.. ipython:: python
   :suppress:

    import numpy as np
    import pandas as pd
    import xarray as xr
    np.random.seed(123456)

• For combining datasets or data arrays along a single dimension, see concatenate.
• For combining datasets with different variables, see merge.
• For combining datasets or data arrays with different indexes or missing values, see combine.
• For combining datasets or data arrays along multiple dimensions see combining.multi.

To combine arrays along existing or new dimension into a larger array, you can use :py:func:`~xarray.concat`. concat takes an iterable of DataArray or Dataset objects, as well as a dimension name, and concatenates along that dimension:

.. ipython:: python

    arr = xr.DataArray(np.random.randn(2, 3),
                       [('x', ['a', 'b']), ('y', [10, 20, 30])])
    arr[:, :1]
    # this resembles how you would use np.concatenate
    xr.concat([arr[:, :1], arr[:, 1:]], dim='y')

In addition to combining along an existing dimension, concat can create a new dimension by stacking lower dimensional arrays together:

.. ipython:: python

    arr[0]
    # to combine these 1d arrays into a 2d array in numpy, you would use np.array
    xr.concat([arr[0], arr[1]], 'x')

If the second argument to concat is a new dimension name, the arrays will be concatenated along that new dimension, which is always inserted as the first dimension:

.. ipython:: python

    xr.concat([arr[0], arr[1]], 'new_dim')

The second argument to concat can also be an :py:class:`~pandas.Index` or :py:class:`~xarray.DataArray` object as well as a string, in which case it is used to label the values along the new dimension:

.. ipython:: python

    xr.concat([arr[0], arr[1]], pd.Index([-90, -100], name='new_dim'))

Of course, concat also works on Dataset objects:

.. ipython:: python

    ds = arr.to_dataset(name='foo')
    xr.concat([ds.sel(x='a'), ds.sel(x='b')], 'x')

:py:func:`~xarray.concat` has a number of options which provide deeper control over which variables are concatenated and how it handles conflicting variables between datasets. With the default parameters, xarray will load some coordinate variables into memory to compare them between datasets. This may be prohibitively expensive if you are manipulating your dataset lazily using :ref:`dask`.

To combine variables and coordinates between multiple DataArray and/or Dataset objects, use :py:func:`~xarray.merge`. It can merge a list of Dataset, DataArray or dictionaries of objects convertible to DataArray objects:

.. ipython:: python

    xr.merge([ds, ds.rename({'foo': 'bar'})])
    xr.merge([xr.DataArray(n, name='var%d' % n) for n in range(5)])

If you merge another dataset (or a dictionary including data array objects), by default the resulting dataset will be aligned on the union of all index coordinates:

.. ipython:: python

    other = xr.Dataset({'bar': ('x', [1, 2, 3, 4]), 'x': list('abcd')})
    xr.merge([ds, other])

This ensures that merge is non-destructive. xarray.MergeError is raised if you attempt to merge two variables with the same name but different values:

.. ipython::

    @verbatim
    In [1]: xr.merge([ds, ds + 1])
    MergeError: conflicting values for variable 'foo' on objects to be combined:
    first value: <xarray.Variable (x: 2, y: 3)>
    array([[ 0.4691123 , -0.28286334, -1.5090585 ],
           [-1.13563237,  1.21211203, -0.17321465]])
    second value: <xarray.Variable (x: 2, y: 3)>
    array([[ 1.4691123 ,  0.71713666, -0.5090585 ],
           [-0.13563237,  2.21211203,  0.82678535]])

The same non-destructive merging between DataArray index coordinates is used in the :py:class:`~xarray.Dataset` constructor:

.. ipython:: python

    xr.Dataset({'a': arr[:-1], 'b': arr[1:]})

The instance method :py:meth:`~xarray.DataArray.combine_first` combines two datasets/data arrays and defaults to non-null values in the calling object, using values from the called object to fill holes. The resulting coordinates are the union of coordinate labels. Vacant cells as a result of the outer-join are filled with NaN. For example:

.. ipython:: python

    ar0 = xr.DataArray([[0, 0], [0, 0]], [('x', ['a', 'b']), ('y', [-1, 0])])
    ar1 = xr.DataArray([[1, 1], [1, 1]], [('x', ['b', 'c']), ('y', [0, 1])])
    ar0.combine_first(ar1)
    ar1.combine_first(ar0)

For datasets, ds0.combine_first(ds1) works similarly to xr.merge([ds0, ds1]), except that xr.merge raises MergeError when there are conflicting values in variables to be merged, whereas .combine_first defaults to the calling object's values.

