Roughness Measurements of Soil Surfaces by Acoustic Backscatter

surfaces may have the same roughness index but one surface may have the roughness on average spaced farThe measurement of the roughness of soil surfaces on centimeter ther apart on the surface. A more complete characterizascales is important to modeling local soil erodibility. An acoustic backscatter technique was examined for its ability to quantify the tion would describe not only vertical scales of roughness roughness of porous soil on centimeter scales. Acoustic backscatter but also the horizontal scales. offers the possibility of an inexpensive, mobile, and rapid means of Römkens and Wang (1987) proposed two new paramestimating statistical properties of soil surfaces. Four soil plots were eters to describe both the roughness with elevation and constructed with varying amounts of roughness. Surface roughness the horizontal scale, or spatial dependency, of the roughof the four soil plots was measured with the acoustic backscatter ness. One roughness parameter used to describe a trantechnique and a laser microreliefmeter. The roughness power spectra sect of a rough surface was introduced by Römkens and for the surface plots were obtained from surface profiles measured by Wang (1986a) as the laser microreliefmeter and by the acoustic backscatter technique. Statistical values of the RMS (root mean square) height and correlaR A F [1] tion length of surface roughness for each plot were calculated from the acoustic backscatter power spectra and laser microreliefmeter where A is the microrelief index (mm) and F is the peak power spectra and compared. Agreement between the two techniques frequency factor (mm 1). A and F were used to describe for estimating roughness statistics was shown to be good ( 13% the average-clod size and clod frequency, respectively. difference) when an adequate amount of data points were used to map The microrelief index, A, is defined as the area per unit out the roughness power spectra. The acoustic backscatter technique length between the measured surface profile and the appears to be a potential alternative to rapidly and inexpensively regression line of least squares through all measured quantify the roughness of soil surfaces. elevations on a transect. The spatial distribution and the spatial dependence of the roughness were evaluated by the autocorrelation Q descriptions of surface roughness are function, , of the roughness parameter, R, of successive important in evaluating tillage and in simulating transects. The correlation length for spatial indepenerosion processes. Few studies involving quantitative dence was determined where the correlation function measures of surface roughness have been conducted. dropped to 0.2 of its initial value. A smaller spatial The major concern for describing a rough surface is independence was found for surfaces that had been chisconstructing an adequate model to characterize the apeled repeatedly as opposed to surface with little tillage parent random nature of surface roughness and then (Römkens and Wang, 1987). The more a surface is chisfinding an adequate means of measuring model parameled the smaller the clod sizes. Smaller scaled roughness eters. should tend to become uncorrelated at shorter lengths Kuipers (1957) first introduced parameters that have than larger scaled roughness. been used in the past to describe surface roughness. Huang (1998) proposed an alternate description of Kuipers defined a roughness index RK 100 log( ) surface roughness that would measure vertical and horiin which is the standard deviation of the elevations zontal scales of roughness. The statistics by Huang (1998) readings of the surface. Following this, Allmaras et al. utilized the fractal nature of random rough surfaces to (1966) refined Kuipers roughness index by measuring describe the roughness. The fractal dimension, D, and the standard error of measured elevation points referthe crossover length, l, were used to describe the semivaenced to some plane. Several studies involving roughness riance function characterization on surfaces used these parameters (Mit(h) 0.5E(|Zx Zx h|) [2] chell, 1970; Moore and Larson, 1979; Linden, 1979; Onstad, 1984). where Zx and Zx h are the roughness heights at positions A major critique with using the roughness index was separated by a horizontal distance h and E () is the that this roughness parameter did not describe the spaexpectation. The crossover length and fractal dimension tial dependence of the roughness elements. The roughdescribed the relative magnitude and slope of the seminess index characterized the variation of heights, or variance function, respectively. Huang and Bradford vertical roughness, but did not describe the spatial distri(1992) used the semivariance description to characterize bution of roughness on the surface. For example, two roughness of soil plots as they changed because of rainfall. Several instruments have been used in the past to M.L. Oelze, Department of Electrical and Computer Engineering, obtain the surface roughness statistical characterizations University of Illinois, Urbana, IL 61801; and J.M. Sabatier and R. from measured elevation data. Contact type microreliefRaspet, National Center for Physical Acoustics, The University of meters have been used to measure surface roughness Mississippi, Coliseum Drive, University, MS 38677. Received 9 July 2001. *Corresponding author ([email protected]). Abbreviations: RMS, root mean square. Published in Soil Sci. Soc. Am. J. 67:241–250 (2003).