# Xarray in 45 minutes#

In this lesson, we cover the basics of Xarray data structures. By the end of the lesson, we will be able to:

• Understand the basic data structures in Xarray

• Inspect DataArray and Dataset objects.

• Read and write netCDF files using Xarray.

• Understand that there are many packages that build on top of xarray

We’ll start by reviewing the various components of the Xarray data model, represented here visually:

import matplotlib.pyplot as plt
import numpy as np
import xarray as xr

xr.set_options(keep_attrs=True, display_expand_data=False)
np.set_printoptions(threshold=10, edgeitems=2)

%xmode minimal
%matplotlib inline
%config InlineBackend.figure_format='retina'

Exception reporting mode: Minimal


Xarray has a few small real-world tutorial datasets hosted in the xarray-data GitHub repository.

Here we’ll use air temperature from the National Center for Environmental Prediction. Xarray objects have convenient HTML representations to give an overview of what we’re working with:

ds = xr.tutorial.load_dataset("air_temperature")
ds

<xarray.Dataset> Size: 31MB
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 31MB 241.2 242.5 243.5 ... 296.2 295.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

Note that behind the scenes the tutorial.open_dataset downloads a file. It then uses xarray.open_dataset function to open that file (which for this datasets is a netCDF file).

A few things are done automatically upon opening, but controlled by keyword arguments. For example, try passing the keyword argument mask_and_scale=False… what happens?

## What’s in a Dataset?#

Many DataArrays!

Datasets are dictionary-like containers of “DataArray”s. They are a mapping of variable name to DataArray:

# pull out "air" dataarray with dictionary syntax
ds["air"]

<xarray.DataArray 'air' (time: 2920, lat: 25, lon: 53)> Size: 31MB
241.2 242.5 243.5 244.0 244.1 243.9 ... 297.9 297.4 297.2 296.5 296.2 295.7
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:     4xDaily Air temperature at sigma level 995
units:         degK
precision:     2
GRIB_id:       11
GRIB_name:     TMP
var_desc:      Air temperature
dataset:       NMC Reanalysis
level_desc:    Surface
statistic:     Individual Obs
parent_stat:   Other
actual_range:  [185.16 322.1 ]

You can save some typing by using the “attribute” or “dot” notation. This won’t work for variable names that clash with a built-in method name (like mean for example).

# pull out dataarray using dot notation
ds.air

<xarray.DataArray 'air' (time: 2920, lat: 25, lon: 53)> Size: 31MB
241.2 242.5 243.5 244.0 244.1 243.9 ... 297.9 297.4 297.2 296.5 296.2 295.7
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:     4xDaily Air temperature at sigma level 995
units:         degK
precision:     2
GRIB_id:       11
GRIB_name:     TMP
var_desc:      Air temperature
dataset:       NMC Reanalysis
level_desc:    Surface
statistic:     Individual Obs
parent_stat:   Other
actual_range:  [185.16 322.1 ]

## What’s in a DataArray?#

data + (a lot of) metadata

### Name (optional)#

da = ds.air

da.name

'air'


### Named dimensions#

.dims correspond to the axes of your data.

In this case we have 2 spatial dimensions (latitude and longitude are store with shorthand names lat and lon) and one temporal dimension (time).

da.dims

('time', 'lat', 'lon')


### Coordinate variables#

.coords is a simple data container for coordinate variables.

Here we see the actual timestamps and spatial positions of our air temperature data:

da.coords

Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00


Coordinates objects support similar indexing notation

# extracting coordinate variables
da.lon

<xarray.DataArray 'lon' (lon: 53)> Size: 212B
200.0 202.5 205.0 207.5 210.0 212.5 ... 317.5 320.0 322.5 325.0 327.5 330.0
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
Attributes:
standard_name:  longitude
long_name:      Longitude
units:          degrees_east
axis:           X
# extracting coordinate variables from .coords
da.coords["lon"]

<xarray.DataArray 'lon' (lon: 53)> Size: 212B
200.0 202.5 205.0 207.5 210.0 212.5 ... 317.5 320.0 322.5 325.0 327.5 330.0
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
Attributes:
standard_name:  longitude
long_name:      Longitude
units:          degrees_east
axis:           X

It is useful to think of the values in these coordinate variables as axis “labels” such as “tick labels” in a figure. These are coordinate locations on a grid at which you have data.

