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Computes the gradient of an array that is on a gaussian grid using spherical harmonics.


	procedure gradsg (
		z    : numeric,          
		gzx  : float or double,  
		gzy  : float or double   



The array to compute the gradient of (input, two or more dimensions, rightmost two dimensions must be nlat x nlon).

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


Gradient arrays (output, same dimensions as z, values will be in ascending latitude order)


gradsg computes the gradient given an array z, and returns the results in the arrays gzx and gzy. gradsg operates on a gaussian grid. If the input array z is on a fixed grid, gradsf should be used.

This procedure does not handle missing values, and the input array z must be on a global grid. If any missing values are encountered in a particular 2D input grid, then all of the values in the corresponding output grids will be set to the missing value defined by the output grids' _FillValue attributes.

Note: The underlying Spherepack routines use radians. Thus, for say, temperature (T, units K), the Spherepack units would be dT/dtheta => K/radian. The interface scales these values by the radius of the earth (R=6.37122e06 meters) which is equivalent to one radian: (K/radian)*(one_radian/R)=>(K/meter).

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

See Also

gradsf, igradsg, igradsf, igradsF, igradsG, lderuvf, lderuvg


A requirement is that the global grid(s) be ordered South-to-North (S==>N). Some gridded data sets are ordered N==>S. These must be reordered prior to use. This can be done via NCL-syntax. For example: T(time,lev,lat,lon) then

      T = T(:,:,::-1,:)     ; reorder the gridded data and coordinate variables

Example 1

Given a scalar array T, compute the latitudinal and longitudinal derivatives, and then recompute T. T is on a gaussian grid.

  T_grad_lon = T                ; create arrays to hold output, same size and type as input
  T_grad_lat = T                
                                ; this procedure will overwrite
                                ; values in T_grad_lon and T_grad_lat
  gradsg (T, T_grad_lon, T_grad_lat)   

  T_grad_lon@long_name = "longitudinal gradient (derivative)"
  T_grad_lat@long_name = "latitudinal gradient (derivative)"
  T_grad_lat@units     = "K/m"
  T_grad_lon@units     = "K/m"

  igradsg (T_grad_lon, T_grad_lat, T)  


If jer or ker is equal to:

1 : error in the specification of nlat
2 : error in the specification of nlon
4 : error in the specification of N (jer only)