example_triangle_interpolation

This example shows how interpolation between points on a spherical triangle appears.

The first function (example_three_points) creates three arbitrary points on the sphere and demonstrates that the values taken between the corners vary linearly (in great circle distance).

The second (example_terra) uses a subset of the TERRA mesh at ~22 km spacing and applies a smooth function, which we then interpolate between, demonstrating that the field is correctly interpolated.

We begin by importing the required things:

In [1]:

import matplotlib.pyplot as plt
import numpy as np

from terratools.terra_model import read_netcdf
from terratools.example_data import example_terra_model

from terratools.geographic import triangle_interpolation

import matplotlib.pyplot as plt import numpy as np from terratools.terra_model import read_netcdf from terratools.example_data import example_terra_model from terratools.geographic import triangle_interpolation

Next define a function to create a grid of points.

In [2]:

def grid(lon1, lon2, lat1, lat2, delta):
    lons = np.arange(lon1, lon2, delta)
    lats = np.arange(lat1, lat2, delta)
    return lons, lats

def grid(lon1, lon2, lat1, lat2, delta): lons = np.arange(lon1, lon2, delta) lats = np.arange(lat1, lat2, delta) return lons, lats

Download and read in the example model.

In [3]:

# get the path to the downloaded model
path = example_terra_model()

# read in the model
model = read_netcdf([path])

# get the path to the downloaded model path = example_terra_model() # read in the model model = read_netcdf([path])

Define a grid of points to perform the interpolation on. Note that we extract the points from the model itself using model get_lateral_points().

In [4]:

# extract points
lon, lat = model.get_lateral_points()

# create grid
delta = 10
gridlon, gridlat = grid(-180, 180, -90, 90, delta)
nlon, nlat = len(gridlon), len(gridlat)

# extract points lon, lat = model.get_lateral_points() # create grid delta = 10 gridlon, gridlat = grid(-180, 180, -90, 90, delta) nlon, nlat = len(gridlon), len(gridlat)

Perform the interpolation using model.evaluate() with the triangle method at 5000 km radius.

In [5]:

# loop over the grid of points

interpolated_values = np.empty((nlon, nlat))
for i in range(nlon):
    for j in range(nlat):
        interpolated_values[i, j] = model.evaluate(
            gridlon[i], gridlat[j], 5000, "t", method="triangle"
        )

# loop over the grid of points interpolated_values = np.empty((nlon, nlat)) for i in range(nlon): for j in range(nlat): interpolated_values[i, j] = model.evaluate( gridlon[i], gridlat[j], 5000, "t", method="triangle" )

Plot!

In [6]:

plt.pcolormesh(gridlon, gridlat, np.transpose(interpolated_values))
plt.scatter(lon, lat, edgecolors="white", s=0.5)
plt.colorbar()
plt.show()

plt.pcolormesh(gridlon, gridlat, np.transpose(interpolated_values)) plt.scatter(lon, lat, edgecolors="white", s=0.5) plt.colorbar() plt.show()

In [ ]: