# center_finite_diff

Performs a centered finite difference operation on the rightmost dimension.

## Prototype

function center_finite_diff ( q : numeric, r : numeric, rCyclic : logical, opt : 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. These do need not be equally spaced from a computational
point of view. However, they must be monotonic along the operable dimension.

- scalar:
*r*assumed to be the (constant) distance between adjacent points. - one-dimensional (and the same size as the rightmost 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.

## Description

Performs a centered finite difference operation on the rightmost 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))

**Use center_finite_diff_n if the dimension to do the
calculation on is not the rightmost dimension and reordering is not
desired. This function can be significantly faster
than center_finite_diff.**

## See Also

## Examples

**Example 1**

q = (/30,33,39,36,41,37/) r = 2. ; constant dqdr =center_finite_diff(q,r,False,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(theta,p,False,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(theta,p,False,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. This requires that T be reordered to put level in the rightmost dimension.

Note: in V5.2.0 or later you can use **center_finite_diff_n**
to avoid having to reorder the data.

dTdP =center_finite_diff(T(time|:,lat|:,lon|:,lev|:),P,False,0) ; returns dTdP (time,lat,lon,lev). this variable can be reordered ; again to place it back in the original order ; In version 5.2.0 or later: ; dTdP =center_finite_diff_n(T,P,False,0,1) ; returns dTdP (time,lev,lat,lon)

**Example 5**

Now P is also four-dimensional and requires reordering:

dTdP =center_finite_diff(T(time|:,lat|:,lon|:,lev|:) \ ,P(time|:,lat|:,lon|:,lev|:), False,0) ; returns dTdP(time,lat,lon,lev) ; In version 5.2.0 or later: ; 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 =new( (/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,:) =center_finite_diff(T(:,:,nl;,:), dX , True,0) end do ; result: dTdX(time,lev,lat,lon)