# Data Structures

## DataArray

`xarray.DataArray` is xarray’s implementation of a labeled, multi-dimensional array. It has several key properties:

- `values`: a `numpy.ndarray` holding the array’s values

- `dims`: dimension names for each axis (e.g., `('x', 'y', 'z')`)

- `coords`: a dict-like container of arrays (coordinates) that label each point (e.g., 1-dimensional arrays of numbers, datetime objects or strings)

- `attrs`: `dict` to hold arbitrary metadata (attributes)

Xarray uses `dims` and `coords` to enable its core metadata aware operations. Dimensions provide names that xarray uses instead of the `axis` argument found in many numpy functions. Coordinates enable fast label based indexing and alignment, building on the functionality of the `index` found on a pandas `DataFrame` or `Series`.

DataArray objects also can have a `name` and can hold arbitrary metadata in the form of their `attrs` property. Names and attributes are strictly for users and user-written code: xarray makes no attempt to interpret them, and propagates them only in unambiguous cases (see FAQ, What is your approach to metadata?).

### Creating a DataArray

The `DataArray` constructor takes:

- `data`: a multi-dimensional array of values (e.g., a numpy ndarray, `Series`, `DataFrame` or `pandas.Panel`)

- `coords`: a list or dictionary of coordinates. If a list, it should be a list of tuples where the first element is the dimension name and the second element is the corresponding coordinate array_like object.

- `dims`: a list of dimension names. If omitted and `coords` is a list of tuples, dimension names are taken from `coords`.

- `attrs`: a dictionary of attributes to add to the instance

- `name`: a string that names the instance

    In [1]: data = np.random.rand(4, 3)

    In [2]: locs = ["IA", "IL", "IN"]

    In [3]: times = pd.date_range("2000-01-01", periods=4)

    In [4]: foo = xr.DataArray(data, coords=[times, locs], dims=["time", "space"])

    In [5]: foo
    Out[5]:
    <xarray.DataArray (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'

Only `data` is required; all of other arguments will be filled in with default values:

    In [6]: xr.DataArray(data)
    Out[6]:
    <xarray.DataArray (dim_0: 4, dim_1: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Dimensions without coordinates: dim_0, dim_1

As you can see, dimension names are always present in the xarray data model: if you do not provide them, defaults of the form `dim_N` will be created. However, coordinates are always optional, and dimensions do not have automatic coordinate labels.

Note

This is different from pandas, where axes always have tick labels, which default to the integers `[0, ..., n-1]`.

Prior to xarray v0.9, xarray copied this behavior: default coordinates for each dimension would be created if coordinates were not supplied explicitly. This is no longer the case.

Coordinates can be specified in the following ways:

- A list of values with length equal to the number of dimensions, providing coordinate labels for each dimension. Each value must be of one of the following forms:

  - A `DataArray` or `Variable`

  - A tuple of the form `(dims, data[, attrs])`, which is converted into arguments for `Variable`

  - A pandas object or scalar value, which is converted into a `DataArray`

  - A 1D array or list, which is interpreted as values for a one dimensional coordinate variable along the same dimension as it’s name

- A dictionary of `{coord_name: coord}` where values are of the same form as the list. Supplying coordinates as a dictionary allows other coordinates than those corresponding to dimensions (more on these later). If you supply `coords` as a dictionary, you must explicitly provide `dims`.

As a list of tuples:

    In [7]: xr.DataArray(data, coords=[("time", times), ("space", locs)])
    Out[7]:
    <xarray.DataArray (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'

As a dictionary:

    In [8]: xr.DataArray(
       ...:     data,
       ...:     coords={
       ...:         "time": times,
       ...:         "space": locs,
       ...:         "const": 42,
       ...:         "ranking": ("space", [1, 2, 3]),
       ...:     },
       ...:     dims=["time", "space"],
       ...: )
       ...:
    Out[8]:
    <xarray.DataArray (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
        const    int64 42
        ranking  (space) int64 1 2 3

As a dictionary with coords across multiple dimensions:

