COMMENT ON ARCVIEW SPLINE FUNCTION FOR FARM APPLICATION

LUBOS MITAS, HELENA MITASOVA, DIANE SZAFONI, DOUGLAS M. JOHNSTON
National Center for Supercomputing Applications and Geographic Modeling Systems Laboratory, University of Illinois at Urbana-Champaign

The problem was fixed in Spatial Analyst version 1.1 which was released in March 1998, therefore the comment is relevant only for previous versions of ArcView Spatial Analyst.

Introduction

The ArcView Spatial Analyst tutorial includes an interesting application for a large corporate farmer, illustrating the creation and analysis of surface data. Spline interpolation is used in the examples and several raster maps are created from the given point data sets. All of these maps have significant anisotropy in the N-S direction. We have run several experiments and comparisons in an effort to find the reason for this anisotropy with the following results.

Interpolation of potassium from ArcView Spatial Analyst p. 22-24

Soil potassium content was measured in 74 points and interpolated to a raster map using regularized spline. There is no indication in the manual that an anisotropy in N-S direction is present in the modeled phenomena, however, the result of ArcView spline interpolation shows such anisotropy, while the results of other functions (e.g. IDW) don't. This indicates a possible bug or impropper implementation of the spline interpolation function.

The artificial anisotropy can be illustrated by comparison of contour maps and surfaces interpolated by:

• SPLINE in ArcView, contours and surface (Figure 1a)
• Regularized Spline with Tension (RST), contours and surface (Figure 1b)

Interpolation of organic matter from ArcView Spatial Analyst p. 59-60

We have done a similar comparison with the data representing organic matter:

• IDW in ArcView (Figure 2a)
• SPLINE in ArcView (Figure 2b)
• RST (Figure 2c)

with similar results, indicating artificial anisotropy introduced by the spline function in ArcView.

Interpolation of crop yield from ArcView Spatial Analyst p. 52-55

The distortion was very strong for a surface computed for crop yield data:

• SPLINE in ArcView, contours and surface (Figure 3a)
• RST, contours and surface (Figure 3b)

Interpolation on a subset of data from experimental farm in Germany

We have imported our data describing the elevation surface at an experimental farm in Germany into ArcView, performed the spline interpolation and compared the results with the surface interpolated by our RST method with the following results:

• SPLINE in ArcView, contours and surface (Figure 4a)
• RST, contours and surface (Figure 4b)

Again, the result from ArcView is distorted, with strong anisotropy in the E-W direction.

Conclusion

Our experiments both with the data provided by the ESRI and with our test data show that the spline function in ArcView Spatial Analyst has a potential incorrect implementation and in certain cases produces maps with strong artificial anisotropy. Therefore we believe that the maps published in the book on pages 22-24, 59-60, 52-55 provide distorted information about the spatial distributions of phenomena which they represent.

Notes:
The distortion is probably caused by improper normalization of data, which assumes that the data are always interpolated within a square area. Therefore surfaces interpolated for square areas don't exhibit the distortion, as illustrated by a square subarea for the data from the previous example (elevations at experimental farm):

• SPLINE in ArcView, contours and surface (Figure 5a)
• Regularized Spline with Tension (RST), contours and surface (Figure 5b)

Contacts

Helena Mitasova (GMSLab)
helena@gis.uiuc.edu
Lubos Mitas (NCSA)
lmitas@ncsa.uiuc.edu

GMSL Modeling & Visualization
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