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Indexing and Selecting Data

Indexing and Selecting Data#

Learning Objectives#

  • Select data by position using .isel with values or slices

  • Select data by label using .sel with values or slices

  • Select timeseries data by date/time with values or slices

  • Use nearest-neighbor lookups with .sel

Why do we need label-based indexing?#

Scientific data is inherently labeled. For example, time series data includes timestamps that label individual periods or points in time, spatial data has coordinates (e.g. longitude, latitude, elevation), and model or laboratory experiments are often identified by unique identifiers.

import xarray as xr

%config InlineBackend.figure_format='retina'

ds = xr.open_dataset("../../data/sst.mnmean.nc")
ds

<xarray.Dataset> Size: 8MB
Dimensions:  (lat: 89, lon: 180, time: 128)
Coordinates:
  * lat      (lat) float32 356B 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0
  * lon      (lon) float32 720B 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Data variables:
    sst      (time, lat, lon) float32 8MB ...
Attributes: (12/37)
    climatology:               Climatology is based on 1971-2000 SST, Xue, Y....
    description:               In situ data: ICOADS2.5 before 2007 and NCEP i...
    keywords_vocabulary:       NASA Global Change Master Directory (GCMD) Sci...
    keywords:                  Earth Science > Oceans > Ocean Temperature > S...
    instrument:                Conventional thermometers
    source_comment:            SSTs were observed by conventional thermometer...
    ...                        ...
    creator_url_original:      https://www.ncei.noaa.gov
    license:                   No constraints on data access or use
    comment:                   SSTs were observed by conventional thermometer...
    summary:                   ERSST.v5 is developed based on v4 after revisi...
    dataset_title:             NOAA Extended Reconstructed SST V5
    data_modified:             2020-09-07

NumPy Positional Indexing#

When working with numpy, indexing is done by position (slices/ranges/scalars).

t = ds["sst"].data  # numpy array
t
Hide code cell output 
array([[[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],

       [[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],

       [[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],

       ...,

       [[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],

       [[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],

       [[-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        [-1.8, -1.8, -1.8, ..., -1.8, -1.8, -1.8],
        ...,
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan],
        [ nan,  nan,  nan, ...,  nan,  nan,  nan]]], dtype=float32)

t.shape

(128, 89, 180)

# extract a time-series for one spatial location
t[:, 20, 40]
Hide code cell output 
array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan],
      dtype=float32)
but wait, what labels go with 20 and 40? Was that lat/lon or lon/lat? Where are the timestamps that go along with this time-series?

Indexing with xarray#

xarray offers extremely flexible indexing routines that combine the best features of NumPy and pandas for data selection.

da = ds["sst"]  # Extract data array
da
Hide code cell output 
<xarray.DataArray 'sst' (time: 128, lat: 89, lon: 180)> Size: 8MB
array([[[-1.8, -1.8, ..., -1.8, -1.8],
        [-1.8, -1.8, ..., -1.8, -1.8],
        ...,
        [ nan,  nan, ...,  nan,  nan],
        [ nan,  nan, ...,  nan,  nan]],

       [[-1.8, -1.8, ..., -1.8, -1.8],
        [-1.8, -1.8, ..., -1.8, -1.8],
        ...,
        [ nan,  nan, ...,  nan,  nan],
        [ nan,  nan, ...,  nan,  nan]],

       ...,

       [[-1.8, -1.8, ..., -1.8, -1.8],
        [-1.8, -1.8, ..., -1.8, -1.8],
        ...,
        [ nan,  nan, ...,  nan,  nan],
        [ nan,  nan, ...,  nan,  nan]],

