# Data Structures

## DataArray

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

- `values`: a `numpy.ndarray` or numpy-like array 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. For reading and writing attributes xarray relies on the capabilities of the supported backends. (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, a numpy-like array, `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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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)> Size: 96B
    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]], shape=(4, 3))
    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 its 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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
        const    int64 8B 42
        ranking  (space) int64 24B 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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
        const    int64 8B 42
        ranking  (time, space) int64 96B 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)> Size: 32B
    array([[0, 2],
           [1, 3]])
    Coordinates:
      * abc      (abc) object 16B 'a' 'b'
      * xyz      (xyz) object 16B '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]], shape=(4, 3))

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

    In [17]: foo.coords
    Out[17]:
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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)> Size: 96B
    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]], shape=(4, 3))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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)> Size: 32B
    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] 32B 2000-01-01 2000-01-02 ... 2000-01-04

    In [26]: foo["time"]
    Out[26]:
    <xarray.DataArray 'time' (time: 4)> Size: 32B
    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] 32B 2000-01-01 2000-01-02 ... 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] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
        ranking  (space) int64 24B 1 2 3

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

    In [30]: foo.coords
    Out[30]:
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B '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 its 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 this example dataset, we will represent measurements of the temperature and pressure that were made under various conditions:

- the measurements were made on four different days;

- they were made at two separate locations, which we will represent using their latitude and longitude; and

- they were made using instruments by three different manufacturers, which we will refer to as `'manufac1'`, `'manufac2'`, and `'manufac3'`.

    In [31]: np.random.seed(0)

    In [32]: temperature = 15 + 8 * np.random.randn(2, 3, 4)

    In [33]: precipitation = 10 * np.random.rand(2, 3, 4)

    In [34]: lon = [-99.83, -99.32]

    In [35]: lat = [42.25, 42.21]

    In [36]: instruments = ["manufac1", "manufac2", "manufac3"]

    In [37]: time = pd.date_range("2014-09-06", periods=4)

    In [38]: reference_time = pd.Timestamp("2014-09-05")

    # 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 [39]: ds = xr.Dataset(
       ....:     {
       ....:         "temperature": (["loc", "instrument", "time"], temperature),
       ....:         "precipitation": (["loc", "instrument", "time"], precipitation),
       ....:     },
       ....:     coords={
       ....:         "lon": (["loc"], lon),
       ....:         "lat": (["loc"], lat),
       ....:         "instrument": instruments,
       ....:         "time": time,
       ....:         "reference_time": reference_time,
       ....:     },
       ....: )
       ....:

    In [40]: ds
    Out[40]:
    <xarray.Dataset> Size: 552B
    Dimensions:         (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lon             (loc) float64 16B -99.83 -99.32
        lat             (loc) float64 16B 42.25 42.21
      * instrument      (instrument) <U8 96B 'manufac1' 'manufac2' 'manufac3'
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc
    Data variables:
        temperature     (loc, instrument, time) float64 192B 29.11 18.2 ... 9.063
        precipitation   (loc, instrument, time) float64 192B 4.562 5.684 ... 1.613

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

    In [41]: xr.Dataset(dict(bar=foo))
    Out[41]:
    <xarray.Dataset> Size: 152B
    Dimensions:  (time: 4, space: 3)
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) <U2 24B 'IA' 'IL' 'IN'
    Data variables:
        bar      (time, space) float64 96B 0.127 0.9667 0.2605 ... 0.543 0.373 0.448

    In [42]: xr.Dataset(dict(bar=foo.to_pandas()))
    Out[42]:
    <xarray.Dataset> Size: 152B
    Dimensions:  (time: 4, space: 3)
    Coordinates:
      * time     (time) datetime64[ns] 32B 2000-01-01 2000-01-02 ... 2000-01-04
      * space    (space) object 24B 'IA' 'IL' 'IN'
    Data variables:
        bar      (time, space) float64 96B 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 [43]: "temperature" in ds
    Out[43]: True

