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Point-surface interpolation. Day 1: point-surface interpolation. Principles Tobler’s First Law of Geography and spatial interpolation Classification of methods Common methods Thiessen polygons Trend surfaces Inverse distance weighting (IDW) TINs Geostatistical Analyst in ArcMap.

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## Point-surface interpolation

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**Day 1: point-surface interpolation**• Principles • Tobler’s First Law of Geography and spatial interpolation • Classification of methods • Common methods • Thiessen polygons • Trend surfaces • Inverse distance weighting (IDW) • TINs • Geostatistical Analyst in ArcMap**Principles of interpolation**• Tobler’s First Law of Geography • “Everything is related to everything else, but near things are more related than distant things.”1 • Spatial interpolation • The procedure of estimating the values of properties at unsampled sites within an area covered by existing observations • important in addressing problem of data availability • quick fix for partial data coverage • interpolation of point data to raster surface • role of filling in the gaps between observations 1W. R. Tobler, (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(2): 234-240.**Classification of methods**• Methods of spatial interpolation: • many different methods available • e.g. Thiessen polygons • e.g. Inverse distance weighting • classification according to: • exact or approximate • deterministic or stochastic • local or global • gradual or abrupt • Remember! Tobler’s First Law of Geography**Common methods**• Thiessen polygons • Gradual or abrupt? • Exact or approximate? • Local or global? • Deterministic or stochastic?**Common methods**• Trend surfaces • Gradual or abrupt? • Exact or approximate? • Local or global? • Deterministic or stochastic?**Common methods**• Inverse Distance Weighting (IDW) • Gradual or abrupt? • Exact or approximate? • Local or global? • Deterministic or stochastic?**Common methods**• Triangulated Irregular Networks (TINs) • Gradual or abrupt? • Exact or approximate? • Local or global? • Deterministic or stochastic?**Geostatistical analyst**• Geostatistical analyst in ArcMap**Practical exercise**• Hands-on Exercise #2 • Interpolating point data in ArcGIS

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