# 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 pyinterp
import pyinterp.backends.xarray
import pyinterp.tests
import xarray
```

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:

```mss = interpolator.bivariate(
coords=dict(lon=mx.ravel(), lat=my.ravel())).reshape(mx.shape)
```

Let’s visualize the original grid and the result of the interpolation.

```fig = matplotlib.pyplot.figure(figsize=(10, 8))
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',
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',
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()
```

Out:

```/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:825: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
if len(multi_line_string) > 1:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:836: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
line_strings = list(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:836: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
line_strings = list(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:877: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
for line in multi_line_string:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:944: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
if len(p_mline) > 0:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:982: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
line_strings.extend(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:982: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
line_strings.extend(multi_line_string)
```

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:

```mss = interpolator.bicubic(coords=dict(lon=mx.ravel(), lat=my.ravel()),
nx=3,
ny=3).reshape(mx.shape)
```

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))
211, projection=cartopy.crs.PlateCarree(central_longitude=180))
pcm = ax1.pcolormesh(lons,
lats,
ds.mss.T,
cmap='jet',
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',
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()
```

Out:

```/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:825: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
if len(multi_line_string) > 1:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:836: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
line_strings = list(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:836: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
line_strings = list(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:877: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
for line in multi_line_string:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:944: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
if len(p_mline) > 0:
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:982: ShapelyDeprecationWarning: Iteration over multi-part geometries is deprecated and will be removed in Shapely 2.0. Use the `geoms` property to access the constituent parts of a multi-part geometry.
line_strings.extend(multi_line_string)
/home/docs/checkouts/readthedocs.org/user_builds/pangeo-pyinterp/conda/latest/lib/python3.7/site-packages/cartopy/crs.py:982: ShapelyDeprecationWarning: __len__ for multi-part geometries is deprecated and will be removed in Shapely 2.0. Check the length of the `geoms` property instead to get the  number of parts of a multi-part geometry.
line_strings.extend(multi_line_string)
```

Total running time of the script: ( 0 minutes 9.391 seconds)

Gallery generated by Sphinx-Gallery