    In [9]: xr.DataArray(
       ...:     data,
       ...:     coords={
       ...:         "time": times,
       ...:         "space": locs,
       ...:         "const": 42,
       ...:         "ranking": (("time", "space"), np.arange(12).reshape(4, 3)),
       ...:     },
       ...:     dims=["time", "space"],
       ...: )
       ...:
    Out[9]:
    <xarray.DataArray (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
        const    int64 42
        ranking  (time, space) int64 0 1 2 3 4 5 6 7 8 9 10 11

If you create a `DataArray` by supplying a pandas `Series`, `DataFrame` or `pandas.Panel`, any non-specified arguments in the `DataArray` constructor will be filled in from the pandas object:

    In [10]: df = pd.DataFrame({"x": [0, 1], "y": [2, 3]}, index=["a", "b"])

    In [11]: df.index.name = "abc"

    In [12]: df.columns.name = "xyz"

    In [13]: df
    Out[13]:
    xyz  x  y
    abc
    a    0  2
    b    1  3

    In [14]: xr.DataArray(df)
    Out[14]:
    <xarray.DataArray (abc: 2, xyz: 2)>
    array([[0, 2],
           [1, 3]])
    Coordinates:
      * abc      (abc) object 'a' 'b'
      * xyz      (xyz) object 'x' 'y'

### DataArray properties

Let’s take a look at the important properties on our array:

    In [15]: foo.values
    Out[15]:
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])

    In [16]: foo.dims
    Out[16]: ('time', 'space')

    In [17]: foo.coords
    Out[17]:
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'

    In [18]: foo.attrs
    Out[18]: {}

    In [19]: print(foo.name)
    None

You can modify `values` inplace:

    In [20]: foo.values = 1.0 * foo.values

Note

The array values in a `DataArray` have a single (homogeneous) data type. To work with heterogeneous or structured data types in xarray, use coordinates, or put separate `DataArray` objects in a single `Dataset` (see below).

Now fill in some of that missing metadata:

    In [21]: foo.name = "foo"

    In [22]: foo.attrs["units"] = "meters"

    In [23]: foo
    Out[23]:
    <xarray.DataArray 'foo' (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
    Attributes:
        units:    meters

The `rename()` method is another option, returning a new data array:

    In [24]: foo.rename("bar")
    Out[24]:
    <xarray.DataArray 'bar' (time: 4, space: 3)>
    array([[0.127, 0.967, 0.26 ],
           [0.897, 0.377, 0.336],
           [0.451, 0.84 , 0.123],
           [0.543, 0.373, 0.448]])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
    Attributes:
        units:    meters

### DataArray Coordinates

The `coords` property is `dict` like. Individual coordinates can be accessed from the coordinates by name, or even by indexing the data array itself:

    In [25]: foo.coords["time"]
    Out[25]:
    <xarray.DataArray 'time' (time: 4)>
    array(['2000-01-01T00:00:00.000000000', '2000-01-02T00:00:00.000000000',
           '2000-01-03T00:00:00.000000000', '2000-01-04T00:00:00.000000000'],
          dtype='datetime64[ns]')
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04

    In [26]: foo["time"]
    Out[26]:
    <xarray.DataArray 'time' (time: 4)>
    array(['2000-01-01T00:00:00.000000000', '2000-01-02T00:00:00.000000000',
           '2000-01-03T00:00:00.000000000', '2000-01-04T00:00:00.000000000'],
          dtype='datetime64[ns]')
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04

These are also `DataArray` objects, which contain tick-labels for each dimension.

Coordinates can also be set or removed by using the dictionary like syntax:

    In [27]: foo["ranking"] = ("space", [1, 2, 3])

    In [28]: foo.coords
    Out[28]:
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
        ranking  (space) int64 1 2 3

    In [29]: del foo["ranking"]

    In [30]: foo.coords
    Out[30]:
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'

For more details, see Coordinates below.

## Dataset

`xarray.Dataset` is xarray’s multi-dimensional equivalent of a `DataFrame`. It is a dict-like container of labeled arrays (`DataArray` objects) with aligned dimensions. It is designed as an in-memory representation of the data model from the netCDF file format.

