Add a notebook about (gaussian) grid/bounds/weights generation

[jypeter]

A colleague (@dmr-dj) told me this morning that he had no easy way to create cell boundaries for a gaussian grid. I sent him the following lines, that could probably be integrated into a new notebook/tutorial, since grid/bounds/weights generation are an asset of cdms2 (not sure if you can find this in netcdf4 and xarray)

>>> dir(cdms2)
['AbstractAxis', ...'createAxis', 'createDataset', 'createEqualAreaAxis', 'createGaussianAxis', 'createGaussianGrid', 'createGenericGrid', 'createGlobalMeanGrid', 'createRectGrid', 'createUniformGrid', 'createUniformLatitudeAxis', 'createUniformLongitudeAxis', 'createVariable', 'createZonalGrid', ... ]

>>> help(cdms2.createGaussianGrid)

createGaussianGrid(nlats, xorigin=0.0, order='yx')
    createGaussianGrid(nlats, xorigin=0.0)
    Create a Gaussian grid, with shape (nlats, 2*nlats).

    Parameters
    ----------
         nlats:
              is the number of latitudes.

         xorigin:
              is the origin of the longitude axis

         order:
              is either "yx" or "xy"

>>> gr32 = cdms2.createGaussianGrid(32)
>>> lat32 = gr32.getLatitude()
>>> lat32
   id: latitude
   Designated a latitude axis.
   units:  degrees_north
   Length: 32
   First:  85.7605871204438
   Last:   -85.7605871204438
   Other axis attributes:
      axis: Y
   Python id:  0x2b9a4bcc2438

>>> lat32[:]
array([ 85.76058712,  80.26877907,  74.74454037,  69.21297617,
        63.67863556,  58.14295405,  52.60652603,  47.06964206,
        41.53246125,  35.99507841,  30.45755396,  24.91992863,
        19.38223135,  13.84448373,   8.30670286,   2.76890301,
        -2.76890301,  -8.30670286, -13.84448373, -19.38223135,
       -24.91992863, -30.45755396, -35.99507841, -41.53246125,
       -47.06964206, -52.60652603, -58.14295405, -63.67863556,
       -69.21297617, -74.74454037, -80.26877907, -85.76058712])
>>> lat32.getBounds()
array([[ 9.00000000e+01,  8.32076896e+01],
       [ 8.32076896e+01,  7.76092666e+01],
       [ 7.76092666e+01,  7.20479751e+01],
       [ 7.20479751e+01,  6.64972690e+01],
       [ 6.64972690e+01,  6.09510468e+01],
...
       [-7.76092666e+01, -8.32076896e+01],
       [-8.32076896e+01, -9.00000000e+01]])
>>> lat32_w, lon32_w = gr32.getWeights()
>>> lat32_w.sum(), lon32_w.sum()
(1.0, 1.0)

>>> len(lat32_w), len(lon32_w)
(32, 64)
>>> weights32 = np.outer(lat32_w, lon32_w)
>>> weights32.shape
(32, 64)
>>> weights32.sum()
1.0

>>> weights32[0, :]
array([5.48328907e-05, 5.48328907e-05, 5.48328907e-05, 5.48328907e-05,
...
       5.48328907e-05, 5.48328907e-05, 5.48328907e-05, 5.48328907e-05])
>>> weights32[:, 0]
array([5.48328907e-05, 1.27143709e-04, 1.98375510e-04, 2.67764554e-04,
       3.34655453e-04, 3.98422338e-04, 4.58469480e-04, 5.14236115e-04,
...
       5.14236115e-04, 4.58469480e-04, 3.98422338e-04, 3.34655453e-04,
       2.67764554e-04, 1.98375510e-04, 1.27143709e-04, 5.48328907e-05])