Interpolation over an irregular grid

So, I have three numpy arrays which store latitude, longitude, and some property value on a grid -- that is, I have LAT(y,x), LON(y,x), and, say temperature T(y,x), for some limits of x and y. The grid isn't necessarily regular -- in fact, it's tripolar.

I then want to interpolate these property (temperature) values onto a bunch of different lat/lon points (stored as lat1(t), lon1(t), for about 10,000 t...) which do not fall on the actual grid points. I've tried matplotlib.mlab.griddata, but that takes far too long (it's not really designed for what I'm doing, after all). I've also tried scipy.interpolate.interp2d, but I get a MemoryError (my grids are about 400x400).

Is there any sort of slick, preferably fast way of doing this? I can't help but think the answer is something obvious... Thanks!!

Solution 1:

Try the combination of inverse-distance weighting and scipy.spatial.KDTree described in SO inverse-distance-weighted-idw-interpolation-with-python. Kd-trees work nicely in 2d 3d ..., inverse-distance weighting is smooth and local, and the k= number of nearest neighbours can be varied to tradeoff speed / accuracy.

Solution 2:

There is a nice inverse distance example by Roger Veciana i Rovira along with some code using GDAL to write to geotiff if you're into that.

This is of coarse to a regular grid, but assuming you project the data first to a pixel grid with pyproj or something, all the while being careful what projection is used for your data.

A copy of his algorithm and example script:

from math import pow  
from math import sqrt  
import numpy as np  
import matplotlib.pyplot as plt  
  
def pointValue(x,y,power,smoothing,xv,yv,values):  
    nominator=0  
    denominator=0  
    for i in range(0,len(values)):  
        dist = sqrt((x-xv[i])*(x-xv[i])+(y-yv[i])*(y-yv[i])+smoothing*smoothing);  
        #If the point is really close to one of the data points, return the data point value to avoid singularities  
        if(dist<0.0000000001):  
            return values[i]  
        nominator=nominator+(values[i]/pow(dist,power))  
        denominator=denominator+(1/pow(dist,power))  
    #Return NODATA if the denominator is zero  
    if denominator > 0:  
        value = nominator/denominator  
    else:  
        value = -9999  
    return value  
  
def invDist(xv,yv,values,xsize=100,ysize=100,power=2,smoothing=0):  
    valuesGrid = np.zeros((ysize,xsize))  
    for x in range(0,xsize):  
        for y in range(0,ysize):  
            valuesGrid[y][x] = pointValue(x,y,power,smoothing,xv,yv,values)  
    return valuesGrid  
      
  
if __name__ == "__main__":  
    power=1  
    smoothing=20  
  
    #Creating some data, with each coodinate and the values stored in separated lists  
    xv = [10,60,40,70,10,50,20,70,30,60]  
    yv = [10,20,30,30,40,50,60,70,80,90]  
    values = [1,2,2,3,4,6,7,7,8,10]  
      
    #Creating the output grid (100x100, in the example)  
    ti = np.linspace(0, 100, 100)  
    XI, YI = np.meshgrid(ti, ti)  
  
    #Creating the interpolation function and populating the output matrix value  
    ZI = invDist(xv,yv,values,100,100,power,smoothing)  
  
  
    # Plotting the result  
    n = plt.normalize(0.0, 100.0)  
    plt.subplot(1, 1, 1)  
    plt.pcolor(XI, YI, ZI)  
    plt.scatter(xv, yv, 100, values)  
    plt.title('Inv dist interpolation - power: ' + str(power) + ' smoothing: ' + str(smoothing))  
    plt.xlim(0, 100)  
    plt.ylim(0, 100)  
    plt.colorbar()  
  
    plt.show()