In addition to the dict-like interface of the dataset itself, which can be used to access any variable in a dataset, datasets have four key properties:

- `dims`: a dictionary mapping from dimension names to the fixed length of each dimension (e.g., `{'x': 6, 'y': 6, 'time': 8}`)

- `data_vars`: a dict-like container of DataArrays corresponding to variables

- `coords`: another dict-like container of DataArrays intended to label points used in `data_vars` (e.g., arrays of numbers, datetime objects or strings)

- `attrs`: `dict` to hold arbitrary metadata

The distinction between whether a variable falls in data or coordinates (borrowed from CF conventions) is mostly semantic, and you can probably get away with ignoring it if you like: dictionary like access on a dataset will supply variables found in either category. However, xarray does make use of the distinction for indexing and computations. Coordinates indicate constant/fixed/independent quantities, unlike the varying/measured/dependent quantities that belong in data.

Here is an example of how we might structure a dataset for a weather forecast:

In this example, it would be natural to call `temperature` and `precipitation` “data variables” and all the other arrays “coordinate variables” because they label the points along the dimensions. (see 1 for more background on this example).

### Creating a Dataset

To make an `Dataset` from scratch, supply dictionaries for any variables (`data_vars`), coordinates (`coords`) and attributes (`attrs`).

- `data_vars` should be a dictionary with each key as the name of the variable and each value as one of:

  - A `DataArray` or `Variable`

  - A tuple of the form `(dims, data[, attrs])`, which is converted into arguments for `Variable`

  - A pandas object, which is converted into a `DataArray`

  - A 1D array or list, which is interpreted as values for a one dimensional coordinate variable along the same dimension as it’s name

- `coords` should be a dictionary of the same form as `data_vars`.

- `attrs` should be a dictionary.

Let’s create some fake data for the example we show above:

    In [31]: temp = 15 + 8 * np.random.randn(2, 2, 3)

    In [32]: precip = 10 * np.random.rand(2, 2, 3)

    In [33]: lon = [[-99.83, -99.32], [-99.79, -99.23]]

    In [34]: lat = [[42.25, 42.21], [42.63, 42.59]]

    # for real use cases, its good practice to supply array attributes such as
    # units, but we won't bother here for the sake of brevity
    In [35]: ds = xr.Dataset(
       ....:     {
       ....:         "temperature": (["x", "y", "time"], temp),
       ....:         "precipitation": (["x", "y", "time"], precip),
       ....:     },
       ....:     coords={
       ....:         "lon": (["x", "y"], lon),
       ....:         "lat": (["x", "y"], lat),
       ....:         "time": pd.date_range("2014-09-06", periods=3),
       ....:         "reference_time": pd.Timestamp("2014-09-05"),
       ....:     },
       ....: )
       ....:

    In [36]: ds
    Out[36]:
    <xarray.Dataset>
    Dimensions:         (x: 2, y: 2, time: 3)
    Coordinates:
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        lat             (x, y) float64 42.25 42.21 42.63 42.59
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature     (x, y, time) float64 11.04 23.57 20.77 ... 6.301 9.61 15.91
        precipitation   (x, y, time) float64 5.904 2.453 3.404 ... 3.435 1.709 3.947

Here we pass `xarray.DataArray` objects or a pandas object as values in the dictionary:

    In [37]: xr.Dataset(dict(bar=foo))
    Out[37]:
    <xarray.Dataset>
    Dimensions:  (time: 4, space: 3)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) <U2 'IA' 'IL' 'IN'
    Data variables:
        bar      (time, space) float64 0.127 0.9667 0.2605 ... 0.543 0.373 0.448

    In [38]: xr.Dataset(dict(bar=foo.to_pandas()))
    Out[38]:
    <xarray.Dataset>
    Dimensions:  (time: 4, space: 3)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 2000-01-02 2000-01-03 2000-01-04
      * space    (space) object 'IA' 'IL' 'IN'
    Data variables:
        bar      (time, space) float64 0.127 0.9667 0.2605 ... 0.543 0.373 0.448

Where a pandas object is supplied as a value, the names of its indexes are used as dimension names, and its data is aligned to any existing dimensions.

