Calculating Climatology and Departures from Time Series Data

Calculating Climatology and Departures from Time Series Data#

Author: Tom Vo & Jiwoo Lee

Updated: 03/14/25 [xcdat v0.8.0]

Related APIs:

Overview#

Suppose we have two netCDF4 files for air temperature data (tas).

  • File 1: Monthly frequency from 1850-01-16 to 1874-12-31

    • We want to calculate the annual and seasonal cycle climatologies and departures using this file.

  • File 2: Hourly frequency from 2010-01-01 to 2015-01-01

    • We want to calculate the daily cycle climatologies and departures using this file.

The data used in this example can be found in the xcdat-data repository.

Notebook Kernel Setup#

Users can install their own instance of xcdat and follow these examples using their own environment (e.g., with VS Code, Jupyter, Spyder, iPython) or enable xcdat with existing JupyterHub instances.

First, create the conda environment:

conda create -n xcdat_notebook -c conda-forge xcdat xesmf matplotlib ipython ipykernel cartopy nc-time-axis gsw-xarray jupyter pooch

Then install the kernel from the xcdat_notebook environment using ipykernel and name the kernel with the display name (e.g., xcdat_notebook):

python -m ipykernel install --user --name xcdat_notebook --display-name xcdat_notebook

Then to select the kernel xcdat_notebook in Jupyter to use this kernel.

[1]:

%matplotlib inline

import matplotlib.pyplot as plt
import pandas as pd
import xcdat as xc

1. Open Sample Datasets#

File 1: Monthly Frequency#

[2]:

ds = xc.tutorial.open_dataset("tas_amon_access", use_cftime=True)

# Unit adjust (-273.15, K to C)
ds["tas"] = ds.tas - 273.15

ds_monthly = ds.copy()
ds_monthly

[2]:

<xarray.Dataset> Size: 7MB
Dimensions:    (time: 60, bnds: 2, lat: 145, lon: 192)
Coordinates:
  * lat        (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon        (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 354.4 356.2 358.1
    height     float64 8B 2.0
  * time       (time) object 480B 1870-01-16 12:00:00 ... 1874-12-16 12:00:00
Dimensions without coordinates: bnds
Data variables:
    time_bnds  (time, bnds) object 960B ...
    lat_bnds   (lat, bnds) float64 2kB ...
    lon_bnds   (lon, bnds) float64 3kB ...
    tas        (time, lat, lon) float32 7MB -29.36 -29.36 ... -31.07 -31.07
Attributes: (12/48)
    Conventions:                     CF-1.7 CMIP-6.2
    activity_id:                     CMIP
    branch_method:                   standard
    branch_time_in_child:            0.0
    branch_time_in_parent:           87658.0
    creation_date:                   2020-06-05T04:06:11Z
    ...                              ...
    variant_label:                   r10i1p1f1
    version:                         v20200605
    license:                         CMIP6 model data produced by CSIRO is li...
    cmor_version:                    3.4.0
    tracking_id:                     hdl:21.14100/af78ae5e-f3a6-4e99-8cfe-5f2...
    DODS_EXTRA.Unlimited_Dimension:  time

2: Hourly Frequency#

[3]:

ds_hourly = xc.tutorial.open_dataset("tas_3hr_access", add_bounds="T")

# Unit adjust (-273.15, K to C)
ds_hourly["tas"] = ds_hourly.tas - 273.15
ds_hourly

[3]:

<xarray.Dataset> Size: 25MB
Dimensions:    (lat: 25, bnds: 2, lon: 17, time: 14608)
Coordinates:
  * lat        (lat) float64 200B 15.0 16.25 17.5 18.75 ... 42.5 43.75 45.0
  * lon        (lon) float64 136B 15.0 16.88 18.75 20.62 ... 41.25 43.12 45.0
    height     float64 8B 2.0
  * time       (time) object 117kB 2010-01-01 03:00:00 ... 2015-01-01 00:00:00
Dimensions without coordinates: bnds
Data variables:
    lat_bnds   (lat, bnds) float64 400B ...
    lon_bnds   (lon, bnds) float64 272B ...
    tas        (time, lat, lon) float32 25MB 12.32 13.32 14.73 ... 0.9856 1.557
    time_bnds  (time, bnds) object 234kB 2010-01-01 03:00:00 ... 2015-01-01 0...
Attributes: (12/47)
    Conventions:            CF-1.7 CMIP-6.2
    activity_id:            CMIP
    branch_method:          standard
    branch_time_in_child:   0.0
    branch_time_in_parent:  87658.0
    creation_date:          2020-06-05T04:54:56Z
    ...                     ...
    variable_id:            tas
    variant_label:          r10i1p1f1
    version:                v20200605
    license:                CMIP6 model data produced by CSIRO is licensed un...
    cmor_version:           3.4.0
    tracking_id:            hdl:21.14100/b79e6a05-c482-46cf-b3b8-83b9a7d0cfdd

