Author: Joe Hamman
The data used for this example can be found in the xray-data repository. You may need to change the path to rasm.nc below.
Suppose we have a netCDF or xray 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.
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.
In [1]:
%matplotlib inline
import numpy as np
import pandas as pd
import xarray as xr
from netCDF4 import num2date
import matplotlib.pyplot as plt
print("numpy version : ", np.__version__)
print("pandas version : ", pd.__version__)
print("xarray version : ", xr.__version__)
In [2]:
dpm = {'noleap': [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'365_day': [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'standard': [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'gregorian': [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'proleptic_gregorian': [0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'all_leap': [0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'366_day': [0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31],
'360_day': [0, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30]}
In [3]:
def leap_year(year, calendar='standard'):
"""Determine if year is a leap year"""
leap = False
if ((calendar in ['standard', 'gregorian',
'proleptic_gregorian', 'julian']) and
(year % 4 == 0)):
leap = True
if ((calendar == 'proleptic_gregorian') and
(year % 100 == 0) and
(year % 400 != 0)):
leap = False
elif ((calendar in ['standard', 'gregorian']) and
(year % 100 == 0) and (year % 400 != 0) and
(year < 1583)):
leap = False
return leap
def get_dpm(time, calendar='standard'):
"""
return a array of days per month corresponding to the months provided in `months`
"""
month_length = np.zeros(len(time), dtype=np.int)
cal_days = dpm[calendar]
for i, (month, year) in enumerate(zip(time.month, time.year)):
month_length[i] = cal_days[month]
if leap_year(year, calendar=calendar):
month_length[i] += 1
return month_length
In [4]:
ds = xr.tutorial.open_dataset('rasm').load()
print(ds)
In [5]:
# Make a DataArray with the number of days in each month, size = len(time)
month_length = xr.DataArray(get_dpm(ds.time.to_index(), calendar='noleap'),
coords=[ds.time], name='month_length')
# Calculate the weights by grouping by 'time.season'.
# Conversion to float type ('astype(float)') only necessary for Python 2.x
weights = month_length.groupby('time.season') / month_length.astype(float).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')
In [6]:
print(ds_weighted)
In [7]:
# only used for comparisons
ds_unweighted = ds.groupby('time.season').mean('time')
ds_diff = ds_weighted - ds_unweighted
In [8]:
# 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)
Out[8]:
In [9]:
# Wrap it into a simple function
def season_mean(ds, calendar='standard'):
# Make a DataArray of season/year groups
year_season = xr.DataArray(ds.time.to_index().to_period(freq='Q-NOV').to_timestamp(how='E'),
coords=[ds.time], name='year_season')
# Make a DataArray with the number of days in each month, size = len(time)
month_length = xr.DataArray(get_dpm(ds.time.to_index(), calendar=calendar),
coords=[ds.time], name='month_length')
# 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')
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