Spatial Interpolation (Kriging)

Objectives

• Understand the general procedures for spatial interpolation

• Explore the use of Kriging for spatial interpolation

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

Review of Kriging

• Semi-variogram

γ(h) = 1/2 var [z(s+h) – z(s)]

= 1/2 E{[z(s+h) – z(s)]2} if E[z(s+h)] = E[z(s)] (ie, no trend)

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• Ordinary Kriging– Assume:

• z(s) is intrinsically stationary, ie z(s) = m + e(s)• known semi-variogramγ• know values at z(s1) …… z(sn)

– Want to predicted z(s0) using a linear predictor

– With the objectives

Review of Kriging (cont.)

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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

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

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

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

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

Step 4: Choose a proper model

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

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

Step 5: Perform interpolation (cont.)

• Display the interpolation via– ArcMap

– Or Grid• Display 9999• Mape s50_1s• Gridpaint s50_1s # linear # gray

Step 6: Quality evaluation

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

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

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