Kringing Algorithm

I’m working with this recently. It was use to interpolate the unmeasured data in environment. I asked chatgpt to explain the algorithm for me.

How are the weights chosen?
Kriging looks at
– Distance: closer points are more relevant
– Spatial correlation: how similar nearby points tend to be (modeled by a variogram)

The variogram describes how values “change” with distance. For example:
If points 1 meter apart are almost always similar → strong correlation
If points quickly become unrelated as you move away → weak correlation

from pykrige.ok import OrdinaryKriging
OK = OrdinaryKriging(
    x, y, values,
    variogram_model='gaussian',
    variogram_parameters=None,
    nlags=6,
    weight=True,
    enable_plotting=False,
    coordinates_type='euclidean'
)
z, ss = OK.execute('grid', gridx, gridy)
z[z < 0] = np.nan   # post-process results by masking negatives

variogram_model: controls how spatial correlation decays including linear, power, gaussian(default), spherical, exponential
variogram_parameters = {‘sill’: 0.8, ‘range’: 10, ‘nugget’: 0.1}
nlags: controls how many lag bins are used to calculate the experimental variogram. More bins is more smoother fitting, but slower.
If weight is True, It weight the variogram fitting by number of point pairs per lag.
coordinates_type
-euclidean: x, y in linear units (e.g., meters)
-geographic: lat/lon in degrees
Execute option: grid for mesh, points for specific locations

#If you want even more control (e.g., kernels, noise, trend), use GaussianProcessRegressor:

from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, WhiteKernel, ConstantKernel

kernel = ConstantKernel() * RBF(length_scale=10.0) + WhiteKernel(noise_level=0.1)
gpr = GaussianProcessRegressor(kernel=kernel)