Gridding with splines (cross-validated)

The verde.Spline has two main parameters that need to be configured:

  1. mindist: the minimum distance between forces and data points

  2. damping: the regularization parameter controlling smoothness

These parameters can be determined through cross-validation (see Model Selection) automatically using verde.SplineCV. It is very similar to verde.Spline but takes a set of parameter values instead of only one value. When calling, the class will:

  1. Create a spline for each combination of the input parameter sets

  2. Calculate the cross-validation score for each spline using verde.cross_val_score

  3. Pick the spline with the highest score



Score: 0.853

Best spline configuration:
  mindist: 50000.0
  damping: 0.001
/home/travis/build/fatiando/verde/examples/ UserWarning: Tight layout not applied. The left and right margins cannot be made large enough to accommodate all axes decorations.

import matplotlib.pyplot as plt
import as ccrs
import pyproj
import numpy as np
import verde as vd

# We'll test this on the air temperature data from Texas
data = vd.datasets.fetch_texas_wind()
coordinates = (data.longitude.values, data.latitude.values)
region = vd.get_region(coordinates)

# Use a Mercator projection for our Cartesian gridder
projection = pyproj.Proj(proj="merc", lat_ts=data.latitude.mean())

# The output grid spacing will 15 arc-minutes
spacing = 15 / 60

# This spline will automatically perform cross-validation and search for the optimal
# parameter configuration.
spline = vd.SplineCV(dampings=(1e-5, 1e-3, 1e-1), mindists=(10e3, 50e3, 100e3))

# Fit the model on the data. Under the hood, the class will perform K-fold
# cross-validation for each the 3*3=9 parameter combinations and pick the one with the
# highest R² score.*coordinates), data.air_temperature_c)

# We can show the best R² score obtained in the cross-validation
print("\nScore: {:.3f}".format(spline.scores_.max()))

# And then the best spline parameters that produced this high score.
print("\nBest spline configuration:")
print("  mindist:", spline.mindist_)
print("  damping:", spline.damping_)

# Now we can create a geographic grid of air temperature by providing a projection
# function to the grid method and mask points that are too far from the observations
grid_full = spline.grid(
    dims=["latitude", "longitude"],
grid = vd.distance_mask(
    coordinates, maxdist=3 * spacing * 111e3, grid=grid_full, projection=projection

# Plot the grid and the original data points
plt.figure(figsize=(8, 6))
ax = plt.axes(projection=ccrs.Mercator())
ax.set_title("Air temperature gridded with biharmonic spline")
ax.plot(*coordinates, ".k", markersize=1, transform=ccrs.PlateCarree())
tmp = grid.temperature.plot.pcolormesh(
    ax=ax, cmap="plasma", transform=ccrs.PlateCarree(), add_colorbar=False
plt.colorbar(tmp).set_label("Air temperature (C)")
# Use an utility function to add tick labels and land and ocean features to the map.
vd.datasets.setup_texas_wind_map(ax, region=region)

Total running time of the script: ( 0 minutes 0.558 seconds)

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