    In [44]: ds["temperature"]
    Out[44]:
    <xarray.DataArray 'temperature' (loc: 2, instrument: 3, time: 4)> Size: 192B
    array([[[29.112, 18.201, 22.83 , 32.927],
            [29.94 ,  7.182, 22.601, 13.789],
            [14.174, 18.285, 16.152, 26.634]],

           [[21.088, 15.973, 18.551, 17.669],
            [26.953, 13.359, 17.505,  8.167],
            [-5.424, 20.229, 21.915,  9.063]]], shape=(2, 3, 4))
    Coordinates:
        lon             (loc) float64 16B -99.83 -99.32
        lat             (loc) float64 16B 42.25 42.21
      * instrument      (instrument) <U8 96B 'manufac1' 'manufac2' 'manufac3'
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc

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 [45]: ds.data_vars
    Out[45]:
    Data variables:
        temperature    (loc, instrument, time) float64 192B 29.11 18.2 ... 9.063
        precipitation  (loc, instrument, time) float64 192B 4.562 5.684 ... 1.613

    In [46]: ds.coords
    Out[46]:
    Coordinates:
        lon             (loc) float64 16B -99.83 -99.32
        lat             (loc) float64 16B 42.25 42.21
      * instrument      (instrument) <U8 96B 'manufac1' 'manufac2' 'manufac3'
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05

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

    In [47]: ds.attrs
    Out[47]: {}

    In [48]: ds.attrs["title"] = "example attribute"

    In [49]: ds
    Out[49]:
    <xarray.Dataset> Size: 552B
    Dimensions:         (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lon             (loc) float64 16B -99.83 -99.32
        lat             (loc) float64 16B 42.25 42.21
      * instrument      (instrument) <U8 96B 'manufac1' 'manufac2' 'manufac3'
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc
    Data variables:
        temperature     (loc, instrument, time) float64 192B 29.11 18.2 ... 9.063
        precipitation   (loc, instrument, time) float64 192B 4.562 5.684 ... 1.613
    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 [50]: ds.temperature
    Out[50]:
    <xarray.DataArray 'temperature' (loc: 2, instrument: 3, time: 4)> Size: 192B
    array([[[29.112, 18.201, 22.83 , 32.927],
            [29.94 ,  7.182, 22.601, 13.789],
            [14.174, 18.285, 16.152, 26.634]],

           [[21.088, 15.973, 18.551, 17.669],
            [26.953, 13.359, 17.505,  8.167],
            [-5.424, 20.229, 21.915,  9.063]]], shape=(2, 3, 4))
    Coordinates:
        lon             (loc) float64 16B -99.83 -99.32
        lat             (loc) float64 16B 42.25 42.21
      * instrument      (instrument) <U8 96B 'manufac1' 'manufac2' 'manufac3'
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc

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 [51]: ds = xr.Dataset()

    In [52]: ds["temperature"] = (("loc", "instrument", "time"), temperature)

    In [53]: ds["temperature_double"] = (("loc", "instrument", "time"), temperature * 2)

    In [54]: ds["precipitation"] = (("loc", "instrument", "time"), precipitation)

    In [55]: ds.coords["lat"] = (("loc",), lat)

    In [56]: ds.coords["lon"] = (("loc",), lon)

    In [57]: ds.coords["time"] = pd.date_range("2014-09-06", periods=4)

    In [58]: 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 [59]: ds[["temperature"]]
    Out[59]:
    <xarray.Dataset> Size: 264B
    Dimensions:         (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lat             (loc) float64 16B 42.25 42.21
        lon             (loc) float64 16B -99.83 -99.32
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature     (loc, instrument, time) float64 192B 29.11 18.2 ... 9.063

    In [60]: ds[["temperature", "temperature_double"]]
    Out[60]:
    <xarray.Dataset> Size: 456B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature         (loc, instrument, time) float64 192B 29.11 ... 9.063
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13

    In [61]: ds.drop_vars("temperature")
    Out[61]:
    <xarray.Dataset> Size: 456B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13
        precipitation       (loc, instrument, time) float64 192B 4.562 ... 1.613

