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)

Ordinary Kriging –Assume: z(s) is intrinsically stationary, ie z(s) = m + e(s) known semi-variogramγ know values at z(s 1 ) …… z(s n ) –Want to predicted z(s 0 ) using a linear predictor –With the objectives Review of Kriging (cont.)

Ordinary Kriging –With the objectives Differentiating and set the partial derivatives to zero can get w i and Review of Kriging (cont.)

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 –Kriging sample s50_1 vars50_1 value # graph gaussian sample –Kriging sample s50_1 vars50_1 value # graph circular sample –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 –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