Spatial%20Interpolation%20(Kriging)

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Spatial Interpolation (Kriging)
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Objectives

• Understand the general procedures for spatial
  interpolation
• Explore the use of Kriging for spatial
  interpolation

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General Procedures

• Examine the spatial continuity in sample data
  used to construct a semivariogram
• Choose a proper model to describe the observed
  spatial continuity
• Perform interpolation of values at un-visited
  locations
• Examine the quality of the interpolation

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Review of Kriging

• Semi-variogram
• ?(h) 1/2 var z(sh) z(s)
• 1/2 Ez(sh) z(s)2 if
  Ez(sh) Ez(s) (ie, no trend)

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Review of Kriging (cont.)

• Ordinary Kriging
• Assume
• z(s) is intrinsically stationary, ie z(s) m
  e(s)
• known semi-variogram?
• know values at z(s1) z(sn)
• Want to predicted z(s0) using a linear predictor
• With the objectives

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Review of Kriging (cont.)

• Ordinary Kriging
• With the objectives

• Differentiating and set the partial derivatives
  to zero can get wi and

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Step 1 get data

• Get data
• Start arc
• Createworkspace workspace (workspace must not
  already exist)
• createworkspace d\geog579\lab05
• Copy sample.e00 and test.e00 to your workspace
  using Windows copy and paste command
• Use the following command to import e00 files
• Import cover sample sample
• Import cover test test
• Show available coverage in the workspace
• lc
• Use dir info to list Arc/Info files
• dir info
• Use list to see the information in the files
• list sample.pat

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Step 2 Examine data

• Examine the data via
• ArcMap
• From ArcMap ? add data ? sample
• Or Arcplot
• From arc, use the following commands
• to plot the data
• Display 9999
• Arcplot (Launch Arcplot)
• Clear
• Mape sample
• Points sample noids

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Step 3 Examine spatial continuity in the sample
data

• In ARC using the following statement to examine
  the spatial continuity of the sample data
• Kriging sample s50_1 vars50_1 value graph
  spherical sample 12 50

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Step 3 Examine spatial continuity in the sample
data (cont.)

• Use list s50_1.svg to examine the model fitted
  semivariance
• Examine the data using other semi-variogram
  models (exponential, gaussian, circular, and
  linear models)
• Kriging sample s50_1 vars50_1 value graph
  exponential sample 12 50
• Kriging sample s50_1 vars50_1 value graph
  gaussian sample 12 50
• Kriging sample s50_1 vars50_1 value graph
  circular sample 12 50
• Kriging sample s50_1 vars50_1 value graph
  linear sample 12 50

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Step 3 Examine spatial continuity in the sample
data (cont.)

• Launch arcplot to display the semi-variogram
• Clear
• Semivariogram s50_1.svg
• Use arcplot and the commands outlined in the
  handout to print/save the image

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Step 4 Choose a proper model

• Choose a semi-variogram model based on the shape
  of the sample semi-variogram

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Step 5 Perform interpolation

• Perform interpolation
• For example
• Kriging sample s50_1s vars50_1s value lattice
  spherical sample 12 50
• Name conventions
• Differentiate of sample points, maximum
  radius, resolution, semivariogram model

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Step 5 Perform interpolation (cont.)

• Display the interpolation via
• ArcMap
• Or Grid
• Display 9999
• Mape s50_1s
• Gridpaint s50_1s linear gray

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Step 6 Quality evaluation

• Use ArcMap or Arc/Info grid subsystem to
  print/save the interpolation variance map

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Step 6 Quality evaluation (cont.)

• Compare RMSE
• Copy rmse.eaf, edriveaml.bat, rmse.aml and
  aml.bat to your local storage
• In Arcplot use a locally develop program to
  report RMSE and ME
• run rmse test value s50_1s

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Step 7 Repeat

• Repeat
• Change search radius from 50 ? 20 (other
  parameter unchanged)
• Change spatial resolution from 1 ? 3
• Change search sample points from 12 ? 30
• Do comparison