None

Note

This tutorial was generated from an IPython notebook that can be accessed from github.

In this tutorial we will show how to create 2D integer mask for arbitrary latitude and longitude grids.

Note

2D masks are good for plotting. However, to calculate weighted regional averages 3D boolean masks are more convenient. See the tutorial on 3D masks. See #226 how weighted regional averages can be calculated with 2D integer mask (this may also offer some speed gains).

Import regionmask and check the version:

```import regionmask

```
```'0.10.0'
```

Load xarray and the tutorial data:

```import xarray as xr
import numpy as np

xr.set_options(display_style="text", display_width=60)
```
```<xarray.core.options.set_options at 0x7fbf7b1594e0>
```

Define a lon/ lat grid with a 1° grid spacing, where the points define the center of the grid.

```lon = np.arange(-179.5, 180)
lat = np.arange(-89.5, 90)
```

We will create a mask with the SREX regions (Seneviratne et al., 2012).

```regionmask.defined_regions.srex
```
```<regionmask.Regions 'SREX'>
Source:   Seneviratne et al., 2012 (https://www.ipcc.ch/site/assets/uploads/2...
overlap:  False

Regions:
3 WNA         W. North America
4 CNA         C. North America
5 ENA         E. North America
..  ..                      ...
22 EAS                  E. Asia
23 SAS                  S. Asia
24 SEA                S.E. Asia
25 NAU             N. Australia
26 SAU S. Australia/New Zealand

[26 regions]
```

The function `mask` determines which gridpoints lie within the polygon making up the each region:

```mask = regionmask.defined_regions.srex.mask(lon, lat)
```
```<xarray.DataArray 'mask' (lat: 180, lon: 360)>
array([[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan],
...,
[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan]])
Coordinates:
* lat      (lat) float64 -89.5 -88.5 -87.5 ... 88.5 89.5
* lon      (lon) float64 -179.5 -178.5 ... 178.5 179.5
Attributes:
standard_name:  region
flag_values:    [ 1  2  3  4  5  6  7  8  9 10 11 12 ...
flag_meanings:  ALA CGI WNA CNA ENA CAM AMZ NEB WSA S...```

`mask` is now a `xarray.Dataset` with shape `lat x lon` (if you need a numpy array use `mask.values`). Gridpoints that do not fall in a region are `NaN`, the gridpoints that fall in a region are encoded with the number of the region (here 1 to 26).

We can now plot the `mask`:

```import cartopy.crs as ccrs
import matplotlib.pyplot as plt

f, ax = plt.subplots(subplot_kw=dict(projection=ccrs.PlateCarree()))
ax.coastlines()

)

```
```<cartopy.mpl.geocollection.GeoQuadMesh at 0x7fbf35dad030>
```

masks can be used to select data in a certain region and to calculate regional averages - let’s illustrate this with a ‘real’ dataset:

```airtemps = xr.tutorial.load_dataset("air_temperature")
```

The example data is a temperature field over North America. Let’s plot the first time step:

```# choose a good projection for regional maps
proj = ccrs.LambertConformal(central_longitude=-100)

ax = plt.subplot(111, projection=proj)

airtemps.isel(time=1).air.plot.pcolormesh(ax=ax, transform=ccrs.PlateCarree())

ax.coastlines();
```

Conveniently we can directly pass an xarray object to the `mask` function. It gets the longitude and latitude from the `DataArray`/ `Dataset` and creates the `mask`. Per default regionmask assumes the longitude and latitude are called `"lon"` and `"lat"`. If they have another name, you can pass them individually, e.g. `region.mask(ds.longitude, ds.latitude)`.

