1. Labs Labs 5 & 6 are on the website. Lab 5 is due Tuesday (Oct. 31st).
Lab 6 is due Thursday (Nov. 2nd).
No class Tuesday.
Lecture 12B

2. Project Progress Report
Due: Nov. 9th
Description of what you have accomplished to date and your data dictionary.
The data dictionary and data sources will be included as appendices to your final project report.
Lecture 12B

3. The Table Inventory
BIOLOGICAL INVENTORY
Comprehensive Inventory Program for Birds at Six Pennsylvania National Parks,
BirdEvents
Events
Locations
LocCanopy
LocGroundCover
LocHerbVegHeight
LocOverstory
LocUnderstory&Shrub
OwlSurvey
PointCountSurvey
RaptorSurvey
RiparianBirdSurvey
RoadSurvey
ShrikeSurvey
LinkObservers
BirdSpecies
ParkName
Lecture 12B

4. BirdEvents Table Field Name Type Width Field Description EventID Text50
Sampling Event ID such as EISE_BIRDS_SHRIKE_2000-May-15_00:01 where EISE=park code, BIRDS=general survey type, SHRIKE=specific survey type, 2000-May-15=date, 00:01=time where applicable or 00:00 where the last digit(s) are the survey point
Temp
Double 8
Temperature in degrees Fahrenheit
Wind
Wind speed in miles per hour
Clouds
Percentage of cloud cover
Precip
Indication of precipitation: 0 = none and 1 = light snow during winter or mist to light drizzle during spring, breed, or fall.
Snow
Long 4
Snow depth in centimeters
Lecture 12B

5. Appendices to Final Report
Appendix A
Data used in project and its source.
Appendix B
Table Inventory
Appendix C
Data Dictionary
Lecture 12B

6. Spatial Estimation Chapter 12 – Part 2
Lecture 12B

7. The Farm
Lecture 12B

8. Fixed-Radius – Local Averaging
INTERPOLATION
Fixed-Radius – Local Averaging
Lecture 12B

9. Fixed Radius
Radius 0.17
Radius 0.34
Radius 0.68
Lecture 12B

10. INTERPOLATION Inverse Distance Weighted (IDW)
Zi is value of known point
Dij is distance to known point
Zj is the unknown point
n is a user selected exponent
Lecture 12B

11. IDW
Power 1
Power 2
Power 4
Lecture 12B

12. Global Mathematical Functions Polynomial Trend Surface
Lecture 12B

13. Polynomial Trend Function
Order 1
Order 2
Order 4
Order 8
Lecture 12B

14. Kriging Kriging (weighted average technique)
Measures distances between all possible pairs of sample points - Lags
Models the spatial autocorrelation for the surface
Tailors its calculations to the surface
Analyzing all the data points to find out how much autocorrelation they exhibit
Factors that information into the weighted average estimation
Incorporates trends as expressed through the data's variogram
Lecture 12B

15. Kriging - Quantifying Spatial Autocorrelation
Lecture 12B

16. Kriging Kriging (weighted average technique) The variogram model
Mathematically specifies the spatial variability
Mathematically specifies the resulting grid
Geostatistics assume that adjoining points are spatially related
Variogram models the correlation between spatial variables
Modeling the variogram
Allows quantification of the correlation between any two values separated by a distance (lag)
Uses this to apply the most appropriate interpolation procedure
Lecture 12B

17. Kriging Interpolating a surface using Kriging
Spatial autocorrelation is determined for the sample point set
Best-fit model is automatically applied to the data
Unknown values are predicted
Lecture 12B

18. Kriging - Semivariogram Model
(h)
Nugget
Partial
Sill
Range
Lecture 12B

19. Kriging - Fitting a Semivariogram Model
Lecture 12B

20. Kriging
Typically the initial kriged surface is considered a first draft
Surface against which future iterations can be compared
Kriging methods
Ordinary Kriging
Assumes there is no trend in the data
Highly reliable and is recommended for most data sets
Universal Kriging
Assumes that there is an overriding trend in the data
Lecture 12B

21. Kriging
A surface created with Kriging can exceed the value range of the sample points but will not pass through the points.
Lecture 12B

22. Kriging
Simple Kriging
Ordinary Kriging
Universal Kriging
Lecture 12B

23. Core Area Mapping Mean Center and Mean Circle Convex Hulls
Kernel Mapping
Time-Geographic Density Mapping
Lecture 12B

24. Mean Center and Mean Circle
The mean center is the average of the X and Y coordinates of the sample points.
Mean circles are defined by a radius measured from the mean center.
Farthest distance
Average distance of sample points
Or some other statistical measure
Lecture 12B

25. Mean Center and Mean Circle
Advantages:
Simplicity
Ease of contruction
Disadvantage
They assume a uniformly circular shape for the core area.
Lecture 12B

26. Convex Hulls (Minimum Convex Polygon)
The simplest way to identify core areas with an irregular shape.
The smallest polygon created by edges that completely enclose a set of points and for which all exterior angles are greater than or equal to 180o.
Concave – some angles less than 180o.
Convex.
Lecture 12B

27. Kernel Mapping
Uses a set of sample locations to estimate a continuous density surface.
Based on a density distribution for each sample.
Lecture 12B

28. Results of Kernel Mapping Depends on Method
Lecture 12B

29. Kernel Mapping
Polynomial Order 0
Polynomial Order 1

30. Problems in Interpolation
When performing any of the methods of interpolation
Four factors need to be considered:
The number of control points
The location of control points
The problem of saddle points
The area containing data points
Lecture 12B

31. Problems in Interpolation
The number / location of control points
Generally it is safe to say that the more sample points…
More accurate the interpolation will be
More like the surface will be our model
Eventually reach a point of diminishing returns
Increases in computation time
Too much data will tend to produce unusual results
Data clusters may create an unevenly generalized surface
Having more data points does not always improve accuracy
The more complex the surface, the more data points you need
Sure of capturing the necessary detail
Lecture 12B

32. Problems in Interpolation
 The saddle-point problem
Both members of one pair of diagonally opposite Z values are located below and both members of the second pair lie above the value the interpolation algorithm is attempting to solve
This generally occurs only in linear interpolation
Any distance weighting will likely solve the problem
Software is presented with two probable solutions
Average the interpolated values produced
Place this average value at the center of the diagonal
Lecture 12B

33. Problems in Interpolation
The area containing data points
Interpolation data must have control points on all sides
Need to interpolate points near the margins of the study area
The map border precludes any data points beyond the margin
 In the absence of these surrounding data points
Algorithm will use whatever is available 
The interpolation is performed…it will tend to underestimate
Solution…extend the borders of the elevation coverage
Margins of the study area can be used to shave the edges
Extending the margins 10% will guarantee good results
Lecture 12B

34. Assignment
Read Chapter 12
Lecture 12B