# [Met_help] [rt.rap.ucar.edu #53003] History for Regarding scale specification in wavelet-stat tool of MET

John Halley Gotway via RT met_help at ucar.edu
Fri Jan 27 09:53:14 MST 2012

```----------------------------------------------------------------
Initial Request
----------------------------------------------------------------

I wish to use wavelet stat tool for verification.
I am using tile_dim=64
so NSCALE is 6
now according to my understanding, ISCALE 0 to 5 (i.e. n=0 to n-1) is for
mother wavelet component and ISCALE = 6 is for father wavelet component
(domain mean), then ISCALE=7 stands for what ? There are in total 8
categories of ISCALE (i.e. 0 to 7) are appearing on line type ___isc.txt .
Kindly explain.

Thanks and Regards
Mansi Bhowmick
Project Scientist
India Meteorological Department

----------------------------------------------------------------
Complete Ticket History
----------------------------------------------------------------

Subject: Regarding scale specification in wavelet-stat tool of MET
From: John Halley Gotway
Time: Wed Jan 25 08:52:04 2012

Mansi,

I ran a test case of Wavelet-Stat using a tile dimension of 64 (which
is 2 to the 6th power), and I attached some images of the output.

Also below, I've listed an excerpt from section 7.2.1 of the MET
User's Guide:

-----------------------------------------------------------------------------

The binary forecast and observation fields obtained from the
thresholding are then decomposed into the sum of components on
different scales, by using a 2D Haar wavelet filter (Fig 7.2). Note
that the
scale components are fields, and their sum adds up to the original
binary field. For a forecast defined over square domain of 2^n grid-
points, the scale components are n+1: n mother wavelet
components + the largest father wavelet (or scale-function) component.
The n mother wavelet components have resolution equal to 1, 2, 4, ...
2^(n-1) grid-points. The largest father wavelet component
is a constant field over the 2^n grid-point domain with value equal to
the field mean.

-----------------------------------------------------------------------------

In the case of 64 = 2^6, we have 6 mother wavelet components with
resolutions equal to 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and
2^5 = 32 grid points.  And we have the largest father wavelet
which is constant over the 2^6 = 64 grid-point domain.  So in the
attached output images, you should see pictures for the raw field, the
thresholded binary field, 6 mother wavelets, and one father
wavelet.

In the process of looking at this, I do see that our documentation
says "2^n x 2^n" in a few places when it should just say "2^n".
Perhaps that's a source of confusion.  I'll make sure we correct
that for the next release.

Thanks,
John Halley Gotway
met_help at ucar.edu

On 01/25/2012 03:03 AM, Mansi via RT wrote:
>
> Wed Jan 25 03:03:50 2012: Request 53003 was acted upon. Transaction:
Ticket created by mansibhowmick at gmail.com Queue: met_help Subject:
Regarding scale specification in wavelet-stat tool of MET
> Owner: Nobody Requestors: mansibhowmick at gmail.com Status: new
Ticket<URL: https://rt.rap.ucar.edu/rt/Ticket/Display.html?id=53003>
>
>
>
> I wish to use wavelet stat tool for verification. I am using
tile_dim=64 so NSCALE is 6 now according to my understanding, ISCALE 0
to 5 (i.e. n=0 to n-1) is for mother wavelet component and ISCALE
> = 6 is for father wavelet component (domain mean), then ISCALE=7
stands for what ? There are in total 8 categories of ISCALE (i.e. 0 to
7) are appearing on line type ___isc.txt . Kindly explain.
>
> Thanks and Regards Mansi Bhowmick Project Scientist India
Meteorological Department

------------------------------------------------
Subject: Re: [rt.rap.ucar.edu #53003] Regarding scale specification in wavelet-stat tool of MET
From: John Halley Gotway
Time: Wed Jan 25 09:02:55 2012

Mansi,

says 2^n x 2^n in section 7.2.1 of the documentation is correct.  I
was just confusing myself!

Thanks,
John

On 01/25/2012 08:52 AM, John Halley Gotway wrote:
> Mansi,
>
> I ran a test case of Wavelet-Stat using a tile dimension of 64
(which is 2 to the 6th power), and I attached some images of the
output.
>
> Also below, I've listed an excerpt from section 7.2.1 of the MET
User's Guide:
>
>
-----------------------------------------------------------------------------
>
> The binary forecast and observation fields obtained from the
thresholding are then decomposed into the sum of components on
different scales, by using a 2D Haar wavelet filter (Fig 7.2). Note
that the
> scale components are fields, and their sum adds up to the original
binary field. For a forecast defined over square domain of 2^n grid-
points, the scale components are n+1: n mother wavelet
> components + the largest father wavelet (or scale-function)
component. The n mother wavelet components have resolution equal to 1,
2, 4, ... 2^(n-1) grid-points. The largest father wavelet component
> is a constant field over the 2^n grid-point domain with value equal
to the field mean.
>
>
-----------------------------------------------------------------------------
>
> In the case of 64 = 2^6, we have 6 mother wavelet components with
resolutions equal to 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and
2^5 = 32 grid points. And we have the largest father wavelet
> which is constant over the 2^6 = 64 grid-point domain. So in the
attached output images, you should see pictures for the raw field, the
thresholded binary field, 6 mother wavelets, and one father
> wavelet.
