Re: drawing Taylor diagram ...

On 05/17/2010 12:30 PM, u.utku.turuncoglu@be.itu.edu.tr wrote:
> Hi,
>
> I try to plot a Taylor diagram to compare the different model simulations
> with observations. So, i have some basic question about the procedure;
Hi Ufuk,

[1] No.

[2] See Example 7 at

http://www.ncl.ucar.edu/Applications/taylor.shtml

>
> 1 - I am using monthly mean precipitation rate field (mm/day) and surface
> temperature that is averaged over specified region (i will plot them in
> different Taylor diagrams). Is it necessary to interpolate all model
> results and observation into a common grid before calculating variances
> and cross correlation?

It is easy to compute the variances on the original grids. However, the
correlations requires the same grid. Hence, it is best to interpolate
to a common grid. This grid is commonly the reference grid configuration
but that is up to you.

>
> 2 - As you already know that the Taylor diagram NCL function basically
> expects the ratio of the standardized variances and cross correlation
> between model and observation. To calculate the variance, i am using
> "variance" function but i think i have to standardize the fields before
> applying variance function. Is it correct?

vcntl => reference or control variable
vtest => model variable

If the region being tested is 'large' then a weight variable [wgt]
should be created. If your region is 'small', you can ignore the
weight [wgt=1]. Given that you are looking at a very small area, you
can ignore any weighting. Also you have masked out all points outside
your area of interest.

              var_cntl = variance(vcntl)
              var_test = variance(vtest)

              ratio = var_test/var_cntl

By definition, the correlation is already standardized [-1 to +1]
So, if var_test and var_cntl are on the same grid and you are not
applying weighting then the pattern correlation is

              cc = escorc( ndtooned(var_cntl), ndtooned(var_test) )

===
For a 'large' area, you will have to apply weighting [same grids]

              wgt = conform(vcntl, wt , rank-2)
            ;;wgt = mask(wgt, lsflag.eq.0, False) ; if desired
            ;;wgt = mask(wgt, lsflag.eq.1, False)

                                          ; temporary variables
              sumw = sum(wgt)
              sumwc = sum(wgt*vcntl)
              sumwt = sum(wgt*vtest)
                                          ; wgted areal mean
              wmean_cntl = sumwc/sumw
              wmean_test = sumwt/sumw
                                          ; wgted areal variance
              wvar_cntl = sum(wgt*(vcntl-wmean_cntl)^2)/sumw
              wvar_test = sum(wgt*(vtest-wmean_test)^2)/sumw

                                          ; wgted correlation coef
              wcc = (sum(wgt*vcntl*vtest) - sumwc*sumwt/sumw )/ \
                           ((sum(wgt*vcntl^2) - sumwc^2/sumw) * \
                            (sum(wgt*vtest^2) -sumwt^2/sumw))^0.5

=======

Good luck
D

If yes, can i use the
> "dim_standardize" to do that? The current structure of my scripts seems
> like,
>
> model1_variance = variance(model1)
> obs_variance = variance(obs)
>
> cc = escorc(obs, model1)
> ratio = model1_variance/obs_variance
>
> but i think that it must be,
>
> model1_variance = variance(dim_standardize (model1))
> obs_variance = variance(dim_standardize (obs))
>
> cc = escorc(obs, model1)
> ratio = model1_variance/obs_variance
>
> PS: you can find my taylor NCL scripts as attachment.
>
> Any suggestions can be helpful.
> Thanks,
>
> --ufuk
>
>
>
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-- 
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Dennis J. Shea                  tel: 303-497-1361    |
P.O. Box 3000                   fax: 303-497-1333    |
Climate Analysis Section                             |
Climate & Global Dynamics Div.                       |
National Center for Atmospheric Research             |
Boulder, CO  80307                                   |
USA                        email: shea 'at' ucar.edu |
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