Note
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2D interpolation#
Interpolation of a two-dimensional regular grid.
Bivariate#
Perform a bivariate
interpolation of gridded
data points.
The distribution contains a 2D field mss.nc
that will be used in this help.
This file is located in the src/pyinterp/tests/dataset
directory at the root
of the project.
Warning
This file is an old version of the sub-sampled quarter step MSS CNES/CLS. Please do not use it for scientific purposes, download the latest updated high-resolution version instead here.
import cartopy.crs
import matplotlib
import matplotlib.pyplot
import numpy
import xarray
import pyinterp
import pyinterp.backends.xarray
import pyinterp.tests
The first step is to load the data into memory and create the interpolator object:
Note
An exception will be thrown if the constructor is not able to determine
which axes are the longitudes and latitudes. You can force the data to be
read by specifying on the longitude and latitude axes the respective
degrees_east
and degrees_north
attribute units
. If your grid
does not contain geodetic coordinates, set the geodetic
option of the
constructor to False
.
ds = xarray.open_dataset(pyinterp.tests.grid2d_path())
interpolator = pyinterp.backends.xarray.Grid2D(ds.mss)
We will then build the coordinates on which we want to interpolate our grid:
Note
The coordinates used for interpolation are shifted to avoid using the points of the bivariate function.
mx, my = numpy.meshgrid(numpy.arange(-180, 180, 1) + 1 / 3.0,
numpy.arange(-89, 89, 1) + 1 / 3.0,
indexing='ij')
The grid is interpolated
to the desired coordinates:
Let’s visualize the original grid and the result of the interpolation.
fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax1 = fig.add_subplot(
211, projection=cartopy.crs.PlateCarree(central_longitude=180))
lons, lats = numpy.meshgrid(ds.lon, ds.lat, indexing='ij')
pcm = ax1.pcolormesh(lons,
lats,
ds.mss.T,
cmap='jet',
shading='auto',
transform=cartopy.crs.PlateCarree(),
vmin=-0.1,
vmax=0.1)
ax1.coastlines()
ax1.set_title("Original MSS")
ax2 = fig.add_subplot(212, projection=cartopy.crs.PlateCarree())
pcm = ax2.pcolormesh(mx,
my,
mss,
cmap='jet',
shading='auto',
transform=cartopy.crs.PlateCarree(),
vmin=-0.1,
vmax=0.1)
ax2.coastlines()
ax2.set_title("Bilinear Interpolated MSS")
fig.colorbar(pcm, ax=[ax1, ax2], shrink=0.8)
fig.show()

Values can be interpolated with several methods: bilinear, nearest, and inverse distance weighting. Distance calculations, if necessary, are calculated using the Haversine formula.
Bicubic#
To interpolate data points on a regular two-dimensional grid. The interpolated surface is smoother than the corresponding surfaces obtained by bilinear interpolation. Spline functions provided by GSL achieve bicubic interpolation.
Warning
When using this interpolator, pay attention to the undefined values. Because as long as the calculation window uses an indefinite point, the interpolator will compute indeterminate values. In other words, this interpolator increases the area covered by the masked values. To avoid this behavior, it is necessary to pre-process the grid to delete undefined values.
The interpolation bicubic
function has more parameters to define the data frame used by the spline
functions and how to process the edges of the regional grids:
Warning
The grid provided must have strictly increasing axes to meet the specifications of the GSL library. When building the grid, specify the
increasing_axes
option to flip the decreasing axes and the grid automatically. For example:
interpolator = pyinterp.backends.xarray.Grid2D(
ds.mss, increasing_axes=True)
fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax1 = fig.add_subplot(
211, projection=cartopy.crs.PlateCarree(central_longitude=180))
pcm = ax1.pcolormesh(lons,
lats,
ds.mss.T,
cmap='jet',
shading='auto',
transform=cartopy.crs.PlateCarree(),
vmin=-0.1,
vmax=0.1)
ax1.coastlines()
ax1.set_title("Original MSS")
ax2 = fig.add_subplot(212, projection=cartopy.crs.PlateCarree())
pcm = ax2.pcolormesh(mx,
my,
mss,
cmap='jet',
shading='auto',
transform=cartopy.crs.PlateCarree(),
vmin=-0.1,
vmax=0.1)
ax2.coastlines()
ax2.set_title("Bicubic Interpolated MSS")
fig.colorbar(pcm, ax=[ax1, ax2], shrink=0.8)
fig.show()

Total running time of the script: ( 0 minutes 9.277 seconds)