Spectral Interpolation

There are 2 codes to interpolate SEOM results to an arbitrary set of points:

interp2d: a 2-dimensional interpolation package to use with SEOM-2D
interp3d: a 3-dimensional interpolation package to use with SEOM-3D.

The code can be downloaded . To install edit the Makefile and do:


make interp2d 

make interp3d

To run the code just issue the command interp2d . By default the input is read from a file called interp2d.dat. Idem for interp3d. The structures of the input files are listed below.

interp2d.dat

sphere (logical flag)
T if sphere, F otherwise
grid_file (character)
SEOM horizontal grid file name
point_file (character)
Name of file holding coordinates of points to interpolate to. There are 2 possible forms for this file:
- If the file name is 'structured_grid', the following 2 lines (lines 4 and 5) must contain the corner points of the structured grid in the horizontal direction. The points are assumed to be on a regular grid, with grid spacings of
```
              dlon=(lon1-lon0)/(nxi-1)
              dlat=(lat1-lat0)/(nyi-1)
              dz=(z1-z0)/(nzi-1) 
```
- The file actually exist, then it must have the following form: read(88,*) nxi, nyi do ij = 1,nxi*nyi read(88,*) alon(ij), alat(ij) enddo
lon0, lon1, nxi (real, real, integer)
min and max longitude, and number of points in x, if necessary
lat0, lat1, nyi (real, real, integer)
min and max latitude, and number of points in y, if necessary
input_file (character)
Name of input spectral element data
output_file (character)
Name of output interpolated data

interp3d.dat

Here is the structure of an interp3d.dat file. It is the data file read by the program interp3d and must reside in the directory where the command is issued.

sphere (logical flag)
T if sphere, F otherwise
grid_file (character)
SEOM horizontal grid file name
point_file (character)
Name of file holding coordinates of points to interpolate to. There are 2 possible forms for this file:
- If the file name is 'structured_grid', the following 2 lines (lines 4 and 5) must contain the corner points of the structured grid in the horizontal direction. The points are assumed to be on a regular grid, with grid spacings of
```
              dlon=(lon1-lon0)/(nxi-1)
              dlat=(lat1-lat0)/(nyi-1)
              dz=(z1-z0)/(nzi-1) 
```
- The file actually exist, then it must have the following form: read(88,*) nxi, nyi do ij = 1,nxi*nyi read(88,*) alon(ij), alat(ij) enddo
lon0, lon1, nxi (real, real, integer)
min and max longitude, and number of points in x, if necessary
lat0, lat1, nyi (real, real, integer)
min and max latitude, and number of points in y, if necessary
z0, z1, nzi (real, real, integer)
min and max altitude, and number of points in z, if necessary
nelem_vt, npts_vt (integer, integer)
- npts_vt: number of the spectral element in the vertical
- npts_vt: spectral truncation in the vertical.
elev_file (character)
Name of elevation file
input_file (character)
Name of input spectral element data
output_file (character)
Name of output interpolated data

Notes on "interp3d.dat"

To get a 2D slice of the data along a coordinate line set nxi=1 for a latitude-z slice, nyi=1 for a longitude z-slice, or nzi=1 for a longitude latitude slice. A 1D slice can be obtained by setting any pair of the (nxi,nyi,nzi) triplets to 1.
Points that are not on the grid are filled with the special value set in NCARSPV =-999999.0_r8 .
The first time the user runs interp3d, the location of the interpolation points within each spectral element must be computed. This is a rather lengthy operation (and error-prone if the elements are distorted). To save computational time for later interpolation operations, this one-time information is saved in 2 files: structured_grid.loc, and structured_grid.sav. The former is an ASCII file holding the location of the points in the SEOM grid and can be inspected by the user. The latter file is a binary form of the ASCII file and is read the next time interp3d is run. If a file called structured_grid.sav is found, and the information of the structured grid in it matches what is found in interp3d.dat, this information is used. Otherwise, the location of the points is computed again.
It is possible to produce a sigma-like structured grid if a vertical slice is produced. The trick is to set z0=1, and z1=-1. A message alerting you that this is a sigma-map is then printed. The structured grid points are then mapped such that
```
         dsig= (z1-z0)/(nzi-1)
         sig(k) = z0 + (j-1) * dsig 
         z(k) = h/2 * (sig(k)-1)
       
```

Below are sample interp3d.dat files:

script for interpolating to a latitude section at 55 N on a structured grid of 1/2 degree ranging from 100 West to 20 East, and going from a depth of -5500 to 0 by 27.5 m increments.
script Same as above but interpolating to a sigma-like grid in the vertical using only 41 points.
script lon-lat grid at a fixed geopotential level.