2. Calculate Climatology#

Related API: xarray.Dataset.temporal.climatology()

In this example, we will be calculating the weighted climatology of the tas variable for its seasonal, annual, and daily cycles.

Helpful knowledge:

  • Masked (missing) data is automatically handled.

    • The weight of masked (missing) data is excluded when averages are calculated. This is the same as giving them a weight of 0.

  • If desired, use the reference_period argument to calculate a climatology based on a climatological reference period (a subset of the entire time series). If no value is provided, the climatological reference period will be the full period covered by the dataset.

Seasonal Climatology#

Groups time coordinates by season

The season_config dictionary keyword argument can be passed to .climatology() for more granular configuration. We will be sticking with the default settings.

[4]:

season_climo = ds_monthly.temporal.climatology(
    "tas",
    freq="season",
    weighted=True,
    season_config={"dec_mode": "DJF", "drop_incomplete_djf": True},
)

[5]:

notnull = pd.notnull(season_climo["tas"][0])
tas_season = season_climo.tas

fig, axes = plt.subplots(nrows=4, ncols=1, figsize=(14, 12))
for i, season in enumerate(("DJF", "MAM", "JJA", "SON")):
    tas_season.isel(time=i).where(notnull).plot.pcolormesh(
        ax=axes[i],
        vmin=-30,
        vmax=30,
        cmap="Spectral_r",
        add_colorbar=True,
        extend="both",
    )
    axes[i].set_ylabel(season)

for ax in axes.flat:
    ax.axes.get_xaxis().set_ticklabels([])
    ax.axes.get_yaxis().set_ticklabels([])
    ax.axes.axis("tight")
    ax.set_xlabel("")

plt.tight_layout()
fig.suptitle("Seasonal Surface Air Temperature", fontsize=16, y=1.02)

[5]:

Text(0.5, 1.02, 'Seasonal Surface Air Temperature')
../_images/examples_climatology-and-departures_12_1.png

Notice that the time coordinates are cftime objects, with each season (“DJF”, “MAM”, “JJA”, and “SON”) represented by its middle month.

cftime objects are used because the time coordinates are outside the Timestamp-valid range (approximately between years 1678 and 2262).

[6]:

season_climo.time

[6]:

<xarray.DataArray 'time' (time: 4)> Size: 32B
array([cftime.DatetimeProlepticGregorian(1, 1, 1, 0, 0, 0, 0, has_year_zero=True),
       cftime.DatetimeProlepticGregorian(1, 4, 1, 0, 0, 0, 0, has_year_zero=True),
       cftime.DatetimeProlepticGregorian(1, 7, 1, 0, 0, 0, 0, has_year_zero=True),
       cftime.DatetimeProlepticGregorian(1, 10, 1, 0, 0, 0, 0, has_year_zero=True)],
      dtype=object)
Coordinates:
    height   float64 8B 2.0
  * time     (time) object 32B 0001-01-01 00:00:00 ... 0001-10-01 00:00:00
Attributes:
    bounds:         time_bnds
    axis:           T
    long_name:      time
    standard_name:  time
    _ChunkSizes:    1

Custom Seasonal Climatology#

Groups time coordinates by season

To calculate custom seasonal cycle climatology, we must first define our custom seasons using the season_config dictionary and the "custom_seasons" key.

"custom_seasons" must be a list of sublists containing month strings, with each sublist representing a custom season.

