1. Ran TAO rtao2@uncc.edu Missing Spatial Data

2. 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

3. 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

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

5. 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

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

7. Example: Kriging This one is kind of in between—because it fits an equation through point, but weights it based on probabilities

8. Theissen

9. Inverse Distance Weighting

10. Kriging