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[GEMPAK #MJB-537359]: Error in dfgwfs?

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  • Subject: [GEMPAK #MJB-537359]: Error in dfgwfs?
  • Date: Wed, 22 Sep 2010 10:02:22 -0600
Jack,

The definition of sigma in dfgwfs includes the factor of 2 (or sqrt of 2) that 
would conventionally be expressed inside the weighting function.

sgma = (float)nwl / ( PI * sqrt ( 2.0 ) );

which results in

sig2 = sgma**2 = nwl**2 / 2 * PI**2 

therefore the factor of 2 is included in sig2 the variable aa:

aa = 1. / ( sig2 * PI );

which is expressed in the weighting function (with sig2 rather than 2 * sig2):

w[iw-1][jw-1] = aa * exp ( - ( x*x + y*y ) / sig2 );



if the factor of 2 were not included in sgma, it would be accounted for in aa 
and w as:

aa = 1. / ( 2 ** sig2 * PI );

which is expressed in the weighting function:

w[iw-1][jw-1] = aa * exp ( - ( x*x + y*y ) / 2 ** sig2 );

so essentially we're only changing the definition of sgma in dfgwfs.f to 
include the factor of 2 so we don't need to account for it in aa and w.

I did a quick napkin run-down of the terms and the math seems correct.  Do you 
agree?

Michael James
Unidata


> Hi,
> 
> I was looking at the code for the Gaussian smoother in GEMPAK called dfgwfs 
> and came across what might be an error, but I wanted to run it by you to make 
> sure.  The weighting function used is:
> 
> 
> 
> Where  and N is the number of grid points in a wavelength.  I'm wondering if 
> ? should be given instead by .  This value for sigma seems to be correct 
> given your definition of W.  Would someone please take a look?
> 
> 
> 
> Thanks,
> 
> Jack
> 
> 
> 
> Jack Dostalek
> 
> Cooperative Institute for Research in the Atmosphere
> 
> Colorado State University
> 
> Foothills Campus
> 
> 1375 Campus Delivery
> 
> Fort Collins, CO 80523-1375
> 
> (970) 491-8326
> 
> address@hidden
> 
> 
> 
> 
> 
> 
> 
> 
> 


Ticket Details
===================
Ticket ID: MJB-537359
Department: Support GEMPAK
Priority: Normal
Status: Open