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.. _interp:
Interpolating data
==================
.. ipython:: python
:suppress:
import numpy as np
import pandas as pd
import xarray as xr
np.random.seed(123456)
xarray offers flexible interpolation routines, which have a similar interface
to our :ref:`indexing <indexing>`.
.. note::
``interp`` requires `scipy` installed.
Scalar and 1-dimensional interpolation
--------------------------------------
Interpolating a :py:class:`~xarray.DataArray` works mostly like labeled
indexing of a :py:class:`~xarray.DataArray`,
.. ipython:: python
da = xr.DataArray(
np.sin(0.3 * np.arange(12).reshape(4, 3)),
[("time", np.arange(4)), ("space", [0.1, 0.2, 0.3])],
)
# label lookup
da.sel(time=3)
# interpolation
da.interp(time=2.5)
Similar to the indexing, :py:meth:`~xarray.DataArray.interp` also accepts an
array-like, which gives the interpolated result as an array.
.. ipython:: python
# label lookup
da.sel(time=[2, 3])
# interpolation
da.interp(time=[2.5, 3.5])
To interpolate data with a :py:doc:`numpy.datetime64 <reference/arrays.datetime>` coordinate you can pass a string.
.. ipython:: python
da_dt64 = xr.DataArray(
[1, 3], [("time", pd.date_range("1/1/2000", "1/3/2000", periods=2))]
)
da_dt64.interp(time="2000-01-02")
The interpolated data can be merged into the original :py:class:`~xarray.DataArray`
by specifying the time periods required.
.. ipython:: python
da_dt64.interp(time=pd.date_range("1/1/2000", "1/3/2000", periods=3))
Interpolation of data indexed by a :py:class:`~xarray.CFTimeIndex` is also
allowed. See :ref:`CFTimeIndex` for examples.
.. note::
Currently, our interpolation only works for regular grids.
Therefore, similarly to :py:meth:`~xarray.DataArray.sel`,
only 1D coordinates along a dimension can be used as the
original coordinate to be interpolated.
Multi-dimensional Interpolation
-------------------------------
Like :py:meth:`~xarray.DataArray.sel`, :py:meth:`~xarray.DataArray.interp`
accepts multiple coordinates. In this case, multidimensional interpolation
is carried out.
.. ipython:: python
# label lookup
da.sel(time=2, space=0.1)
# interpolation
da.interp(time=2.5, space=0.15)
Array-like coordinates are also accepted:
.. ipython:: python
# label lookup
da.sel(time=[2, 3], space=[0.1, 0.2])
# interpolation
da.interp(time=[1.5, 2.5], space=[0.15, 0.25])
:py:meth:`~xarray.DataArray.interp_like` method is a useful shortcut. This
method interpolates an xarray object onto the coordinates of another xarray
object. For example, if we want to compute the difference between
two :py:class:`~xarray.DataArray` s (``da`` and ``other``) staying on slightly
different coordinates,
.. ipython:: python
other = xr.DataArray(
np.sin(0.4 * np.arange(9).reshape(3, 3)),
[("time", [0.9, 1.9, 2.9]), ("space", [0.15, 0.25, 0.35])],
)
it might be a good idea to first interpolate ``da`` so that it will stay on the
same coordinates of ``other``, and then subtract it.
:py:meth:`~xarray.DataArray.interp_like` can be used for such a case,
.. ipython:: python
# interpolate da along other's coordinates
interpolated = da.interp_like(other)
interpolated
It is now possible to safely compute the difference ``other - interpolated``.
Interpolation methods
---------------------
We use :py:class:`scipy.interpolate.interp1d` for 1-dimensional interpolation and
:py:func:`scipy.interpolate.interpn` for multi-dimensional interpolation.
The interpolation method can be specified by the optional ``method`` argument.
.. ipython:: python
da = xr.DataArray(
np.sin(np.linspace(0, 2 * np.pi, 10)),
dims="x",
coords={"x": np.linspace(0, 1, 10)},
)
da.plot.line("o", label="original")
da.interp(x=np.linspace(0, 1, 100)).plot.line(label="linear (default)")
da.interp(x=np.linspace(0, 1, 100), method="cubic").plot.line(label="cubic")
@savefig interpolation_sample1.png width=4in
plt.legend()
Additional keyword arguments can be passed to scipy's functions.
.. ipython:: python
# fill 0 for the outside of the original coordinates.
da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={"fill_value": 0.0})
# 1-dimensional extrapolation
da.interp(x=np.linspace(-0.5, 1.5, 10), kwargs={"fill_value": "extrapolate"})
# multi-dimensional extrapolation
da = xr.DataArray(
np.sin(0.3 * np.arange(12).reshape(4, 3)),
[("time", np.arange(4)), ("space", [0.1, 0.2, 0.3])],
)
da.interp(time=4, space=np.linspace(-0.1, 0.5, 10), kwargs={"fill_value": None})
Advanced Interpolation
----------------------
:py:meth:`~xarray.DataArray.interp` accepts :py:class:`~xarray.DataArray`
as similar to :py:meth:`~xarray.DataArray.sel`, which enables us more advanced interpolation.
Based on the dimension of the new coordinate passed to :py:meth:`~xarray.DataArray.interp`, the dimension of the result are determined.
