Geo Interpolation

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    Peter TelekGEOG 586 - Fall 2008

    Project 5 - Page 1

    Project 5: Interpolation Methods

    Part I: Inverse Distance Weighted Interpolation (1)

    Figures 1a-c shows three outputs as the number of points were varied from 6 to 12 to 24 for theInverse Distance Weighted Interpolation of 597 randomly selected elevation height values incentral PA. As the number of points increase, then contour "smoothness" decreases. I chose the12 point (figure 1b) as the final data set for later work.

    Figure 1d shows the output of a fixed radius of 2500 m. Since the spacing in the area of interestis neither uniform nor dense, there are several points or areas that have a distance greater than2500 meters. Therefore the interpolation is incomplete and has "holes" in the result.

    According to ArcGIS, "Inverse distance weighted (IDW) interpolation determines cell valuesusing a linearly weighted combination of a set of sample points. The weight is a function of inverse distance. The surface being interpolated should be that of a locationally dependentvariable.

    The {power} option of IDW lets you control the significance of known points on the interpolatedvalues, based on their distance from the output point. It is a positive, real number. The defaultvalue is 2.

    By defining the higher {power} option, more emphasis can be put on the nearest points. Thus,nearby data will have the most influence, and the surface will have more detail (be less smooth).As the power increases, the interpolated values begin to approach the value of the nearest samplepoint. Specifying a lower value for power will provide a bit more influence to surrounding pointsa little farther away. Since the IDW formula is not linked to any real physical process, there is noway to determine that a particular power value is too large. As a general guideline, a power of 30would be considered extremely large, and thus of questionable use.

    An optimal value for the power can be considered to be where the minimum mean absolute erroris at its lowest. ArcGIS Geostatistical Analyst provides a way to investigate this.

    IDW relies mainly on the inverse of the distance raised to the power. If the distances are large, orthe power value is large, the results may be incorrect.

    The characteristics of the interpolated surface can also be controlled by limiting the input pointsfor calculating each interpolated point. The input can be limited by the number of sample pointsto be used or by a radius within which there are points to be used in the calculation of theinterpolated points."

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 1a. Inverse Distance Weighted Interpolation of 597 random height values in central PAusing ArcMap with following options: power = 2, variable size search radius, number of points= 6, and output cell size = 500.

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    Peter TelekGEOG 586 - Fall 2008

    Project 5 - Page 3

    Figure 1b. Inverse Distance Weighted Interpolation of 597 random height values in central PAusing ArcMap with following options: power = 2, variable size search radius, number of points= 12, and output cell size = 500.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 1c. Inverse Distance Weighted Interpolation of 597 random height values in central PAusing ArcMap with following options: power = 2, variable size search radius, number of points= 24, and output cell size = 500.

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    Peter TelekGEOG 586 - Fall 2008

    Project 5 - Page 5

    Figure 1d. Inverse Distance Weighted Interpolation of 597 random height values in central PAusing ArcMap with following options: power = 2, fixed size search radius, distance = 2500, min# of pts = 0, and output cell size = 500.

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    Peter TelekGEOG 586 - Fall 2008

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    Part II: Inverse Distance Weighted Interpolation (2) - Interpolation Errors

    Figure 2a shows error calculation map (estimate - truth). The large differences are dark red(negative) values and dark green (positive) are shown while the lightest colors show small or nodifference between estimated and truth values in elevation in central PA. Figure 2b is a zoomedin area with error contours. The greatest errors appear to be furthest from the points. The leastdifference between the random points and the truth are near and at the randomly selected points.This makes sense since the closer you get to the point with IWD, the better the estimate; andidentical for the point itself if the algorithm is coded correctly.

    Figure 2a. Error calculation map (estimate - truth). The large differences are dark red (negative)values and dark green (positive) are shown while the lightest colors show small or no differencebetween estimated and truth values in elevation in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 2b. Zoomed in Error calculation map (estimate - truth) with error contours. The largedifferences are dark red (negative) values and dark green (positive) are shown while the lightestcolors show small or no difference between estimated and truth values in elevation in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Part III: Kriging Using the Geostatistical Analyst

    Note: I had to use an evaluation copy of Geostatistical Analyst for ArcMap v9.2 software for thispart of the project. It seemed to work.

    Figure 3a-c are results from ArcMap using the isotropy case to create an interpolated map byKriging from the 597 randomly selected elevations in central PA used in Part I.

    Anisotropy, directional influences on the semivariogram/covariance, is a types of directionalcomponent that can affect the predictions in the output surface. For anisotropy, the shape of thesemivariogram may vary with direction. Isotropy exists when the semivariogram does not varyaccording to direction.

    In this example, the Pennsylvania hills or ridges appear to be oriented southwest to northeast.Since there is a directional trend, I'd expect that an anisotropy result to be better than an isotropyresult. Figure 3g shows an elliptical shape oriented SW-NE for specifying searchingneighborhood for anisotropy case.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3a. Interpolated map by kriging from 597 randomly selected elevations in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3b. Contour lines of interpolated map by kriging randomly selected elevations displayedover the actual elevation data in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3c. Specifying the isotropy semivariogram model to work with in kriging.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3d. Specifying the ansotropy semivariogram model to work with in kriging.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3e. Interpolated map by kriging from 597 randomly selected elevations in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3f. Contour lines of interpolated map by Kriging randomly selected elevations displayedover the actual elevation data in central PA.

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    Peter TelekGEOG 586 - Fall 2008

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    Figure 3g. Specifying searching neighborhood for anisotropy case. Notice the elliptical shapeoriented SW-NE.