Using geostatistics and spectral analysis to study spatial patterns in the topography of southeastern Washington State, U.S.A.

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AbstractTopography for four areas in the Palouse region of southeastern Washington State having different patterns and encompassing areas of about 900 ha each were quantitatively compared and described using two‐dimensional semi‐variograms and periodograms. The four areas studied were from the Garfield, La Crosse, Thornton, and Wilcox quadrangle topographic maps.Semivariance of elevation residuals were modelled using a combination of spherical, periodic, or linear semivariogram models. The range of the spherical component was interpreted as a relatively short‐range scale of correlation which was not periodic. For each of the study areas a model was developed to describe the variation in range with orientation. Values for the range from this model reached maximum values of from about 700 m to 800 m at an orientation of from 35° to 55° (approximately northeast) in each study area. This orientation was interpreted as the dominant direction of non‐periodic small‐scale landscape features. The wavelength and amplitude of the periodic semivariogram component, which were highly correlated, were interpreted in terms of parallel northeast‐trending ridges having relatively long scales of periodic correlation varying in size from about 1350 m to 2100 m. This attempt to identify the dominant orientation of periodic landscape features using models for the wavelength and amplitude was, however, not completely definitive.Two‐dimensional spectral analysis provided significantly more detail concerning orientation and wavelengths of the periodic topographic patterns than the semivariogram analysis. In the Garfield study area, spectral analysis identified north‐trending ridge systems separated by a wavelength of 1494 m and northeast‐trending systems with a wavelength of 747 m. In the La Crosse study area, both north and northeast‐trending patterns were identified having periodic spacings of 980 and 735 m. North‐trending ridges separated by wavelengths of 996 m and northeast‐trending ridges separated by wavelengths of 747 or 996 m were the predominant periodic features of topography in the Thornton study area. In the Wilcox study area, northeast‐trending ridge systems separated by wavelengths of 373, 498, or 996 m were detected.A comparison of the results from geostatistical and spectral analysis of these complex topographic surfaces shows that each approach had significant strengths and weaknesses. Two‐dimensional analysis with semivariograms was the only method which could be used for identifying the correlation scale and orientation of relatively small non‐periodic landscape features. Two‐dimensional spectral analysis accurately identified the predominant orientation of relatively large periodic features in topography, whereas semivariogram analysis was somewhat inconclusive. Also, semivariograms were generally unable to detect the presence of multiple or harmonic periodicities operating at different wavelengths along a given orientation.