# Re: cross-corelation coherence

From: Maria Gehne <mgehne_at_nyahnyahspammersnyahnyah>
Date: Tue Oct 29 2013 - 11:11:15 MDT

Hi Xi,

I don't think it is very difficult, maybe a little tedious (because you
probably want this for multiple latitudes and heights). The paper gives
you an excellent, very detailed description of how to compute the
cross-spectra and you can use existing ncl routines for most of the
calculations.

Here is a suggestion of how you could try to go about this:

1) choose two latitudes and heights that you want to compare (see the
paper you mentioned, page 921)

2) this gives you two arrays of size (nt,nx), the Z1 and Z2 in the paper

3) use ezfftf on both of these (as Dennis already mentioned). ezfftf
works on the right-most dimension if there is more than one so you will
end up with two arrays of size (2,nt,nk), where the last one is the
number of zonal wavenumbers

4) choose which zonal wavenumber you want, this leaves you with 4 time
series S1, S2, C1, C2 for the Fourier coefficients at that wavenumber

5) to get CO(tau) you can use the ncl function esccr: CO =
esccr(S1,S2,mxlag)+ esccr(C1,C2,mxlag)

6) similarly you can use that for the quadrature as well: QD =
esccr(S1,C2,mxlag)- esccr(C1,S2,mxlag)

7) use these to compute the coherence and phase at the different lags
(as in equations 1c and 1d in the paper)

Hope this helps,
Maria

On 10/29/2013 09:18 AM, Xi Chang wrote:
> I think, it's still difficultto use "ezfftf" in this case, since this
> method needs to find a coherence (based on "le Fourier coefficient")
>
> ==> let's say for k=1 --> Cohr= (CO^2 + QD^2) ^1/2
>
> is it possible to use "specxy_anal" in this case,, however I have no
> idea to retain a specific wavenumber in this case.
>
> Xi
>
>
> On Tue, Oct 29, 2013 at 3:22 PM, Dennis Shea <shea@ucar.edu
> <mailto:shea@ucar.edu>> wrote:
>
> To my knowledge, this has not been done. Pretty specialized!
>
> Use ezfftf to perform the Fourier analysis at each
> time, level and latitude. This will provide the Fourier coefficients
> [his S1(t) and C1(t)]. You specify the desired wave number, k.
>
> http://www.ncl.ucar.edu/Document/Functions/Built-in/ezfftf.shtml
>
>
> On 10/29/13 7:13 AM, Xi Chang wrote:
>
> Hallo NCL folks,
>
> Anyone here has ever used the cross-spectral correlation or cross
> corelation coherence (Randel 1987) using NCL? maybe you could
> share the
> main idea/function underlying this diagnostic tool?
>
> Thanks,
> Xi
>
>
>
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```--
Maria Gehne
Postdoctoral Fellow
NCAR/CGD/CAS
P.O. Box 3000
Boulder, CO 80307

```

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Received on Tue Oct 29 11:11:31 2013

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