You can also create an dataset from:

- A `pandas.DataFrame` or `pandas.Panel` along its columns and items respectively, by passing it into the `Dataset` directly

- A `pandas.DataFrame` with `Dataset.from_dataframe`, which will additionally handle MultiIndexes See Working with pandas

- A netCDF file on disk with `open_dataset()`. See Reading and writing files.

### Dataset contents

`Dataset` implements the Python mapping interface, with values given by `xarray.DataArray` objects:

    In [39]: "temperature" in ds
    Out[39]: True

    In [40]: ds["temperature"]
    Out[40]:
    <xarray.DataArray 'temperature' (x: 2, y: 2, time: 3)>
    array([[[11.041, 23.574, 20.772],
            [ 9.346,  6.683, 17.175]],

           [[11.6  , 19.536, 17.21 ],
            [ 6.301,  9.61 , 15.909]]])
    Coordinates:
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        lat             (x, y) float64 42.25 42.21 42.63 42.59
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y

Valid keys include each listed coordinate and data variable.

Data and coordinate variables are also contained separately in the `data_vars` and `coords` dictionary-like attributes:

    In [41]: ds.data_vars
    Out[41]:
    Data variables:
        temperature    (x, y, time) float64 11.04 23.57 20.77 ... 6.301 9.61 15.91
        precipitation  (x, y, time) float64 5.904 2.453 3.404 ... 3.435 1.709 3.947

    In [42]: ds.coords
    Out[42]:
    Coordinates:
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        lat             (x, y) float64 42.25 42.21 42.63 42.59
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05

Finally, like data arrays, datasets also store arbitrary metadata in the form of attributes:

    In [43]: ds.attrs
    Out[43]: {}

    In [44]: ds.attrs["title"] = "example attribute"

    In [45]: ds
    Out[45]:
    <xarray.Dataset>
    Dimensions:         (x: 2, y: 2, time: 3)
    Coordinates:
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        lat             (x, y) float64 42.25 42.21 42.63 42.59
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature     (x, y, time) float64 11.04 23.57 20.77 ... 6.301 9.61 15.91
        precipitation   (x, y, time) float64 5.904 2.453 3.404 ... 3.435 1.709 3.947
    Attributes:
        title:    example attribute

Xarray does not enforce any restrictions on attributes, but serialization to some file formats may fail if you use objects that are not strings, numbers or `numpy.ndarray` objects.

As a useful shortcut, you can use attribute style access for reading (but not setting) variables and attributes:

    In [46]: ds.temperature
    Out[46]:
    <xarray.DataArray 'temperature' (x: 2, y: 2, time: 3)>
    array([[[11.041, 23.574, 20.772],
            [ 9.346,  6.683, 17.175]],

           [[11.6  , 19.536, 17.21 ],
            [ 6.301,  9.61 , 15.909]]])
    Coordinates:
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        lat             (x, y) float64 42.25 42.21 42.63 42.59
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y

This is particularly useful in an exploratory context, because you can tab-complete these variable names with tools like IPython.

### Dictionary like methods

We can update a dataset in-place using Python’s standard dictionary syntax. For example, to create this example dataset from scratch, we could have written:

    In [47]: ds = xr.Dataset()

    In [48]: ds["temperature"] = (("x", "y", "time"), temp)

    In [49]: ds["temperature_double"] = (("x", "y", "time"), temp * 2)

    In [50]: ds["precipitation"] = (("x", "y", "time"), precip)

    In [51]: ds.coords["lat"] = (("x", "y"), lat)

    In [52]: ds.coords["lon"] = (("x", "y"), lon)

    In [53]: ds.coords["time"] = pd.date_range("2014-09-06", periods=3)

    In [54]: ds.coords["reference_time"] = pd.Timestamp("2014-09-05")

To change the variables in a `Dataset`, you can use all the standard dictionary methods, including `values`, `items`, `__delitem__`, `get` and `update()`. Note that assigning a `DataArray` or pandas object to a `Dataset` variable using `__setitem__` or `update` will automatically align the array(s) to the original dataset’s indexes.

