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Calculating Seasonal Averages from Timeseries of Monthly Means¶
Author: Joe Hamman
The data used for this example can be found in the xarray-data repository. You may need to change the path to rasm.nc
below.
Suppose we have a netCDF or xarray.Dataset
of monthly mean data and we want to calculate the seasonal average. To do this properly, we need to calculate the weighted average considering that each month has a different number of days.
[1]:
%matplotlib inline
import numpy as np
import pandas as pd
import xarray as xr
import matplotlib.pyplot as plt
Open the Dataset
¶
[2]:
ds = xr.tutorial.open_dataset('rasm').load()
ds
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
<ipython-input-2-0eb806e38f7f> in <module>
----> 1 ds = xr.tutorial.open_dataset('rasm').load()
2 ds
/build/python-xarray-6p5Afb/python-xarray-0.16.0/xarray/tutorial.py in open_dataset(name, cache, cache_dir, github_url, branch, **kws)
76 # May want to add an option to remove it.
77 if not _os.path.isdir(longdir):
---> 78 _os.mkdir(longdir)
79
80 url = "/".join((github_url, "raw", branch, fullname))
FileNotFoundError: [Errno 2] No such file or directory: '/sbuild-nonexistent/.xarray_tutorial_data'
Now for the heavy lifting:¶
We first have to come up with the weights, - calculate the month lengths for each monthly data record - calculate weights using groupby('time.season')
Finally, we just need to multiply our weights by the Dataset
and sum allong the time dimension. Creating a DataArray
for the month length is as easy as using the days_in_month
accessor on the time coordinate. The calendar type, in this case 'noleap'
, is automatically considered in this operation.
[3]:
month_length = ds.time.dt.days_in_month
month_length
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-3-ec6a7921a622> in <module>
----> 1 month_length = ds.time.dt.days_in_month
2 month_length
NameError: name 'ds' is not defined
[4]:
# Calculate the weights by grouping by 'time.season'.
weights = month_length.groupby('time.season') / month_length.groupby('time.season').sum()
# Test that the sum of the weights for each season is 1.0
np.testing.assert_allclose(weights.groupby('time.season').sum().values, np.ones(4))
# Calculate the weighted average
ds_weighted = (ds * weights).groupby('time.season').sum(dim='time')
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-4-51dd727eba52> in <module>
1 # Calculate the weights by grouping by 'time.season'.
----> 2 weights = month_length.groupby('time.season') / month_length.groupby('time.season').sum()
3
4 # Test that the sum of the weights for each season is 1.0
5 np.testing.assert_allclose(weights.groupby('time.season').sum().values, np.ones(4))
NameError: name 'month_length' is not defined
[5]:
ds_weighted
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-5-3bfc08fe27f1> in <module>
----> 1 ds_weighted
NameError: name 'ds_weighted' is not defined
[6]:
# only used for comparisons
ds_unweighted = ds.groupby('time.season').mean('time')
ds_diff = ds_weighted - ds_unweighted
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-6-993ccc0e89d8> in <module>
1 # only used for comparisons
----> 2 ds_unweighted = ds.groupby('time.season').mean('time')
3 ds_diff = ds_weighted - ds_unweighted
NameError: name 'ds' is not defined
[7]:
# Quick plot to show the results
notnull = pd.notnull(ds_unweighted['Tair'][0])
fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(14,12))
for i, season in enumerate(('DJF', 'MAM', 'JJA', 'SON')):
ds_weighted['Tair'].sel(season=season).where(notnull).plot.pcolormesh(
ax=axes[i, 0], vmin=-30, vmax=30, cmap='Spectral_r',
add_colorbar=True, extend='both')
ds_unweighted['Tair'].sel(season=season).where(notnull).plot.pcolormesh(
ax=axes[i, 1], vmin=-30, vmax=30, cmap='Spectral_r',
add_colorbar=True, extend='both')
ds_diff['Tair'].sel(season=season).where(notnull).plot.pcolormesh(
ax=axes[i, 2], vmin=-0.1, vmax=.1, cmap='RdBu_r',
add_colorbar=True, extend='both')
axes[i, 0].set_ylabel(season)
axes[i, 1].set_ylabel('')
axes[i, 2].set_ylabel('')
for ax in axes.flat:
ax.axes.get_xaxis().set_ticklabels([])
ax.axes.get_yaxis().set_ticklabels([])
ax.axes.axis('tight')
ax.set_xlabel('')
axes[0, 0].set_title('Weighted by DPM')
axes[0, 1].set_title('Equal Weighting')
axes[0, 2].set_title('Difference')
plt.tight_layout()
fig.suptitle('Seasonal Surface Air Temperature', fontsize=16, y=1.02)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-7-ded3065dafd3> in <module>
1 # Quick plot to show the results
----> 2 notnull = pd.notnull(ds_unweighted['Tair'][0])
3
4 fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(14,12))
5 for i, season in enumerate(('DJF', 'MAM', 'JJA', 'SON')):
NameError: name 'ds_unweighted' is not defined
[8]:
# Wrap it into a simple function
def season_mean(ds, calendar='standard'):
# Make a DataArray with the number of days in each month, size = len(time)
month_length = ds.time.dt.days_in_month
# Calculate the weights by grouping by 'time.season'
weights = month_length.groupby('time.season') / month_length.groupby('time.season').sum()
# Test that the sum of the weights for each season is 1.0
np.testing.assert_allclose(weights.groupby('time.season').sum().values, np.ones(4))
# Calculate the weighted average
return (ds * weights).groupby('time.season').sum(dim='time')