Interpolation & Surfaces

A continuous surface from scattered samples, with its support attached.

The interpolation path, from guessing between samples to cross-validating the surface you built. a continuous surface from scattered samples, with its support attached1the guess betweenand where to measure2IDWand its bullseyes3the variogramhow far a sample reaches4krige & validatewith the varianceIt ends in cross-validation because an interpolated surface is a claim, and claims get checked

Interpolation produces a value for every cell, including the cells a kilometre from the nearest observation, and the output gives no hint which is which. These guides cover the methods — IDW, kriging, TIN and areal interpolation — but spend as much time on what they cannot tell you: why cross-validation is optimistic where the samples are dense, why kriging variance is a map of sample geometry rather than of error, why a finer cell size buys nothing, and how to ship a distance-to-nearest-sample raster so the reader can see where the surface is measurement and where it is arithmetic.

The variogram guide in the middle is the hinge. Before it, interpolation is a choice of formula; after it, it is a statement about how far a measurement reaches, which is what lets kriging report a variance and what makes the cross-validation at the end mean something.

The full path, in order

The concepts underneath the work, then each task, then the errors that task produces. Work down, or jump to the step you need.

  1. Sample Design Explained: Where to Measure sample design explained 🧭 Concept
  2. How to Interpolate Points to a Grid with IDW in Python idw interpolation python ⚙️ How-To
  3. My IDW Surface Is Full of Bullseyes idw bullseyes 🔧 Fix
  4. The Variogram Explained: How Far Does a Measurement Reach variogram explained 🧭 Concept
  5. How to Fit a Variogram and Krige a Surface in Python kriging python ⚙️ How-To
  6. My Kriging Fit Fails or Returns a Flat Surface kriging fit fails flat surface 🔧 Fix
  7. How to Build a TIN and Interpolate Elevations tin interpolation python ⚙️ How-To
  8. IDW, Kriging, Splines or TIN? Choosing an Interpolator choosing an interpolator explained 🧭 Concept
  9. How to Cross-Validate an Interpolated Surface cross validate interpolation python ⚙️ How-To
  10. How to Choose a Cell Size for an Interpolated Surface choose cell size interpolation ⚙️ How-To
  11. My Interpolated Surface Extends Far Beyond the Data interpolation extends beyond data 🔧 Fix
  12. How to Interpolate to Polygons Instead of a Grid areal interpolation python ⚙️ How-To

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