You can copy a `Dataset` by calling the `copy()` method. By default, the copy is shallow, so only the container will be copied: the arrays in the `Dataset` will still be stored in the same underlying `numpy.ndarray` objects. You can copy all data by calling `ds.copy(deep=True)`.

### Transforming datasets

In addition to dictionary-like methods (described above), xarray has additional methods (like pandas) for transforming datasets into new objects.

For removing variables, you can select and drop an explicit list of variables by indexing with a list of names or using the `drop_vars()` methods to return a new `Dataset`. These operations keep around coordinates:

    In [55]: ds[["temperature"]]
    Out[55]:
    <xarray.Dataset>
    Dimensions:         (x: 2, y: 2, time: 3)
    Coordinates:
        lat             (x, y) float64 42.25 42.21 42.63 42.59
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature     (x, y, time) float64 11.04 23.57 20.77 ... 6.301 9.61 15.91

    In [56]: ds[["temperature", "temperature_double"]]
    Out[56]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature         (x, y, time) float64 11.04 23.57 20.77 ... 9.61 15.91
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82

    In [57]: ds.drop_vars("temperature")
    Out[57]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82
        precipitation       (x, y, time) float64 5.904 2.453 3.404 ... 1.709 3.947

To remove a dimension, you can use `drop_dims()` method. Any variables using that dimension are dropped:

    In [58]: ds.drop_dims("time")
    Out[58]:
    <xarray.Dataset>
    Dimensions:         (x: 2, y: 2)
    Coordinates:
        lat             (x, y) float64 42.25 42.21 42.63 42.59
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
        reference_time  datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        *empty*

As an alternate to dictionary-like modifications, you can use `assign()` and `assign_coords()`. These methods return a new dataset with additional (or replaced) values:

    In [59]: ds.assign(temperature2=2 * ds.temperature)
    Out[59]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temperature         (x, y, time) float64 11.04 23.57 20.77 ... 9.61 15.91
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82
        precipitation       (x, y, time) float64 5.904 2.453 3.404 ... 1.709 3.947
        temperature2        (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82

There is also the `pipe()` method that allows you to use a method call with an external function (e.g., `ds.pipe(func)`) instead of simply calling it (e.g., `func(ds)`). This allows you to write pipelines for transforming your data (using “method chaining”) instead of writing hard to follow nested function calls:

    # these lines are equivalent, but with pipe we can make the logic flow
    # entirely from left to right
    In [60]: plt.plot((2 * ds.temperature.sel(x=0)).mean("y"))
    Out[60]: [<matplotlib.lines.Line2D at 0x7f3d2ae791e0>]

    In [61]: (ds.temperature.sel(x=0).pipe(lambda x: 2 * x).mean("y").pipe(plt.plot))
    Out[61]: [<matplotlib.lines.Line2D at 0x7f3d2ad9fa90>]

Both `pipe` and `assign` replicate the pandas methods of the same names (`DataFrame.pipe` and `DataFrame.assign`).

With xarray, there is no performance penalty for creating new datasets, even if variables are lazily loaded from a file on disk. Creating new objects instead of mutating existing objects often results in easier to understand code, so we encourage using this approach.

### Renaming variables

Another useful option is the `rename()` method to rename dataset variables:

    In [62]: ds.rename({"temperature": "temp", "precipitation": "precip"})
    Out[62]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
    Dimensions without coordinates: x, y
    Data variables:
        temp                (x, y, time) float64 11.04 23.57 20.77 ... 9.61 15.91
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82
        precip              (x, y, time) float64 5.904 2.453 3.404 ... 1.709 3.947

The related `swap_dims()` method allows you do to swap dimension and non-dimension variables:

    In [63]: ds.coords["day"] = ("time", [6, 7, 8])

    In [64]: ds.swap_dims({"time": "day"})
    Out[64]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, day: 3)
    Coordinates:
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
        time                (day) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
      * day                 (day) int64 6 7 8
    Dimensions without coordinates: x, y
    Data variables:
        temperature         (x, y, day) float64 11.04 23.57 20.77 ... 9.61 15.91
        temperature_double  (x, y, day) float64 22.08 47.15 41.54 ... 19.22 31.82
        precipitation       (x, y, day) float64 5.904 2.453 3.404 ... 1.709 3.947

