Re: [ferret_users] Why does ferret fail to support swapping integraland differential?

[Ansley Manke <ansley.b.manke@xxxxxxxx>]

Hi Feng,
You could redefine your coordinate axes so their units are not longitude and latitude, for the purposes of this calculation.  Then the order of the integral and derivitive can be interchanged and you should get the result you want.

Ansley

FENG HE wrote:

Hi Ansley 
Thank you for your reply. 
Right now, I understand the curvature of earth gives the difficulty for
this problem. 

I would like to know what is the right way to calculate the
streamfunction using Kessler's script
(http://ferret.pmel.noaa.gov/Ferret/Mail_Archives/fu_2002/msg00155.html)
Mathematically, the solution (Psi = Int{y0:y}u dy - Int{x_0:x}v(x,y_0)
dx) is perfect, but in Ferret, because it could not support swapping
integral and differential, I could not reproduce v using -d(Psi)/dx
Best regards

Feng He 
Center for Climate Research
Atmospheric and Oceanic Sciences
University of Wisconsin - Madison

----- Original Message -----
From: Ansley Manke <Ansley.B.Manke@noaa.gov>
Date: Friday, March 17, 2006 10:02 am
Subject: Re: [ferret_users] Why does ferret fail to support swapping
integral and differential?
To: FENG HE <fenghe@wisc.edu>
Cc: oar.pmel.ferret_users@noaa.gov

  

Hi Feng,
Thank you for sending a clear example.

This turns out to be because derivatives and integrals on fields in 
latitude and longitude are done in units of meters on the earth, 
rather 
than degrees latitude and longitude. The fact that degrees of 
longitude 
are not a constant length over the earth means that the 
computations are 
not linear. Try this case, where the numbers may be easier to 
interpret.
  yes? use coads_climatology
  yes? set reg/x=1:3/y=51:55/L=1

  yes? let uu_ddb = uu[x=@ddb]
  yes? let uu_ddb_iin = uu_ddb[y=@iin]
  yes? let uu_iin = uu[y=@iin]
  yes? let uu_iin_ddb = uu_iin[x=@ddb]

   ! Define a function with simple integer values

  yes? let uu = x[gx=uwnd] + y[gy=uwnd]
  yes? list uu

   ! Set the axes so they are NOT in units of degrees
   ! longitude and latitude.

  yes? set axis/units=" " coadsx
  yes? set axis/units=" " coadsy

   ! The results are as you would expect.

  yes? list uu_ddb
  yes? list uu_iin
  yes? list uu_ddb_iin
  yes? list uu_iin_ddb