### Arbitrary attributes#

.attrs is a dictionary that can contain arbitrary Python objects (strings, lists, integers, dictionaries, etc.) Your only limitation is that some attributes may not be writeable to certain file formats.

da.attrs

{'long_name': '4xDaily Air temperature at sigma level 995',
'units': 'degK',
'precision': 2,
'GRIB_id': 11,
'GRIB_name': 'TMP',
'var_desc': 'Air temperature',
'dataset': 'NMC Reanalysis',
'level_desc': 'Surface',
'statistic': 'Individual Obs',
'parent_stat': 'Other',
'actual_range': array([185.16, 322.1 ], dtype=float32)}

# assign your own attributes!
da.attrs["who_is_awesome"] = "xarray"
da.attrs

{'long_name': '4xDaily Air temperature at sigma level 995',
'units': 'degK',
'precision': 2,
'GRIB_id': 11,
'GRIB_name': 'TMP',
'var_desc': 'Air temperature',
'dataset': 'NMC Reanalysis',
'level_desc': 'Surface',
'statistic': 'Individual Obs',
'parent_stat': 'Other',
'actual_range': array([185.16, 322.1 ], dtype=float32),
'who_is_awesome': 'xarray'}

da

<xarray.DataArray 'air' (time: 2920, lat: 25, lon: 53)> Size: 31MB
241.2 242.5 243.5 244.0 244.1 243.9 ... 297.9 297.4 297.2 296.5 296.2 295.7
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray

### Underlying data#

.data contains the numpy array storing air temperature values.

Xarray structures wrap underlying simpler array-like data structures. This part of Xarray is quite extensible allowing for distributed array, GPU arrays, sparse arrays, arrays with units etc. We’ll briefly look at this later in this tutorial.

da.data

array([[[241.2 , 242.5 , ..., 235.5 , 238.6 ],
[243.8 , 244.5 , ..., 235.3 , 239.3 ],
...,
[295.9 , 296.2 , ..., 295.9 , 295.2 ],
[296.29, 296.79, ..., 296.79, 296.6 ]],

[[242.1 , 242.7 , ..., 233.6 , 235.8 ],
[243.6 , 244.1 , ..., 232.5 , 235.7 ],
...,
[296.2 , 296.7 , ..., 295.5 , 295.1 ],
[296.29, 297.2 , ..., 296.4 , 296.6 ]],

...,

[[245.79, 244.79, ..., 243.99, 244.79],
[249.89, 249.29, ..., 242.49, 244.29],
...,
[296.29, 297.19, ..., 295.09, 294.39],
[297.79, 298.39, ..., 295.49, 295.19]],

[[245.09, 244.29, ..., 241.49, 241.79],
[249.89, 249.29, ..., 240.29, 241.69],
...,
[296.09, 296.89, ..., 295.69, 295.19],
[297.69, 298.09, ..., 296.19, 295.69]]])

# what is the type of the underlying data
type(da.data)

numpy.ndarray


### Review#

Xarray provides two main data structures:

1. DataArrays that wrap underlying data containers (e.g. numpy arrays) and contain associated metadata

2. Datasets that are dictionary-like containers of DataArrays

DataArrays contain underlying arrays and associated metadata:

1. Name

2. Dimension names

3. Coordinate variables

4. and arbitrary attributes.

## Why Xarray?#

Metadata provides context and provides code that is more legible. This reduces the likelihood of errors from typos and makes analysis more intuitive and fun!