For example, if you want to interpolate a two dimensional array along a particular dimension, as illustrated below,
you can pass two 1-dimensional :py:class:`~xarray.DataArray` s with
a common dimension as new coordinate.
.. image:: _static/advanced_selection_interpolation.svg
:height: 200px
:width: 400 px
:alt: advanced indexing and interpolation
:align: center
For example:
.. ipython:: python
da = xr.DataArray(
np.sin(0.3 * np.arange(20).reshape(5, 4)),
[("x", np.arange(5)), ("y", [0.1, 0.2, 0.3, 0.4])],
)
# advanced indexing
x = xr.DataArray([0, 2, 4], dims="z")
y = xr.DataArray([0.1, 0.2, 0.3], dims="z")
da.sel(x=x, y=y)
# advanced interpolation
x = xr.DataArray([0.5, 1.5, 2.5], dims="z")
y = xr.DataArray([0.15, 0.25, 0.35], dims="z")
da.interp(x=x, y=y)
where values on the original coordinates
``(x, y) = ((0.5, 0.15), (1.5, 0.25), (2.5, 0.35))`` are obtained by the
2-dimensional interpolation and mapped along a new dimension ``z``.
If you want to add a coordinate to the new dimension ``z``, you can supply
:py:class:`~xarray.DataArray` s with a coordinate,
.. ipython:: python
x = xr.DataArray([0.5, 1.5, 2.5], dims="z", coords={"z": ["a", "b", "c"]})
y = xr.DataArray([0.15, 0.25, 0.35], dims="z", coords={"z": ["a", "b", "c"]})
da.interp(x=x, y=y)
For the details of the advanced indexing,
see :ref:`more advanced indexing <more_advanced_indexing>`.
Interpolating arrays with NaN
-----------------------------
Our :py:meth:`~xarray.DataArray.interp` works with arrays with NaN
the same way that
`scipy.interpolate.interp1d <https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html>`_ and
`scipy.interpolate.interpn <https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interpn.html>`_ do.
``linear`` and ``nearest`` methods return arrays including NaN,
while other methods such as ``cubic`` or ``quadratic`` return all NaN arrays.
.. ipython:: python
da = xr.DataArray([0, 2, np.nan, 3, 3.25], dims="x", coords={"x": range(5)})
da.interp(x=[0.5, 1.5, 2.5])
da.interp(x=[0.5, 1.5, 2.5], method="cubic")
To avoid this, you can drop NaN by :py:meth:`~xarray.DataArray.dropna`, and
then make the interpolation
.. ipython:: python
dropped = da.dropna("x")
dropped
dropped.interp(x=[0.5, 1.5, 2.5], method="cubic")
If NaNs are distributed randomly in your multidimensional array,
dropping all the columns containing more than one NaNs by
:py:meth:`~xarray.DataArray.dropna` may lose a significant amount of information.
In such a case, you can fill NaN by :py:meth:`~xarray.DataArray.interpolate_na`,
which is similar to :py:meth:`pandas.Series.interpolate`.
.. ipython:: python
filled = da.interpolate_na(dim="x")
filled
This fills NaN by interpolating along the specified dimension.
After filling NaNs, you can interpolate:
.. ipython:: python
filled.interp(x=[0.5, 1.5, 2.5], method="cubic")
For the details of :py:meth:`~xarray.DataArray.interpolate_na`,
see :ref:`Missing values <missing_values>`.
Example
-------
Let's see how :py:meth:`~xarray.DataArray.interp` works on real data.
.. ipython:: python
# Raw data
ds = xr.tutorial.open_dataset("air_temperature").isel(time=0)
fig, axes = plt.subplots(ncols=2, figsize=(10, 4))
ds.air.plot(ax=axes[0])
axes[0].set_title("Raw data")
# Interpolated data
new_lon = np.linspace(ds.lon[0], ds.lon[-1], ds.dims["lon"] * 4)
new_lat = np.linspace(ds.lat[0], ds.lat[-1], ds.dims["lat"] * 4)
dsi = ds.interp(lat=new_lat, lon=new_lon)
dsi.air.plot(ax=axes[1])
@savefig interpolation_sample3.png width=8in
axes[1].set_title("Interpolated data")
Our advanced interpolation can be used to remap the data to the new coordinate.
Consider the new coordinates x and z on the two dimensional plane.
The remapping can be done as follows
.. ipython:: python
# new coordinate
x = np.linspace(240, 300, 100)
z = np.linspace(20, 70, 100)
# relation between new and original coordinates
lat = xr.DataArray(z, dims=["z"], coords={"z": z})
lon = xr.DataArray(
(x[:, np.newaxis] - 270) / np.cos(z * np.pi / 180) + 270,
dims=["x", "z"],
coords={"x": x, "z": z},
)
fig, axes = plt.subplots(ncols=2, figsize=(10, 4))
ds.air.plot(ax=axes[0])
# draw the new coordinate on the original coordinates.
for idx in [0, 33, 66, 99]:
axes[0].plot(lon.isel(x=idx), lat, "--k")
for idx in [0, 33, 66, 99]:
axes[0].plot(*xr.broadcast(lon.isel(z=idx), lat.isel(z=idx)), "--k")
axes[0].set_title("Raw data")
dsi = ds.interp(lon=lon, lat=lat)
dsi.air.plot(ax=axes[1])
@savefig interpolation_sample4.png width=8in
axes[1].set_title("Remapped data")
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