Spatial interpolation

In your life as a spatial data scientist, you will find yourself in a situation where you have plenty of data to work with, just linked to different geometries or representing slightly different locations that you need. When this happens, you need to interpolate the data from one set of geometries, on which the data is shipped, to the other, the one you are interested in.

Any interpolation method is necessarily an approximation but some are better than others.

import geopandas as gpd
import tobler
import pyinterpolate
import numpy as np
import matplotlib.pyplot as plt

from libpysal import graph
from sklearn import neighbors
from scipy import interpolate

/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/distance/distance.py:176: SyntaxWarning: invalid escape sequence '\s'
  """Function calculates distance between two blocks based on how they are divided (into the point support grid).
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:37: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates circular model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:93: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates cubic model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:167: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates exponential model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:212: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates gaussian model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:259: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates linear model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:310: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates power model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/theoretical/models/variogram_models.py:362: SyntaxWarning: invalid escape sequence '\g'
  """Function calculates spherical model of semivariogram.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/utils/metrics.py:14: SyntaxWarning: invalid escape sequence '\s'
  """Function calculates forecast bias of prediction.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/utils/metrics.py:53: SyntaxWarning: invalid escape sequence '\s'
  """Function calculates forecast bias of prediction.
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/utils/metrics.py:93: SyntaxWarning: invalid escape sequence '\s'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/utils/metrics.py:135: SyntaxWarning: invalid escape sequence '\s'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/utils/metrics.py:206: SyntaxWarning: invalid escape sequence '\s'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/regularization/block/inblock_semivariance.py:48: SyntaxWarning: invalid escape sequence '\g'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/regularization/block/avg_inblock_semivariances.py:53: SyntaxWarning: invalid escape sequence '\g'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/variogram/regularization/deconvolution.py:783: SyntaxWarning: invalid escape sequence '\g'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/kriging/models/block/weight.py:14: SyntaxWarning: invalid escape sequence '\g'
  """
/home/runner/work/sds/sds/.pixi/envs/default/lib/python3.12/site-packages/pyinterpolate/kriging/models/block/weight.py:123: SyntaxWarning: invalid escape sequence '\g'
  """

This chapter of the course covers two types of interpolation - from one set of polygons to another set of polygons, and from a sparse set of points to other locations in the same area.

Areal interpolation and dasymetric mapping

The first use case is the interpolation of data from one set of geometries to the other one, otherwise known as areal interpolation or dasymetric mapping.

Data zones and H3

You are already familiar with the Scottish Index of Multiple Deprivation, so let’s use it as an example of areal interpolation. Load the subset of SIMD 2020 for the City of Edinburgh.

simd = gpd.read_file(
    "https://martinfleischmann.net/sds/interpolation/data/edinburgh_simd_2020.gpkg"
)
simd.head(2)

	DataZone	DZName	LAName	SAPE2017	WAPE2017	Rankv2	Quintilev2	Decilev2	Vigintilv2	Percentv2	...	CrimeRate	CrimeRank	HouseNumOC	HouseNumNC	HouseOCrat	HouseNCrat	HouseRank	Shape_Leng	Shape_Area	geometry
0	S01008417	Balerno and Bonnington Village - 01	City of Edinburgh	708	397	5537	4	8	16	80	...	86	5392.0	17	8	2%	1%	6350.0	20191.721420	1.029993e+07	POLYGON ((315157.369 666212.846, 315173.727 66...
1	S01008418	Balerno and Bonnington Village - 02	City of Edinburgh	691	378	6119	5	9	18	88	...	103	5063.0	7	10	1%	1%	6650.0	25944.861787	2.357050e+07	POLYGON ((317816 666579, 318243 666121, 318495...

2 rows × 52 columns

Alternative

Instead of reading the file directly off the web, it is possible to download it manually, store it on your computer, and read it locally. To do that, you can follow these steps:

Download the file by right-clicking on this link and saving the file
Place the file in the same folder as the notebook where you intend to read it
Replace the code in the cell above with:

simd = gpd.read_file(
    "edinburgh_simd_2020.gpkg",
)

Get an interactive map with one of the variables to get more familiar with the data.

simd[["EmpNumDep", "geometry"]].explore("EmpNumDep", tiles="CartoDB Positron")

Make this Notebook Trusted to load map: File -> Trust Notebook