### Analysis without xarray: X(#

# plot the first timestep
lat = ds.air.lat.data  # numpy array
lon = ds.air.lon.data  # numpy array
temp = ds.air.data  # numpy array

plt.figure()
plt.pcolormesh(lon, lat, temp[0, :, :]);

temp.mean(axis=1)  ## what did I just do? I can't tell by looking at this line.

array([[279.398 , 279.6664, ..., 280.3152, 280.6624],
[279.0572, 279.538 , ..., 280.27  , 280.7976],
...,
[279.398 , 279.666 , ..., 280.342 , 280.834 ],
[279.27  , 279.354 , ..., 279.97  , 280.482 ]])


### Analysis with xarray =)#

ds.air.isel(time=0).plot(x="lon");


Use dimension names instead of axis numbers

ds.air.mean(dim="time").plot(x="lon")

<matplotlib.collections.QuadMesh at 0x7fc03087e9d0>


## Extracting data or “indexing”#

Xarray supports

• label-based indexing using .sel

• position-based indexing using .isel

See the user guide for more.

### Label-based indexing#

Xarray inherits its label-based indexing rules from pandas; this means great support for dates and times!

# here's what ds looks like
ds

<xarray.Dataset> Size: 31MB
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 31MB 241.2 242.5 243.5 ... 296.2 295.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# pull out data for all of 2013-May
ds.sel(time="2013-05")

<xarray.Dataset> Size: 1MB
Dimensions:  (lat: 25, time: 124, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 992B 2013-05-01 ... 2013-05-31T18:00:00
Data variables:
air      (time, lat, lon) float64 1MB 259.2 259.3 259.1 ... 297.6 297.5
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# demonstrate slicing
ds.sel(time=slice("2013-05", "2013-07"))

<xarray.Dataset> Size: 4MB
Dimensions:  (lat: 25, time: 368, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 3kB 2013-05-01 ... 2013-07-31T18:00:00
Data variables:
air      (time, lat, lon) float64 4MB 259.2 259.3 259.1 ... 299.5 299.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
ds.sel(time="2013")

<xarray.Dataset> Size: 15MB
Dimensions:  (lat: 25, time: 1460, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 12kB 2013-01-01 ... 2013-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 15MB 241.2 242.5 243.5 ... 295.1 294.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# demonstrate "nearest" indexing
ds.sel(lon=240.2, method="nearest")

<xarray.Dataset> Size: 607kB
Dimensions:  (lat: 25, time: 2920)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
lon      float32 4B 240.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat) float64 584kB 239.6 237.2 240.1 ... 294.8 296.9 298.4
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# "nearest indexing at multiple points"
ds.sel(lon=[240.125, 234], lat=[40.3, 50.3], method="nearest")

<xarray.Dataset> Size: 117kB
Dimensions:  (lat: 2, time: 2920, lon: 2)
Coordinates:
* lat      (lat) float32 8B 40.0 50.0
* lon      (lon) float32 8B 240.0 235.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 93kB 268.1 283.0 265.5 ... 256.8 268.6
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

### Position-based indexing#

This is similar to your usual numpy array[0, 2, 3] but with the power of named dimensions!

ds.air.data[0, 2, 3]

247.5

# pull out time index 0, lat index 2, and lon index 3
ds.air.isel(time=0, lat=2, lon=3)  #  much better than ds.air[0, 2, 3]

<xarray.DataArray 'air' ()> Size: 8B
247.5
Coordinates:
lat      float32 4B 70.0
lon      float32 4B 207.5
time     datetime64[ns] 8B 2013-01-01
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray
# demonstrate slicing
ds.air.isel(lat=slice(10))

<xarray.DataArray 'air' (time: 2920, lat: 10, lon: 53)> Size: 12MB
241.2 242.5 243.5 244.0 244.1 243.9 ... 273.4 273.8 273.5 273.8 275.0 276.2
Coordinates:
* lat      (lat) float32 40B 75.0 72.5 70.0 67.5 65.0 62.5 60.0 57.5 55.0 52.5
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray

## Concepts for computation#

Consider calculating the mean air temperature per unit surface area for this dataset. Because latitude and longitude correspond to spherical coordinates for Earth’s surface, each 2.5x2.5 degree grid cell actually has a different surface area as you move away from the equator! This is because latitudinal length is fixed ($$\delta Lat = R \delta \phi$$), but longitudinal length varies with latitude ($$\delta Lon = R \delta \lambda \cos(\phi)$$)