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

    In [62]: ds.drop_dims("time")
    Out[62]:
    <xarray.Dataset> Size: 40B
    Dimensions:         (loc: 2)
    Coordinates:
        lat             (loc) float64 16B 42.25 42.21
        lon             (loc) float64 16B -99.83 -99.32
        reference_time  datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc
    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 [63]: ds.assign(temperature2=2 * ds.temperature)
    Out[63]:
    <xarray.Dataset> Size: 840B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature         (loc, instrument, time) float64 192B 29.11 ... 9.063
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13
        precipitation       (loc, instrument, time) float64 192B 4.562 ... 1.613
        temperature2        (loc, instrument, time) float64 192B 58.22 ... 18.13

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 [64]: plt.plot((2 * ds.temperature.sel(loc=0)).mean("instrument"))
    Out[64]: [<matplotlib.lines.Line2D at 0x7c5f964d65d0>]

    In [65]: (ds.temperature.sel(loc=0).pipe(lambda x: 2 * x).mean("instrument").pipe(plt.plot))
    Out[65]: [<matplotlib.lines.Line2D at 0x7c5f964d79d0>]

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 [66]: ds.rename({"temperature": "temp", "precipitation": "precip"})
    Out[66]:
    <xarray.Dataset> Size: 648B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
    Dimensions without coordinates: loc, instrument
    Data variables:
        temp                (loc, instrument, time) float64 192B 29.11 ... 9.063
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13
        precip              (loc, instrument, time) float64 192B 4.562 ... 1.613

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

    In [67]: ds.coords["day"] = ("time", [6, 7, 8, 9])

    In [68]: ds.swap_dims({"time": "day"})
    Out[68]:
    <xarray.Dataset> Size: 680B
    Dimensions:             (loc: 2, instrument: 3, day: 4)
    Coordinates:
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
        time                (day) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
      * day                 (day) int64 32B 6 7 8 9
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature         (loc, instrument, day) float64 192B 29.11 18.2 ... 9.063
        temperature_double  (loc, instrument, day) float64 192B 58.22 36.4 ... 18.13
        precipitation       (loc, instrument, day) float64 192B 4.562 ... 1.613

## DataTree

`DataTree` is `xarray`’s highest-level data structure, able to organise heterogeneous data which could not be stored inside a single `Dataset` object. This includes representing the recursive structure of multiple groups within a netCDF file or Zarr Store.

Each `DataTree` object (or “node”) contains the same data that a single `xarray.Dataset` would (i.e. `DataArray` objects stored under hashable keys), and so has the same key properties:

- `dims`: a dictionary mapping of dimension names to lengths, for the variables in this node, and this node’s ancestors,

- `data_vars`: a dict-like container of DataArrays corresponding to variables in this node,

- `coords`: another dict-like container of DataArrays, corresponding to coordinate variables in this node, and this node’s ancestors,

- `attrs`: dict to hold arbitrary metadata relevant to data in this node.

A single `DataTree` object acts much like a single `Dataset` object, and has a similar set of dict-like methods defined upon it. However, `DataTree`s can also contain other `DataTree` objects, so they can be thought of as nested dict-like containers of both `xarray.DataArray`s and `DataTree`s.

A single datatree object is known as a “node”, and its position relative to other nodes is defined by two more key properties:

- `children`: An dictionary mapping from names to other `DataTree` objects, known as its “child nodes”.

- `parent`: The single `DataTree` object whose children this datatree is a member of, known as its “parent node”.

Each child automatically knows about its parent node, and a node without a parent is known as a “root” node (represented by the `parent` attribute pointing to `None`). Nodes can have multiple children, but as each child node has at most one parent, there can only ever be one root node in a given tree.

The overall structure is technically a connected acyclic undirected rooted graph, otherwise known as a “Tree”.

`DataTree` objects can also optionally have a `name` as well as `attrs`, just like a `DataArray`. Again these are not normally used unless explicitly accessed by the user.

### Creating a DataTree

One way to create a `DataTree` from scratch is to create each node individually, specifying the nodes’ relationship to one another as you create each one.

The `DataTree` constructor takes:

- `dataset`: The data that will be stored in this node, represented by a single `xarray.Dataset`, or a named `xarray.DataArray`.

- `children`: The various child nodes (if there are any), given as a mapping from string keys to `DataTree` objects.

- `name`: A string to use as the name of this node.

Let’s make a single datatree node with some example data in it:

    In [69]: ds1 = xr.Dataset({"foo": "orange"})

    In [70]: dt = xr.DataTree(name="root", dataset=ds1)

    In [71]: dt
    Out[71]:
    <xarray.DataTree 'root'>
    Group: /
        Dimensions:  ()
        Data variables:
            foo      <U6 24B 'orange'

At this point we have created a single node datatree with no parent and no children.

    In [72]: dt.parent is None
    Out[72]: True

    In [73]: dt.children
    Out[73]: Frozen({})

We can add a second node to this tree, assigning it to the parent node `dt`:

    In [74]: dataset2 = xr.Dataset({"bar": 0}, coords={"y": ("y", [0, 1, 2])})

    In [75]: dt2 = xr.DataTree(name="a", dataset=dataset2)

    # Add the child Datatree to the root node
    In [76]: dt.children = {"child-node": dt2}

    In [77]: dt
    Out[77]:
    <xarray.DataTree 'root'>
    Group: /
    │   Dimensions:  ()
    │   Data variables:
    │       foo      <U6 24B 'orange'
    └── Group: /child-node
            Dimensions:  (y: 3)
            Coordinates:
              * y        (y) int64 24B 0 1 2
            Data variables:
                bar      int64 8B 0

More idiomatically you can create a tree from a dictionary of `Datasets` and `DataTrees`. In this case we add a new node under `dt["child-node"]` by providing the explicit path under `"child-node"` as the dictionary key:

    # create a third Dataset
    In [78]: ds3 = xr.Dataset({"zed": np.nan})

    # create a tree from a dictionary of DataTrees and Datasets
    In [79]: dt = xr.DataTree.from_dict({"/": dt, "/child-node/new-zed-node": ds3})

We have created a tree with three nodes in it:

    In [80]: dt
    Out[80]:
    <xarray.DataTree>
    Group: /
    │   Dimensions:  ()
    │   Data variables:
    │       foo      <U6 24B 'orange'
    └── Group: /child-node
        │   Dimensions:  (y: 3)
        │   Coordinates:
        │     * y        (y) int64 24B 0 1 2
        │   Data variables:
        │       bar      int64 8B 0
        └── Group: /child-node/new-zed-node
                Dimensions:  ()
                Data variables:
                    zed      float64 8B nan

Consistency checks are enforced. For instance, if we try to create a cycle, where the root node is also a child of a descendant, the constructor will raise an (`InvalidTreeError`):

    In [81]: dt["child-node"].children = {"new-child": dt}
    InvalidTreeError: Cannot set parent, as intended parent is already a descendant of this node.

Alternatively you can also create a `DataTree` object from:

- A dictionary mapping directory-like paths to either `DataTree` nodes or data, using `xarray.DataTree.from_dict()`,

- A well formed netCDF or Zarr file on disk with `open_datatree()`. See reading and writing files.

For data files with groups that do not not align see `xarray.open_groups()` or target each group individually `xarray.open_dataset(group='groupname')`. For more information about coordinate alignment see DataTree Inheritance

### DataTree Contents

Like `Dataset`, `DataTree` implements the python mapping interface, but with values given by either `DataArray` objects or other `DataTree` objects.

    In [82]: dt["child-node"]
    Out[82]:
    <xarray.DataTree 'child-node'>
    Group: /child-node
    │   Dimensions:  (y: 3)
    │   Coordinates:
    │     * y        (y) int64 24B 0 1 2
    │   Data variables:
    │       bar      int64 8B 0
    └── Group: /child-node/new-zed-node
            Dimensions:  ()
            Data variables:
                zed      float64 8B nan

    In [83]: dt["foo"]
    Out[83]:
    <xarray.DataArray 'foo' ()> Size: 24B
    array('orange', dtype='<U6')

Iterating over keys will iterate over both the names of variables and child nodes.

