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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Overlapping regions
Two or more on regions can share the same area - they overlap, as for example region 3 and 4 of the PRUDENCE regions This notebook illustrates how overlapping regions can be treated in regionmask.
In short
Thus, when creating your own Regions you need to tell regionmask if they are overlapping.
python
region = regionmask.Regions(..., overlap=True)
region = regionmask.from_geopandas(..., overlap=True)
If you have two overlapping regions and overlap=False regionmask will silently assign the gridpoints of the overlapping regions to the one with the higher number, e.g., region 4 for PRUDENCE (this may change in a future version).
Note that overlap is correctly defined in regionmask.defined_regions.
Example
To illustrate the problem we construct two regions in North America that partially overlap. One is horizontal, the other vertical.
Preparation
Import regionmask and check the version
Step1:  Other imports
Step2:  Define some colors
Step3:  Define helper function
Step4:  Define the polygons
Step5:  Default behavior (overlap=False)
Fe first test what happens if we keep the default value of overlap=False
Step6:  Create a mask
Step7:  Plot the masked regions
Step8:  The small gray points show the gridpoint center and the vertical and horizontal lines are the gridpoint boundaries. The colored rectangles are the two regions. The vertical region has the number 1 and the horizontal region the number 2.
We can see that only the gridpoints in the lower part of the vertical (magenta) region were assigned to it. All gridpoints of the overlapping part are now assigned to the horizontal (orange) region. As mentioned the gridpoints are assigned to the region with the higher number By switching the order of the regions you could have the common gridpoints assigned to the vertical region.
Setting overlap=True
As mentioned regionmask assumes regions are not overlapping, so you need to pass overlap=True to the constructor
Step9:  Now it says overlap
Step10:  and plot it
Step11:  Now the gridpoints in the overlapping part are assigned to both regions.
PRUDENCE regions
The PRUDENCE regions are a real-world example of overlapping areas. The prudence regions already set overlap=True.
Step12:  Regions 3 and 4 overlap in Western France
Step13:  Create mask of PRUDENCE regions
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Python Code:
import regionmask
regionmask.__version__
Explanation: Overlapping regions
Two or more on regions can share the same area - they overlap, as for example region 3 and 4 of the PRUDENCE regions This notebook illustrates how overlapping regions can be treated in regionmask.
In short
Thus, when creating your own Regions you need to tell regionmask if they are overlapping.
python
region = regionmask.Regions(..., overlap=True)
region = regionmask.from_geopandas(..., overlap=True)
If you have two overlapping regions and overlap=False regionmask will silently assign the gridpoints of the overlapping regions to the one with the higher number, e.g., region 4 for PRUDENCE (this may change in a future version).
Note that overlap is correctly defined in regionmask.defined_regions.
Example
To illustrate the problem we construct two regions in North America that partially overlap. One is horizontal, the other vertical.
Preparation
Import regionmask and check the version:
End of explanation
import xarray as xr
import numpy as np
import cartopy.crs as ccrs
import matplotlib.pyplot as plt
from matplotlib import colors as mplc
from shapely.geometry import Polygon
import matplotlib.patheffects as pe
Explanation: Other imports
End of explanation
cmap = mplc.ListedColormap(["none", "#9ecae1"])
Explanation: Define some colors:
End of explanation
def plot_region_vh(mask):
    fg = mask.plot(
        subplot_kws=dict(projection=ccrs.PlateCarree()),
        col="region",
        cmap=cmap,
        add_colorbar=False,
        transform=ccrs.PlateCarree(),
        ec="0.5",
        lw=0.25,
    )
    for ax in fg.axes.flatten():
        region_vh[[0]].plot(ax=ax, add_label=False, line_kws=dict(color="#6a3d9a"))
        region_vh[[1]].plot(ax=ax, add_label=False, line_kws=dict(color="#ff7f00"))
        ax.set_extent([-105, -75, 25, 55], ccrs.PlateCarree())
        ax.plot(
            ds_US.LON, ds_US.lat, "*", color="0.5", ms=0.5, transform=ccrs.PlateCarree()
        )
Explanation: Define helper function:
End of explanation
coords_v = np.array([[-90.0, 50.0], [-90.0, 28.0], [-100.0, 28.0], [-100.0, 50.0]])
coords_h = np.array([[-80.0, 50.0], [-80.0, 40.0], [-100.0, 40.0], [-100.0, 50.0]])
Explanation: Define the polygons:
End of explanation
region_vh = regionmask.Regions([coords_v, coords_h])
Explanation: Default behavior (overlap=False)
Fe first test what happens if we keep the default value of overlap=False:
End of explanation
ds_US = regionmask.core.utils.create_lon_lat_dataarray_from_bounds(
    *(-160, -29, 2), *(76, 13, -2)
)
mask_vh = region_vh.mask_3D(ds_US)
Explanation: Create a mask
End of explanation
plot_region_vh(mask_vh)
Explanation: Plot the masked regions:
End of explanation
region_overlap = regionmask.Regions([coords_v, coords_h], overlap=True)
region_overlap
Explanation: The small gray points show the gridpoint center and the vertical and horizontal lines are the gridpoint boundaries. The colored rectangles are the two regions. The vertical region has the number 1 and the horizontal region the number 2.
We can see that only the gridpoints in the lower part of the vertical (magenta) region were assigned to it. All gridpoints of the overlapping part are now assigned to the horizontal (orange) region. As mentioned the gridpoints are assigned to the region with the higher number By switching the order of the regions you could have the common gridpoints assigned to the vertical region.
Setting overlap=True
As mentioned regionmask assumes regions are not overlapping, so you need to pass overlap=True to the constructor:
End of explanation
mask_overlap = region_overlap.mask_3D(ds_US)
Explanation: Now it says overlap:  True - and we can again create a mask:
End of explanation
plot_region_vh(mask_overlap)
Explanation: and plot it
End of explanation
prudence = regionmask.defined_regions.prudence
prudence
Explanation: Now the gridpoints in the overlapping part are assigned to both regions.
PRUDENCE regions
The PRUDENCE regions are a real-world example of overlapping areas. The prudence regions already set overlap=True.
End of explanation
proj = ccrs.LambertConformal(central_longitude=10)
text_kws = dict(
    bbox=dict(color="none"),
    path_effects=[pe.withStroke(linewidth=3, foreground="w")],
    color="#67000d",
)
ax = prudence.plot(
    projection=proj, text_kws=text_kws, resolution="50m", line_kws=dict(lw=0.75)
)
ax.set_extent([-10.0, 30.0, 40.0, 55.0], ccrs.PlateCarree())
Explanation: Regions 3 and 4 overlap in Western France:
End of explanation
lon = np.arange(-12, 33, 0.5)
lat = np.arange(72, 33, -0.5)
mask_prudence = prudence.mask_3D(lon, lat)
proj = ccrs.LambertConformal(central_longitude=10)
fg = mask_prudence.sel(region=[3, 4]).plot(
    subplot_kws=dict(projection=proj),
    col="region",
    cmap=cmap,
    add_colorbar=False,
    transform=ccrs.PlateCarree(),
)
for ax in fg.axes.flatten():
    regionmask.defined_regions.prudence.plot(
        ax=ax, add_label=False, resolution="50m", line_kws=dict(lw=0.75)
    )
Explanation: Create mask of PRUDENCE regions
End of explanation
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