Re: [ferret_users] Sverdrup Streamfunction - indefinite integral withirregular boarders

["Dr. Theodor Yemenis" <yemenis@xxxxxxxxxxxxxxxxxx>]

Hi Ansley,

thanks for your  answer but something doesnt  work properly.

my curl_tau is missing over land, so I don't need the land-mask.

if I define PSI  like:

    LET PSI = IF curl_tau[x=150E:0] THEN (1/(beta*rho_ocean))*( 
(-1)*curl_tau[x=150E:0@iin] + curl_tau[x=150E:0@din] )/1E06

the result looks like in the attached image.

The calculation breaks at the boundaries and behind missing values 
(islands).
I think  @iin doesnt like missing values but I dont know how to filter 
them out
so that  the integration would be executed only over non-missing values.


best regards
Theodor

Ansley Manke wrote:

> Hi Theodor,
> I admit to looking at this just briefly, so I may be missing 
> something. Is your variable curl_tau missing over land? In that case, 
> in your definition of psi you should leave off the ELSE 0.  The result 
> will be missing wherever  the expresssion  curl_tau[x=160E:0@iin]  is 
> false. On this kind of definition there is an implied "ELSE missing"
>
> Otherwise you need to apply a mask to the data as outlined in this FAQ 
> about doing integration or averaging over irregular fields by applying 
> a mask;
> http://www.ferret.noaa.gov/Ferret/FAQ/analysis/avg_integ_irreg.html
>
> For your case the mask would be a field which is 1 over water and 
> missing over land.You could make such a variable from one of the 
> topography data sets, choosing one which has a resolution similar to 
> the grid your data is on
>
>   yes? use etopo20 
>   yes? let mask = IF rose[d=etopo20,gxy=curl_tau[d=1]] LT 0 then 1
>   yes? shade mask  ! Look at the plot to check the definition
>
> Dr. Theodor Yemenis wrote:
>
> > I am trying to calculate and plot with FERRET the Sverdrup 
> > Streamfunction from the wind stress curl  curl_tau
> >
> > acording to the formel:
> >
> > Psi = 1/beta Int_xlim(y) ^x curl(tau)dx,   xlim (y) is the  longitude 
> > of the boundary at each latitude.
> >
> > I use the following definition (for the pacific ocean):
> >
> >   LET PSI = IF curl_tau[x=160E:0@iin] THEN (1/(beta*rho_ocean))*( 
> > (-1)*curl_tau[x=160E:0@iin] + curl_tau[x=160E:0@din] )/1E06 ELSE 0
> >
> >   fill PSI ; go land
> >
> > the result is as in the attached GIF-image, but it is not sutisfing. 
> > I have the following problem:
> >
> > - the islands(Hawaii, New Zeland, ...) and the Continent (Australia) 
> > disdurb the calculation (no streamfunction behind the land-boarders).
> > The problem is computing an indefinite integral in an area with 
> > irregular boundaries.
> > How can I solve this? Can someone help?
> >
> > best regards
> > Theodor
> >
> >
> >
> >
> > ------------------------------------------------------------------------


--
--------------------------------------
Dr. Theodoros Yemenis
Center for Marine and Atmospheric Research
University of Hamburg
Institute of Oceanography
Bundesstrasse 53
D-20146 Hamburg
Germany
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phone:   +49 40 42838 6104
 fax:   +49 40 42838 7063
        +49 40 36 801 801
email:   yemenis@ifm.zmaw.de   
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