Semivariogram

[DeepananthanDhanasekaran1]

Hi,

While plotting the semivariogram, we generally take the expectation of the semivariance values of each lag and then plot it (literally we will have one point per lag) ! but why do Geostatistical analyst plots many points in each lag? Also the lag distance along x axis has 10^-ve values (example h.10^-3). Is this correct? can somebody clarify this?

Thanks
Deep

[EricKrause]

Hi Deep,

The Wizard help describes the points as:

"Binned points (the red dots) are generated by grouping (binning) empirical semivariogram/covariance points together using square cells that are one lag wide. Average points (the blue crosses, which are new in ArcGIS 10) are generated by binning empirical semivariogram/covariance points that fall within angular sectors. The graph can display binned points, average points, or both. Binned points show local variation in the semivariogram/covariance values, whereas average values show smooth semivariogram/covariance value variation."


As for the h.10^-5 on x axis, it is using the formula: x = h(10^-5).  Scientific notation often takes the form h = x(10^5).  The difference is whether you are writing the scale relative to h or relative to the value on the x-axis.  We chose this way because that is historically how the scale of the semivariogram is written.

If you require further information or clarification, let me know.  I've attached an image of a typical semivariogram from the Geostatistical Wizard in ArcGIS 10.

[DeepananthanDhanasekaran1]

Hi Eric,

I don't have ArcGIS 10, my version is 9.2.
I don't clearly understand the following sentence, specifically the last part of it.
"Binned points (the red dots) are generated by grouping (binning) empirical semivariogram/covariance points together using square cells that are one lag wide."

What do you mean by square cells that are one lag wide? do you mean the lag width. Is there some help available stating how binning is done in Arc?

Thanks
Deep

[EricKrause]

The points are binned in the following way:

For each pair of points, a vector is created between them.  One point in the pair is plotted at the origin, and the other point in the pair is plotted according to it's distance in the x and y direction (the point chosen to be at the origin is the one that will keep the vector in the first or second quadrant).  For example, if one point was located at (5,5), and the other point was at (8,9), then the semivariance between the two points would be plotted at (3,4).  After all pairs are plotted this way, the result is a scatterplot of semivariance values in the first and second quadrants.  These semivariance values are then binned together using a grid of cells that are each 1 lag by 1 lag.  The average semivariance is calculated for each cell.  Then, each of these binned averages is plotted on the semivariogram in the wizard. 

We use binned values because plotting a point for every pair would overburden the semivariogram; with that many points, it would be hard to visually determine what is going on. 

I've attached a rough picture of how the semivariances are binned.  Let me know if you need more detail or clarification.

[wangsen]

The points are binned in the following way:

For each pair of points, a vector is created between them.  One point in the pair is plotted at the origin, and the other point in the pair is plotted according to it's distance in the x and y direction (the point chosen to be at the origin is the one that will keep the vector in the first or second quadrant).  For example, if one point was located at (5,5), and the other point was at (8,9), then the semivariance between the two points would be plotted at (3,4).  After all pairs are plotted this way, the result is a scatterplot of semivariance values in the first and second quadrants.  These semivariance values are then binned together using a grid of cells that are each 1 lag by 1 lag.  The average semivariance is calculated for each cell.  Then, each of these binned averages is plotted on the semivariogram in the wizard. 

We use binned values because plotting a point for every pair would overburden the semivariogram; with that many points, it would be hard to visually determine what is going on. 

I've attached a rough picture of how the semivariances are binned.  Let me know if you need more detail or clarification.

Thanks a lot!

[SabinePeukert]

Hey,
How can I understand the units 10>-2? I need to present my semivariogram with distances in meters, how could I convert the given units to this to create a presentable semivariogram?

Cheers,
Sab

[EricKrause]

The x-axis units are the map units.  So, if your data is in meters, the x-axis is in meters. 

If the scale is in the form:
(Distance) x 10^(-2),

then this means than if you see .12 on the x-axis, it corresponds to 12 meters because 12 x 10^(-2) = .12.