       [[-1.8, -1.8, ..., -1.8, -1.8],
        [-1.8, -1.8, ..., -1.8, -1.8],
        ...,
        [ nan,  nan, ...,  nan,  nan],
        [ nan,  nan, ...,  nan,  nan]]], dtype=float32)
Coordinates:
  * lat      (lat) float32 356B 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0
  * lon      (lon) float32 720B 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Attributes:
    long_name:     Monthly Means of Sea Surface Temperature
    units:         degC
    var_desc:      Sea Surface Temperature
    level_desc:    Surface
    statistic:     Mean
    dataset:       NOAA Extended Reconstructed SST V5
    parent_stat:   Individual Values
    actual_range:  [-1.8     42.32636]
    valid_range:   [-1.8 45. ]

  • NumPy style indexing still works (but preserves the labels/metadata)

da[:, 20, 40]
Hide code cell output 
<xarray.DataArray 'sst' (time: 128)> Size: 512B
array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan], dtype=float32)
Coordinates:
    lat      float32 4B 48.0
    lon      float32 4B 80.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Attributes:
    long_name:     Monthly Means of Sea Surface Temperature
    units:         degC
    var_desc:      Sea Surface Temperature
    level_desc:    Surface
    statistic:     Mean
    dataset:       NOAA Extended Reconstructed SST V5
    parent_stat:   Individual Values
    actual_range:  [-1.8     42.32636]
    valid_range:   [-1.8 45. ]

  • Positional indexing using dimension names

da.isel(lat=60, lon=40).plot();
../../_images/31d9dc46a85fca7b791537dfba4c821c62a2505ceba0059fea5f8e1df1bedc1b.png

  • Label-based indexing

da.sel(lat=-32, lon=80).plot();
../../_images/31d9dc46a85fca7b791537dfba4c821c62a2505ceba0059fea5f8e1df1bedc1b.png 
da.sel(lat=50.0, lon=200.0, time="2020")

<xarray.DataArray 'sst' (time: 8)> Size: 32B
array([ 5.501727,  5.015851,  4.808821,  5.837058,  7.285223,  8.64473 ,
       11.524967, 12.405846], dtype=float32)
Coordinates:
    lat      float32 4B 50.0
    lon      float32 4B 200.0
  * time     (time) datetime64[ns] 64B 2020-01-01 2020-02-01 ... 2020-08-01
Attributes:
    long_name:     Monthly Means of Sea Surface Temperature
    units:         degC
    var_desc:      Sea Surface Temperature
    level_desc:    Surface
    statistic:     Mean
    dataset:       NOAA Extended Reconstructed SST V5
    parent_stat:   Individual Values
    actual_range:  [-1.8     42.32636]
    valid_range:   [-1.8 45. ]
# demonstrate slicing
ds.sel(time=slice("2019-05", "2020-07"))

<xarray.Dataset> Size: 962kB
Dimensions:  (lat: 89, lon: 180, time: 15)
Coordinates:
  * lat      (lat) float32 356B 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0
  * lon      (lon) float32 720B 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0
  * time     (time) datetime64[ns] 120B 2019-05-01 2019-06-01 ... 2020-07-01
Data variables:
    sst      (time, lat, lon) float32 961kB -1.8 -1.8 -1.8 -1.8 ... nan nan nan
Attributes: (12/37)
    climatology:               Climatology is based on 1971-2000 SST, Xue, Y....
    description:               In situ data: ICOADS2.5 before 2007 and NCEP i...
    keywords_vocabulary:       NASA Global Change Master Directory (GCMD) Sci...
    keywords:                  Earth Science > Oceans > Ocean Temperature > S...
    instrument:                Conventional thermometers
    source_comment:            SSTs were observed by conventional thermometer...
    ...                        ...
    creator_url_original:      https://www.ncei.noaa.gov
    license:                   No constraints on data access or use
    comment:                   SSTs were observed by conventional thermometer...
    summary:                   ERSST.v5 is developed based on v4 after revisi...
    dataset_title:             NOAA Extended Reconstructed SST V5
    data_modified:             2020-09-07

