[MITgcm-devel] diagnostics: fixing variances

[Jean-Michel Campin]

Hello Ed,

I don't understand exactly this "elegant" solution,
and I have seen 2 recent modifications that were
supposed to fix this precision problem:
1) the new "fflags" (to write 1 file in real*8).
2) new diagnostics: SALTanom and SALTSQan
my question is what is the problem with those 2 solutions ?

Thanks,

Jean-Michel

On Sun, May 08, 2005 at 12:55:35AM -0400, Ed Hill wrote:
> 
> Hi Jean-Michel, Andrea, Gael, & Dimitris,
> 
> Heres an idea for improving the diagnostics package that will, I think,
> elegantly solve the output-precision problem for variances.
> 
> The problem is: if one wants to compute variances within diagnostics,
> one currently has to choose between doubling the size of the output
> using REAL*8, facing very serious (catastrophic as Gael has seen w/
> SALT) precision loss using REAL*4 output, or messing with some sort of
> scaling to try to subtract a mean.  All are bad choices.  But there is a
> deeply satisfying fix!  Instead of computing a mean and a mean-of-
> squares as we currently do (eg. SALT, SALTSQ) and then squashing them
> into REAL*4 for the output, we should instead compute a mean and a
> standard deviation together within the model
> 
>   VAR_STD = sqrt( mean(VAR^2) - (mean(VAR))^2 )
> 
> as another kind of "pair-wise" diagnostic.  The benefits are:
> 
>  - its the *same* information but with absolutely minimal loss 
>      of precision since the rounding occurs ***after*** the critical 
>      bits are computed
>  - it adds no additional storage to either the model or the output
>  - Dimitris (and others with huge simulations) get to use the 
>      more compact REAL*4 for all output
> 
> The only down-side is that we need to re-work the code a bit.  But its
> not a massive re-write.  The diagnostics package can certainly handle
> this sort of thing within its design.
> 
> Attached is an example plot and a MatLAB script used to draw it.  It
> shows how this approach can maintain precision over 4+ additional orders
> of magnitude (green line) over what we currently do (red line).
> 
> Ed
> 
> -- 
> Edward H. Hill III, PhD
> office:  MIT Dept. of EAPS;  Rm 54-1424;  77 Massachusetts Ave.
>              Cambridge, MA 02139-4307
> emails:  eh3 at mit.edu                ed at eh3.com
> URLs:    http://web.mit.edu/eh3/    http://eh3.com/
> phone:   617-253-0098
> fax:     617-253-4464



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