fast-barnes-py 1.0.0

Fast Barnes Interpolation

Fast Barnes Interpolation

This Python package provides an implementation of the formal algorithms for fast Barnes interpolation as presented in the corresponding paper (preprint available at GMD).

Barnes interpolation is a method that is widely used in geospatial sciences like meteorology to remodel data values recorded at irregularly distributed points into a representative analytical field.

Naive computation of Barnes interpolation leads to an algorithmic complexity of O(N x W x H), where N is the number of sample points and W x H the size of the underlying grid.
As shown in the paper, a good approximation of Barnes interpolation with a drastically reduced algorithmic complexity O(N + W x H) can be obtained by calculating a convolutional expression.

Example

The code below demonstrates how Barnes interpolation can be computed given a few sample points of mean sea level pressure values located over the British islands.

import numpy as np

# definition of 50 sample points with longitude, latitude and mean sea level pressure QFF
input_data = np.asarray([
    [-3.73,56.33,995.1], [2.64,47.05,1012.5], [-8.40,47.50,1011.3], [2.94,54.33,1006.0], [-2.90,49.90,1006.3],
    [-8.98,53.72,1002.1], [1.20,58.60,1002.6], [1.60,50.73,1009.1], [-7.38,57.36,997.7], [-1.25,53.01,1000.4],
    [-4.74,52.79,998.4], [-0.61,47.48,1013.0], [-6.10,50.10,1004.3], [-6.46,54.87,996.4], [-3.22,47.29,1012.8],
    [-1.60,55.42,996.6], [2.30,56.60,1004.5], [1.12,52.95,1003.6], [-0.90,57.80,999.9], [-7.90,51.40,1002.6],
    [-0.70,50.10,1007.5], [2.53,49.02,1010.8], [-5.06,48.47,1008.5], [-3.10,53.60,997.5], [-5.63,57.86,997.8],
    [-6.90,52.85,1000.9], [-4.15,51.09,1002.6], [-1.99,51.50,1002.7], [1.21,47.68,1011.7], [-5.70,56.30,995.5],
    [-1.98,53.13,998.5], [1.09,49.93,1009.0], [1.72,58.42,1002.9], [-6.30,52.30,999.4], [0.70,57.70,1001.9],
    [-3.50,53.60,995.9], [1.38,48.06,1011.6], [-4.37,51.71,1001.1], [-3.09,58.45,998.5], [2.00,56.40,1003.9],
    [1.90,57.00,1003.3], [0.45,51.90,1004.9], [-8.25,51.80,1002.5], [-1.87,53.81,997.4], [-2.38,55.71,995.1],
    [-4.01,54.80,992.1], [0.88,53.37,1002.6], [-1.69,51.86,1002.1], [-4.57,52.14,999.6], [-0.20,58.40,1001.1],
])

lon_lat_data = input_data[:, 0:2]
qff_values = input_data[:, 2]

The target grid has to be specified and then the data and the grid are passed with the Gaussian width parameter to the interpolation.barnes() method, which returns a representative gridded field.

# definition of a 12° x 12° grid starting at 9°W / 47°N
resolution = 32.0
step = 1.0 / resolution
x0 = np.asarray([-9.0, 47.0], dtype=np.float64)
size = (int(12.0 / step), int(12.0 / step))

# calculate Barnes interpolation
from fastbarnes import interpolation
sigma = 1.0
field = interpolation.barnes(lon_lat_data, qff_values, sigma, x0, step, size)

The resulting field can then be further processed, for instance visualized by a matplotlib contour plot.

# draw graphic with labeled contours and scattered sample points
import matplotlib.pyplot as plt
plt.figure(figsize=(5, 5))

gridX = np.arange(x0[0], x0[0]+size[1]*step, step)
gridY = np.arange(x0[1], x0[1]+size[0]*step, step)
levels = np.arange(976, 1026, 2)
cs = plt.contour(gridX, gridY, field, levels)
plt.clabel(cs, levels[::2], fmt='%d', fontsize=9)

plt.scatter(lon_lat_data[:, 0], lon_lat_data[:, 1], color='red', s=20, marker='.')

plt.show()

Note that due to the just-in-time compilation of the underlying code, the first execution of Barnes interpolation takes considerable more time than the succeeding ones.