We can also access all the data in a single node, and its inherited coordinates, through a dataset-like view

    In [84]: dt["child-node"].dataset
    Out[84]:
    <xarray.DatasetView> Size: 32B
    Dimensions:  (y: 3)
    Coordinates:
      * y        (y) int64 24B 0 1 2
    Data variables:
        bar      int64 8B 0

This demonstrates the fact that the data in any one node is equivalent to the contents of a single `Dataset` object. The `DataTree.dataset` property returns an immutable view, but we can instead extract the node’s data contents as a new and mutable `Dataset` object via `DataTree.to_dataset()`:

    In [85]: dt["child-node"].to_dataset()
    Out[85]:
    <xarray.Dataset> Size: 32B
    Dimensions:  (y: 3)
    Coordinates:
      * y        (y) int64 24B 0 1 2
    Data variables:
        bar      int64 8B 0

Like with `Dataset`, you can access the data and coordinate variables of a node separately via the `data_vars` and `coords` attributes:

    In [86]: dt["child-node"].data_vars
    Out[86]:
    Data variables:
        bar      int64 8B 0

    In [87]: dt["child-node"].coords
    Out[87]:
    Coordinates:
      * y        (y) int64 24B 0 1 2

### Dictionary-like methods

We can update a datatree in-place using Python’s standard dictionary syntax, similar to how we can for Dataset objects. For example, to create this example DataTree from scratch, we could have written:

    In [88]: dt = xr.DataTree(name="root")

    In [89]: dt["foo"] = "orange"

    In [90]: dt["child-node"] = xr.DataTree(
       ....:     dataset=xr.Dataset({"bar": 0}, coords={"y": ("y", [0, 1, 2])})
       ....: )
       ....:

    In [91]: dt["child-node/new-zed-node/zed"] = np.nan

    In [92]: dt
    Out[92]:
    <xarray.DataTree 'root'>
    Group: /
    │   Dimensions:  ()
    │   Data variables:
    │       foo      <U6 24B 'orange'
    └── Group: /child-node
        │   Dimensions:  (y: 3)
        │   Coordinates:
        │     * y        (y) int64 24B 0 1 2
        │   Data variables:
        │       bar      int64 8B 0
        └── Group: /child-node/new-zed-node
                Dimensions:  ()
                Data variables:
                    zed      float64 8B nan

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

If you copy a `DataTree` using the `copy()` function or the `xarray.DataTree.copy()` method it will copy the subtree, meaning that node and children below it, but no parents above it. Like for `Dataset`, this copy is shallow by default, but you can copy all the underlying data arrays by calling `dt.copy(deep=True)`.

### DataTree Inheritance

DataTree implements a simple inheritance mechanism. Coordinates, dimensions and their associated indices are propagated from downward starting from the root node to all descendent nodes. Coordinate inheritance was inspired by the NetCDF-CF inherited dimensions, but DataTree’s inheritance is slightly stricter yet easier to reason about.

The constraint that this puts on a DataTree is that dimensions and indices that are inherited must be aligned with any direct descendant node’s existing dimension or index. This allows descendants to use dimensions defined in ancestor nodes, without duplicating that information. But as a consequence, if a dimension-name is defined in on a node and that same dimension-name exists in one of its ancestors, they must align (have the same index and size).

