Calculating Seasonal Averages from Timeseries of Monthly Means

Calculating Seasonal Averages from Timeseries of Monthly Means

The data used for this example can be found in thexarray-data repository.

Suppose we have a netCDF or xarray.Dataset of monthly mean data andwe want to calculate the seasonal average. To do this properly, we needto calculate the weighted average considering that each month has adifferent number of days.

%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__)

numpy version  :  1.11.1
pandas version :  0.18.1
xarray version :  0.8.2

Some calendar information so we can support any netCDF calendar.

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]}

A few calendar functions to determine the number of days in each month

If you were just using the standard calendar, it would be easy to usethe calendar.month_range function.

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

Open the Dataset

ds = xr.tutorial.load_dataset('rasm')
print(ds)

<xarray.Dataset>
Dimensions:  (time: 36, x: 275, y: 205)
Coordinates:
  * time     (time) datetime64[ns] 1980-09-16T12:00:00 1980-10-17 ...
  * y        (y) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
  * x        (x) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
Data variables:
    Tair     (time, y, x) float64 nan nan nan nan nan nan nan nan nan nan ...
    yc       (y, x) float64 16.53 16.78 17.02 17.27 17.51 17.76 18.0 18.25 ...
    xc       (y, x) float64 189.2 189.4 189.6 189.7 189.9 190.1 190.2 190.4 ...
Attributes:
    title: /workspace/jhamman/processed/R1002RBRxaaa01a/lnd/temp/R1002RBRxaaa01a.vic.ha.1979-09-01.nc
    institution: U.W.
    source: RACM R1002RBRxaaa01a
    output_frequency: daily
    output_mode: averaged
    convention: CF-1.4
    references: Based on the initial model of Liang et al., 1994, JGR, 99, 14,415- 14,429.
    comment: Output from the Variable Infiltration Capacity (VIC) model.
    nco_openmp_thread_number: 1
    NCO: 4.3.7
    history: history deleted for brevity

Now for the heavy lifting:

We first have to come up with the weights, - calculate the month lengthsfor each monthly data record - calculate weights usinggroupby('time.season')

Finally, we just need to multiply our weights by the Dataset and sumalong the time dimension.

# 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')

print(ds_weighted)

<xarray.Dataset>
Dimensions:  (season: 4, x: 275, y: 205)
Coordinates:
  * y        (y) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
  * x        (x) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
  * season   (season) object 'DJF' 'JJA' 'MAM' 'SON'
Data variables:
    Tair     (season, y, x) float64 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ...
    xc       (season, y, x) float64 189.2 189.4 189.6 189.7 189.9 190.1 ...
    yc       (season, y, x) float64 16.53 16.78 17.02 17.27 17.51 17.76 18.0 ...

# only used for comparisons
ds_unweighted = ds.groupby('time.season').mean('time')
ds_diff = ds_weighted - ds_unweighted

# 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)

<matplotlib.text.Text at 0x117c18048>

# 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')