1. Steve Kopp and Steve Lynch
July 2011
Creating Surfaces
Steve Kopp and Steve Lynch

2. Overview
Learn the types of surfaces and the data structures used to store them
Emphasis on surface interpolation
Understand how interpolators work
Learn the interpolation workflow
Understand how to choose an appropriate interpolation technique and its parameters
Additional useful tips and notes
Questions / Answers

3. Types of Surfaces Elevation Soil chemistry Water quality Population
Income
Disease occurrence

4. What kind of surfaces do you create?
What is the source data?
Points, lines, polygons, raster
Is quality a concern
What is the phenomena?
Measurements, counts, something else
Anything special or odd about it?
Discontinuous
Highs and lows sampled or not
What do you want/expect for a result?
Raster, TIN, contour lines or polygons, estimates at points, estimate of surface quality

5. Storing surfaces in ArcGIS78 74 72 67 69 56 71 49 58 50 64 53 44 55 37 22 38 31 48 24 68 61 47 34 21 12 16 11 19 46
Raster
TIN / Terrain
Points
LAS
Isolines / Contours
Geostatistical Layer
Note: in ArcGIS 10.1 LAS files are supported for direct use in Terrains and Mosaic Datasets

6. TIN and Terrain Maintain accuracy of measured locations
Discontinuities are handled with breaklines
Hard breaklines (cliff, fault)
Soft breaklines (road, stream)

7. Where do I find these capabilities?
Spatial Analyst – raster, contour
3D Analyst – raster, contour, TIN, terrain
Geostatistical Analyst – raster, contour line, filled contour polygon, point, geostatistical layer

8. 2 common types of surfaces
Density surfaces of count per unit area
Interpolated surfaces of measured quantities
This session is about interpolation

9. Density Density surfaces are maps of magnitude per unit area
Count occurrences of a phenomena within an area and distribute it through the area.
Simple Density and Kernel Density
Use points or lines as input.
Population per Km2
Road density per Mi2

10. Interpolation
Interpolation is the process of taking measurements of a continuous phenomena and transforming it into a continuous surface representation
Estimating new values at unsampled locations

11. Types of input for Interpolation
Points
Continuous values
LAS
Polylines
Contours
Polygon
Centriod
Areal Interpolation
Dasymetric mapping
Raster
Fill in missing values
Change resolution through Resampling or Interpolation
Modify surface with supplemental data

12. Interpolation Workflow
Understand your data
Choose an appropriate interpolator and parameters
Evaluate the surface
Repeat…

13. Exploratory Spatial Data Analysis
Where is the data located?
What are the values of the data points?
How does the location of a point relate to its value?

14. Understanding your data
Exploratory Spatial Data Analysis (ESDA)
Outliers
Incorrect data or the most influential data ?
Spatial Dependency
If not, why use Geostatistics ?
Distribution
How close to Gaussian distribution ?
Stationarity
Data preprocessing if non-stationary ?

15. Exploring your Data
Demonstration

16. Two parts of all interpolators
Neighborhood definition – where do I find known points to estimate a new value
Estimation function – from those points, how do I calculate a new value

17. Searching neighborhood
Variable number of points
Specify a maximum search distance and number of points, a smaller number of points may be used.
Can result in NoData cells
Fixed number of points
Specify a minimum number of points, and the search distance is increased until that number of points is found.
Tobler’s first law of geography applies "Everything is related to everything else, but near things are more related than distant things."

18. Multiple sectors - Geostatistical Analyst
Multi-sector neighborhoods are very useful for data with an irregular spatial distribution or clustering

19. Choosing an appropriate interpolation tool
Natural Neighbors
Minimum Curvature Spline
Spline with Barriers
Radial Basis Functions
TopoToRaster
Local Polynomial
Global Polynomial
Diffusion Interpolation with Barriers
Kernel Interpolation with Barriers
Inverse Distance Weighted
Kriging
Cokriging
Moving Window Kriging
Geostatistical Simulation

20. Considerations in choosing an interpolator
Standard error of prediction
Stationarity
Normally distributed
Exact interpolator
Support barriers
Speed

21. The simplest, safest interpolator – Natural Neighbor

22. Local Polynomial Interpolation (LPI)
Sta

23. Easy Interpolations of Ozone Concentration
Demonstration

24. You want a prediction standard error map
Choose from:
Local Polynomial Interpolation
Kernel Interpolation
Kriging

25. You want an exact interpolator that honors the points
Choose from:
IDW
Natural Neighbors
Spline
Radial Basis Function

26. The high and low values have not been sampled… and are important
Do not use
Natural Neighbors
IDW

27. You want smooth interpolation
10.1
10.3
12.5
9.1
Unlike smoothing the output,
this method modifies the weights
Smooth interpolation is an option in the Geostatistical Analyst interpolators

28. When to use Kriging Assumptions:
Spatially correlated
Stationary *
Normally distributed
Want prediction and prediction standard error

29. You know the phenomena is correlated with something measured more
If you have a sparsely measured variable such as temperature, which is correlated with another variable such as elevation that has much more sampling…
Use CoKriging

30. Kriging Ozone Concentration
Demonstration

31. There are cliffs, faults, or barriers in my data
IDW
Spline with Barriers
Kernel Interpolation with Barriers
Diffusion Interpolation with Barriers

32. Interpolation with Barriers
Non Euclidean distance
Line of sight ?
Barrier ?
Barrier
IDW
Kernel Interpolation with Barriers
Diffusion Interpolation with Barriers
Spline with Barriers
Cost Raster

33. Geologic Interpolation with barriers
Demonstration

34. For contour input, and creating hydrologic DEMs
Topo To Raster
ANUDEM
Inputs
Spot heights
Contours
Streams
Sinks
Lakes
Optional drainage enforcement

35. TopoToRaster for DEM Creation
Demonstration

36. How good is your surface?
Standard Error surface
Cross Validation
Subset Features

37. Subset Features

38. Your input is equally spaced points
If input points are already equally spaced on a regular grid, you probably don’t need to interpolate, just use PointsToRaster

39. You have many input points per output cell
If your data is highly oversampled, you probably do not need to interpolate, you can just use the PointsToRaster tool, and select the statistic of interest.

40. Working with VERY large input point data
Point To Raster
Most frequent
Sum, mean std. deviation
Minimum, maximum, range, count
Smaller input extent
Subset Features

41. Handling Coincident/Duplicate Points

42. Why don’t all softwares create the same result?
12.2
11.2
9.7
10.1
Equidistant points
Duplicate points
Zeros or Nulls

43. New in 10.1 for surface creation
Direct read and surface rendering of LAS files
TopoToRaster update (ANUDEM 5.3)
Areal Interpolation
Empirical Bayesian Kriging

44. Better Interpolation and Heat Maps
Statistically robust method for making heat maps from polygons
Obesity by school zone
Obesity surface and error surface
Obesity by census block
Statistically robust method for aggregating back to other polygons
Easier kriging interpolation that works better with large spatial extents

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