Some examples:

    # Set up coordinates
    In [93]: time = xr.DataArray(data=["2022-01", "2023-01"], dims="time")

    In [94]: stations = xr.DataArray(data=list("abcdef"), dims="station")

    In [95]: lon = [-100, -80, -60]

    In [96]: lat = [10, 20, 30]

    # Set up fake data
    In [97]: wind_speed = xr.DataArray(np.ones((2, 6)) * 2, dims=("time", "station"))

    In [98]: pressure = xr.DataArray(np.ones((2, 6)) * 3, dims=("time", "station"))

    In [99]: air_temperature = xr.DataArray(np.ones((2, 6)) * 4, dims=("time", "station"))

    In [100]: dewpoint = xr.DataArray(np.ones((2, 6)) * 5, dims=("time", "station"))

    In [101]: infrared = xr.DataArray(np.ones((2, 3, 3)) * 6, dims=("time", "lon", "lat"))

    In [102]: true_color = xr.DataArray(np.ones((2, 3, 3)) * 7, dims=("time", "lon", "lat"))

    In [103]: dt2 = xr.DataTree.from_dict(
       .....:     {
       .....:         "/": xr.Dataset(
       .....:             coords={"time": time},
       .....:         ),
       .....:         "/weather": xr.Dataset(
       .....:             coords={"station": stations},
       .....:             data_vars={
       .....:                 "wind_speed": wind_speed,
       .....:                 "pressure": pressure,
       .....:             },
       .....:         ),
       .....:         "/weather/temperature": xr.Dataset(
       .....:             data_vars={
       .....:                 "air_temperature": air_temperature,
       .....:                 "dewpoint": dewpoint,
       .....:             },
       .....:         ),
       .....:         "/satellite": xr.Dataset(
       .....:             coords={"lat": lat, "lon": lon},
       .....:             data_vars={
       .....:                 "infrared": infrared,
       .....:                 "true_color": true_color,
       .....:             },
       .....:         ),
       .....:     },
       .....: )
       .....:

    In [104]: dt2
    Out[104]:
    <xarray.DataTree>
    Group: /
    │   Dimensions:  (time: 2)
    │   Coordinates:
    │     * time     (time) <U7 56B '2022-01' '2023-01'
    ├── Group: /weather
    │   │   Dimensions:     (station: 6, time: 2)
    │   │   Coordinates:
    │   │     * station     (station) <U1 24B 'a' 'b' 'c' 'd' 'e' 'f'
    │   │   Data variables:
    │   │       wind_speed  (time, station) float64 96B 2.0 2.0 2.0 2.0 ... 2.0 2.0 2.0 2.0
    │   │       pressure    (time, station) float64 96B 3.0 3.0 3.0 3.0 ... 3.0 3.0 3.0 3.0
    │   └── Group: /weather/temperature
    │           Dimensions:          (time: 2, station: 6)
    │           Data variables:
    │               air_temperature  (time, station) float64 96B 4.0 4.0 4.0 4.0 ... 4.0 4.0 4.0
    │               dewpoint         (time, station) float64 96B 5.0 5.0 5.0 5.0 ... 5.0 5.0 5.0
    └── Group: /satellite
            Dimensions:     (lat: 3, lon: 3, time: 2)
            Coordinates:
              * lat         (lat) int64 24B 10 20 30
              * lon         (lon) int64 24B -100 -80 -60
            Data variables:
                infrared    (time, lon, lat) float64 144B 6.0 6.0 6.0 6.0 ... 6.0 6.0 6.0
                true_color  (time, lon, lat) float64 144B 7.0 7.0 7.0 7.0 ... 7.0 7.0 7.0

Here there are four different coordinate variables, which apply to variables in the DataTree in different ways:

`time` is a shared coordinate used by both `weather` and `satellite` variables `station` is used only for `weather` variables `lat` and `lon` are only use for `satellite` images

Coordinate variables are inherited to descendent nodes, which is only possible because variables at different levels of a hierarchical DataTree are always aligned. Placing the `time` variable at the root node automatically indicates that it applies to all descendent nodes. Similarly, `station` is in the base `weather` node, because it applies to all weather variables, both directly in `weather` and in the `temperature` sub-tree. Notice the inherited coordinates are explicitly shown in the tree representation under `Inherited coordinates:`.

