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ilapsf

Inverts the Laplacian (on a fixed grid) using spherical harmonics.

Prototype

	procedure ilapsf (
		zlap    : numeric,          
		zlmbda  : numeric,          
		z       : float or double   
	)

Arguments

zlap

the Laplacian array to invert (input, two or more dimensions, last two dimensions must be nlat x nlon)

input values must be in ascending latitude order
input array must be on a global grid

zlmbda

If zlap is a two dimensional array then zlmbda may be a constant. If zlap has 3 or more dimensions then zlmbda must be an array with the same dimensions as zlap (minus the rightmost two dimensions). If zlmbda is identically zero, the poisson equation is solved. Otherwise, the Helmholtz equation is solved.

the inverted Laplacian array (output, same dimensions as zlap, values will be in ascending latitude order)

Description

ilapsf inverts the Laplacian zlap and returns it in the array z. ilapsf operates on a fixed grid.

This procedure does not handle missing values (defined by the _FillValue attribute). If any missing values are encountered in a particular 2D input grid, then all of the values in the corresponding output grid will be set to the default missing value appropriate to the type of the output.

Note: For the arrays whose last two dimensions are nlat x nlon, the rest of the dimensions (if any) are collectively referred to as N. If the input/output arrays are just two dimensions, then N can either be considered equal to 1 or nothing at all.

Arrays which have dimensions N x nlat x nlon should not include the cyclic (wraparound) points when invoking the procedures and functions which use spherical harmonics (Spherepack).

For example, if an array x has dimensions nlat = 64 and nlon = 129, where the "129" represents the cyclic points, then the user should pass the data to the procedure/function via:

    z = sample ( x([...],:,0:nlon-2) )  ; does not include cyclic points

If the input array zlap is on a gaussian grid, ilapsg should be used. Also, note that ilapsf is the procedural version of ilapsF.

Examples

Example 1

Read Z (on a fixed grid) from a netCDF file and compute the inverse laplacian, solving the Poisson equation (k=0):

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_code.ncl"
load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_csm.ncl"
begin
   a = addfile("/cgd/cas/shea/MURPHYS/ATMOS/80.fixed.nc","r")
   z200 = a->Z(0,{189.},:,:)			; z200 is dimensioned nlat x nlon
   printVarSummary(z200)
   ilapl = z200			; preallocate space for return array
   ilapsf(z200,0,ilapl)
end

Errors

If jer or ker is equal to: