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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

center_finite_diff

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 = 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:nl,:) = center_finite_diff_n (T(:,:,nl:nl,:), dX , True,0,3)
  end do
; result: dTdX(time,lev,lat,lon)
The reason for the 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,:) = center_finite_diff_n (T(:,:,nl,:), dX , True,0,2)
The arrays are 'temporarily' reduced to 3D and the longitude dimension number is 2, not 3.