  • Month strings must be in the three letter format (e.g., ‘Jan’)

  • Each month must be included once in a custom season

  • Order of the months in each custom season does not matter

  • Custom seasons can vary in length

[7]:

custom_seasons = [
    ["Jan", "Feb", "Mar"],  # "JanFebMar"
    ["Apr", "May", "Jun"],  # "AprMayJun"
    ["Jul", "Aug", "Sep"],  # "JunJulAug"
    ["Oct", "Nov", "Dec"],  # "OctNovDec"
]

c_season_climo = ds_monthly.temporal.climatology(
    "tas",
    freq="season",
    weighted=True,
    season_config={"custom_seasons": custom_seasons},
)

[8]:

c_season_climo.tas

[8]:

<xarray.DataArray 'tas' (time: 4, lat: 145, lon: 192)> Size: 891kB
array([[[-39.19532013, -39.19532013, -39.19532013, ..., -39.19532013,
         -39.19532013, -39.19532013],
        [-37.01573944, -37.04970169, -37.08385849, ..., -36.91618729,
         -36.94950867, -36.98220444],
        [-36.18674469, -36.29411697, -36.40126038, ..., -35.86174393,
         -35.97014999, -36.07756042],
        ...,
        [-33.77421951, -33.72594452, -33.67987442, ..., -33.93065262,
         -33.8719902 , -33.82394409],
        [-33.88726044, -33.86452866, -33.84161377, ..., -33.96446609,
         -33.93911743, -33.91221619],
        [-34.45789719, -34.45789719, -34.45789719, ..., -34.45789719,
         -34.45789719, -34.45789719]],

       [[-56.66869736, -56.66869736, -56.66869736, ..., -56.66869736,
         -56.66869736, -56.66869736],
        [-52.51451492, -52.56056595, -52.60503387, ..., -52.37384796,
         -52.4212532 , -52.46620178],
        [-51.41792679, -51.53495407, -51.64799118, ..., -51.03515244,
         -51.16582108, -51.29377365],
...
        [ -4.33746576,  -4.34009361,  -4.33881092, ...,  -4.33952332,
          -4.33847046,  -4.33966684],
        [ -4.34618855,  -4.34531164,  -4.3482523 , ...,  -4.34492779,
          -4.35151768,  -4.35107231],
        [ -4.43647957,  -4.43647957,  -4.43647957, ...,  -4.43647957,
          -4.43647957,  -4.43647957]],

       [[-38.69176865, -38.69176865, -38.69176865, ..., -38.69176865,
         -38.69176865, -38.69176865],
        [-36.53458786, -36.5655098 , -36.59703064, ..., -36.44615936,
         -36.47403336, -36.50304413],
        [-35.67700195, -35.77786636, -35.87950897, ..., -35.37251282,
         -35.47246933, -35.57453918],
        ...,
        [-25.41450691, -25.35720825, -25.29871559, ..., -25.59947968,
         -25.53376579, -25.47436333],
        [-25.7094574 , -25.68809891, -25.66363525, ..., -25.78791618,
         -25.76446152, -25.73705673],
        [-26.46623611, -26.46623611, -26.46623611, ..., -26.46623611,
         -26.46623611, -26.46623611]]])
Coordinates:
  * lat      (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon      (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 352.5 354.4 356.2 358.1
    height   float64 8B 2.0
  * time     (time) object 32B 0001-02-01 00:00:00 ... 0001-11-01 00:00:00
Attributes:
    operation:                temporal_avg
    mode:                     climatology
    freq:                     season
    weighted:                 True
    drop_incomplete_seasons:  False
    custom_seasons:           ['JanFebMar', 'AprMayJun', 'JulAugSep', 'OctNov...
[9]:

notnull = pd.notnull(c_season_climo["tas"][0])
tas_c_season = c_season_climo.tas

fig, axes = plt.subplots(nrows=4, ncols=1, figsize=(14, 12))
for i, season in enumerate(tas_c_season.attrs["custom_seasons"]):
    tas_c_season.isel(time=i).where(notnull).plot.pcolormesh(
        ax=axes[i],
        vmin=-30,
        vmax=30,
        cmap="Spectral_r",
        add_colorbar=True,
        extend="both",
    )
    axes[i].set_ylabel(season)

for ax in axes.flat:
    ax.axes.get_xaxis().set_ticklabels([])
    ax.axes.get_yaxis().set_ticklabels([])
    ax.axes.axis("tight")
    ax.set_xlabel("")

plt.tight_layout()
fig.suptitle("Seasonal Surface Air Temperature", fontsize=16, y=1.02)