```mask = regionmask.defined_regions.srex.mask(airtemps)
```

Note

`regionmask` automatically detects whether the longitude needs to be wrapped around, i.e. if the regions extend from -180° E to 180° W, while the grid goes from 0° to 360° W as in our example:

```lon = airtemps.lon.values
print("Grid extent:    {:3.0f}°E to {:3.0f}°E".format(lon.min(), lon.max()))

print("Region extent: {:3.0f}°E to {:3.0f}°E".format(bounds[0], bounds[2]))
```
```Grid extent:    200°E to 330°E
Region extent: -168°E to 180°E
```

Let’s plot the mask of the regions:

```proj = ccrs.LambertConformal(central_longitude=-100)
ax = plt.subplot(111, projection=proj)

levels = np.arange(low - 0.5, high + 1)

)

# for colorbar: find abbreviations of all regions that were selected
reg = reg[~np.isnan(reg)]

cbar = plt.colorbar(h, orientation="horizontal", fraction=0.075, pad=0.05)

cbar.set_ticks(reg)
cbar.set_ticklabels(abbrevs)
cbar.set_label("Region")

ax.coastlines()

# fine tune the extent
ax.set_extent([200, 330, 10, 75], crs=ccrs.PlateCarree())
```

Select a specific region - using cf_xarray

If cf_xarray is installed and imported we can select any individual region using the flags saved in the attributes (`attrs`) of the mask (new in regionmask 0.10.0):

```import cf_xarray
```
```mask
```
```<xarray.DataArray 'mask' (lat: 25, lon: 53)>
array([[nan, nan, nan, ...,  2.,  2.,  2.],
[ 1.,  1.,  1., ...,  2.,  2.,  2.],
[ 1.,  1.,  1., ...,  2.,  2.,  2.],
...,
[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan],
[nan, nan, nan, ..., nan, nan, nan]])
Coordinates:
* lat      (lat) float32 75.0 72.5 70.0 ... 20.0 17.5 15.0
* lon      (lon) float32 200.0 202.5 205.0 ... 327.5 330.0
Attributes:
standard_name:  region
flag_values:    [1 2 3 4 5 6]
flag_meanings:  ALA CGI WNA CNA ENA CAM```

Thus to select the region named “Central North America” (abbreviated “CNA”) we can do:

```mask_CNA = mask.cf == "CNA"

# show a subset
```
```<xarray.DataArray 'mask' (lon: 9)>
array([False, False, False, False, False, False, False,  True,  True])
Coordinates:
lat      float32 30.0
* lon      (lon) float32 240.0 242.5 245.0 ... 257.5 260.0```

Warning

`flag_meanings` cannot contain spaces - they will be replaced by underscores:

```mask_names = regionmask.defined_regions.srex.mask(airtemps, flag="names")

try:
except ValueError:
print("error raised")

mask_names.cf == "C. North America".replace(" ", "_")
```
```error raised
```
```<xarray.DataArray 'mask' (lat: 25, lon: 53)>
array([[False, False, False, ..., False, False, False],
[False, False, False, ..., False, False, False],
[False, False, False, ..., False, False, False],
...,
[False, False, False, ..., False, False, False],
[False, False, False, ..., False, False, False],
[False, False, False, ..., False, False, False]])
Coordinates:
* lat      (lat) float32 75.0 72.5 70.0 ... 20.0 17.5 15.0
* lon      (lon) float32 200.0 202.5 205.0 ... 327.5 330.0```

Select a specific region - without cf_xarray

We first need to find out which number the region ‘C. North America’ corresponds to:

```CNA_index = regionmask.defined_regions.srex.map_keys("C. North America")
CNA_index
```
```4
```
```mask_CNA = mask == CNA_index
```

To replace all grid points outside of CNA we use the `where` method of `xr.Dataset` (documentation), which filters elements from this object according to a condition:

```airtemps_CNA = airtemps.where(mask_CNA)
```

Check everything went well by repeating the first plot with the selected region:

```# choose a good projection for regional maps
proj = ccrs.LambertConformal(central_longitude=-100)

ax = plt.subplot(111, projection=proj)

airtemps_CNA.isel(time=1).air.plot.pcolormesh(ax=ax, transform=ccrs.PlateCarree())

ax.coastlines();
```

Looks good - with this we can calculate the region average.

Calculate weighted regional average

From version 0.15.1 xarray includes a function to calculate the weighted mean - we use `cos(lat)` as proxy of the grid cell area

Note

It is better to use a model’s original grid cell area (e.g. `areacella`). `cos(lat)` works reasonably well for regular lat/ lon grids. For irregular grids (regional models, ocean models, …) it is not appropriate.

```weights = np.cos(np.deg2rad(airtemps.lat))

ts_airtemps_CNA = airtemps_CNA.weighted(weights).mean(dim=("lat", "lon")) - 273.15
```

We plot the resulting time series:

```f, ax = plt.subplots()
ts_airtemps_CNA.air.plot.line(ax=ax, label="Central North America")

ax.axhline(0, color="0.1", lw=0.5)

plt.legend();
```

To get the regional average for each region you would need to loop over them. However, it’s easier to use a 3D mask.

