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Next, open the sample data file water.dat (File -> Open). We will roughly follow the flow chart in Figure 6-2 to analyze this data set. Initial questions you should have since you are not familiar with this data set, are 1) how are the data distributed, and 2) how many samples are in the data set (there are 659, greater than the 50 sample rule of thumb). To examine the data set, select the View -> Post Data menu item. A new window displaying the scatter data will be displayed (again after a number of additional files are downloaded):
If you want to examine some area more closely, you can zoom into and area by drawing a rectangle around the desired area (using mouse, point at location on map to start rectangle, click and hold down left mouse button, drag mouse pointer to create desired zoom rectangle, and release mouse); this process can be repeated for finer zooming (to un-zoom, left click mouse button without moving mouse).
This data set is a collection of scattered data samples which were digitized along ground water, water-table, contour lines (a synthetic data set). There is some clustering in the Northern area of the map (North to top), but it is not severe. To examine the actual sample values, in the Spatial Data window, select the Data -> Set Data Columns menu item. A new dialog:
This dialog display the number of samples, and each sample location (X, Y; this is still beta software, the Z coordinate and point value will eventually be displayed - all values are used in the semivariogram calculation as appropriate). Now that you have a basic feel for the data set, you are ready to calcualte the experimental semivariogram. Bring the Experimental Semivariogram toolbar forward.
For this data set, each sample has only one value, based on a continuous variable. Calculating a classic semivariogram is appropriate for this data set (normally you wil set the equation type can be set by using the Experimental -> Spatial Equations menu item, but this is not yet implemented). After defing the spatial equation, we can set the basic serach parameters. Use the Experimental -> Search parameter -> Point Data menu item, to bring up the Point Data Search Parameter dialog:
The software will automatically pick values for the Lag Distance, Maximum Search Distance, Direction Bandwidth, Plunge Bandwidth, Horizontal Search Direction, Vertical Search Direction, Horizontal Half-Angle, and Vertical Half-Angle. Depending on the data set these values may or may not be reasonable. Initially only one model is defined, but it is possible to calculate several different models at once (you could, but don't, press Add; multiple models would only confuse the process at this point).
At this point, we have enough information to calculate an experimental semivariogram; press the Calculate button. After a brief pause, a new graph will appear displaying the experimental semivariogram:
This is a good quality isotropic experimental semivariogram (Horizontal and Vertical Half-Angles = 90o's; no Bandwidth limitations). If it weren't, you might experiment with the lag and other parameters, to try to create a better model. Given this good isotropic model, you should now check for anisotropy. Since this model is calculated reasonbly quickly, we will keep it, and add another model (press Add). Now we can begin to experiment. Since this is a 2D data set, we don't need to (and shouldn't) modify any of the vertical parameters. A good place to start is by reducing the Horizontal Half-Angle (as long as it is 90o's, you are calculating an isotropic semivariogram; this assuming the Bandwidth is unlimited). To identify anisotropy, you want the angle as small as possible, but if you make it too small, there are to few sample pairs for each lag calculation, and the model quality degrades. With some data sets, it is not possible to get a good quality model, with a small half-angle. For this data set, try 10o's (on the second row of the table in the Point Data SearchParameter dialog, change the Horz. HA from 90.0 to 10.0, and hit the RETURN key), and press the Calculate button. Shortly you will see the figure:
While the models differ significantly past a distance of 1.2, the lag estimates are very similar for all the lags less then 1.3 (approximately where samples exceed the data set variance). If the lag estimates for the model are similar at lags prior to the model reaching the variance, the model is isotropic. If models are significantly different over this range, the data set is anisotropic. We cannot determine whether this model is isotropic yet (you've only calculated one directional experimental model). For the next step, calcualte directional models with Horizontal Search Directions (Horz. Dir.) of 30o's, 60o's, 90o's, 120o's, and 150o's.
Do you think this data set is isotropic or anisotropic?
If you plot all the models together, you will get the following figure:
(In this figure only the shorter lags are displayed). Although the different directional models are not identical, the results for the lags less than 1.0 are very similar. Under most circumstances it would be reasonable to assume this data set is isotropic based on these models.
The next example will lead you through fitting a model semivariogram to the original isotropic experimental semivariogram calculated in this exercise.
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