[9]:

Text(0.5, 1.02, 'Seasonal Surface Air Temperature')
../_images/examples_climatology-and-departures_18_1.png

Annual Climatology#

Groups time coordinates by month

[10]:

annual_climo = ds_monthly.temporal.climatology("tas", freq="month", weighted=True)

[11]:

annual_climo.tas

[11]:

<xarray.DataArray 'tas' (time: 12, lat: 145, lon: 192)> Size: 3MB
array([[[-29.06313705, -29.06313705, -29.06313705, ..., -29.06313705,
         -29.06313705, -29.06313705],
        [-28.08530235, -28.11272812, -28.14105415, ..., -28.01033974,
         -28.03586197, -28.05913353],
        [-27.52668381, -27.62425613, -27.72285843, ..., -27.22868156,
         -27.326931  , -27.42668152],
        ...,
        [-33.98196411, -33.93555069, -33.89547729, ..., -34.13406372,
         -34.07303238, -34.02735901],
        [-33.84999084, -33.82824707, -33.80555725, ..., -33.92643738,
         -33.90127945, -33.87459183],
        [-34.257267  , -34.257267  , -34.257267  , ..., -34.257267  ,
         -34.257267  , -34.257267  ]],

       [[-37.60506439, -37.60506439, -37.60506439, ..., -37.60506439,
         -37.60506439, -37.60506439],
        [-36.16939926, -36.2160759 , -36.2623558 , ..., -36.02677917,
         -36.07527161, -36.12286377],
        [-35.75842667, -35.87947083, -36.00115204, ..., -35.38283539,
         -35.5104866 , -35.63329315],
...
        [-24.32939911, -24.24647331, -24.155159  , ..., -24.5884037 ,
         -24.50076294, -24.41546249],
        [-24.88113976, -24.85075569, -24.81808472, ..., -24.99034882,
         -24.95741653, -24.92110443],
        [-25.88207817, -25.88207817, -25.88207817, ..., -25.88207817,
         -25.88207817, -25.88207817]],

       [[-28.29774857, -28.29774857, -28.29774857, ..., -28.29774857,
         -28.29774857, -28.29774857],
        [-27.16428185, -27.19420052, -27.2231102 , ..., -27.07938766,
         -27.10679245, -27.13484001],
        [-26.44675827, -26.54774094, -26.64871025, ..., -26.14484024,
         -26.24298477, -26.34383011],
        ...,
        [-31.27905464, -31.22894287, -31.1820488 , ..., -31.44397545,
         -31.38128471, -31.33101273],
        [-31.66051483, -31.63742447, -31.61308861, ..., -31.73810959,
         -31.71916199, -31.68753624],
        [-32.59217453, -32.59217453, -32.59217453, ..., -32.59217453,
         -32.59217453, -32.59217453]]])
Coordinates:
  * lat      (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon      (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 352.5 354.4 356.2 358.1
    height   float64 8B 2.0
  * time     (time) object 96B 0001-01-01 00:00:00 ... 0001-12-01 00:00:00
Attributes:
    operation:  temporal_avg
    mode:       climatology
    freq:       month
    weighted:   True

Daily Climatology#

Groups time coordinates by month and day.

Leap days (if present) are dropped if the CF calendar type is "gregorian", "proleptic_gregorian", or "standard".

[12]:

daily_climo = ds_hourly.temporal.climatology("tas", freq="day", weighted=True)

[13]:

daily_climo.tas

[13]:

<xarray.DataArray 'tas' (time: 365, lat: 25, lon: 17)> Size: 1MB
array([[[17.27717972, 18.28470039, 20.56212997, ..., 24.01642036,
         22.2651577 , 18.01205444],
        [15.63191414, 16.40312004, 18.61579514, ..., 25.43622398,
         21.73271751, 17.26057434],
        [15.77403927, 16.43821526, 16.8564167 , ..., 25.21095467,
         19.33696747, 14.54894066],
        ...,
        [10.21639633, 11.54874611,  6.83477879, ..., -1.93490219,
         -1.85050786, -2.05440116],
        [ 7.95682573,  1.64279783, -0.69631803, ..., -1.64676321,
         -2.02924085, -3.6966176 ],
        [ 3.34392548, -2.73531485, -3.0223999 , ..., -2.79192901,
         -4.44235325, -5.27707195]],

