Topic 6: Spatial Interpolation 第六讲 空 间 插 值

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 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 Chapter 13 outline (1)

Box 13.5 Radial Basis Functions 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 Chapter 13 outline (2)

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

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.

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

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

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.

(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.

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.

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.

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.

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

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

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

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

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

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

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

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

      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.

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

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

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

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

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

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

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.

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

WEPP (Water Erosion Prediction Project) 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/ Chapter 14 websites

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