# Terminology#

*Xarray terminology differs slightly from CF, mathematical conventions, and
pandas; so we’ve put together a glossary of its terms. Here,* `arr`

*refers to an xarray* `DataArray`

*in the examples. For more
complete examples, please consult the relevant documentation.*

- DataArray#
A multi-dimensional array with labeled or named dimensions.

`DataArray`

objects add metadata such as dimension names, coordinates, and attributes (defined below) to underlying “unlabeled” data structures such as numpy and Dask arrays. If its optional`name`

property is set, it is a*named DataArray*.- Dataset#
A dict-like collection of

`DataArray`

objects with aligned dimensions. Thus, most operations that can be performed on the dimensions of a single`DataArray`

can be performed on a dataset. Datasets have data variables (see**Variable**below), dimensions, coordinates, and attributes.- Variable#
A NetCDF-like variable consisting of dimensions, data, and attributes which describe a single array. The main functional difference between variables and numpy arrays is that numerical operations on variables implement array broadcasting by dimension name. Each

`DataArray`

has an underlying variable that can be accessed via`arr.variable`

. However, a variable is not fully described outside of either a`Dataset`

or a`DataArray`

.Note

The

`Variable`

class is low-level interface and can typically be ignored. However, the word “variable” appears often enough in the code and documentation that is useful to understand.- Dimension#
In mathematics, the

*dimension*of data is loosely the number of degrees of freedom for it. A*dimension axis*is a set of all points in which all but one of these degrees of freedom is fixed. We can think of each dimension axis as having a name, for example the “x dimension”. In xarray, a`DataArray`

object’s*dimensions*are its named dimension axes`da.dims`

, and the name of the`i`

-th dimension is`da.dims[i]`

. If an array is created without specifying dimension names, the default dimension names will be`dim_0`

,`dim_1`

, and so forth.- Coordinate#
An array that labels a dimension or set of dimensions of another

`DataArray`

. In the usual one-dimensional case, the coordinate array’s values can loosely be thought of as tick labels along a dimension. We distinguish Dimension coordinate vs. Non-dimension coordinate and Indexed coordinate vs. Non-indexed coordinate. A coordinate named`x`

can be retrieved from`arr.coords[x]`

. A`DataArray`

can have more coordinates than dimensions because a single dimension can be labeled by multiple coordinate arrays. However, only one coordinate array can be a assigned as a particular dimension’s dimension coordinate array.- Dimension coordinate#
A one-dimensional coordinate array assigned to

`arr`

with both a name and dimension name in`arr.dims`

. Usually (but not always), a dimension coordinate is also an Indexed coordinate so that it can be used for label-based indexing and alignment, like the index found on a`pandas.DataFrame`

or`pandas.Series`

.- Non-dimension coordinate#
A coordinate array assigned to

`arr`

with a name in`arr.coords`

but*not*in`arr.dims`

. These coordinates arrays can be one-dimensional or multidimensional, and they are useful for auxiliary labeling. As an example, multidimensional coordinates are often used in geoscience datasets when the data’s physical coordinates (such as latitude and longitude) differ from their logical coordinates. Printing`arr.coords`

will print all of`arr`

’s coordinate names, with the corresponding dimension(s) in parentheses. For example,`coord_name (dim_name) 1 2 3 ...`

.- Indexed coordinate#
A coordinate which has an associated Index. Generally this means that the coordinate labels can be used for indexing (selection) and/or alignment. An indexed coordinate may have one or more arbitrary dimensions although in most cases it is also a Dimension coordinate. It may or may not be grouped with other indexed coordinates depending on whether they share the same index. Indexed coordinates are marked by an asterisk

`*`

when printing a`DataArray`

or`Dataset`

.- Non-indexed coordinate#
A coordinate which has no associated Index. It may still represent fixed labels along one or more dimensions but it cannot be used for label-based indexing and alignment.