Calculate regional statistics using `groupby`

Warning

Using `groupby` offers some convenience and is faster than using `where` and a loop. However, xarray does currently not natively support to combine `groupby` with `weighted` (pydata/xarray#3937), see #226 for a workaround. Overall, I recommend working with a 3D mask.

```# you can group over all integer values of the mask
airtemps_all
```
```<xarray.Dataset>
Coordinates:
* time     (time) datetime64[ns] 2013-01-01 ... 2014-12...
Data variables:
air      (mask, time) float32 255.9 255.7 ... 294.9
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridd...```

However, `groupby` is the way to go when calculating a (unweighted) regional median:

```# you can group over all integer values of the mask
airtemps_reg_median.isel(time=0)
```
```<xarray.Dataset>
Coordinates:
time     datetime64[ns] 2013-01-01
Data variables:
air      (mask) float32 255.7 250.8 ... 282.9 296.0
Attributes:
Conventions:  COARDS
title:        4x daily NMC reanalysis (1948)
description:  Data is from NMC initialized reanalysis...
platform:     Model
references:   http://www.esrl.noaa.gov/psd/data/gridd...```

Multidimensional coordinates

Regionmask can also handle mutltidimensional longitude/ latitude grids (e.g. from a regional climate model). As xarray provides such an example dataset, we will use it to illustrate it. See also in the xarray documentation.

```rasm = xr.tutorial.load_dataset("rasm")
```

The example data is a temperature field over the Northern Hemisphere. Let’s plot the first time step:

```# choose a projection
proj = ccrs.NorthPolarStereo()

ax = plt.subplot(111, projection=proj)
ax.set_global()

rasm.isel(time=1).Tair.plot.pcolormesh(
ax=ax, x="xc", y="yc", transform=ccrs.PlateCarree()
)

# add the abbreviation of the regions
)

ax.set_extent([-180, 180, 43, 90], ccrs.PlateCarree())

ax.coastlines();
```

Again we pass the xarray object to regionmask. Here, cf_xarray is used to detect `rasm.xc` and `rasm.yc` as longitude and latitude coordinates (new in regionmask 0.10.0). Without cf_xarray we would need to pass the coordinates explicitely (i.e. `srex.mask(rasm.xc, rasm.yc`):

```mask = regionmask.defined_regions.srex.mask(rasm)
```
```<xarray.DataArray 'mask' (y: 205, x: 275)>
array([[nan, nan, nan, ...,  5.,  5.,  5.],
[nan, nan, nan, ...,  5.,  5.,  5.],
[nan, nan, nan, ...,  5.,  5.,  5.],
...,
[24., 24., 24., ..., 14., 14., 14.],
[24., 24., 24., ..., 14., 14., 14.],
[24., 24., 24., ..., 14., 14., 14.]])
Coordinates:
xc       (y, x) float64 189.2 189.4 ... 17.15 16.91
yc       (y, x) float64 16.53 16.78 ... 27.76 27.51
Dimensions without coordinates: y, x
Attributes:
standard_name:  region
flag_values:    [ 1  2  3  4  5 11 12 13 14 18 19 20 ...
flag_meanings:  ALA CGI WNA CNA ENA NEU CEU MED SAH N...```

We want to select the region ‘NAS’ (Northern Asia).

Select using `where`

Using the cf_xarray accessor (from regionmask 0.10.0) we can directly use the name of the region (otherwise we need to select by the the number of the region):

```rasm_NAS = rasm.where(mask.cf == "NAS")
```

Check everything went well by repeating the first plot with the selected region:

```# choose a projection
proj = ccrs.NorthPolarStereo()

ax = plt.subplot(111, projection=proj)
ax.set_global()

rasm_NAS.isel(time=1).Tair.plot.pcolormesh(
ax=ax, x="xc", y="yc", transform=ccrs.PlateCarree()
)

# add the abbreviation of the regions