$\delta A = R^2 \delta\phi \, \delta\lambda \cos(\phi)$

where $$\phi$$ is latitude, $$\delta \phi$$ is the spacing of the points in latitude, $$\delta \lambda$$ is the spacing of the points in longitude, and $$R$$ is Earth’s radius. (In this formula, $$\phi$$ and $$\lambda$$ are measured in radians)

# Earth's average radius in meters
R = 6.371e6

# Coordinate spacing for this dataset is 2.5 x 2.5 degrees

dlat = R * dϕ * xr.ones_like(ds.air.lon)
dlon = R * dλ * np.cos(np.deg2rad(ds.air.lat))
dlon.name = "dlon"
dlat.name = "dlat"


There are two concepts here:

1. you can call functions like np.cos and np.deg2rad (“numpy ufuncs”) on Xarray objects and receive an Xarray object back.

2. We used ones_like to create a DataArray that looks like ds.air.lon in all respects, except that the data are all ones

# returns an xarray DataArray!

<xarray.DataArray 'lat' (lat: 25)> Size: 100B
0.2588 0.3007 0.342 0.3827 0.4226 0.4617 ... 0.9063 0.9239 0.9397 0.9537 0.9659
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
Attributes:
standard_name:  latitude
long_name:      Latitude
units:          degrees_north
axis:           Y
# cell latitude length is constant with longitude
dlat

<xarray.DataArray 'dlat' (lon: 53)> Size: 212B
2.78e+05 2.78e+05 2.78e+05 2.78e+05 ... 2.78e+05 2.78e+05 2.78e+05 2.78e+05
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
Attributes:
standard_name:  longitude
long_name:      Longitude
units:          degrees_east
axis:           X
# cell longitude length changes with latitude
dlon

<xarray.DataArray 'dlon' (lat: 25)> Size: 100B
7.195e+04 8.359e+04 9.508e+04 1.064e+05 ... 2.612e+05 2.651e+05 2.685e+05
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
Attributes:
standard_name:  latitude
long_name:      Latitude
units:          degrees_north
axis:           Y

Our longitude and latitude length DataArrays are both 1D with different dimension names. If we multiple these DataArrays together the dimensionality is expanded to 2D by broadcasting:

cell_area = dlon * dlat
cell_area

<xarray.DataArray (lat: 25, lon: 53)> Size: 5kB
2e+10 2e+10 2e+10 2e+10 2e+10 ... 7.464e+10 7.464e+10 7.464e+10 7.464e+10
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
Attributes:
standard_name:  latitude
long_name:      Latitude
units:          degrees_north
axis:           Y

The result has two dimensions because xarray realizes that dimensions lon and lat are different so it automatically “broadcasts” to get a 2D result. See the last row in this image from Jake VanderPlas Python Data Science Handbook

Because xarray knows about dimension names we avoid having to create unnecessary size-1 dimensions using np.newaxis or .reshape. For more, see the user guide

### Alignment: putting data on the same grid#

When doing arithmetic operations xarray automatically “aligns” i.e. puts the data on the same grid. In this case cell_area and ds.air are at the same lat, lon points we end up with a result with the same shape (25x53):

ds.air.isel(time=1) / cell_area

<xarray.DataArray (lat: 25, lon: 53)> Size: 11kB
1.21e-08 1.213e-08 1.215e-08 1.217e-08 ... 3.971e-09 3.971e-09 3.974e-09
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
time     datetime64[ns] 8B 2013-01-01T06:00:00
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray

Now lets make cell_area unaligned i.e. change the coordinate labels

# make a copy of cell_area
# then add 1e-5 degrees to latitude
cell_area_bad["lat"] = cell_area.lat + 1e-5  # latitudes are off by 1e-5 degrees!