- Index#
An

*index*is a data structure optimized for efficient data selection and alignment within a discrete or continuous space that is defined by coordinate labels (unless it is a functional index). By default, Xarray creates a`PandasIndex`

object (i.e., a`pandas.Index`

wrapper) for each Dimension coordinate. For more advanced use cases (e.g., staggered or irregular grids, geospatial indexes), Xarray also accepts any instance of a specialized`Index`

subclass that is associated to one or more arbitrary coordinates. The index associated with the coordinate`x`

can be retrieved by`arr.xindexes[x]`

(or`arr.indexes["x"]`

if the index is convertible to a`pandas.Index`

object). If two coordinates`x`

and`y`

share the same index,`arr.xindexes[x]`

and`arr.xindexes[y]`

both return the same`Index`

object.- name#
The names of dimensions, coordinates, DataArray objects and data variables can be anything as long as they are hashable. However, it is preferred to use

`str`

typed names.- scalar#
By definition, a scalar is not an array and when converted to one, it has 0 dimensions. That means that, e.g.,

`int`

,`float`

, and`str`

objects are “scalar” while`list`

or`tuple`

are not.- duck array#
Duck arrays are array implementations that behave like numpy arrays. They have to define the

`shape`

,`dtype`

and`ndim`

properties. For integration with`xarray`

, the`__array__`

,`__array_ufunc__`

and`__array_function__`

protocols are also required.- Aligning#
Aligning refers to the process of ensuring that two or more DataArrays or Datasets have the same dimensions and coordinates, so that they can be combined or compared properly.

In [1]: x = xr.DataArray( ...: [[25, 35], [10, 24]], ...: dims=("lat", "lon"), ...: coords={"lat": [35.0, 40.0], "lon": [100.0, 120.0]}, ...: ) ...: In [2]: y = xr.DataArray( ...: [[20, 5], [7, 13]], ...: dims=("lat", "lon"), ...: coords={"lat": [35.0, 42.0], "lon": [100.0, 120.0]}, ...: ) ...: In [3]: x Out[3]: <xarray.DataArray (lat: 2, lon: 2)> Size: 32B array([[25, 35], [10, 24]]) Coordinates: * lat (lat) float64 16B 35.0 40.0 * lon (lon) float64 16B 100.0 120.0 In [4]: y Out[4]: <xarray.DataArray (lat: 2, lon: 2)> Size: 32B array([[20, 5], [ 7, 13]]) Coordinates: * lat (lat) float64 16B 35.0 42.0 * lon (lon) float64 16B 100.0 120.0

- Broadcasting#
A technique that allows operations to be performed on arrays with different shapes and dimensions. When performing operations on arrays with different shapes and dimensions, xarray will automatically attempt to broadcast the arrays to a common shape before the operation is applied.

# 'a' has shape (3,) and 'b' has shape (4,) In [5]: a = xr.DataArray(np.array([1, 2, 3]), dims=["x"]) In [6]: b = xr.DataArray(np.array([4, 5, 6, 7]), dims=["y"]) # 2D array with shape (3, 4) In [7]: a + b Out[7]: <xarray.DataArray (x: 3, y: 4)> Size: 96B array([[ 5, 6, 7, 8], [ 6, 7, 8, 9], [ 7, 8, 9, 10]]) Dimensions without coordinates: x, y

- Merging#
Merging is used to combine two or more Datasets or DataArrays that have different variables or coordinates along the same dimensions. When merging, xarray aligns the variables and coordinates of the different datasets along the specified dimensions and creates a new

`Dataset`

containing all the variables and coordinates.# create two 1D arrays with names In [8]: arr1 = xr.DataArray( ...: [1, 2, 3], dims=["x"], coords={"x": [10, 20, 30]}, name="arr1" ...: ) ...: In [9]: arr2 = xr.DataArray( ...: [4, 5, 6], dims=["x"], coords={"x": [20, 30, 40]}, name="arr2" ...: ) ...: # merge the two arrays into a new dataset In [10]: merged_ds = xr.Dataset({"arr1": arr1, "arr2": arr2}) In [11]: merged_ds Out[11]: <xarray.Dataset> Size: 96B Dimensions: (x: 4) Coordinates: * x (x) int64 32B 10 20 30 40 Data variables: arr1 (x) float64 32B 1.0 2.0 3.0 nan arr2 (x) float64 32B nan 4.0 5.0 6.0