       [[18.07527542, 19.41358376, 21.73988342, ..., 23.84286499,
         22.06729889, 17.94522667],
        [16.30291557, 17.35409355, 19.68123817, ..., 25.38882065,
         21.60221481, 17.15660095],
        [16.38220406, 17.03896523, 17.6282177 , ..., 25.10874939,
         19.60748482, 15.19600296],
...
        [10.0537653 , 10.37064075,  6.2460289 , ..., -0.07122867,
         -0.41881028, -0.35291451],
        [ 8.59601116,  2.34073639, -0.05397935, ...,  0.37767109,
          0.59887844, -1.20402229],
        [ 3.99511075, -0.92589515, -0.43800527, ...,  0.42250133,
         -1.37440813, -2.37011075]],

       [[17.06862831, 18.31666374, 20.47524643, ..., 24.17832565,
         22.36183167, 18.67901802],
        [15.69621277, 16.47986794, 18.62369728, ..., 25.67900276,
         21.79547691, 17.65401649],
        [16.06197929, 16.58876419, 16.79445457, ..., 25.22506332,
         19.46402168, 14.96523285],
        ...,
        [ 9.90585041, 10.08311176,  5.55598688, ...,  0.44683456,
         -0.25121009, -0.91855931],
        [ 8.56485367,  2.25678468,  0.18535   , ...,  0.17904666,
          0.07626422, -2.15031719],
        [ 4.15226316, -0.89051032, -1.03323781, ..., -0.49040323,
         -2.69038248, -3.31937933]]])
Coordinates:
  * lat      (lat) float64 200B 15.0 16.25 17.5 18.75 ... 41.25 42.5 43.75 45.0
  * lon      (lon) float64 136B 15.0 16.88 18.75 20.62 ... 41.25 43.12 45.0
    height   float64 8B 2.0
  * time     (time) object 3kB 0001-01-01 00:00:00 ... 0001-12-31 00:00:00
Attributes:
    operation:  temporal_avg
    mode:       climatology
    freq:       day
    weighted:   True

3. Calculate Departures (Anomalies)#

Related API: xarray.Dataset.temporal.departures()

In this example, we will be calculating the weighted departures of the tas variable for its seasonal, annual, and daily cycles.

Helpful knowledge:

  • What are anomalies?

    • In climatology, “anomalies” refer to the difference between the value during a given time interval (e.g., the January average surface air temperature) and the long-term average value for that time interval (e.g., the average surface temperature over the last 30 Januaries).

  • How is the climatology calculated?

    • In the departures API, the reference climatology is calculated internally so there is no need to pass one to this method.

    • You can still calculate the reference climatology using the climatology API.

    • If desired, use the reference_period argument to calculate anomalies relative to a climatological reference period (a subset of the entire time series). If no value is provided, the climatological reference period will be the full period covered by the dataset.

  • Masked (missing) data is automatically handled.

    • The weight of masked (missing) data is excluded when averages are calculated. This is the same as giving them a weight of 0.

Seasonal Anomalies#

The season_config dictionary keyword argument can be passed to .departures() for more granular configuration. We will be sticking with the default settings.

[14]:

season_departures = ds_monthly.temporal.departures(
    "tas",
    freq="season",
    weighted=True,
    season_config={"dec_mode": "DJF", "drop_incomplete_djf": True},
)

[15]:

season_departures.tas

[15]:

<xarray.DataArray 'tas' (time: 20, lat: 145, lon: 192)> Size: 4MB
array([[[-0.38632202, -0.38632202, -0.38632202, ..., -0.38632202,
         -0.38632202, -0.38632202],
        [-0.45806122, -0.46568298, -0.47153091, ..., -0.43983078,
         -0.44695663, -0.45316696],
        [-0.40726852, -0.42545319, -0.44137573, ..., -0.3614769 ,
         -0.37729263, -0.39260483],
        ...,
        [ 0.95509338,  0.96128082,  0.95720863, ...,  0.94127274,
          0.94262123,  0.95428467],
        [ 0.8538208 ,  0.86007881,  0.86849403, ...,  0.80337715,
          0.82001877,  0.84108543],
        [ 0.59794998,  0.59794998,  0.59794998, ...,  0.59794998,
          0.59794998,  0.59794998]],