>
> In the process of looking at this, I do see that our documentation
says "2^n x 2^n" in a few places when it should just say "2^n".
Perhaps that's a source of confusion. I'll make sure we correct that
> for the next release.
>
>
> Thanks,
> John Halley Gotway
> met_help at ucar.edu
>
>
> On 01/25/2012 03:03 AM, Mansi via RT wrote:
>>
>> Wed Jan 25 03:03:50 2012: Request 53003 was acted upon.
Transaction: Ticket created by mansibhowmick at gmail.com Queue: met_help
Subject: Regarding scale specification in wavelet-stat tool of MET
>> Owner: Nobody Requestors: mansibhowmick at gmail.com Status: new
Ticket<URL: https://rt.rap.ucar.edu/rt/Ticket/Display.html?id=53003>
>>
>>
>>
>> I wish to use wavelet stat tool for verification. I am using
tile_dim=64 so NSCALE is 6 now according to my understanding, ISCALE 0
to 5 (i.e. n=0 to n-1) is for mother wavelet component and ISCALE
>> = 6 is for father wavelet component (domain mean), then ISCALE=7
stands for what ? There are in total 8 categories of ISCALE (i.e. 0 to
7) are appearing on line type ___isc.txt . Kindly explain.
>>
>> Thanks and Regards Mansi Bhowmick Project Scientist India
Meteorological Department

------------------------------------------------
Subject: Regarding scale specification in wavelet-stat tool of MET
From: Mansi
Time: Thu Jan 26 23:08:09 2012

Respected Sir,

Many thanks for the reply and explanation.
Perhaps I have misunderstood ISCALE=0 as 1st mother wavelet component
,which actually stands for thresholded binary field.

Thanks and regards
Mansi

On 25 January 2012 21:32, John Halley Gotway via RT
<met_help at ucar.edu>wrote:

> Mansi,
>
> Please disregard my comment about the documentation issue - where it
says
> 2^n x 2^n in section 7.2.1 of the documentation is correct.  I was
just
> confusing myself!
>
> Thanks,
> John
>
> On 01/25/2012 08:52 AM, John Halley Gotway wrote:
> > Mansi,
> >
> > I ran a test case of Wavelet-Stat using a tile dimension of 64
(which is
> 2 to the 6th power), and I attached some images of the output.
> >
> > Also below, I've listed an excerpt from section 7.2.1 of the MET
User's
> Guide:
> >
> >
>
-----------------------------------------------------------------------------
> >
> > The binary forecast and observation fields obtained from the
> thresholding are then decomposed into the sum of components on
different
> scales, by using a 2D Haar wavelet filter (Fig 7.2). Note that the
> > scale components are fields, and their sum adds up to the original
> binary field. For a forecast defined over square domain of 2^n grid-
points,
> the scale components are n+1: n mother wavelet
> > components + the largest father wavelet (or scale-function)
component.
> The n mother wavelet components have resolution equal to 1, 2, 4,
...
> 2^(n-1) grid-points. The largest father wavelet component
> > is a constant field over the 2^n grid-point domain with value
equal to
> the field mean.
> >
> >
>
-----------------------------------------------------------------------------
> >
> > In the case of 64 = 2^6, we have 6 mother wavelet components with
> resolutions equal to 2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16,
and 2^5
> = 32 grid points. And we have the largest father wavelet
> > which is constant over the 2^6 = 64 grid-point domain. So in the
> attached output images, you should see pictures for the raw field,
the
> thresholded binary field, 6 mother wavelets, and one father
> > wavelet.
> >
> > In the process of looking at this, I do see that our documentation
says
> "2^n x 2^n" in a few places when it should just say "2^n". Perhaps
that's a
> source of confusion. I'll make sure we correct that
> > for the next release.
> >
confusion,
> >
> > Thanks,
> > John Halley Gotway
> > met_help at ucar.edu
> >
> >
> > On 01/25/2012 03:03 AM, Mansi via RT wrote:
> >>
> >> Wed Jan 25 03:03:50 2012: Request 53003 was acted upon.
Transaction:
> Ticket created by mansibhowmick at gmail.com Queue: met_help Subject:
> Regarding scale specification in wavelet-stat tool of MET
> >> Owner: Nobody Requestors: mansibhowmick at gmail.com Status: new
> Ticket<URL: https://rt.rap.ucar.edu/rt/Ticket/Display.html?id=53003>
> >>
> >>
> >>
> >> I wish to use wavelet stat tool for verification. I am using
> tile_dim=64 so NSCALE is 6 now according to my understanding, ISCALE
0 to 5
> (i.e. n=0 to n-1) is for mother wavelet component and ISCALE
> >> = 6 is for father wavelet component (domain mean), then ISCALE=7
stands
> for what ? There are in total 8 categories of ISCALE (i.e. 0 to 7)
are
> appearing on line type ___isc.txt . Kindly explain.
> >>
> >> Thanks and Regards Mansi Bhowmick Project Scientist India
> Meteorological Department
>
>

------------------------------------------------
```