Type of Spatial Interpolation: Global vs. Local, Exact vs. Inexact and Deterministic vs. Stochastic (Especially for GATE-Geospatial 2022)

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Global vs. Local Interpolation

Diagram Shows First Spatial Interpolation Methods

Global interpolation uses every known point available to estimate an unknown value. Local interpolation uses a sample of known points to estimate an unknown value. This method is designed to capture the local or short-range variation.

A global interpolation method used every known point available to estimate an unknown value. A global interpolation method, on the other hand, uses a sample of known points to estimate an unknown value. Because the difference between the two groups lies in the number of control points used in estimation, one may view the scale from global to local as a continuum.

Conceptually, a global interpolation method is designed to capture the general trend of the surface and a local or short-range variation. For many phenomena, it is more efficient to estimate the unknown value at a point using a local method than a global method.

Exact vs. Inexact Interpolation

Second, spatial interpolation methods can be grouped into exact and inexact interpolation.

Diagram Shows Second Spatial Interpolation Methods

1. Exact Interpolation

An exact interpolation predicts a value at the point location that is the same as is known value. In other words, exact interpolation generates a surface that passes through the control points.

2. Inexact Interpolation

In contrast, inexact interpolation, or approximate interpolation, predicts a value at the point location that differs from its known value.

Image Shows Exact Interpolation and Inexact Interpolation

Deterministic vs. Stochastic

Spatial interpolation methods may be deterministic or stochastic.

Diagram Shows Third Spatial Interpolation Methods

1. Deterministic Interpolation

A deterministic interpolation method provides no assessment of errors with predicted values.

2. Stochastic Interpolation

A stochastic interpolation method, on the other hand, offers assessment of prediction errors with estimated variances.

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