Windowed Computations#
Xarray has built-in support for windowed operations:
In this notebook, we’ll learn to
Compute rolling, or sliding window, means along one or more dimensions.
Compute block averages along a dimension.
Use
construct
to reshape arrays so that a new dimension provides windowed views to the data.
import numpy as np
import xarray as xr
import matplotlib.pyplot as plt
np.set_printoptions(threshold=10, edgeitems=2)
xr.set_options(display_expand_data=False)
%config InlineBackend.figure_format='retina'
ds = xr.tutorial.load_dataset("ersstv5")
ds
<xarray.Dataset> Dimensions: (lat: 89, lon: 180, time: 624, nbnds: 2) Coordinates: * lat (lat) float32 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0 * lon (lon) float32 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0 * time (time) datetime64[ns] 1970-01-01 1970-02-01 ... 2021-12-01 Dimensions without coordinates: nbnds Data variables: time_bnds (time, nbnds) float64 9.969e+36 9.969e+36 ... 9.969e+36 9.969e+36 sst (time, lat, lon) float32 -1.8 -1.8 -1.8 -1.8 ... 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: 2022-06-07
Rolling or moving windows#
Rolling window operations
can be applied along any dimension, or along multiple dimensions.
returns object of same shape as input
pads with NaNs to make (3) possible
Again, all common reduction operations are available
rolling = ds.rolling(time=12, center=True)
rolling
DatasetRolling [time->12(center)]
Tip
Xarrays’ computation methods (groupby
, groupby_bins
, rolling
, coarsen
, weighted
) all return special objects that represent the basic underlying computation pattern. For e.g. rolling
above is a DatasetRolling
object that represents 12-point rolling windows of the data in ds
. It is usually helpful to save and reuse these objects for multiple operations (e.g. a mean and standard deviation calculation).
ds_rolling = rolling.mean()
ds_rolling
<xarray.Dataset> Dimensions: (time: 624, nbnds: 2, lat: 89, lon: 180) Coordinates: * time (time) datetime64[ns] 1970-01-01 1970-02-01 ... 2021-12-01 * lat (lat) float32 88.0 86.0 84.0 82.0 ... -82.0 -84.0 -86.0 -88.0 * lon (lon) float32 0.0 2.0 4.0 6.0 8.0 ... 352.0 354.0 356.0 358.0 Dimensions without coordinates: nbnds Data variables: time_bnds (time, nbnds) float64 nan nan nan nan nan ... nan nan nan nan nan sst (time, lat, lon) float32 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: 2022-06-07
ds.sst.sel(lon=300, lat=50).plot(label="monthly anom")
ds_rolling.sst.sel(lon=300, lat=50).plot(label="12 month rolling mean")
plt.legend()
<matplotlib.legend.Legend at 0x7f5ed71daed0>

We can apply rolling mean along multiple dimensions as a 2D smoother in (lat, lon). Here is an example of a 5-point running mean applied along both the lat
and lon
dimensions
extract = ds.sst.isel(time=0)
smoothed = extract.rolling(lon=5, lat=5, center=True).mean()
f, ax = plt.subplots(2, 1, sharex=True, sharey=True)
extract.plot(ax=ax[0], robust=True)
smoothed.plot(ax=ax[1], robust=True)
f.set_size_inches((10, 7))
plt.tight_layout()

