Point Interpolation

Compares different point interpolation approaches.

import cartopy.crs as ccrs
import cartopy.feature as cfeature
from matplotlib.colors import BoundaryNorm
import matplotlib.pyplot as plt
import numpy as np

from metpy.cbook import get_test_data
from metpy.interpolate import (interpolate_to_grid, remove_nan_observations,
                               remove_repeat_coordinates)
from metpy.plots import add_metpy_logo

def basic_map(proj, title):
    """Make our basic default map for plotting"""
    fig = plt.figure(figsize=(15, 10))
    add_metpy_logo(fig, 0, 80, size='large')
    view = fig.add_axes([0, 0, 1, 1], projection=proj)
    view.set_title(title)
    view.set_extent([-120, -70, 20, 50])
    view.add_feature(cfeature.STATES.with_scale('50m'))
    view.add_feature(cfeature.OCEAN)
    view.add_feature(cfeature.COASTLINE)
    view.add_feature(cfeature.BORDERS, linestyle=':')
    return fig, view


def station_test_data(variable_names, proj_from=None, proj_to=None):
    with get_test_data('station_data.txt') as f:
        all_data = np.loadtxt(f, skiprows=1, delimiter=',',
                              usecols=(1, 2, 3, 4, 5, 6, 7, 17, 18, 19),
                              dtype=np.dtype([('stid', '3S'), ('lat', 'f'), ('lon', 'f'),
                                              ('slp', 'f'), ('air_temperature', 'f'),
                                              ('cloud_fraction', 'f'), ('dewpoint', 'f'),
                                              ('weather', '16S'),
                                              ('wind_dir', 'f'), ('wind_speed', 'f')]))

    all_stids = [s.decode('ascii') for s in all_data['stid']]

    data = np.concatenate([all_data[all_stids.index(site)].reshape(1, ) for site in all_stids])

    value = data[variable_names]
    lon = data['lon']
    lat = data['lat']

    if proj_from is not None and proj_to is not None:

        try:

            proj_points = proj_to.transform_points(proj_from, lon, lat)
            return proj_points[:, 0], proj_points[:, 1], value

        except Exception as e:

            print(e)
            return None

    return lon, lat, value


from_proj = ccrs.Geodetic()
to_proj = ccrs.AlbersEqualArea(central_longitude=-97.0000, central_latitude=38.0000)

levels = list(range(-20, 20, 1))
cmap = plt.get_cmap('magma')
norm = BoundaryNorm(levels, ncolors=cmap.N, clip=True)

x, y, temp = station_test_data('air_temperature', from_proj, to_proj)

x, y, temp = remove_nan_observations(x, y, temp)
x, y, temp = remove_repeat_coordinates(x, y, temp)

Scipy.interpolate linear

gx, gy, img = interpolate_to_grid(x, y, temp, interp_type='linear', hres=75000)
img = np.ma.masked_where(np.isnan(img), img)
fig, view = basic_map(to_proj, 'Linear')
mmb = view.pcolormesh(gx, gy, img, cmap=cmap, norm=norm)
fig.colorbar(mmb, shrink=.4, pad=0, boundaries=levels)

Out:

<matplotlib.colorbar.Colorbar object at 0x7f7a9f4f0ca0>

Natural neighbor interpolation (MetPy implementation)

Reference

gx, gy, img = interpolate_to_grid(x, y, temp, interp_type='natural_neighbor', hres=75000)
img = np.ma.masked_where(np.isnan(img), img)
fig, view = basic_map(to_proj, 'Natural Neighbor')
mmb = view.pcolormesh(gx, gy, img, cmap=cmap, norm=norm)
fig.colorbar(mmb, shrink=.4, pad=0, boundaries=levels)

Out:

<matplotlib.colorbar.Colorbar object at 0x7f7a788c76d0>

Cressman interpolation

search_radius = 100 km

grid resolution = 25 km

min_neighbors = 1

gx, gy, img = interpolate_to_grid(x, y, temp, interp_type='cressman', minimum_neighbors=1,
                                  hres=75000, search_radius=100000)
img = np.ma.masked_where(np.isnan(img), img)
fig, view = basic_map(to_proj, 'Cressman')
mmb = view.pcolormesh(gx, gy, img, cmap=cmap, norm=norm)
fig.colorbar(mmb, shrink=.4, pad=0, boundaries=levels)

Out:

<matplotlib.colorbar.Colorbar object at 0x7f7aa00101c0>

Barnes Interpolation

search_radius = 100km

min_neighbors = 3

gx, gy, img1 = interpolate_to_grid(x, y, temp, interp_type='barnes', hres=75000,
                                   search_radius=100000)
img1 = np.ma.masked_where(np.isnan(img1), img1)
fig, view = basic_map(to_proj, 'Barnes')
mmb = view.pcolormesh(gx, gy, img1, cmap=cmap, norm=norm)
fig.colorbar(mmb, shrink=.4, pad=0, boundaries=levels)

Out:

<matplotlib.colorbar.Colorbar object at 0x7f7a79d34a60>

Radial basis function interpolation

linear

gx, gy, img = interpolate_to_grid(x, y, temp, interp_type='rbf', hres=75000, rbf_func='linear',
                                  rbf_smooth=0)
img = np.ma.masked_where(np.isnan(img), img)
fig, view = basic_map(to_proj, 'Radial Basis Function')
mmb = view.pcolormesh(gx, gy, img, cmap=cmap, norm=norm)
fig.colorbar(mmb, shrink=.4, pad=0, boundaries=levels)

plt.show()

Wind and Sea Level Pressure Interpolation Inverse Distance Verification: Cressman and Barnes