  • Nearest Neighbor Lookups

da.sel(lat=52.25, lon=251.8998, method="nearest")
Hide code cell output 
<xarray.DataArray 'sst' (time: 128)> Size: 512B
array([nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
       nan, nan], dtype=float32)
Coordinates:
    lat      float32 4B 52.0
    lon      float32 4B 252.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Attributes:
    long_name:     Monthly Means of Sea Surface Temperature
    units:         degC
    var_desc:      Sea Surface Temperature
    level_desc:    Surface
    statistic:     Mean
    dataset:       NOAA Extended Reconstructed SST V5
    parent_stat:   Individual Values
    actual_range:  [-1.8     42.32636]
    valid_range:   [-1.8 45. ]

  • All of these indexing methods work on the dataset too:

ds.sel(lat=52.25, lon=251.8998, method="nearest")

<xarray.Dataset> Size: 2kB
Dimensions:  (time: 128)
Coordinates:
    lat      float32 4B 52.0
    lon      float32 4B 252.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Data variables:
    sst      (time) float32 512B nan nan nan nan nan nan ... nan nan nan nan nan
Attributes: (12/37)
    climatology:               Climatology is based on 1971-2000 SST, Xue, Y....
    description:               In situ data: ICOADS2.5 before 2007 and NCEP i...
    keywords_vocabulary:       NASA Global Change Master Directory (GCMD) Sci...
    keywords:                  Earth Science > Oceans > Ocean Temperature > S...
    instrument:                Conventional thermometers
    source_comment:            SSTs were observed by conventional thermometer...
    ...                        ...
    creator_url_original:      https://www.ncei.noaa.gov
    license:                   No constraints on data access or use
    comment:                   SSTs were observed by conventional thermometer...
    summary:                   ERSST.v5 is developed based on v4 after revisi...
    dataset_title:             NOAA Extended Reconstructed SST V5
    data_modified:             2020-09-07

Vectorized Indexing#

Like numpy and pandas, xarray supports indexing many array elements at once in a vectorized manner:

# generate a coordinates for a transect of points
lat_points = xr.DataArray([60, 80, 90], dims="points")
lon_points = xr.DataArray([250, 250, 250], dims="points")
lat_points

<xarray.DataArray (points: 3)> Size: 24B
array([60, 80, 90])
Dimensions without coordinates: points
lon_points

<xarray.DataArray (points: 3)> Size: 24B
array([250, 250, 250])
Dimensions without coordinates: points
# nearest neighbor selection along the transect
da.sel(lat=lat_points, lon=lon_points, method="nearest").plot();
../../_images/7fd59dd8e83545137160706c198b33d4648aebabe2a5c41b8878ede1e80b96a5.png

Indexing with where()#

# Let's replace the missing values (nan) with some placeholder
ds.sst.where(ds.sst.notnull(), -99)
Hide code cell output 
<xarray.DataArray 'sst' (time: 128, lat: 89, lon: 180)> Size: 8MB
array([[[ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        ...,
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ]],

       [[ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        ...,
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ]],

       [[ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        ...,
...
        ...,
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ]],

       [[ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        ...,
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ]],

       [[ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        [ -1.8,  -1.8,  -1.8, ...,  -1.8,  -1.8,  -1.8],
        ...,
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ],
        [-99. , -99. , -99. , ..., -99. , -99. , -99. ]]], dtype=float32)
Coordinates:
  * lat      (lat) float32 356B 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0
  * lon      (lon) float32 720B 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0
  * time     (time) datetime64[ns] 1kB 2010-01-01 2010-02-01 ... 2020-08-01
Attributes:
    long_name:     Monthly Means of Sea Surface Temperature
    units:         degC
    var_desc:      Sea Surface Temperature
    level_desc:    Surface
    statistic:     Mean
    dataset:       NOAA Extended Reconstructed SST V5
    parent_stat:   Individual Values
    actual_range:  [-1.8     42.32636]
    valid_range:   [-1.8 45. ]

Going Further#

Previous: xarray fundamentals

Next: Computation

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