Highly erratic spatial variability of soil-pH on Iping Common, West Sussex

• Published in: Catena (Giessen) Vol. 13; no. 1; pp. 81 - 98
• Main Author: Culling, W.E.H.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1986
• ISSN: 0341-8162; 1872-6887
• DOI: 10.1016/S0341-8162(86)80006-6

The notion of sets of fractional dimension is applied to the spatial variation of soil-pH values collected from a transect of Iping Common. The soil is a well developed humo-ferric podsol. A preliminary estimation gives a value for the Hausdorff dimension of 1.7–1.9 corresponding to the highly erratic variation. A second set of samples were collected and tested under improved and standardised conditions. The incremental values follow a Gaussian distribution but fail to show the martingale property of equal liklihood of a positive or negative increment at each sample interval and therefore indicate the presence of some dependence. Thus the line graph approximates to a fractional Brownian process of dimension 1.8. This implies a surface of values of dimension 2.8 and the consequences of such a high value for measurement, mapping and experiment are detailed.