Note the addition of NaNs at the data boundaries and near continental boundaries.
Custom reductions#
While common reductions are implemented by default, sometimes it is useful to apply our own windowed operations. For these uses, Xarray provides the construct
methods for DataArray.rolling and Dataset.rolling.
For rolling over a dimension time
with a window size N
, construct
adds a new dimension (with user-provided name) of size N
.
We illustrate with a simple example array:
simple = xr.DataArray(np.arange(10), dims="time", coords={"time": np.arange(10)})
simple
<xarray.DataArray (time: 10)> 0 1 2 3 4 5 6 7 8 9 Coordinates: * time (time) int64 0 1 2 3 4 5 6 7 8 9
We call construct
and provide a name for the new dimension: window
# adds a new dimension "window"
simple.rolling(time=5, center=True).construct("window")
<xarray.DataArray (time: 10, window: 5)> nan nan 0.0 1.0 2.0 nan 0.0 1.0 2.0 3.0 ... 7.0 8.0 9.0 nan 7.0 8.0 9.0 nan nan Coordinates: * time (time) int64 0 1 2 3 4 5 6 7 8 9 Dimensions without coordinates: window
Exercise 9
Illustrate the difference between center=True
and center=False
for rolling by looking at the construct
-ed array.
Solution to Exercise 9
display("center=True")
display(simple.rolling(time=5, center=True).construct("window"))
display("center=False")
display(simple.rolling(time=5, center=False).construct("window"))
Coarsening#
coarsen
does something similar to rolling
, but allows us to work with discrete non-overlapping blocks of data.
You will need to specify boundary
if the length of the dimension is not a multiple of the window size (“block size”). You can choose to
trim
the excess valuespad
with NaNs
Again, all standard reductions are implemented.
coarse = ds.coarsen(lon=5, lat=5)
coarse
DatasetCoarsen [windows->{'lon': 5, 'lat': 5},side->left]
Xarrays’ computation methods (groupby, groupby_bins, rolling, coarsen, weighted) all return special objects that represent the basic underlying computation pattern. For e.g. coarse
above is a DatasetCoarsen
object that represents 5-point windows along lat, lon of the data in ds
. It is usually helpful to save and reuse these objects for multiple operations (e.g. a mean and standard deviation calculation).
# we expect an error here because lat has size 89, which is not divisible by block size 5
coarse.mean()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
Cell In[10], line 2
1 # we expect an error here because lat has size 89, which is not divisible by block size 5
----> 2 coarse.mean()
File ~/micromamba/envs/xarray-tutorial/lib/python3.11/site-packages/xarray/core/rolling.py:1098, in DatasetCoarsen._reduce_method.<locals>.wrapped_func(self, keep_attrs, **kwargs)
1096 reduced = {}
1097 for key, da in self.obj.data_vars.items():
-> 1098 reduced[key] = da.variable.coarsen(
1099 self.windows,
1100 func,
1101 self.boundary,
1102 self.side,
1103 keep_attrs=keep_attrs,
1104 **kwargs,
1105 )
1107 coords = {}
1108 for c, v in self.obj.coords.items():
1109 # variable.coarsen returns variables not containing the window dims
1110 # unchanged (maybe removes attrs)
File ~/micromamba/envs/xarray-tutorial/lib/python3.11/site-packages/xarray/core/variable.py:2515, in Variable.coarsen(self, windows, func, boundary, side, keep_attrs, **kwargs)
2512 if not windows:
2513 return self._replace(attrs=_attrs)
-> 2515 reshaped, axes = self.coarsen_reshape(windows, boundary, side)
2516 if isinstance(func, str):
2517 name = func
File ~/micromamba/envs/xarray-tutorial/lib/python3.11/site-packages/xarray/core/variable.py:2551, in Variable.coarsen_reshape(self, windows, boundary, side)
2549 if boundary[d] == "exact":
2550 if n * window != size:
-> 2551 raise ValueError(
2552 f"Could not coarsen a dimension of size {size} with "
2553 f"window {window} and boundary='exact'. Try a different 'boundary' option."
2554 )
2555 elif boundary[d] == "trim":
2556 if side[d] == "left":
ValueError: Could not coarsen a dimension of size 89 with window 5 and boundary='exact'. Try a different 'boundary' option.
coarse = ds.coarsen(lat=5, lon=5, boundary="trim").mean()
coarse
<xarray.Dataset> Dimensions: (time: 624, nbnds: 2, lat: 17, lon: 36) Coordinates: * lat (lat) float32 84.0 74.0 64.0 54.0 ... -46.0 -56.0 -66.0 -76.0 * lon (lon) float32 4.0 14.0 24.0 34.0 44.0 ... 324.0 334.0 344.0 354.0 * time (time) datetime64[ns] 1970-01-01 1970-02-01 ... 2021-12-01 Dimensions without coordinates: nbnds Data variables: time_bnds (time, nbnds) float64 9.969e+36 9.969e+36 ... 9.969e+36 9.969e+36 sst (time, lat, lon) float32 -1.757 -1.78 -1.8 ... -1.716 -1.685 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: 2022-06-07
coarse.sst.isel(time=0).plot();

Custom reductions#
Like rolling
, coarsen
also provides a construct
method for custom block operations.
Tip
coarsen.construct
is a handy way to reshape Xarray objects.
Consider a “monthly” 1D timeseries. This simple example has one value per month for 2 years
months = xr.DataArray(
np.tile(np.arange(1, 13), reps=2),
dims="time",
coords={"time": np.arange(1, 25)},
)
months
<xarray.DataArray (time: 24)> 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Coordinates: * time (time) int64 1 2 3 4 5 6 7 8 9 10 ... 15 16 17 18 19 20 21 22 23 24
Now we reshape to get one new dimension year
of size 12.
# break "time" into two new dimensions: "year", "month"
months.coarsen(time=12).construct(time=("year", "month"))
<xarray.DataArray (year: 2, month: 12)> 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Coordinates: time (year, month) int64 1 2 3 4 5 6 7 8 9 ... 17 18 19 20 21 22 23 24 Dimensions without coordinates: year, month
Exercise 10
Imagine the array months
was one element shorter. Use boundary="pad"
and the side
kwarg to reshape months.isel(time=slice(1, None))
to a 2D DataArray with the following values:
array([[nan, 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.],
[ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12.]])
Solution to Exercise 10
months.isel(time=slice(1, None)).coarsen({"time": 12}, boundary="pad", side="right").construct(
time=("year", "month")
)
Note that coarsen
pads with NaNs. For more control over padding, use
DataArray.pad explicitly.
Going further#
Follow the tutorial on high-level computational patterns