Pitney Bowes MapInfo Vertical Mapper - Manual (Page 47)

Chapter 3: Creating Grids Using Interpolation
User Guide
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The Search Radius box enables you to define the maximum size, in map units, of a circular zone
centred on each grid node within which point values from the original data are selected based on the
quadrant search technique. The default setting is calculated as a percentage of the total extent of
the map area and is appropriate for most data.
The File name box enables you to enter a new file name.
The Extents button displays a summary of the geographic size and the z-value range of the original
point database, the density of the points, and the data value units.
Kriging Interpolation
Kriging is a geostatistical interpolation technique that considers both the distance and the degree of
variation between known data points when estimating values in unknown areas. A kriged estimate is
a weighted linear combination of the known sample values around the point to be estimated. Applied
properly, kriging allows you to derive weights that result in optimal and unbiased estimates. It
attempts to minimize the error variance and set the mean of the prediction errors to zero so that
there are no overestimates or underestimates.
Included with the kriging function is the ability to construct a semivariogram of the data, which is
used to weight nearby sample points. It also provides a means for you to understand and model the
directional (for example, north-south, east-west) trends of your data. A unique feature of kriging is
that it provides an estimation of the error at each interpolated cell, providing a measure of
confidence in the modeled surface.
The effectiveness of kriging depends on the correct specification of several parameters that describe
the semivariogram and the model of the drift (such as the mean value does or does not change over
distance). Because kriging is a robust interpolation technique, even a naïve selection of parameters
will provide an estimate comparable to many other grid estimation procedures. The trade-off for
estimating the optimal solution for each point by kriging is computation time. Given the additional
trial and error time necessary to select appropriate parameters, kriging should be applied where best
estimates are required, data quality is good, and error estimates are essential.
Vertical Mapper provides three different methods of kriging interpolation: ordinary kriging, simple
kriging, and universal kriging.
How Kriging Works
Kriging is a weighted moving average technique that is similar to Inverse Distance Weighting (IDW)
interpolation. With IDW, each grid node is estimated using sample points that fall within a circular
radius. The degree of influence each point has on the calculated value is based upon the weighted
distance of each point from the grid node being estimated. In other words, points that are closer to
the node will have a greater degree of influence on the calculated value than those points farther
away.
The general relationship between the amount of influence a sample point has with respect to its
distance is determined by the IDW Exponent setting, as shown below.