    In [105]: dt2["/weather"]
    Out[105]:
    <xarray.DataTree 'weather'>
    Group: /weather
    │   Dimensions:     (time: 2, station: 6)
    │   Coordinates:
    │     * station     (station) <U1 24B 'a' 'b' 'c' 'd' 'e' 'f'
    │   Inherited coordinates:
    │     * time        (time) <U7 56B '2022-01' '2023-01'
    │   Data variables:
    │       wind_speed  (time, station) float64 96B 2.0 2.0 2.0 2.0 ... 2.0 2.0 2.0 2.0
    │       pressure    (time, station) float64 96B 3.0 3.0 3.0 3.0 ... 3.0 3.0 3.0 3.0
    └── Group: /weather/temperature
            Dimensions:          (time: 2, station: 6)
            Data variables:
                air_temperature  (time, station) float64 96B 4.0 4.0 4.0 4.0 ... 4.0 4.0 4.0
                dewpoint         (time, station) float64 96B 5.0 5.0 5.0 5.0 ... 5.0 5.0 5.0

Accessing any of the lower level trees through the `.dataset` property automatically includes coordinates from higher levels (e.g., `time` and `station`):

    In [106]: dt2["/weather/temperature"].dataset
    Out[106]:
    <xarray.DatasetView> Size: 272B
    Dimensions:          (time: 2, station: 6)
    Coordinates:
      * time             (time) <U7 56B '2022-01' '2023-01'
      * station          (station) <U1 24B 'a' 'b' 'c' 'd' 'e' 'f'
    Data variables:
        air_temperature  (time, station) float64 96B 4.0 4.0 4.0 4.0 ... 4.0 4.0 4.0
        dewpoint         (time, station) float64 96B 5.0 5.0 5.0 5.0 ... 5.0 5.0 5.0

Similarly, when you retrieve a Dataset through `to_dataset()` , the inherited coordinates are included by default unless you exclude them with the `inherit` flag:

    In [107]: dt2["/weather/temperature"].to_dataset()
    Out[107]:
    <xarray.Dataset> Size: 272B
    Dimensions:          (time: 2, station: 6)
    Coordinates:
      * time             (time) <U7 56B '2022-01' '2023-01'
      * station          (station) <U1 24B 'a' 'b' 'c' 'd' 'e' 'f'
    Data variables:
        air_temperature  (time, station) float64 96B 4.0 4.0 4.0 4.0 ... 4.0 4.0 4.0
        dewpoint         (time, station) float64 96B 5.0 5.0 5.0 5.0 ... 5.0 5.0 5.0

    In [108]: dt2["/weather/temperature"].to_dataset(inherit=False)
    Out[108]:
    <xarray.Dataset> Size: 192B
    Dimensions:          (time: 2, station: 6)
    Dimensions without coordinates: time, station
    Data variables:
        air_temperature  (time, station) float64 96B 4.0 4.0 4.0 4.0 ... 4.0 4.0 4.0
        dewpoint         (time, station) float64 96B 5.0 5.0 5.0 5.0 ... 5.0 5.0 5.0

For more examples and further discussion see alignment and coordinate inheritance.

## Coordinates

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

    In [109]: ds.coords
    Out[109]:
    Coordinates:
        lat             (loc) float64 16B 42.25 42.21
        lon             (loc) float64 16B -99.83 -99.32
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
        day             (time) int64 32B 6 7 8 9

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 [110]: ds.reset_coords()
    Out[110]:
    <xarray.Dataset> Size: 680B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature         (loc, instrument, time) float64 192B 29.11 ... 9.063
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13
        precipitation       (loc, instrument, time) float64 192B 4.562 ... 1.613
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
        reference_time      datetime64[ns] 8B 2014-09-05
        day                 (time) int64 32B 6 7 8 9