## Coordinates

Coordinates are ancillary variables stored for `DataArray` and `Dataset` objects in the `coords` attribute:

    In [65]: ds.coords
    Out[65]:
    Coordinates:
        lat             (x, y) float64 42.25 42.21 42.63 42.59
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
        day             (time) int64 6 7 8

Unlike attributes, xarray does interpret and persist coordinates in operations that transform xarray objects. There are two types of coordinates in xarray:

- dimension coordinates are one dimensional coordinates with a name equal to their sole dimension (marked by `*` when printing a dataset or data array). They are used for label based indexing and alignment, like the `index` found on a pandas `DataFrame` or `Series`. Indeed, these “dimension” coordinates use a `pandas.Index` internally to store their values.

- non-dimension coordinates are variables that contain coordinate data, but are not a dimension coordinate. They can be multidimensional (see Working with Multidimensional Coordinates), and there is no relationship between the name of a non-dimension coordinate and the name(s) of its dimension(s). Non-dimension coordinates can be useful for indexing or plotting; otherwise, xarray does not make any direct use of the values associated with them. They are not used for alignment or automatic indexing, nor are they required to match when doing arithmetic (see Coordinates).

Note

Xarray’s terminology differs from the CF terminology, where the “dimension coordinates” are called “coordinate variables”, and the “non-dimension coordinates” are called “auxiliary coordinate variables” (see GH1295 for more details).

### Modifying coordinates

To entirely add or remove coordinate arrays, you can use dictionary like syntax, as shown above.

To convert back and forth between data and coordinates, you can use the `set_coords()` and `reset_coords()` methods:

    In [66]: ds.reset_coords()
    Out[66]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
    Dimensions without coordinates: x, y
    Data variables:
        temperature         (x, y, time) float64 11.04 23.57 20.77 ... 9.61 15.91
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82
        precipitation       (x, y, time) float64 5.904 2.453 3.404 ... 1.709 3.947
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
        reference_time      datetime64[ns] 2014-09-05
        day                 (time) int64 6 7 8

    In [67]: ds.set_coords(["temperature", "precipitation"])
    Out[67]:
    <xarray.Dataset>
    Dimensions:             (x: 2, y: 2, time: 3)
    Coordinates:
        temperature         (x, y, time) float64 11.04 23.57 20.77 ... 9.61 15.91
        precipitation       (x, y, time) float64 5.904 2.453 3.404 ... 1.709 3.947
        lat                 (x, y) float64 42.25 42.21 42.63 42.59
        lon                 (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time                (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time      datetime64[ns] 2014-09-05
        day                 (time) int64 6 7 8
    Dimensions without coordinates: x, y
    Data variables:
        temperature_double  (x, y, time) float64 22.08 47.15 41.54 ... 19.22 31.82

    In [68]: ds["temperature"].reset_coords(drop=True)
    Out[68]:
    <xarray.DataArray 'temperature' (x: 2, y: 2, time: 3)>
    array([[[11.041, 23.574, 20.772],
            [ 9.346,  6.683, 17.175]],

           [[11.6  , 19.536, 17.21 ],
            [ 6.301,  9.61 , 15.909]]])
    Coordinates:
      * time     (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
    Dimensions without coordinates: x, y

Notice that these operations skip coordinates with names given by dimensions, as used for indexing. This mostly because we are not entirely sure how to design the interface around the fact that xarray cannot store a coordinate and variable with the name but different values in the same dictionary. But we do recognize that supporting something like this would be useful.

