/mailman/listinfo/mitgcm-devel
>>> 
>>> <ATT00001.txt>
>> 
>> <ATT00001.txt>
> 
> _______________________________________________
> MITgcm-devel mailing list
> MITgcm-devel at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-devel

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20110520/1dfadff5/attachment.htm>