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Rust Interpolate

A learning project to implement geospatial interpolation using ordinary kriging in Rust.

Specifically my goals are:

  • Parse a file of XYZ points representing observations
  • Create a spatial index of the observations
  • Create an empirical semivariogram from a sample of the input observations
  • Create a mathematical model of the empirical semivariogram
  • Estimate a raster grid covering the data extent
    • For every unknown point in the grid, use the model to predict the value and variance
  • Write the predicted grid to a raster or vector file format.
    • For now, stick to simple human readable text formats.

Kriging

Kriging is a geostatistical technique for predicting the value of a spatial phenonmenon at an unobserved location. Kriging is a form of interpolation that takes into account the spatial relationship between the data and provides, along with an estimated value, the variance or uncertainty in the value.

Principles of Geographical Information Systems by Burrough and McDonnel (1998) was my primary source of inspiration and the gory mathematical details, particularly Chapters 5 and 6.

Build

cargo build --release

Test

Input: a text file with X, Y and Z values, tab-delimited. (see test.xyz)

Outputs:

  1. Prediction grid in ArcInfo ASCII Grid format
  2. Standard deviation grid in ArcInfo ASCII Grid format
  3. Prediction points as geojson features (contains both predicted value and standard deviation as properties)

time ./target/release/rust-interpolate test2.xyz

The stderr logs

Parse XYZ file...
Create spatial index and removing dups...
extent [-125.0029566667, 41.481515, -124.66719, 42.0182683333]
Empirical semivariogram ...
Making predictions on grid... 256 x 410 with cellsize 0.0013115885417968598
./target/release/rust-interpolate --points test.xyz --range 0.2 >   20.67s user 0.00s system 99% cpu 20.673 total

➥ gdalinfo /tmp/estimates.grd -mm
Driver: AAIGrid/Arc/Info ASCII Grid
Files: /tmp/estimates.grd
Size is 256, 410
Origin = (-125.002956666700001,42.018268333300000)
Pixel Size = (0.001311588541797,-0.001311588541797)
Corner Coordinates:
Upper Left  (-125.0029567,  42.0182683)
Lower Left  (-125.0029567,  41.4805170)
Upper Right (-124.6671900,  42.0182683)
Lower Right (-124.6671900,  41.4805170)
Center      (-124.8350733,  41.7493927)
Band 1 Block=256x1 Type=Float32, ColorInterp=Undefined
    Computed Min/Max=-1124.295,-556.319
  NoData Value=-9999

Maybe, someday?

This is a side project so I'm not likely to get around to this anytime soon. I welcome ideas and contributions though!

  • Fit the model automatically, see scipy
  • Support other models: Exponential, Linear, Gaussian, see scikit-gstat
  • Cross-validation, MSPE on a subset of the original (removed prior to constructing empirical semivariogram)
  • Parallel processing
  • Python wrapper
  • Refactor API and write unit tests
  • Other distance metrics: geodesic distance, great circle distance, ECEF 3D distance
  • Co-kriging
  • Trend elimination (ie Universal Kriging)
  • Subsetting and combining overlapping variogram models
  • Anisotropy
  • Bayesian estimation

For a more complete implementation in Rust, check out the GeoStat framework's GSTools-Core.