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United States Department of Agriculture

Agricultural Research Service

Title: Comment on the Letter-to-the-Editor "on the Characteristic Aggregate Size for Estimating Fractal Dimensions of Soil"

item Pachepsky, Yakov

Submitted to: Soil Science Society of America Journal
Publication Type: Research Notes
Publication Acceptance Date: February 13, 2001
Publication Date: April 1, 2001

Interpretive Summary: Particle and aggregate size distributions are measured by determining the mass of particles in several ranges of particle radius. These ranges have to be characterized with a single, characteristic radius to relate relative abundance of particles to their radius. Several methods to define the characteristic radius were suggested in literature. The letter-to-editor suggests one more method. This comment analyzes this method and shows that it has neither theoretical justification nor practical advantages. The work seems to be an aimless one.

Technical Abstract: The letter proposes defining the characteristic size of grains within a range of sizes as the geometric mean of the upper and the lower boundary sizes for the range. There is no justified theoretical or conceptual need to introduce the geometric mean radius. Earlier authors did not assume the scaling valid within the size ranges and were free to choose a convenient formula for the characteristic size. Later the characteristic size was defined assuming that the fractal scaling law is applicable not only among the size ranges but also within the size ranges. So, using the geometric mean radius is not correct from the recent standpoint and is not advantageous from the standpoints of earlier authors. There is no practical difference between conditions to use geometric mean radius and the other characteristic sizes. To summarize, the Letter-to-the-Editor does not contribute to the methodology of studying scaling in soils.

Last Modified: 4/22/2015