Topic 6: Spatial Interpolation

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

2. Chapter Outline • 13.1 Introduction • Box 13.1 A Survey of Spatial Interpolation among GIS Packages • 13.2 Elements of Spatial Interpolation • 13.2.1 Control Points • 13.2.2 Type of Spatial Interpolation • 13.3 Global Methods • 13.3.1 Trend Surface Analysis • 13.3.2 Regression Models • 13.4 Local Method • Box 13.2 A Worked Example of Trend Surface Analysis • 13.4.1 Thiessen Polygons • 13.4.2 Density Estimation • Box 13.3 A Worked Example of Kernel Estimation • 13.4.3 Inverse Distance Weighted Interpolated • Box 13.4 A Worked Example of Using the Inverse Distance Weighted Method for Estimation

3. 13.4.4 Thin-plate Splines • Box 13.5 Radial Basis Functions • Box 13.6 A Worked Example of Thin-plate Splines with Tension • 13.4.5 Kriging • 13.4.5.1 Ordinary Kriging • Box 13.7 A Worked Example of Using Ordinary Kriging for Estimation • 13.4.5.2 Universal Kriging • Box 13.8 A Worked Example of Using Universal Kriging for Estimation • 13.4.5.3 Other Kriging Methods • 13.5 Comparison of Spatial Interpolation Methods • Box 13.9 Spatial Interpolation using ArcGIS

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

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

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) 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 deterministicinterpolation method provides no assessment of errors with predicted values. A stochasticinterpolation method, on the other hand, offers assessment of prediction errors with estimated variances.

12. A classification of spatial interpolation methods *Given some required assumptions, trend surface analysis can be treated as a special case of regression analysis and thus a stochastic method.

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

14. 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.

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

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

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

19. An isohyet map created by the regularized splines method

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

21. Five mathematical models for fitting semivariograms: Gaussian, linear, spherical, circular, and exponential 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

23. 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

25. 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.

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

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. 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. Conservation Reserve Program (CRP), Farm Service Agency (FSA) of the U.S. Department of Agriculture http://www.fsa.usda.gov/dafp/cepd/crp.htm California LESA model http://www.consrv.ca.gov/DLRP/qh_lesa.htm/ WEPP (Water Erosion Prediction Project) http://topsoil.nserl.purdue.edu/nserlweb/weppmain/wepp.html SWAT http://waterhome.tamu.edu/NRCSdata/SWAT_SSURGO Better Assessment Science Integrating point and Nonpoint Sources (BASINS) system http://www.epa.gov/waterscience/BASINS/

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