In contrast to merge, :py:meth:`~xarray.Dataset.update` modifies a dataset in-place without checking for conflicts, and will overwrite any existing variables with new values:

.. ipython:: python

    ds.update({'space': ('space', [10.2, 9.4, 3.9])})

However, dimensions are still required to be consistent between different Dataset variables, so you cannot change the size of a dimension unless you replace all dataset variables that use it.

update also performs automatic alignment if necessary. Unlike merge, it maintains the alignment of the original array instead of merging indexes:

.. ipython:: python

    ds.update(other)

The exact same alignment logic when setting a variable with __setitem__ syntax:

.. ipython:: python

    ds['baz'] = xr.DataArray([9, 9, 9, 9, 9], coords=[('x', list('abcde'))])
    ds.baz

xarray objects can be compared by using the :py:meth:`~xarray.Dataset.equals`, :py:meth:`~xarray.Dataset.identical` and :py:meth:`~xarray.Dataset.broadcast_equals` methods. These methods are used by the optional compat argument on concat and merge.

:py:attr:`~xarray.Dataset.equals` checks dimension names, indexes and array values:

.. ipython:: python

    arr.equals(arr.copy())

:py:attr:`~xarray.Dataset.identical` also checks attributes, and the name of each object:

.. ipython:: python

    arr.identical(arr.rename('bar'))

:py:attr:`~xarray.Dataset.broadcast_equals` does a more relaxed form of equality check that allows variables to have different dimensions, as long as values are constant along those new dimensions:

.. ipython:: python

    left = xr.Dataset(coords={'x': 0})
    right = xr.Dataset({'x': [0, 0, 0]})
    left.broadcast_equals(right)

Like pandas objects, two xarray objects are still equal or identical if they have missing values marked by NaN in the same locations.

In contrast, the == operation performs element-wise comparison (like numpy):

.. ipython:: python

    arr == arr.copy()

Note that NaN does not compare equal to NaN in element-wise comparison; you may need to deal with missing values explicitly.

The compat argument 'no_conflicts' is only available when combining xarray objects with merge. In addition to the above comparison methods it allows the merging of xarray objects with locations where either have NaN values. This can be used to combine data with overlapping coordinates as long as any non-missing values agree or are disjoint:

.. ipython:: python

    ds1 = xr.Dataset({'a': ('x', [10, 20, 30, np.nan])}, {'x': [1, 2, 3, 4]})
    ds2 = xr.Dataset({'a': ('x', [np.nan, 30, 40, 50])}, {'x': [2, 3, 4, 5]})
    xr.merge([ds1, ds2], compat='no_conflicts')

Note that due to the underlying representation of missing values as floating point numbers (NaN), variable data type is not always preserved when merging in this manner.

For combining many objects along multiple dimensions xarray provides :py:func:`~xarray.combine_nested`` and :py:func:`~xarray.combine_by_coords`. These functions use a combination of concat and merge across different variables to combine many objects into one.

:py:func:`~xarray.combine_nested`` requires specifying the order in which the objects should be combined, while :py:func:`~xarray.combine_by_coords` attempts to infer this ordering automatically from the coordinates in the data.

:py:func:`~xarray.combine_nested` is useful when you know the spatial relationship between each object in advance. The datasets must be provided in the form of a nested list, which specifies their relative position and ordering. A common task is collecting data from a parallelized simulation where each processor wrote out data to a separate file. A domain which was decomposed into 4 parts, 2 each along both the x and y axes, requires organising the datasets into a doubly-nested list, e.g:

.. ipython:: python

    arr = xr.DataArray(name='temperature', data=np.random.randint(5, size=(2, 2)), dims=['x', 'y'])
    arr
    ds_grid = [[arr, arr], [arr, arr]]
    xr.combine_nested(ds_grid, concat_dim=['x', 'y'])

:py:func:`~xarray.combine_nested` can also be used to explicitly merge datasets with different variables. For example if we have 4 datasets, which are divided along two times, and contain two different variables, we can pass None to 'concat_dim' to specify the dimension of the nested list over which we wish to use merge instead of concat:

.. ipython:: python

    temp = xr.DataArray(name='temperature', data=np.random.randn(2), dims=['t'])
    precip = xr.DataArray(name='precipitation', data=np.random.randn(2), dims=['t'])
    ds_grid = [[temp, precip], [temp, precip]]
    xr.combine_nested(ds_grid, concat_dim=['t', None])

:py:func:`~xarray.combine_by_coords` is for combining objects which have dimension coordinates which specify their relationship to and order relative to one another, for example a linearly-increasing 'time' dimension coordinate.

Here we combine two datasets using their common dimension coordinates. Notice they are concatenated in order based on the values in their dimension coordinates, not on their position in the list passed to combine_by_coords.

.. ipython:: python
    :okwarning:

    x1 = xr.DataArray(name='foo', data=np.random.randn(3), coords=[('x', [0, 1, 2])])
    x2 = xr.DataArray(name='foo', data=np.random.randn(3), coords=[('x', [3, 4, 5])])
    xr.combine_by_coords([x2, x1])

These functions can be used by :py:func:`~xarray.open_mfdataset` to open many files as one dataset. The particular function used is specified by setting the argument 'combine' to 'by_coords' or 'nested'. This is useful for situations where your data is split across many files in multiple locations, which have some known relationship between one another.