# Time series data

A major use case for xarray is multi-dimensional time-series data. Accordingly, we’ve copied many of features that make working with time-series data in pandas such a joy to xarray. In most cases, we rely on pandas for the core functionality.

## Creating datetime64 data

Xarray uses the numpy dtypes `datetime64[ns]` and `timedelta64[ns]` to represent datetime data, which offer vectorized (if sometimes buggy) operations with numpy and smooth integration with pandas.

To convert to or create regular arrays of `datetime64` data, we recommend using `pandas.to_datetime()` and `pandas.date_range()`:

    In [1]: pd.to_datetime(["2000-01-01", "2000-02-02"])
    Out[1]: DatetimeIndex(['2000-01-01', '2000-02-02'], dtype='datetime64[ns]', freq=None)

    In [2]: pd.date_range("2000-01-01", periods=365)
    Out[2]:
    DatetimeIndex(['2000-01-01', '2000-01-02', '2000-01-03', '2000-01-04',
                   '2000-01-05', '2000-01-06', '2000-01-07', '2000-01-08',
                   '2000-01-09', '2000-01-10',
                   ...
                   '2000-12-21', '2000-12-22', '2000-12-23', '2000-12-24',
                   '2000-12-25', '2000-12-26', '2000-12-27', '2000-12-28',
                   '2000-12-29', '2000-12-30'],
                  dtype='datetime64[ns]', length=365, freq='D')

Alternatively, you can supply arrays of Python `datetime` objects. These get converted automatically when used as arguments in xarray objects:

    In [3]: import datetime

    In [4]: xr.Dataset({"time": datetime.datetime(2000, 1, 1)})
    Out[4]:
    <xarray.Dataset>
    Dimensions:  ()
    Data variables:
        time     datetime64[ns] 2000-01-01

When reading or writing netCDF files, xarray automatically decodes datetime and timedelta arrays using CF conventions (that is, by using a `units` attribute like `'days since 2000-01-01'`).

Note

When decoding/encoding datetimes for non-standard calendars or for dates before year 1678 or after year 2262, xarray uses the cftime library. It was previously packaged with the `netcdf4-python` package under the name `netcdftime` but is now distributed separately. `cftime` is an optional dependency of xarray.

You can manual decode arrays in this form by passing a dataset to `decode_cf()`:

    In [5]: attrs = {"units": "hours since 2000-01-01"}

    In [6]: ds = xr.Dataset({"time": ("time", [0, 1, 2, 3], attrs)})

    In [7]: xr.decode_cf(ds)
    Out[7]:
    <xarray.Dataset>
    Dimensions:  (time: 4)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-01-01T03:00:00
    Data variables:
        *empty*

One unfortunate limitation of using `datetime64[ns]` is that it limits the native representation of dates to those that fall between the years 1678 and 2262. When a netCDF file contains dates outside of these bounds, dates will be returned as arrays of `cftime.datetime` objects and a `CFTimeIndex` will be used for indexing. `CFTimeIndex` enables a subset of the indexing functionality of a `pandas.DatetimeIndex` and is only fully compatible with the standalone version of `cftime` (not the version packaged with earlier versions `netCDF4`). See Non-standard calendars and dates outside the Timestamp-valid range for more information.

## Datetime indexing

Xarray borrows powerful indexing machinery from pandas (see Indexing and selecting data).

This allows for several useful and succinct forms of indexing, particularly for datetime64 data. For example, we support indexing with strings for single items and with the slice object:

    In [8]: time = pd.date_range("2000-01-01", freq="H", periods=365 * 24)

    In [9]: ds = xr.Dataset({"foo": ("time", np.arange(365 * 24)), "time": time})

    In [10]: ds.sel(time="2000-01")
    Out[10]:
    <xarray.Dataset>
    Dimensions:  (time: 744)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-01-31T23:00:00
    Data variables:
        foo      (time) int64 0 1 2 3 4 5 6 7 8 ... 736 737 738 739 740 741 742 743

