Gridding with splines (cross-validated)

The verde.Spline has one main parameter that needs to be configured:

• damping: the regularization parameter controlling smoothness

This parameter 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 verde.SplineCV.fit, the class will:

1. Create a spline for each input parameter value

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

3. Pick the spline with the highest score

Out:

/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/spline.py:245: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  spline = Spline(**params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/spline.py:245: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  spline = Spline(**params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/spline.py:245: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  spline = Spline(**params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/sklearn/base.py:88: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  new_object = klass(**new_object_params)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/model_selection.py:784: FutureWarning: The default scoring will change from R² to negative root mean squared error (RMSE) in Verde 2.0.0. This may change model selection results slightly.
  score = estimator.score(*test_data)
/usr/share/miniconda3/envs/test/lib/python3.9/site-packages/verde/spline.py:261: FutureWarning: The mindist parameter of verde.Spline is no longer required and will be removed in Verde 2.0.0. Use the default value to obtain the future behavior.
  self.spline_ = Spline(**parameter_sets[best])

Score: 0.854

Best damping: 1e-05

import cartopy.crs as ccrs
import matplotlib.pyplot as plt
import pyproj

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))

# Fit the model on the data. Under the hood, the class will perform K-fold
# cross-validation for each the 3 parameter values and pick the one with the
# highest score.
spline.fit(projection(*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 damping parameter that produced this high score.
print("\nBest 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(
    region=region,
    spacing=spacing,
    projection=projection,
    dims=["latitude", "longitude"],
    data_names="temperature",
)
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)
plt.show()