Re: [ferret_users] How to Calulate second order Derivatives

["william s. kessler" <william.s.kessler@xxxxxxxx>]

It is pretty straightforward to write any sort of derivative in  
Ferret. For example, GCMs typically have particular schemes for  
derivatives that are not the same as the simple centered or sideways  
derivatives in DDC, DDB or DDF; in analyzing model output, it is  
often desirable to use the same derivative algorithm as done in the  
actual model run. Here, as an illustration, is an example that  
implements the 4th-order derivative scheme in the Gent-Cane model. In  
this script, the grid shape is hardwired (see definitions of deglen  
and xx), but this could also be a passed argument.

Billy K
---------------------------------------------------------
! finds the 4th-order centered x-difference as in G/C model
! arg1=variable name

! constants etc needed
let pi=4.*atan(1.)
let deglen=111198.6      ! one degree latitude in meters
let deglenx=deglen*cos(pi*y[g=u]/180)    ! one deg lon at latitude y

let xx = x[g=u]                  ! hardwire the grid-defining variable
let delx = deglenx*(xx[i=@shf:1]-xx[i=@shf:-1])/2
let d$1dx = ($1[i=@shf:-2] - 8*$1[i=@shf:-1] + 8*$1[i=@shf:1] - $1 
[i=@shf:2]) / (12*delx)

On 5Jul 2006, at 8:34 AM, Ansley Manke wrote:

> Hi Murali
> Ferret does not have a transformation for second order derivatives.  
> The @DDF, @DDB, and @DDC transformations just apply finite  
> difference approximations for the derivatives. It would not be  
> difficult, I suppose, to write an external function to do finite  
> differences of higher orders.  Has anyone done this?
>
> Ansley
>
> Murali Krishna wrote:
> > Dear Ferreters,
> >
> > To calculate 1st order differntial expression (�P/�x) we are  
> > using the function transformations @DDF, @DDB or @DDC. Then how to  
> > calculate second order derivative (�2P/�x2)? and I saw lot of  
> > the people using the @DDC function for both Differential (dP/dx)  
> > and Partial Differential (�P/�x) expressions. what are the  
> > exact transformations to be used to perform these two operations.  
> > Please help me.
> >
> > Thanks in advance.
> >
> >
> >
> > With Regards,
> >
> > Murali Krishna
> > --------------------------------------------------------------------- 
> > --------------------------
> >
> > S.Murali Krishna,
> > Senior Research Fellow,
> > Indian National Centre for Ocean Information Services (INCOIS),
> > "Ocean Valley", P.B No.21,IDA Jeedimetla P.O,
> > Hyderabad - 500 055, India. Mobile:09885694594
> > smkrishna@incois.gov.in