# center_finite_diff_n

Performs a centered finite difference operation on the given dimension.

*Available in version 5.2.0 and later.*

## Prototype

function center_finite_diff_n ( q : numeric, r : numeric, rCyclic : logical, opt : integer, dim [1] : integer ) return_val [dimsizes(q)] : numeric

## Arguments

*q*

A multi-dimensional array.

*r*

A scalar, one-dimensional, or multi-dimensional array
containing the coordinates along which *q* is to be
differenced. Does need not be equally spaced from a computational
point of view.

- scalar:
*r*assumed to be the (constant) distance between adjacent points. - one-dimensional (and the same size as the
*dim*-th dimension of*q*): applied to all dimensions of*q*. - multi-dimensional: then it must be the same size as
*q*.

*rCyclic*

True: *q* treated as cyclic in *r* and the end values
and all the returned values will be calculated via centered differences.
False: *q* NOT
treated as cyclic in *r* and the end values will use a one-sided
difference scheme for the end points. *q* should not include a
cyclic point.

result(n) = (q(n+1)-q(n))/(r(n+1)-r(n)) for the initial value result(m) = (q(m)-q(m-1))/(r(m)-r(m-1)) for the last value

*opt*

Reserved for future use. Currently not used. Set to an integer.

*dim*

A scalar integer indicating which dimension of *q* to calculate
the center finite difference on. Dimension numbering starts at 0.

## Description

Performs a centered finite difference operation on the *dim*-th
dimension. If
missing
values are present, the calculation will occur at all points
possible, but coordinates which could not be used will set to missing.

result(n) = (q(n+1)-q(n-1))/(r(n+1)-r(n-1))

## See Also

## Examples

**Example 1**

q = (/30,33,39,36,41,37/) r = 2. ; constant dqdr =center_finite_diff_n(q,r,False,0,0)

Result:

dqdr(0) = (33-30)/2 = 1.5 dqdr(1) = (39-30)/4 = 2.25 dqdr(2) = (36-33)/4 = 0.75 dqdr(3) = (41-39)/4 = 0.5 dqdr(4) = (37-36)/4 = 0.25 dqdr(5) = (37-41)/2 = -2.0

**Example 2:**

theta = (/ 298,299,300,302,...,345,355,383/) ; potential temp. p = (/1000,950,900,850,...,200,150,100/) ; pressure (hPa) dtdp =center_finite_diff_n(theta,p,False,0,0)

**Example 3**

p is not equally spaced. Demonstrates defining the appropriate pressure levels when the r coordinate is not equally spaced. The end points are computed via a one-sided difference.

theta = (/ 297, 298,300,302,...,345,350,355,383/) ; potential temp. p = (/1013,1000,900,850,...,200,175,150,100/) ; pressure (hPa) dtdp =center_finite_diff_n(theta,p,False,0,0) np =dimsizes(p) pPlot =new( np, "float" ) ; arithmetic mean pPlot(0) = (p(0)+p(1))*0.5 ; set bottom pPlot(np-1) = (p(np-1)+p(np-2))*0.5 ; set top pPlot(1:np-2) = (p(0:np-3) + p(2:np-1))*0.5 ; mid points ; or ; log (mass) wgted pPlot(0) =exp((log(p(0))+log(p(1)))*0.5) ; set bottom pPlot(np-1) =exp((log(p(np-1))+log(p(np-2)))*0.5) ; set top pPlot(1:np-2) =exp((log(p(0:np-3)) +log(p(2:np-1)))*0.5) ; mid points

**Example 4**

Let T be four-dimensional with dimensions time,level,lat,lon. P is one-dimensional. Perform the finite differencing only in the vertical (level) dimension.

dTdP =center_finite_diff_n(T,P,False,0,1) ; returns dTdP (time,lev,lat,lon).

**Example 5**

Now P is also four-dimensional:

dTdP =center_finite_diff_n(T, P, False, 0, 1) ; returns dTdP(time,lev,lat,lon)

**Example 6**Assume that the longitude coordinate variable associated with T in the examples above is cyclic and is equally spaced in degrees but not in physical space.

dlon = (lon(2)-lon(1))*0.0174533 ; convert to radians ; pre-allocate space dTdX =The reason for thenew( (/ntim,klev,nlat,mlon/),typeof(T), T@_FillValue) do nl=0,nlat-1 ; loop over each latitude dX = 6378388.*cos(0.0174533*lat(nl))*dlon ; constant at this latitude dTdX(:,:,nl:nl,:) =center_finite_diff_n(T(:,:,nl:nl,:), dX , True,0,3) end do ; result: dTdX(time,lev,lat,lon)

**nl:nl**is to preserve the 4D structure of the array.

A subtle issue with NCL is that it removes "degenerate dimensions." If we had used the following

dTdX(:,:,nl,:) =The arrays are 'temporarily' reduced to 3D and the longitude dimension number iscenter_finite_diff_n(T(:,:,nl,:), dX , True,0,2)

**2**, not

**3**.