Structured grids
Dimensions
D depth points, corners of grid cells
Z water level points, cell centres of grid , http://en.wikipedia.org/wiki/Face_(geometry)
UV velocity points, contravariant
Length of dimensions
i number of rows
j number of columns
D = (i+1) * (j+1)
Z = i * j
U = (i+1)j
V = i(j+1)
Netcdf example for collocated grids
dimensions:
imax = 128;
jmax = 64;
nv = 4;
variables:
//coordinates of Z
float lat(imax,jmax);
lat:long_name = "latitude";
lat:units = "degrees_north";
lat:bounds = "lat_bnds";
float lon(imax,jmax);
lon:long_name = "longitude";
lon:units = "degrees_east";
lon:bounds = "lon_bnds";
//coordinates of the boundaries of D
float lat_bnds(imax,jmax,nv);
float lon_bnds(imax,jmax,nv);
Netcdf example for arakawa c grid as used in 3d flow
dimensions:
zimax = 1116 //number of cells in x direction: 1116
zjmax = 7028 //number of cells in y direction: 7028
uimax = 1117 //number of u edges in x direction (i+1)
ujmax = 7028 // number of u edges in y direction (j)
vimax = 1116 //number of v edges in x direction 
vjmax = 7029 // number of v edges in y direction (j+1)
dimax = 1117 // number of d vertices in x direction (i+1)
djmax = 7029 // number of d vertices in y direction (j+1)
D = 7851393 //(i+1) * (j+1)
Z = 7843248 // i * j
U = 7850276 // (i+1)j
V = 7844364 // i(j+1)
variables:
//Z-grid
//coordinates of centres
double zx(zimax, zjmax);
zx:standard_name = "longitude";
zx:units = "degrees_east";
double zy(zimax, zjmax);
zy:standard_name = "latitude";
zy:units = "degrees_north";
//U-grid
//coordinates of u edges
double ux(uimax, ujmax);
ux:standard_name = "longitude";
ux:units = "degrees_east";
double uy(uimax, ujmax);
uy:standard_name = "latitude";
uy:units = "degrees_north";
//V-grid
//coordinates of v edges
double vx(vimax, vjmax);
vx:standard_name = "longitude";
vx:units = "degrees_east";
double vy(vimax, vjmax);
vy:standard_name = "latitude";
vy:units = "degrees_north";
//D-grid
//coordinates of d vertices
double dx(dimax, djmax);
dx:standard_name = "longitude";
dx:units = "degrees_east";
double dy(dimax, djmax);
dy:standard_name = "latitude";
dy:units = "degrees_north";
//Constituents are defined at the Z grid
double c(zimax, zjmax);
c:long_name = "rhodamyne";
c:units= "1e-6"l
//
