The following are interactive exercises based on the EZ Kriging software which is solely meant for learning and to get a"feel" of kriging. It is only for educational purposes. In the EZ kriging, there is only one sample point whose value is being predicted. To outline the process of kriging, see the steps below: 1. Plot all samples or data points on a map 2. Draw all possible lines which connect two sample points 3. Measure the length of a line, this is a "Lag Distance", and also take the square of the difference between the two sample points, this is a "Variogram Value" 4. Do #3 to all the lines 5. Plot them on an x−y plot, where y is the Variogram Value, and x is the Lag Distance Value, this is a Variogram plot 6. A variogram plot shows the relation between the exaggerated difference (variance error) between two sample points vs. the distance between them. 7. Using the Variogram, we can predict the best estimate (mean value) and the errors in the estimate in any given point. 8. Prediction is done by taking a weighted average of the surrounding data values. Now we won't be doing these in the exercise as they are automatically done by programs, but do appreciate the sophistication of Kriging. It would be a good practice to always use all available Kriging Methods as well as use other interpolation methods such as TIN and IDW just to make sure that your Kriging results are reasonable. Things you need: 1. EZ Kriging Manual.pdf - skim the manual and keep in on the side as you use the software. The manual has clickable links within the document. 2. EZ Kriging software - the .exe file Quick refresher on variogram and other terms in Kriging: - Lag Vector (h) (also called Lag Distance) is the vector distance between two data locations. - Variogram value (Gamma) is the average of all the squared differences of pairs of data values with similar Lag Vector values. - Variogram values and Lag Vector values are calculated over all possible combinations of data values and locations throughout the whole dataset. - Variogram plot is the plot of Variogram values vs Lag Vector values - Semivariogram plot is the plot of half (1/2) of Variogram values vs Lag Vector values - Nugget is the minimum value of variance or variogram value. It is the y-intercept of the variogram. - A dataset with no errors in measurements should have Nugget value equal to zero (y-intercept =0) - Remember that at y-intercept, the x value is zero which in the variogram means the distance between two data points is zero. - Now, zero distance means the two data points should be the same, their value should be the same, and the difference between their values should be zero, and their variogram value will also be zero. - However if your measurement system has inherent errors, at the same location, it is possible for the measurements to be different, hence a nonzero variogram value at x=0, and hence a nonzero Nugget value. - As per Deutsch (2019), the ideal way to calculate the nugget is to use a dataset with the greatest number of measurements that are close together. Nugget is then estimated by graphically by constructing a line that passes through the first two points of the variogram up to intersect the Y axis. - At a certain minimum Lag Distance, there may be no significant change in variogram values even with increasing distance. This can be caused by a large region of uniform data values (e.g. a sill or a large tabular body), hence the "sill effect". - Range is the Lag Distance where the Sill or "ceiling" of variogram values take into effect - In Variogram calculation, the search for data pairs can be constrained by Distance Tolerance (e.g. 100±20 meters), Azimuth Tolerance (e.g. 45±5 degrees) and Bandwidth Tolerance (i.e. the maximum "thickness" of the search). - The value of Sill is equal to the Variance of the data. - Range is the Lag Distance in at which the Sill (or the flattening of the curve) starts - A Spherical type of variogram model has a linear pattern at the first 2/3 of its range. - An Exponential type of variogram model has a linear pattern at the first 1/3 of its range. - A Gaussian type of variogram model is used for patterns with short scale continuity (localized patterns) such as topography. Some EZ Kriging symbols - Sample#o (red point) - this is the prediction point, see "results" for its values - co-nugget value - c1-sill - a - range - Prediction - in Kriging, the predicted value is actually a range, as expressed by mean value (prediction) and the variance prediction errors