<xarray.DataArray (lat: 25, lon: 53)> Size: 5kB
2e+10 2e+10 2e+10 2e+10 2e+10 ... 7.464e+10 7.464e+10 7.464e+10 7.464e+10
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
Attributes:
standard_name:  latitude
long_name:      Latitude
units:          degrees_north
axis:           Y
cell_area_bad * ds.air.isel(time=1)

<xarray.DataArray (lat: 0, lon: 53)> Size: 0B

Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* lat      (lat) float32 0B
time     datetime64[ns] 8B 2013-01-01T06:00:00
Attributes:
standard_name:  latitude
long_name:      Latitude
units:          degrees_north
axis:           Y

The result is an empty array with no latitude coordinates because none of them were aligned!

Tip

If you notice extra NaNs or missing points after xarray computation, it means that your xarray coordinates were not aligned exactly.

To make sure variables are aligned as you think they are, do the following:

xr.align(cell_area_bad, ds.air, join="exact")

ValueError: cannot align objects with join='exact' where index/labels/sizes are not equal along these coordinates (dimensions): 'lat' ('lat',)


The above statement raises an error since the two are not aligned.

For more, see the Xarray documentation. This tutorial notebook also covers alignment and broadcasting (highly recommended)

## High level computation#

(groupby, resample, rolling, coarsen, weighted)

Xarray has some very useful high level objects that let you do common computations:

1. groupby : Bin data in to groups and reduce

2. resample : Groupby specialized for time axes. Either downsample or upsample your data.

3. rolling : Operate on rolling windows of your data e.g. running mean

4. coarsen : Downsample your data

5. weighted : Weight your data before reducing

Below we quickly demonstrate these patterns. See the user guide links above and the tutorial for more.

### groupby#

# here's ds
ds

<xarray.Dataset> Size: 31MB
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 31MB 241.2 242.5 243.5 ... 296.2 295.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# seasonal groups
ds.groupby("time.season")

DatasetGroupBy, grouped over 'season'
4 groups with labels 'DJF', 'JJA', 'MAM', 'SON'.

# make a seasonal mean
seasonal_mean = ds.groupby("time.season").mean()
seasonal_mean

<xarray.Dataset> Size: 43kB
Dimensions:  (season: 4, lat: 25, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* season   (season) object 32B 'DJF' 'JJA' 'MAM' 'SON'
Data variables:
air      (season, lat, lon) float64 42kB 247.0 247.0 246.7 ... 299.4 299.5
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

The seasons are out of order (they are alphabetically sorted). This is a common annoyance. The solution is to use .sel to change the order of labels

seasonal_mean = seasonal_mean.sel(season=["DJF", "MAM", "JJA", "SON"])
seasonal_mean

<xarray.Dataset> Size: 43kB
Dimensions:  (season: 4, lat: 25, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* season   (season) object 32B 'DJF' 'MAM' 'JJA' 'SON'
Data variables:
air      (season, lat, lon) float64 42kB 247.0 247.0 246.7 ... 299.4 299.5
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
seasonal_mean.air.plot(col="season")

<xarray.plot.facetgrid.FacetGrid at 0x7fbfdbbf6f10>


### resample#

# resample to monthly frequency
ds.resample(time="M").mean()

/home/runner/micromamba/envs/xarray-tutorial/lib/python3.11/site-packages/xarray/core/groupby.py:668: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
index_grouper = pd.Grouper(

<xarray.Dataset> Size: 255kB
Dimensions:  (time: 24, lat: 25, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 192B 2013-01-31 2013-02-28 ... 2014-12-31
Data variables:
air      (time, lat, lon) float64 254kB 244.5 244.7 244.7 ... 297.7 297.7
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...

### weighted#

# weight by cell_area and take mean over (time, lon)
ds.weighted(cell_area).mean(["lon", "time"]).air.plot(y="lat");


## Visualization#

(.plot)

We have seen very simple plots earlier. Xarray also lets you easily visualize 3D and 4D datasets by presenting multiple facets (or panels or subplots) showing variations across rows and/or columns.

# facet the seasonal_mean
seasonal_mean.air.plot(col="season", col_wrap=2);

# contours

# line plots too? wut
seasonal_mean.air.mean("lon").plot.line(hue="season", y="lat");


For more see the user guide, the gallery, and the tutorial material.