       [[-0.07499695, -0.07499695, -0.07499695, ..., -0.07499695,
         -0.07499695, -0.07499695],
        [-0.21348953, -0.20773697, -0.2016983 , ..., -0.2121315 ,
         -0.21300125, -0.21483612],
        [-0.12429047, -0.12824631, -0.12875748, ..., -0.0993042 ,
         -0.11037064, -0.11869431],
...
        [ 2.56331253,  2.57713127,  2.58680534, ...,  2.53077698,
          2.55092239,  2.55451775],
        [ 2.3217926 ,  2.32055855,  2.33027077, ...,  2.3072319 ,
          2.31292343,  2.31921959],
        [ 2.22647858,  2.22647858,  2.22647858, ...,  2.22647858,
          2.22647858,  2.22647858]],

       [[ 4.89233017,  4.89233017,  4.89233017, ...,  4.89233017,
          4.89233017,  4.89233017],
        [ 5.35656357,  5.37563705,  5.39709663, ...,  5.28821754,
          5.31351471,  5.33597755],
        [ 5.68298912,  5.71720123,  5.73626518, ...,  5.57681656,
          5.61822891,  5.65161705],
        ...,
        [ 0.47870255,  0.43775558,  0.39586639, ...,  0.62412643,
          0.57635117,  0.53154373],
        [-0.10575104, -0.12387848, -0.15367889, ..., -0.0420723 ,
         -0.07511902, -0.08538055],
        [-0.81404877, -0.81404877, -0.81404877, ..., -0.81404877,
         -0.81404877, -0.81404877]]])
Coordinates:
  * lat      (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon      (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 352.5 354.4 356.2 358.1
    height   float64 8B 2.0
  * time     (time) object 160B 1870-04-01 00:00:00 ... 1875-01-01 00:00:00
Attributes:
    operation:            temporal_avg
    mode:                 departures
    freq:                 season
    weighted:             True
    drop_incomplete_djf:  True
    dec_mode:             DJF

Custom Seasonal Anomalies#

To calculate custom seasonal cycle anomalies, we must first define our custom seasons using the season_config dictionary and the "custom_seasons" key.

"custom_seasons" must be a list of sublists containing month strings, with each sublist representing a custom season.

  • Month strings must be in the three letter format (e.g., ‘Jan’)

  • Each month must be included once in a custom season

  • Order of the months in each custom season does not matter

  • Custom seasons can vary in length

[16]:

custom_seasons = [
    ["Jan", "Feb", "Mar"],  # "JanFebMar"
    ["Apr", "May", "Jun"],  # "AprMayJun"
    ["Jul", "Aug", "Sep"],  # "JulAugSep"
    ["Oct", "Nov", "Dec"],  # "OctNovDec"
]
c_season_departs = ds_monthly.temporal.departures(
    "tas",
    freq="season",
    weighted=True,
    season_config={"custom_seasons": custom_seasons},
)

[17]:

c_season_departs.tas

[17]:

<xarray.DataArray 'tas' (time: 20, lat: 145, lon: 192)> Size: 4MB
array([[[-1.07600021, -1.07600021, -1.07600021, ..., -1.07600021,
         -1.07600021, -1.07600021],
        [-0.91370392, -0.90888596, -0.90649796, ..., -0.92504501,
         -0.92197037, -0.91679001],
        [-0.62365341, -0.62122726, -0.61834717, ..., -0.6397171 ,
         -0.63200378, -0.62888718],
        ...,
        [-0.9869957 , -0.98207855, -0.97632599, ..., -1.0029068 ,
         -0.99330139, -0.9924736 ],
        [-0.87341309, -0.86858368, -0.86443329, ..., -0.92316055,
         -0.9064827 , -0.88650513],
        [-1.00656128, -1.00656128, -1.00656128, ..., -1.00656128,
         -1.00656128, -1.00656128]],

