Scaling properties of saturated hydraulic conductivity in soil

Variability of saturated hydraulic conductivity, k(sat), increases when sample size decreases implying that saturated water flow might be a scaling process. The moments of scaling distributions observed at different resolutions can lie related by a power-law function, with the exponent being a single value (simple scaling) or a function (mutiscaling). Our objective was to investigate scaling characteristics of k(sat) using the method of the moments applied to measurements obtained with different sample sizes. We analyzed three data sets of k(sat) measured in: (I) cores with small diameter and increasing length spanning a single soil horizon, (2) columns with increasing cross sectional area and constant length, and (3) columns with increasing cross sectional area and length, the longest column spanning three soil horizons. Visible porosity (macroporosity) was traced on acetate transparency sheets prior to measurement of k(sat) in situation (2). Six moments were calculated assuming that observations followed normal (k(sat), macroporosity) and/or log-normal (k(sat)) distributions. Scaling of k(sat) was observed in all three data sets. Simple scaling was only found when flux occurred in small cross sectional areas of a simple soil horizon (data set (1)). Multiscaling of k(sat) distributions was found when larger soil volumes were involved in the flux process (data sets (2) and (3)). Moments of macroporosity distributions showed multiscaling characteristics, with exponents similar to those from Ink(sat) distributions. The scaling characteristics of k(sat) reported in this paper agree with similar results found at larger scales using semivariograms. Scaling exponents from the semivariogram and the moment techniques could be complemented, as demonstrated by the agreement between macroporosity scaling exponents found with both techniques. (C) 1999 Elsevier Science B.V. Ail rights reserved.