Table of Contents
# Compare weighted and unweighted mean temperature
Author: [Mathias Hauser](https://github.com/mathause/)
We use the `air_temperature` example dataset to calculate the area-weighted temperature over its domain. This dataset has a regular latitude/ longitude grid, thus the grid cell area decreases towards the pole. For this grid we can use the cosine of the latitude as proxy for the grid cell area.
```ipython3
%matplotlib inline
import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import numpy as np
import xarray as xr
```
## Data
Load the data, convert to celsius, and resample to daily values
```ipython3
ds = xr.tutorial.load_dataset("air_temperature")
# to celsius
air = ds.air - 273.15
# resample from 6-hourly to daily values
air = air.resample(time="D").mean()
air
```
Plot the first timestep:
```ipython3
projection = ccrs.LambertConformal(central_longitude=-95, central_latitude=45)
f, ax = plt.subplots(subplot_kw=dict(projection=projection))
air.isel(time=0).plot(transform=ccrs.PlateCarree(), cbar_kwargs=dict(shrink=0.7))
ax.coastlines()
```
## Creating weights
For a rectangular grid the cosine of the latitude is proportional to the grid cell area.
```ipython3
weights = np.cos(np.deg2rad(air.lat))
weights.name = "weights"
weights
```
## Weighted mean
```ipython3
air_weighted = air.weighted(weights)
air_weighted
```
```ipython3
weighted_mean = air_weighted.mean(("lon", "lat"))
weighted_mean
```
## Plot: comparison with unweighted mean
Note how the weighted mean temperature is higher than the unweighted.
```ipython3
weighted_mean.plot(label="weighted")
air.mean(("lon", "lat")).plot(label="unweighted")
plt.legend()
```