16.1.3.3 Example 3: Horizontally isotropic grid

Suppose it was desired to construct a square grid between latitude $65^\circ$S and $65^\circ$N with $3^\circ$ resolution at the equator. The condition is that $\Delta_x = \Delta_y = 3^\circ$ at the equator and in general $\Delta_y$ must shrink with latitude to match the decreasing $\Delta_x$ due to the convergence of the meridians. Consequently,

$$\Delta_y = \Delta_x \cdot \cos\phi.$$ (16.3)

Enabeling option isotropic_grid enforces the above condition and yields a square grid between the bounding longitudes which are set as follows:

c
c     "nxlons"  = number of bounding longitudes to define 1 region
c     "x_lon"   = bounding longitudes {0.0E, 360.0E}
c     "dx_lon"  = resolution centered at "x_lon" {3.0, 3.0}
c     
       parameter (nxlons=2)
       data (x_lon(i), i=1,nxlons)  /0.0, 360.0/
       data (dx_lon(i),i=1,nxlons)  /3.0,   3.0/
c
c     "nylats"  = number of bounding latitudes to define 1 region
c     "y_lat"   = bounding latitudes {-65, 65}
c     "dy_lat"  = resolution centered at equator {3.0, 3.0}
c     
       parameter (nylats=2)
       data (y_lat(j), j=1,nylats)  /-65.0, 65.0/
       data (dy_lat(j),j=1,nylats)  /  3.0,  3.0/

The above specification yields a regional domain with 58 grid cells in latitude between $65.284^\circ$N and $65.284^\circ$S. Resolution is 3.0 degrees on the equator and about 1.26 degrees at the latitudinal boundaries. Note that the regional bounds have been adjusted to fit an integral number of cells.

The isotropic regional domain can be extended to a global domain by enabeling option extend_isotropic_grid. Note that to fit an integral number of cells between $65.284^\circ$ and the poles requires a slight increase in $\Delta_y$ poleward of 65. At the poles, $\Delta_y=1.34$. In general, Delta_y increases slighlty outside the isotropic region to insure the integral constraint.