Analysing soil variation in two dimensions with the discrete wavelet transform

A - Papers appearing in refereed journals

Lark, R. M. and Webster, R. 2004. Analysing soil variation in two dimensions with the discrete wavelet transform. European Journal of Soil Science. 55 (4), pp. 777-797.

AuthorsLark, R. M. and Webster, R.

Complex spatial variation in soil can be analysed by wavelets into contributions at several scales or resolutions. The first applications were to data recorded at regular intervals in one dimension, i.e. on transects. The theory extends readily to two dimensions, but the application to small sets of gridded data such as one is likely to have from a soil survey requires special adaptation. This paper describes the extension of wavelet theory to two dimensions. The adaptation of the wavelet filters near the limits of a region that was successful in one dimension proved unsuitable in two dimensions. We therefore had to pad the data out symmetrically beyond the limits to minimize edge effects. With the above modifications and Daubechies's wavelet with two vanishing moments the analysis is applied to soil thickness, slope gradient, and direct solar beam radiation at the land surface recorded at 100-m intervals on a 60 x 101 square grid in south-west England. The analysis revealed contributions to the variance at several scales and for different directions and correlations between the variables that were not evident in maps of the original data. In particular, it showed how the thickness of the soil increasingly matches the geological structure with increasing dilation of the wavelet, this relationship being local to the strongly aligned outcrops. The analysis reveals a similar pattern in slope gradient, and a negative correlation with soil thickness, most clearly evident at the coarser scales. The solar beam radiation integrates slope gradient and azimuth, and the analysis emphasizes the relations with topography at the various spatial scales and reveals additional effects of aspect on soil thickness.

KeywordsSoil Science
Year of Publication2004
JournalEuropean Journal of Soil Science
Journal citation55 (4), pp. 777-797
Digital Object Identifier (DOI)
Open accessPublished as non-open access
Funder project or code511
Research in statistics relevant to biological processes

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