       [[ 1.73557663,  1.73557663,  1.73557663, ...,  1.73557663,
          1.73557663,  1.73557663],
        [ 1.57818222,  1.56493759,  1.55473709, ...,  1.61846542,
          1.60420227,  1.58953857],
        [ 1.44296646,  1.40348816,  1.36589432, ...,  1.56670761,
          1.52353287,  1.48212433],
...
        [-0.07747459, -0.08188248, -0.0898304 , ..., -0.05021667,
         -0.05778265, -0.06833935],
        [-0.15619373, -0.15584278, -0.15005589, ..., -0.15278625,
         -0.14775133, -0.14955902],
        [-0.12531567, -0.12531567, -0.12531567, ..., -0.12531567,
         -0.12531567, -0.12531567]],

       [[ 0.07812881,  0.07812881,  0.07812881, ...,  0.07812881,
          0.07812881,  0.07812881],
        [-0.31155014, -0.32032776, -0.32696915, ..., -0.28045654,
         -0.29089737, -0.30200577],
        [-0.60416412, -0.6217308 , -0.63963318, ..., -0.56054688,
         -0.5739212 , -0.58827209],
        ...,
        [ 3.15319252,  3.18992233,  3.22689247, ...,  3.02513504,
          3.07551765,  3.11182213],
        [ 2.86530685,  2.88182831,  2.90113068, ...,  2.79384232,
          2.81263733,  2.84139633],
        [ 2.75313568,  2.75313568,  2.75313568, ...,  2.75313568,
          2.75313568,  2.75313568]]])
Coordinates:
  * lat      (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon      (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 352.5 354.4 356.2 358.1
    height   float64 8B 2.0
  * time     (time) object 160B 1870-02-01 00:00:00 ... 1874-11-01 00:00:00
Attributes:
    operation:                temporal_avg
    mode:                     departures
    freq:                     season
    weighted:                 True
    drop_incomplete_seasons:  False
    custom_seasons:           ['JanFebMar', 'AprMayJun', 'JulAugSep', 'OctNov...

Annual Anomalies#

[18]:

annual_departures = ds_monthly.temporal.departures("tas", freq="month", weighted=True)

[19]:

annual_departures.tas

[19]:

<xarray.DataArray 'tas' (time: 60, lat: 145, lon: 192)> Size: 13MB
array([[[-0.29283524, -0.29283524, -0.29283524, ..., -0.29283524,
         -0.29283524, -0.29283524],
        [ 0.08194542,  0.09492111,  0.10429573, ...,  0.04720497,
          0.06009293,  0.07094383],
        [ 0.15577316,  0.17291641,  0.18733597, ...,  0.08950615,
          0.11597824,  0.13424683],
        ...,
        [-2.03436279, -2.08486557, -2.13500977, ..., -1.86698914,
         -1.90568161, -1.96255493],
        [-1.44264221, -1.48994446, -1.539505  , ..., -1.34033203,
         -1.37841415, -1.40650558],
        [-0.69710922, -0.69710922, -0.69710922, ..., -0.69710922,
         -0.69710922, -0.69710922]],

       [[-1.16205597, -1.16205597, -1.16205597, ..., -1.16205597,
         -1.16205597, -1.16205597],
        [-0.87318802, -0.8703804 , -0.87042618, ..., -0.8835907 ,
         -0.88143921, -0.87252808],
        [-0.37824631, -0.38775635, -0.39669037, ..., -0.35071564,
         -0.35512924, -0.36832428],
...
        [ 0.71491241,  0.70773125,  0.69797516, ...,  0.72919655,
          0.73323059,  0.71778488],
        [-0.04808998, -0.05407524, -0.06053162, ..., -0.03354645,
         -0.05242538, -0.04889679],
        [-0.27649117, -0.27649117, -0.27649117, ..., -0.27649117,
         -0.27649117, -0.27649117]],