- Concatenating#
Concatenating is used to combine two or more Datasets or DataArrays along a dimension. When concatenating, xarray arranges the datasets or dataarrays along a new dimension, and the resulting

`Dataset`

or`Dataarray`

will have the same variables and coordinates along the other dimensions.In [12]: a = xr.DataArray([[1, 2], [3, 4]], dims=("x", "y")) In [13]: b = xr.DataArray([[5, 6], [7, 8]], dims=("x", "y")) In [14]: c = xr.concat([a, b], dim="c") In [15]: c Out[15]: <xarray.DataArray (c: 2, x: 2, y: 2)> Size: 64B array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) Dimensions without coordinates: c, x, y

- Combining#
Combining is the process of arranging two or more DataArrays or Datasets into a single

`DataArray`

or`Dataset`

using some combination of merging and concatenation operations.In [16]: ds1 = xr.Dataset( ....: {"data": xr.DataArray([[1, 2], [3, 4]], dims=("x", "y"))}, ....: coords={"x": [1, 2], "y": [3, 4]}, ....: ) ....: In [17]: ds2 = xr.Dataset( ....: {"data": xr.DataArray([[5, 6], [7, 8]], dims=("x", "y"))}, ....: coords={"x": [2, 3], "y": [4, 5]}, ....: ) ....: # combine the datasets In [18]: combined_ds = xr.combine_by_coords([ds1, ds2]) In [19]: combined_ds Out[19]: <xarray.Dataset> Size: 152B Dimensions: (x: 3, y: 4) Coordinates: * x (x) int64 24B 1 2 3 * y (y) int64 32B 3 4 4 5 Data variables: data (x, y) float64 96B 1.0 2.0 nan nan 3.0 4.0 5.0 6.0 nan nan 7.0 8.0

- lazy#
Lazily-evaluated operations do not load data into memory until necessary. Instead of doing calculations right away, xarray lets you plan what calculations you want to do, like finding the average temperature in a dataset. This planning is called “lazy evaluation.” Later, when you’re ready to see the final result, you tell xarray, “Okay, go ahead and do those calculations now!” That’s when xarray starts working through the steps you planned and gives you the answer you wanted. This lazy approach helps save time and memory because xarray only does the work when you actually need the results.

- labeled#
Labeled data has metadata describing the context of the data, not just the raw data values. This contextual information can be labels for array axes (i.e. dimension names) tick labels along axes (stored as Coordinate variables) or unique names for each array. These labels provide context and meaning to the data, making it easier to understand and work with. If you have temperature data for different cities over time. Using xarray, you can label the dimensions: one for cities and another for time.

- serialization#
Serialization is the process of converting your data into a format that makes it easy to save and share. When you serialize data in xarray, you’re taking all those temperature measurements, along with their labels and other information, and turning them into a format that can be stored in a file or sent over the internet. xarray objects can be serialized into formats which store the labels alongside the data. Some supported serialization formats are files that can then be stored or transferred (e.g. netCDF), whilst others are protocols that allow for data access over a network (e.g. Zarr).

- indexing#
Indexing and selecting data is how you select subsets of your data which you are interested in.

Label-based Indexing: Selecting data by passing a specific label and comparing it to the labels stored in the associated coordinates. You can use labels to specify what you want like “Give me the temperature for New York on July 15th.”

Positional Indexing: You can use numbers to refer to positions in the data like “Give me the third temperature value” This is useful when you know the order of your data but don’t need to remember the exact labels.

Slicing: You can take a “slice” of your data, like you might want all temperatures from July 1st to July 10th. xarray supports slicing for both positional and label-based indexing.