[MITgcm-devel] smoothing package for dimensional controls

[Matthew Mazloff]

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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> <ATT00001.txt>

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