Lab2: Modeling Sample Variogram

Geo597: Geostatistics

Spring 2009

Exercise

1. Choose data and interpolation method

In the "Geostatistical Wizard: Choose Input Data and Method" window:
Select the appropriate "Input Data" and "Attribute" for "Dataset 1".
Choose "Kriging" in "Method". -> Next.

2. Select kriging method

In the "Geostatistical Wizard: Step 1 of 4 - Geostatistical Method Selection" window:

(1) In the "Geostatistical Methods" section, choose "Ordinary Kriging" as the geostatistical method, then choose "Prediction Map" as the output.

(2) In the "Dataset 1" section, select the same "Transformation" method as you did when you normalized the histogram (Geostatistical Analyst -> Explore Data -> Histogram). -> Next.

3. Model the sample variogram

In the "Geostatistical Wizard: Step 2 of 4 - Semivariogram/Covariance Modeling" window:

(1) In the Semivariogram/Covariance Surface" section, check the "Show Search Direction" box, then experiment with the parameters of the semivariogram, "Angle Direction", "Angle Tolerance", and "Band Width (Lags)". Or you may interactively change these parameters within the "Semivariogram/Covariance Surface" graph. Complete assignments 1-4.

(2) In the "Models" section, try three different semivariogram models. Complete assignment 5. 

4. Model the sample semivariogram with a single-structure model

(1) Model the anisotropic nature of the sample semivariogram by checking the “Anisotropy" box in the Models section. Multi-directional semivariogram models will appear in the "View -> Semivariogram" section (keep the "Show Search Direction" box un-checked). Select an appropriate model from the model list to fit the sample semivariogram. Print the screen and complete assignment 6.

(2) Experiment with "Lag Size" and "Number of Lags", where
 Lag-Size * Number-of-Lags <= 1/2 of the length or width of your study area.
Find out the distance of your study area by following ArcMap -> right click the layer name -> Properties -> Source, then calculate the length/width based on the "Top", "Left", "Right", and "Bottom" coordinates of your study area. Complete assignment 7.

5. Model the sample semivariogram by a multi-structure model

For a two-structure semivariogram model, provide a "Partial Sill" for "Model 1", which should be less than the default partial sill, then check "Model 2", and then select a semivariogram model for model 2. Continue for "Model 3" if necessary. Complete assignment 8.

Assignment (Due: April 14)

1. Print two anisotropic semivariograms, one in maximum (Major) and the other in minimum (Minor) direction of spatial continuity. Briefly report your observation: do the two semivariograms look alike? If not, what are the differences?
2. Print two anisotropic semivariograms with identical angle direction and band width but different angle tolerances. Briefly report your observation: do the two semivariograms look alike? if not, what are the differences?
3. Print two anisotropic semivariograms with identical angle direction and angle tolerance but different band widths.Briefly report your observation: do the two semivariograms look alike? if not, what are the differences?
4. Print two anisotropic semivariograms with identical angle direction, angle tolerance, and band width but different lag sizes. Briefly report your observation: do the two semivariograms look alike? if not, what are the differences?
5. Fit three different semivariogram models to the sample semivariogram, one at a time, while keeping Angle Direction, Angle Tolerance, and Band Width (Lags) constant. Print results and briefly describe the differences between the models, especially their behavior at the short lag distances.

    6.   Print single-structure, anisotropic semivariogram models.

    7.   Print single-structure anisotropic semivariogram models with customized lag size and number of lags.

    8.   Print multi-structure anisotropic semivariogram models.