# Calculating Seasonal Averages from Timeseries of Monthly Means

Author: Joe Hamman

The data for this example can be found in the xray-data repository. This example is also available in an IPython Notebook that is available here.

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.

``````

In [54]:

%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  :  1.10.4
pandas version :  0.18.0
xarray version   :  0.7.2

``````

## Some calendar information so we can support any netCDF calendar.

``````

In [55]:

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 use the `calendar.month_range` function.

``````

In [56]:

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`

``````

In [57]:

monthly_mean_file = 'RASM_example_data.nc'
ds = xr.open_dataset(monthly_mean_file, decode_coords=False)
print(ds)

``````
``````

<xarray.Dataset>
Dimensions:  (time: 36, x: 275, y: 205)
Coordinates:
* time     (time) datetime64[ns] 1980-09-16T12:00:00 1980-10-17 ...
* x        (x) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
* y        (y) 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 ...
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: 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 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.

``````

In [58]:

# 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'.
seasons = month_length.groupby('time.season')
weights = seasons / seasons.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 [59]:

ds_weighted

``````
``````

Out[59]:

<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 ...

``````
``````

In [60]:

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

``````
``````

In [61]:

# Quick plot to show the results
is_null = np.isnan(ds_unweighted['Tair'][0].values)

fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(14,12))
for i, season in enumerate(('DJF', 'MAM', 'JJA', 'SON')):
plt.sca(axes[i, 0])
vmin=-30, vmax=30, cmap='Spectral_r')
plt.colorbar(extend='both')

plt.sca(axes[i, 1])
vmin=-30, vmax=30, cmap='Spectral_r')
plt.colorbar(extend='both')

plt.sca(axes[i, 2])
vmin=-0.1, vmax=.1, cmap='RdBu_r')
plt.colorbar(extend='both')
for j in range(3):
axes[i, j].axes.get_xaxis().set_ticklabels([])
axes[i, j].axes.get_yaxis().set_ticklabels([])
axes[i, j].axes.axis('tight')

axes[i, 0].set_ylabel(season)

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[61]:

<matplotlib.text.Text at 0x1ea06323240>

``````
``````

In [ ]:

``````