    In [111]: ds.set_coords(["temperature", "precipitation"])
    Out[111]:
    <xarray.Dataset> Size: 680B
    Dimensions:             (loc: 2, instrument: 3, time: 4)
    Coordinates:
        temperature         (loc, instrument, time) float64 192B 29.11 ... 9.063
        precipitation       (loc, instrument, time) float64 192B 4.562 ... 1.613
        lat                 (loc) float64 16B 42.25 42.21
        lon                 (loc) float64 16B -99.83 -99.32
      * time                (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time      datetime64[ns] 8B 2014-09-05
        day                 (time) int64 32B 6 7 8 9
    Dimensions without coordinates: loc, instrument
    Data variables:
        temperature_double  (loc, instrument, time) float64 192B 58.22 ... 18.13

    In [112]: ds["temperature"].reset_coords(drop=True)
    Out[112]:
    <xarray.DataArray 'temperature' (loc: 2, instrument: 3, time: 4)> Size: 192B
    array([[[29.112, 18.201, 22.83 , 32.927],
            [29.94 ,  7.182, 22.601, 13.789],
            [14.174, 18.285, 16.152, 26.634]],

           [[21.088, 15.973, 18.551, 17.669],
            [26.953, 13.359, 17.505,  8.167],
            [-5.424, 20.229, 21.915,  9.063]]], shape=(2, 3, 4))
    Coordinates:
      * time     (time) datetime64[ns] 32B 2014-09-06 2014-09-07 ... 2014-09-09
    Dimensions without coordinates: loc, instrument

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 [113]: ds.coords.to_dataset()
    Out[113]:
    <xarray.Dataset> Size: 104B
    Dimensions:         (loc: 2, time: 4)
    Coordinates:
        lat             (loc) float64 16B 42.25 42.21
        lon             (loc) float64 16B -99.83 -99.32
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
        day             (time) int64 32B 6 7 8 9
    Dimensions without coordinates: loc
    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 [114]: alt = xr.Dataset(coords={"z": [10], "lat": 0, "lon": 0})

    In [115]: ds.coords.merge(alt.coords)
    Out[115]:
    <xarray.Dataset> Size: 80B
    Dimensions:         (time: 4, z: 1)
    Coordinates:
      * time            (time) datetime64[ns] 32B 2014-09-06 ... 2014-09-09
        reference_time  datetime64[ns] 8B 2014-09-05
        day             (time) int64 32B 6 7 8 9
      * z               (z) int64 8B 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 [116]: ds["time"].to_index()
    Out[116]: DatetimeIndex(['2014-09-06', '2014-09-07', '2014-09-08', '2014-09-09'], 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 [117]: ds.indexes
    Out[117]:
    Indexes:
        time     DatetimeIndex(['2014-09-06', '2014-09-07', '2014-09-08', '2014-09-09'], dtype='datetime64[ns]', name='time', freq='D')

### MultiIndex coordinates

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

    In [118]: midx = pd.MultiIndex.from_arrays(
       .....:     [["R", "R", "V", "V"], [0.1, 0.2, 0.7, 0.9]], names=("band", "wn")
       .....: )
       .....:

    In [119]: mda = xr.DataArray(np.random.rand(4), coords={"spec": midx}, dims="spec")

    In [120]: mda
    Out[120]:
    <xarray.DataArray (spec: 4)> Size: 32B
    array([0.653, 0.253, 0.466, 0.244])
    Coordinates:
      * spec     (spec) object 32B MultiIndex
      * band     (spec) object 32B 'R' 'R' 'V' 'V'
      * wn       (spec) float64 32B 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 [121]: mda["band"]
    Out[121]:
    <xarray.DataArray 'band' (spec: 4)> Size: 32B
    array(['R', 'R', 'V', 'V'], dtype=object)
    Coordinates:
      * spec     (spec) object 32B MultiIndex
      * band     (spec) object 32B 'R' 'R' 'V' 'V'
      * wn       (spec) float64 32B 0.1 0.2 0.7 0.9

    In [122]: mda.wn
    Out[122]:
    <xarray.DataArray 'wn' (spec: 4)> Size: 32B
    array([0.1, 0.2, 0.7, 0.9])
    Coordinates:
      * spec     (spec) object 32B MultiIndex
      * band     (spec) object 32B 'R' 'R' 'V' 'V'
      * wn       (spec) float64 32B 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.