Xarray supports many disk formats. Below is a small example using netCDF. For more see the documentation

# write to netCDF
ds.to_netcdf("my-example-dataset.nc")

/tmp/ipykernel_2985/1659397704.py:2: SerializationWarning: saving variable air with floating point data as an integer dtype without any _FillValue to use for NaNs
ds.to_netcdf("my-example-dataset.nc")


Note

To avoid the SerializationWarning you can assign a _FillValue for any NaNs in ‘air’ array by adding the keyword argument encoding=dict(air={_FillValue=-9999})

# read from disk
fromdisk = xr.open_dataset("my-example-dataset.nc")
fromdisk

<xarray.Dataset> Size: 31MB
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Data variables:
air      (time, lat, lon) float64 31MB ...
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis\n(4x/day).  These a...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanaly...
# check that the two are identical
ds.identical(fromdisk)

True


Tip

A common use case to read datasets that are a collection of many netCDF files. See the documentation for how to handle that.

Finally to read other file formats, you might find yourself reading in the data using a different library and then creating a DataArray(docs, tutorial) from scratch. For example, you might use h5py to open an HDF5 file and then create a Dataset from that. For MATLAB files you might use scipy.io.loadmat or h5py depending on the version of MATLAB file you’re opening and then construct a Dataset.

## The scientific python ecosystem#

Xarray ties in to the larger scientific python ecosystem and in turn many packages build on top of xarray. A long list of such packages is here: https://docs.xarray.dev/en/stable/related-projects.html.

Now we will demonstrate some cool features.

### Pandas: tabular data structures#

You can easily convert between xarray and pandas structures. This allows you to conveniently use the extensive pandas ecosystem of packages (like seaborn) for your work.

# convert to pandas dataframe
df = ds.isel(time=slice(10)).to_dataframe()
df

air
lat time lon
75.0 2013-01-01 00:00:00 200.0 241.20
202.5 242.50
205.0 243.50
207.5 244.00
210.0 244.10
... ... ... ...
15.0 2013-01-03 06:00:00 320.0 297.00
322.5 297.29
325.0 296.90
327.5 296.79
330.0 297.10

13250 rows × 1 columns

# convert dataframe to xarray
df.to_xarray()

<xarray.Dataset> Size: 106kB
Dimensions:  (lat: 25, time: 10, lon: 53)
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* time     (time) datetime64[ns] 80B 2013-01-01 ... 2013-01-03T06:00:00
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
Data variables:
air      (lat, time, lon) float64 106kB 241.2 242.5 243.5 ... 296.8 297.1

### Alternative array types#

This notebook has focused on Numpy arrays. Xarray can wrap other array types! For example:

pydata/sparse : sparse arrays

Dask cuts up NumPy arrays into blocks and parallelizes your analysis code across these blocks

# demonstrate dask dataset
"air_temperature",
chunks={"time": 10},  # 10 time steps in each block
)


<xarray.DataArray 'air' (time: 2920, lat: 25, lon: 53)> Size: 31MB
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:     4xDaily Air temperature at sigma level 995
units:         degK
precision:     2
GRIB_id:       11
GRIB_name:     TMP
var_desc:      Air temperature
dataset:       NMC Reanalysis
level_desc:    Surface
statistic:     Individual Obs
parent_stat:   Other
actual_range:  [185.16 322.1 ]

All computations with dask-backed xarray objects are lazy, allowing you to build up a complicated chain of analysis steps quickly

# demonstrate lazy mean

<xarray.DataArray 'air' (time: 2920, lon: 53)> Size: 1MB
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:     4xDaily Air temperature at sigma level 995
units:         degK
precision:     2
GRIB_id:       11
GRIB_name:     TMP
var_desc:      Air temperature
dataset:       NMC Reanalysis
level_desc:    Surface
statistic:     Individual Obs
parent_stat:   Other
actual_range:  [185.16 322.1 ]

To get concrete values, call .compute or .load

# "compute" the mean

<xarray.DataArray 'air' (time: 2920, lon: 53)> Size: 1MB
279.4 279.7 279.7 279.7 280.0 279.9 ... 277.4 278.3 278.9 279.4 280.0 280.5
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:     4xDaily Air temperature at sigma level 995
units:         degK
precision:     2
GRIB_id:       11
GRIB_name:     TMP
var_desc:      Air temperature
dataset:       NMC Reanalysis
level_desc:    Surface
statistic:     Individual Obs
parent_stat:   Other
actual_range:  [185.16 322.1 ]

### HoloViz#

Quickly generate interactive plots from your data!

