Ran TAO Missing Spatial Data

Examples Places cannot be reached E.g. Mountainous area Sample points E.g. Air pollution Damage of data E.g. historical data; falsely delete Mecklenburg Population Density

How to deal with it Use data of known places to predict unknown places Add 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 solutions Trend-surface models Spatial filters and regression techniques Random field models Kriging 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: Spline Note 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 between—because it fits an equation through point, but weights it based on probabilities

Theissen

Inverse Distance Weighting

Kriging