1. Topic 6: Spatial Interpolation
第六讲
空 间 插 值

2. Box 13.1 A Survey of Spatial Interpolation among GIS Packages
Chapter Outline
13.1 Introduction
Box 13.1 A Survey of Spatial Interpolation among GIS Packages
13.2 Elements of Spatial Interpolation
Control Points
Type of Spatial Interpolation
13.3 Global Methods
Trend Surface Analysis
Regression Models
13.4 Local Method
Box 13.2 A Worked Example of Trend Surface Analysis
Thiessen Polygons
Density Estimation
Box 13.3 A Worked Example of Kernel Estimation
Inverse Distance Weighted Interpolated
Box 13.4 A Worked Example of Using the Inverse Distance Weighted Method for Estimation
Chapter 13 outline (1)

3. Box 13.5 Radial Basis Functions
Thin-plate Splines
Box 13.5 Radial Basis Functions
Box 13.6 A Worked Example of Thin-plate Splines with Tension
Kriging
Ordinary Kriging
Box 13.7 A Worked Example of Using Ordinary Kriging for Estimation
Universal Kriging
Box 13.8 A Worked Example of Using Universal Kriging for Estimation
Other Kriging Methods
13.5 Comparison of Spatial Interpolation Methods
Box 13.9 Spatial Interpolation using ArcGIS
Chapter 13 outline (2)

4. Applications: Spatial Interpolation
Task 1: Use Trend Surface Analysis for Global Interpolation
Task 2: Use Kernel Density Estimation for Local Interpolation
Task 3: Use IDW for Local Interpolation
Task 4: Compare Two Splines Methods
Task 5: Use Ordinary Kriging for Local Interpolation
Task 6: Use Universal Kriging for Local Interpolation
Task 7: Use Cokriging for Local Interpolation
Chapter 13 Exercises

5. What is Spatial Interpolation?
Spatial interpolation is the process of using points with known values to estimate values at other points. These points with known values are called known points, control points, sampled points, or observations.
In GIS applications, spatial interpolation is typically applied to a grid with estimates made for all cells. Spatial interpolation is therefore a means of converting point data to surface data so that the surface data can be used with other surfaces for analysis and modeling.

6. Spatial interpolation
A map of 105 weather stations in Idaho and their 30-year average annual precipitation values
Figure 13.1
Spatial interpolation

7. Classification of Spatial Interpolation
Global vs. Local
Exact vs. Inexact
Deterministic vs. Stochastic

8. Global vs. Local
A global interpolation method uses every known point available to estimate an unknown value.
A local interpolation method, on the other hand, uses a sample of known points to estimate an unknown value.

9. (a)
(b)
(c)
Figure 13.4
Three search methods for sample points: (a) find the closest points to the point to be estimated, (b) find points within a radius, and (c) find points within each of the four quadrants.

10. Exact vs. Inexact
Exact interpolation predicts a value at the point location that is the same as its known value. In other words, exact interpolation generates a surface that passes through the control points. In contrast, inexact interpolation or approximate interpolation predicts a value at the point location that differs from its known value.

11. Deterministic vs. Stochastic
A deterministic interpolation method provides no assessment of errors with predicted values. A stochastic interpolation method, on the other hand, offers assessment of prediction errors with estimated variances.

12. A classification of spatial interpolation methods
Global
Local
Deterministic
Stochastic
Trend surface (inexact)*
Regression (inexact)
Thiessen (exact)
Density estimation (inexact)
Inverse distance weighted (exact)
Splines (exact)
Kriging (exact)
Table 13.1
*Given some required assumptions, trend surface analysis can be treated as a special case of regression analysis and thus a stochastic method.

13. Figure 13.3
An isoline map of a third-order trend surface created from 105 points with annual precipitation values

14. Figure 13.5
The diagram shows points, Delaunay triangulation in thinner lines, and Thiessen polygons in thicker lines.

15. The simple density estimation method is used to compute the number of deer sightings per hectare from the point data.
Figure 13.6

16. The kernel estimation method is used to compute the number of sightings per hectare from the point data.
Figure 13.8

17. An annual precipitation surface map created by the inverse distance squared method
Figure 13.9

18. An isohyet map created by the inverse distance squared method
Figure 13.10
An isohyet map created by the inverse distance squared method

19. An isohyet map created by the regularized splines method
Figure 13.11
An isohyet map created by the regularized splines method

20. An isohyet map created by the splines with tension method
Figure 13.12
An isohyet map created by the splines with tension method

21. Five mathematical models for fitting semivariograms: Gaussian, linear, spherical, circular, and exponential
Figure 13.14
A semivariogram constructed from annual precipitation values at 105 weather stations in Idaho. The linear model provides the trend line.

22. An isohyet map created by ordinary kriging with the linear model
Figure 13.15
An isohyet map created by ordinary kriging with the linear model

23. Figure 13.16
The map shows the standard deviation of the annual precipitation surface created by ordinary kriging with the linear model.

24. An isohyet map created by universal kriging with the linear drift
Figure 13.18
An isohyet map created by universal kriging with the linear drift

25. Figure 13.19
The map shows the standard deviation of the annual precipitation surface created by universal kriging with the linear drift.

26. The map shows the difference between surfaces generated from the regularized splines method and the inverse distance squared method. A local operation, in which one surface grid was subtracted from the other, created the map.
Figure 13.20

27. The map shows the difference between surfaces generated from the ordinary kriging with linear model method and the regularized splines method.
Figure 13.21

28. Comparison of Local Methods
Comparison of local methods is usually based on statistical measures, although some studies have also suggested the importance of the visual quality of generated surfaces such as preservation of distinct spatial pattern and visual pleasantness and faithfulness.
Cross validation and validation are two common statistical techniques for comparison.

29. Applications 廖顺宝等. 气温数据栅格化的方法及其比较. 资源科学, 2003,25(6):83～88.
廖顺宝等. 气温数据栅格化的方法及其比较. 资源科学, 2003,25(6):83～88.
Liao Shun-bao et al. Comparison on Methods for Rasterization of Air Temperature Data . Resources Science, 2003,25(6):83～88.
龙 亮等. 基于GIS的精准农业信息流分析方法研究. 资源科学, 2003,25(6):89～95.
Long Liang et al. Information Flow and Interpolation Methods of GIS for Percision Agriculture. Resources Science, 2003,25(6):89～95

30. WEPP (Water Erosion Prediction Project)
Conservation Reserve Program (CRP), Farm Service Agency (FSA) of the U.S. Department of Agriculture
California LESA model
WEPP (Water Erosion Prediction Project)
SWAT
Better Assessment Science Integrating point and Nonpoint Sources (BASINS) system
Chapter 14 websites

31. Thank You !
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