    In [11]: ds.sel(time=slice("2000-06-01", "2000-06-10"))
    Out[11]:
    <xarray.Dataset>
    Dimensions:  (time: 240)
    Coordinates:
      * time     (time) datetime64[ns] 2000-06-01 ... 2000-06-10T23:00:00
    Data variables:
        foo      (time) int64 3648 3649 3650 3651 3652 ... 3883 3884 3885 3886 3887

You can also select a particular time by indexing with a `datetime.time` object:

    In [12]: ds.sel(time=datetime.time(12))
    Out[12]:
    <xarray.Dataset>
    Dimensions:  (time: 365)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01T12:00:00 ... 2000-12-30T12:00:00
    Data variables:
        foo      (time) int64 12 36 60 84 108 132 ... 8628 8652 8676 8700 8724 8748

For more details, read the pandas documentation and the section on Indexing Using Datetime Components (i.e. using the `.dt` acessor).

## Datetime components

Similar to pandas, the components of datetime objects contained in a given `DataArray` can be quickly computed using a special `.dt` accessor.

    In [13]: time = pd.date_range("2000-01-01", freq="6H", periods=365 * 4)

    In [14]: ds = xr.Dataset({"foo": ("time", np.arange(365 * 4)), "time": time})

    In [15]: ds.time.dt.hour
    Out[15]:
    <xarray.DataArray 'hour' (time: 1460)>
    array([ 0,  6, 12, ...,  6, 12, 18])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

    In [16]: ds.time.dt.dayofweek
    Out[16]:
    <xarray.DataArray 'dayofweek' (time: 1460)>
    array([5, 5, 5, ..., 5, 5, 5])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

The `.dt` accessor works on both coordinate dimensions as well as multi-dimensional data.

Xarray also supports a notion of “virtual” or “derived” coordinates for datetime components implemented by pandas, including “year”, “month”, “day”, “hour”, “minute”, “second”, “dayofyear”, “week”, “dayofweek”, “weekday” and “quarter”:

    In [17]: ds["time.month"]
    Out[17]:
    <xarray.DataArray 'month' (time: 1460)>
    array([ 1,  1,  1, ..., 12, 12, 12])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

    In [18]: ds["time.dayofyear"]
    Out[18]:
    <xarray.DataArray 'dayofyear' (time: 1460)>
    array([  1,   1,   1, ..., 365, 365, 365])
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

For use as a derived coordinate, xarray adds `'season'` to the list of datetime components supported by pandas:

    In [19]: ds["time.season"]
    Out[19]:
    <xarray.DataArray 'season' (time: 1460)>
    array(['DJF', 'DJF', 'DJF', ..., 'DJF', 'DJF', 'DJF'], dtype='<U3')
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

    In [20]: ds["time"].dt.season
    Out[20]:
    <xarray.DataArray 'season' (time: 1460)>
    array(['DJF', 'DJF', 'DJF', ..., 'DJF', 'DJF', 'DJF'], dtype='<U3')
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

The set of valid seasons consists of ‘DJF’, ‘MAM’, ‘JJA’ and ‘SON’, labeled by the first letters of the corresponding months.

You can use these shortcuts with both Datasets and DataArray coordinates.

In addition, xarray supports rounding operations `floor`, `ceil`, and `round`. These operations require that you supply a rounding frequency as a string argument.

    In [21]: ds["time"].dt.floor("D")
    Out[21]:
    <xarray.DataArray 'floor' (time: 1460)>
    array(['2000-01-01T00:00:00.000000000', '2000-01-01T00:00:00.000000000',
           '2000-01-01T00:00:00.000000000', ..., '2000-12-30T00:00:00.000000000',
           '2000-12-30T00:00:00.000000000', '2000-12-30T00:00:00.000000000'], dtype='datetime64[ns]')
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

The `.dt` accessor can also be used to generate formatted datetime strings for arrays utilising the same formatting as the standard datetime.strftime.

