Now let's address an important topic, honoring of measured data. By honoring we mean that the predicted concentrations should precisely match the actual data. This is only possible if grid nodes actually match the coordinates of the input (measured) data. Otherwise, we want our predicted distribution to approach our actual data as nodes approach measured sample locations.
This concept of honoring the data seems obvious and hardly worth mentioning. However historically, kriging used a variogram parameter called a nugget. This concept originated with using kriging for predicting ore bodies (which contain randomly dispersed nuggets). If a nugget is used in the variogram (it often seems to make it easier to fit the variogram to the data), the predicted concentrations will not honor the measured data.
First, set the Max Edge Angle on external_edges to 0, and adjust your view in Azimuth & Elevation by setting the Scale to 2.0, Elevation to 0.0 degrees and choose 180 degree Azimuth. It may seem strange that the picture below seems to suggest that EVS does not honor the data. Note that there is an orange sphere with a concentration of 190.0 ppm which is outside of the 5.0 ppm plume.
To see the properties of this sample, hold down the Alt key and click on the orange sphere with your left mouse button. This should pop-up the window below in the upper right corner of your screen.
Because this is an important topic, we wanted to show an example which illustrates the effects of inadequate resolution. You cannot expect a perfect plume geometry if the resolution is too coarse. We set the Max Edge Angle to zero so that the grid would be obvious. Note that the high concentration sphere falls between grid nodes and that the nodes are near lower concentration values. All of the values (within a distance of Reach and up to the maximum Points in the Kriging Parameters) are used to compute the value at each node. Because there were other nearby nodes with lower concentrations, the plume did not extend quite as far as this high concentration value.
EVS's kriging routines will always honor the measured data value if a node falls on (or very near) the value. It will calculate a geostatistically defensible value at all other locations. However, if a plume does not seem to adequately honor the measured data increasing resolution will always fix the problem. Remember, when dealing with 3-D kriging, the resolution must be considered in all three dimensions X, Y, and Z.
In EVS-PRO and MVS, Krig_Z and Krig_3D have adaptive gridding on as the default. We explicitly turned this option off to show the effect for this workbook (and to make the workbook compatible with EVS-Standard).
Adaptive gridding assures that we will have grid nodes at all data points and reduces (almost eliminates) the need for high resolutions.
If we turn Adaptive Gridding on and re-run Krig_3D, the Viewer will show:
The Orange sphere is not enveloped by the plume, but the plume does extend beyond the center of this sphere. The adjacent very low values (non-detects) are still dominating the extent of the plume in this region.
Before proceeding to the next topic adjust the Max Edge Angle back to 60 degrees and set the view to Elevation 12 degrees, Scale 0.7 and Azimuth 210. Also, if you are running EVS-Pro or MVS, turn Adaptive Gridding back off and re-run Krig_3D.