Ran TAO [email protected] Missing Spatial Data. Examples Places cannot be reached E.g. Mountainous area Sample points E.g. Air pollution Damage of data E.g.

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Ran [email protected] Spatial Data

Examples

Places cannot be reachedE.g. Mountainous areaSample pointsE.g. Air pollutionDamage of dataE.g. historical data; falsely delete

Mecklenburg Population DensityHow to deal with itUse data of known places to predict unknown placesAdd hoc methods:replacement of the missing data by the mean or median value of the spatial surface or by a local or regional mean discard the missing data altogether and work only with the observed values. Statistical solutionsTrend-surface modelsSpatial filters and regression techniquesRandom field modelsKriging interpolation

Example Here are some sample elevation points from which surfaces were derived using the three methods

Example: IDW Done with P =2. Notice how it is not as smooth as Spline. This is because of the weighting function introduced through P

Example: SplineNote how smooth the curves of the terrain are; this is because Spline is fitting a simply polynomial equation through the points

Example: Kriging This one is kind of in betweenbecause it fits an equation through point, but weights it based on probabilities

TheissenInverse Distance Weighting

Kriging