05. Interpolation - Multiple Linear Regression#

In this tutorial, we’ll cover the interpolation of point data using the Multiple Linear Regression (MLR) methodology, available in PyMica as mlr. This methodology requires location (lon and lat), predictor variables such as altitude (altitude) or distance to coast line (among others), and value to interpolate.

We’ll use Meteorological Service of Catalonia sample data to demonstrate how to apply this interpolation technique. Therefore, we need to import the required modules. First, we need to load observation data and also the PyMica class.

import json

from pymica.pymica import PyMica

Let’s call the PyMica class with the appropriate parameters, setting the methodology to mlr and the configuration dictionary as follows:

config_file = 'sample-data/configuration_sample.json'

with open('sample-data/configuration_sample.json', 'r') as f_p:
    config = json.load(f_p)

config['mlr']

{'clusters': 'None',
 'variables_files': {'altitude': 'sample-data/explanatory/cat_dem_25831.tif',
  'dist': 'sample-data/explanatory/cat_distance_coast.tif'},
 'interpolation_bounds': [260000, 4488100, 530000, 4750000],
 'resolution': 270,
 'EPSG': 25831}

where:

  • clusters: set to None as no clusters will be used.

  • variables_files: dictionary with predictor variables as keys and their corresponding GeoTIFF path as values. Here, altitude as altitude and distance to coast line as dist.

  • interpolation_bounds: [minimum_x_coordinate, minimum_y_coordinate, maximum_x_coordinate, maximum_y_coordinate], it must be the same as the variable files.

  • resolution: spatial resolution.

  • EPSG: EPSG projection code.

With all these parameters and configurations set, let’s initialize the PyMica class with the methodology set to ‘mlr’.

mlr_method = PyMica(methodology='mlr', config=config_file)

Now that we have the interpolator set, we can input some data for interpolation. We will use data from the Meteorological Service of Catalonia AWS network.

with open('sample-data/data/smc_data.json', 'r') as f_p:
    data = json.load(f_p)

data[0]

{'id': 'C6',
 'value': 8.8,
 'lon': 0.9517200000000001,
 'lat': 41.6566,
 'altitude': 264.0,
 'dist': 0.8587308027349195}

As we can see, the first element of the data meets the requirements of PyMica input data and has the same predictor variables as the ones provided in the configuration dictionary. Therefore, we only need to call the interpolate method from the mlr_method interpolator class.

data_field = mlr_method.interpolate(data)

Now, we can get a quick look of the data_field array using matplotlib.

import matplotlib.pyplot as plt

plt.imshow(data_field)
plt.colorbar(label='Air temperature (\u00b0C)')
_images/05_howto_int_mlr_12_1.png

Finally, we can save the result into a GeoTIFF file using pymica.pymica.PyMica.save_file() from PyMica class.

mlr_method.save_file("sample-data/results/mlr.tif")

We have now completed this tutorial on how to interpolate station data using the mlr methodology. You can experiment with changing the variables_files in the configuration dictionary to observe how the behavior of each variable affects the interpolation result.