Inverse Distance Weighting (IDW)
Inverse Distance Weighting (IDW) Interpolation · Also known as: IDW, inverse distance interpolation, Shepard's method, ters mesafe ağırlıklı enterpolasyon
Inverse distance weighting is a simple, deterministic method for estimating values at unsampled locations by taking a weighted average of nearby measured points, where closer points carry more weight. Introduced by Donald Shepard in 1968, it embodies the first law of geography — near things are more related than distant things — and is one of the most widely used interpolation methods in GIS for mapping continuous fields such as rainfall, elevation, or pollution from scattered samples.
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When to use it
Use IDW for quick, transparent interpolation of a reasonably densely and evenly sampled continuous variable when you want a simple method with no statistical assumptions and no variogram modelling — common for rainfall, temperature, elevation, soil, and pollution surfaces in GIS. It is fast, intuitive, and guarantees predictions within the observed data range. Its weaknesses: it produces characteristic 'bullseye' artefacts around isolated points, cannot predict beyond the observed value range, gives no measure of prediction uncertainty, and is sensitive to the power and search-neighbourhood settings and to uneven sampling. When you need uncertainty estimates, can model spatial correlation, or have anisotropy/trend, kriging (ordinary, universal, or cokriging) is the statistically grounded alternative.
Strengths & limitations
- Simple, fast, and easy to explain — a transparent distance-decay average.
- Requires no distributional assumptions or variogram modelling.
- Exact interpolator: the surface honours the measured sample values.
- Predictions stay within the observed value range, avoiding wild extrapolation.
- Produces 'bullseye' artefacts around isolated data points.
- Cannot predict values beyond the observed minimum and maximum.
- Gives no estimate of prediction uncertainty (unlike kriging).
- Sensitive to the power parameter, search neighbourhood, and uneven sampling.
Frequently asked
How does IDW differ from kriging?
IDW is deterministic — it weights samples purely by distance and makes no statistical model of spatial correlation, so it gives no uncertainty estimate. Kriging models the spatial correlation via a variogram, producing both predictions and a prediction variance, and can incorporate trend (universal kriging) or covariates (cokriging). IDW is simpler and faster; kriging is statistically richer.
What does the power parameter p control?
It controls how quickly a point's influence decays with distance. A high power concentrates weight on the nearest samples, producing sharper, more localized surfaces with pronounced bullseyes; a low power spreads influence to farther points, giving smoother surfaces. The power is commonly tuned by cross-validation.
Why does my IDW map have bullseyes?
Because IDW is an exact interpolator that strongly weights the nearest sample, isolated data points create concentric circular patterns around themselves. Denser, more even sampling and a lower power reduce the effect; kriging or splines avoid it more naturally.
Sources
- Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 23rd ACM National Conference, 517–524. DOI: 10.1145/800186.810616 ↗
- Li, J., & Heap, A. D. (2008). A review of spatial interpolation methods for environmental scientists. Geoscience Australia Record 2008/23. link ↗
How to cite this page
ScholarGate. (2026, June 2). Inverse Distance Weighting (IDW) Interpolation. ScholarGate. https://scholargate.app/en/spatial-analysis/inverse-distance-weighting
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- CokrigingSpatial analysis↔ compare
- Geographically Weighted RegressionSpatial analysis↔ compare
- Universal KrigingSpatial analysis↔ compare