       [[-1.66088486, -1.66088486, -1.66088486, ..., -1.66088486,
         -1.66088486, -1.66088486],
        [-1.57422829, -1.58184624, -1.59149551, ..., -1.54930496,
         -1.55554581, -1.56476021],
        [-1.59505081, -1.61711502, -1.6384449 , ..., -1.53886032,
         -1.55595016, -1.57477951],
        ...,
        [ 1.7876606 ,  1.83859253,  1.89457321, ...,  1.62604332,
          1.68054008,  1.73134232],
        [ 1.56995392,  1.60545731,  1.64182091, ...,  1.43635178,
          1.47557068,  1.52873802],
        [ 1.52529526,  1.52529526,  1.52529526, ...,  1.52529526,
          1.52529526,  1.52529526]]])
Coordinates:
  * lat      (lat) float64 1kB -90.0 -88.75 -87.5 -86.25 ... 87.5 88.75 90.0
  * lon      (lon) float64 2kB 0.0 1.875 3.75 5.625 ... 352.5 354.4 356.2 358.1
    height   float64 8B 2.0
  * time     (time) object 480B 1870-01-16 12:00:00 ... 1874-12-16 12:00:00
Attributes:
    operation:  temporal_avg
    mode:       departures
    freq:       month
    weighted:   True

Daily Anomalies#

Leap days (if present) are dropped if the CF calendar type is "gregorian", "proleptic_gregorian", or "standard".

[20]:

daily_departures = ds_hourly.temporal.departures("tas", freq="day", weighted=True)

[21]:

daily_departures.tas

[21]:

<xarray.DataArray 'tas' (time: 1826, lat: 25, lon: 17)> Size: 6MB
array([[[-0.4617939 , -0.23371887, -0.77225113, ..., -0.43060875,
         -0.26933861, -0.75756836],
        [-0.69361591, -0.14549065, -0.23413849, ..., -0.74233818,
         -2.36725616, -2.93806553],
        [-1.17148685, -1.03936386, -0.30526161, ..., -0.65961075,
         -3.02596664, -6.70324659],
        ...,
        [-1.37778664, -0.22224712,  0.75218296, ..., -6.85112953,
         -4.03730094, -2.19454837],
        [-0.80398989, -0.20715499, -0.41081607, ..., -7.10115302,
         -3.01675773,  0.43061328],
        [-1.63339329, -3.71936607, -3.76028872, ..., -3.54410863,
          0.97883487,  1.92572308]],

       [[-1.09188843, -0.66767693, -1.22796249, ..., -0.19021988,
         -0.39680862, -0.46473503],
        [-1.45289421, -0.85043907, -1.1252079 , ..., -0.39163208,
         -1.62637329, -1.8878212 ],
        [-1.97675514, -1.90818214, -1.56252861, ..., -0.46310425,
         -3.54639244, -4.93937683],
...
        [ 2.8561964 ,  2.77291775,  2.4640975 , ...,  1.72163391,
          1.00494087,  2.70283055],
        [ 3.98282623,  5.14336944,  5.17486805, ...,  0.82676694,
          2.90933529,  4.72999859],
        [ 4.78354692,  6.61546683,  6.10648   , ...,  3.20243555,
          4.11584711,  5.27690649]],

       [[-4.13435745, -3.59619331, -4.52910995, ..., -0.82882881,
         -2.27330589, -6.01483154],
        [-4.14283943, -3.48310661, -3.64786911, ..., -0.42587852,
         -3.67854881, -7.50389099],
        [-4.34801388, -4.29295158, -4.24139595, ...,  0.94807243,
         -5.40727997, -8.04634666],
        ...,
        [ 2.98611832,  1.49663353,  0.34588528, ...,  4.08031845,
          2.43702519,  3.74895072],
        [ 4.54460859,  5.48412478,  4.6792587 , ...,  2.5925945 ,
          5.06738782,  4.55983782],
        [ 5.03025055,  5.57320547,  4.33001709, ...,  5.87710357,
          5.42794895,  6.83362103]]])
Coordinates:
  * lat      (lat) float64 200B 15.0 16.25 17.5 18.75 ... 41.25 42.5 43.75 45.0
  * lon      (lon) float64 136B 15.0 16.88 18.75 20.62 ... 41.25 43.12 45.0
    height   float64 8B 2.0
  * time     (time) object 15kB 2010-01-01 00:00:00 ... 2015-01-01 00:00:00
Attributes:
    operation:  temporal_avg
    mode:       departures
    freq:       day
    weighted:   True
Contents