### Coordinates methods

`Coordinates` objects also have a few useful methods, mostly for converting them into dataset objects:

    In [69]: ds.coords.to_dataset()
    Out[69]:
    <xarray.Dataset>
    Dimensions:         (x: 2, y: 2, time: 3)
    Coordinates:
        lat             (x, y) float64 42.25 42.21 42.63 42.59
        lon             (x, y) float64 -99.83 -99.32 -99.79 -99.23
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
        day             (time) int64 6 7 8
    Dimensions without coordinates: x, y
    Data variables:
        *empty*

The merge method is particularly interesting, because it implements the same logic used for merging coordinates in arithmetic operations (see Computation):

    In [70]: alt = xr.Dataset(coords={"z": [10], "lat": 0, "lon": 0})

    In [71]: ds.coords.merge(alt.coords)
    Out[71]:
    <xarray.Dataset>
    Dimensions:         (time: 3, z: 1)
    Coordinates:
      * time            (time) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08
        reference_time  datetime64[ns] 2014-09-05
        day             (time) int64 6 7 8
      * z               (z) int64 10
    Data variables:
        *empty*

The `coords.merge` method may be useful if you want to implement your own binary operations that act on xarray objects. In the future, we hope to write more helper functions so that you can easily make your functions act like xarray’s built-in arithmetic.

### Indexes

To convert a coordinate (or any `DataArray`) into an actual `pandas.Index`, use the `to_index()` method:

    In [72]: ds["time"].to_index()
    Out[72]: DatetimeIndex(['2014-09-06', '2014-09-07', '2014-09-08'], dtype='datetime64[ns]', name='time', freq='D')

A useful shortcut is the `indexes` property (on both `DataArray` and `Dataset`), which lazily constructs a dictionary whose keys are given by each dimension and whose the values are `Index` objects:

    In [73]: ds.indexes
    Out[73]: time: DatetimeIndex(['2014-09-06', '2014-09-07', '2014-09-08'], dtype='datetime64[ns]', name='time', freq='D')

### MultiIndex coordinates

Xarray supports labeling coordinate values with a `pandas.MultiIndex`:

    In [74]: midx = pd.MultiIndex.from_arrays(
       ....:     [["R", "R", "V", "V"], [0.1, 0.2, 0.7, 0.9]], names=("band", "wn")
       ....: )
       ....:

    In [75]: mda = xr.DataArray(np.random.rand(4), coords={"spec": midx}, dims="spec")

    In [76]: mda
    Out[76]:
    <xarray.DataArray (spec: 4)>
    array([0.642, 0.275, 0.462, 0.871])
    Coordinates:
      * spec     (spec) MultiIndex
      - band     (spec) object 'R' 'R' 'V' 'V'
      - wn       (spec) float64 0.1 0.2 0.7 0.9

For convenience multi-index levels are directly accessible as “virtual” or “derived” coordinates (marked by `-` when printing a dataset or data array):

    In [77]: mda["band"]
    Out[77]:
    <xarray.DataArray 'band' (spec: 4)>
    array(['R', 'R', 'V', 'V'], dtype=object)
    Coordinates:
      * spec     (spec) MultiIndex
      - band     (spec) object 'R' 'R' 'V' 'V'
      - wn       (spec) float64 0.1 0.2 0.7 0.9

    In [78]: mda.wn
    Out[78]:
    <xarray.DataArray 'wn' (spec: 4)>
    array([0.1, 0.2, 0.7, 0.9])
    Coordinates:
      * spec     (spec) MultiIndex
      - band     (spec) object 'R' 'R' 'V' 'V'
      - wn       (spec) float64 0.1 0.2 0.7 0.9

Indexing with multi-index levels is also possible using the `sel` method (see Multi-level indexing).

Unlike other coordinates, “virtual” level coordinates are not stored in the `coords` attribute of `DataArray` and `Dataset` objects (although they are shown when printing the `coords` attribute). Consequently, most of the coordinates related methods don’t apply for them. It also can’t be used to replace one particular level.

Because in a `DataArray` or `Dataset` object each multi-index level is accessible as a “virtual” coordinate, its name must not conflict with the names of the other levels, coordinates and data variables of the same object. Even though xarray sets default names for multi-indexes with unnamed levels, it is recommended that you explicitly set the names of the levels.

1

  Latitude and longitude are 2D arrays because the dataset uses projected coordinates. `reference_time` refers to the reference time at which the forecast was made, rather than `time` which is the valid time for which the forecast applies.