The hvplot package attaches itself to all xarray objects under the .hvplot namespace. So instead of using .plot use .hvplot

import hvplot.xarray

ds.air.hvplot(groupby="time", clim=(270, 300), widget_location='bottom')


Note

The time slider will only work if you’re executing the notebook, rather than viewing the website

### cf_xarray#

cf_xarray is a project that tries to let you make use of other CF attributes that xarray ignores. It attaches itself to all xarray objects under the .cf namespace.

Where xarray allows you to specify dimension names for analysis, cf_xarray lets you specify logical names like "latitude" or "longitude" instead as long as the appropriate CF attributes are set.

For example, the "longitude" dimension in different files might be labelled as: (lon, LON, long, x…), but cf_xarray let’s you always refer to the logical name "longitude" in your code:

import cf_xarray

# describe cf attributes in dataset
ds.air.cf

Coordinates:
CF Axes: * X: ['lon']
* Y: ['lat']
* T: ['time']
Z: n/a

CF Coordinates: * longitude: ['lon']
* latitude: ['lat']
* time: ['time']
vertical: n/a

Cell Measures:   area, volume: n/a

Standard Names: * latitude: ['lat']
* longitude: ['lon']
* time: ['time']

Bounds:   n/a

Grid Mappings:   n/a


The following mean operation will work with any dataset that has appropriate attributes set that allow detection of the “latitude” variable (e.g. units: "degress_north" or standard_name: "latitude")

# demonstrate equivalent of .mean("lat")
ds.air.cf.mean("latitude")

<xarray.DataArray 'air' (time: 2920, lon: 53)> Size: 1MB
279.4 279.7 279.7 279.7 280.0 279.9 ... 277.4 278.3 278.9 279.4 280.0 280.5
Coordinates:
* lon      (lon) float32 212B 200.0 202.5 205.0 207.5 ... 325.0 327.5 330.0
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray
# demonstrate indexing
ds.air.cf.sel(longitude=242.5, method="nearest")

<xarray.DataArray 'air' (time: 2920, lat: 25)> Size: 584kB
241.0 238.0 239.7 246.3 253.7 265.3 ... 289.5 291.4 293.6 295.2 296.8 298.9
Coordinates:
* lat      (lat) float32 100B 75.0 72.5 70.0 67.5 65.0 ... 22.5 20.0 17.5 15.0
lon      float32 4B 242.5
* time     (time) datetime64[ns] 23kB 2013-01-01 ... 2014-12-31T18:00:00
Attributes:
long_name:       4xDaily Air temperature at sigma level 995
units:           degK
precision:       2
GRIB_id:         11
GRIB_name:       TMP
var_desc:        Air temperature
dataset:         NMC Reanalysis
level_desc:      Surface
statistic:       Individual Obs
parent_stat:     Other
actual_range:    [185.16 322.1 ]
who_is_awesome:  xarray

### Other cool packages#

• xgcm : grid-aware operations with xarray objects

• xrft : fourier transforms with xarray

• xclim : calculating climate indices with xarray objects

• intake-xarray : forget about file paths

• rioxarray : raster files and xarray

• xesmf : regrid using ESMF

• MetPy : tools for working with weather data

Check the Xarray Ecosystem page and this tutorial for even more packages and demonstrations.

## Next#

1. Read the tutorial material and user guide

2. See the description of common terms used in the xarray documentation:

3. Answers to common questions on “how to do X” with Xarray are here

4. Ryan Abernathey has a book on data analysis with a chapter on Xarray

5. Project Pythia has foundational and more advanced material on Xarray. Pythia also aggregates other Python learning resources.

6. The Xarray Github Discussions and Pangeo Discourse are good places to ask questions.