    In [22]: ds["time"].dt.strftime("%a, %b %d %H:%M")
    Out[22]:
    <xarray.DataArray 'strftime' (time: 1460)>
    array(['Sat, Jan 01 00:00', 'Sat, Jan 01 06:00', 'Sat, Jan 01 12:00', ..., 'Sat, Dec 30 06:00',
           'Sat, Dec 30 12:00', 'Sat, Dec 30 18:00'], dtype=object)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00

### Indexing Using Datetime Components

You can use use the `.dt` accessor when subsetting your data as well. For example, we can subset for the month of January using the following:

    In [23]: ds.isel(time=(ds.time.dt.month == 1))
    Out[23]:
    <xarray.Dataset>
    Dimensions:  (time: 124)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-01-31T18:00:00
    Data variables:
        foo      (time) int64 0 1 2 3 4 5 6 7 8 ... 116 117 118 119 120 121 122 123

You can also search for multiple months (in this case January through March), using `isin`:

    In [24]: ds.isel(time=ds.time.dt.month.isin([1, 2, 3]))
    Out[24]:
    <xarray.Dataset>
    Dimensions:  (time: 364)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-03-31T18:00:00
    Data variables:
        foo      (time) int64 0 1 2 3 4 5 6 7 8 ... 356 357 358 359 360 361 362 363

## Resampling and grouped operations

Datetime components couple particularly well with grouped operations (see GroupBy: split-apply-combine) for analyzing features that repeat over time. Here’s how to calculate the mean by time of day:

    In [25]: ds.groupby("time.hour").mean()
    Out[25]:
    <xarray.Dataset>
    Dimensions:  (hour: 4)
    Coordinates:
      * hour     (hour) int64 0 6 12 18
    Data variables:
        foo      (hour) float64 728.0 729.0 730.0 731.0

For upsampling or downsampling temporal resolutions, xarray offers a `resample()` method building on the core functionality offered by the pandas method of the same name. Resample uses essentially the same api as `resample` in pandas.

For example, we can downsample our dataset from hourly to 6-hourly:

    In [26]: ds.resample(time="6H")
    Out[26]:
    DatasetResample, grouped over '__resample_dim__'
    1460 groups with labels 2000-01-01, ..., 2000-12-30T1....

This will create a specialized `Resample` object which saves information necessary for resampling. All of the reduction methods which work with `Resample` objects can also be used for resampling:

    In [27]: ds.resample(time="6H").mean()
    Out[27]:
    <xarray.Dataset>
    Dimensions:  (time: 1460)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00
    Data variables:
        foo      (time) float64 0.0 1.0 2.0 3.0 ... 1.457e+03 1.458e+03 1.459e+03

You can also supply an arbitrary reduction function to aggregate over each resampling group:

    In [28]: ds.resample(time="6H").reduce(np.mean)
    Out[28]:
    <xarray.Dataset>
    Dimensions:  (time: 1460)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00
    Data variables:
        foo      (time) float64 0.0 1.0 2.0 3.0 ... 1.457e+03 1.458e+03 1.459e+03

For upsampling, xarray provides six methods: `asfreq`, `ffill`, `bfill`, `pad`, `nearest` and `interpolate`. `interpolate` extends `scipy.interpolate.interp1d` and supports all of its schemes. All of these resampling operations work on both Dataset and DataArray objects with an arbitrary number of dimensions.

In order to limit the scope of the methods `ffill`, `bfill`, `pad` and `nearest` the `tolerance` argument can be set in coordinate units. Data that has indices outside of the given `tolerance` are set to `NaN`.

    In [29]: ds.resample(time="1H").nearest(tolerance="1H")
    Out[29]:
    <xarray.Dataset>
    Dimensions:  (time: 8755)
    Coordinates:
      * time     (time) datetime64[ns] 2000-01-01 ... 2000-12-30T18:00:00
    Data variables:
        foo      (time) float64 0.0 0.0 nan nan nan ... nan nan 1.459e+03 1.459e+03

For more examples of using grouped operations on a time dimension, see Toy weather data.