School of Geography FACULTY OF ENVIRONMENT 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

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 1 W. R. Tobler, (1970) "A computer movie simulating urban growth in the Detroit region". Economic Geography, 46(2):

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