JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. D2, PAGES 3023-3029, FEBRUARY 20, 1993 The Effect of Roughness Elements on Wind Erosion Threshold M. R. RAUPACH CSIRO Centre for Environmental Mechanics, Canberra, Australia D. A. GILLETTE Geophysical Laboratory for Climate Change, Air Resources Laboratory, NOAA, Boulder, Colorado J. F. LEYS Department of Conservation and Land Management, Buronga, New South Wales, Australia A theory is developed to describe the dependenceupon roughness density of the threshold friction velocity ratio R t, the ratio of the thresholdfriction velocity of an erodible surface without roughness to that of the surface with nonerodible roughness present. The roughness density is quantified by the frontal area index A. The prediction is Rt - (1 - mrrA)-•/2(1 + m/3A) -•/2,where/3 isthe ratio ofthe drag coefficient of an isolated roughness element on the surface to the drag coefficient of the substrate surfaceitself; rris the basal-to-frontal area ratio of the roughness elements; and m (< 1) is a parameter accountingfor differencesbetween the average substratesurface stressand the maximum stresson the surface at any one point. The prediction is well verified by four independent data sets. 1. INTRODUCTION It is well known that the erosion of soil by wind is strongly attenuated by the presence of nonerodible roughness ele- ments on the surface. The roughness elements can be of several kinds. Wind erosion suppression is achieved in conservation farming systems by retaining stubbles or crop residues on the ground during fallow periods. On suitable soils, erosion protection is provided by large "nonerodible" soil particles or aggregates, nominally greater than 0.85 mm in diameter [Chepil, 1951]. Protection in grazing or rangeland environments is aided by large roughness elements such as bushes, shrubs, or trees. The basic suppression mechanism is the same in each case: the roughness elements decrease the wind stress on the erodible surface by absorbing a significant fraction of the downward momentum flux from the airflow above. There are two ways in which erosion suppression by roughness has been quantified. The first, older method is through the "soilfluxratio" RQ = QR/Qs, theratioof the streamwise soil flux QR in the presence of roughness ele- ments to the flux Q s over a bare soil without roughness elements, exposed to the same wind conditions. The stream- wisesoil flux (units mass length -• time -1) is usually mea- sured with a portable wind erosion tunnel. (In previous work, R Qhas often been called the"soil loss ratio,"but this terminology is slightly inaccurate because soil loss is actu- ally the streamwise derivative of soil flux.) Fryrear [1985] presented dataon R Q for various kinds of roughness over various soils, including both his own and earlier measure- ments [Chepil, 1944; Siddoway et al., 1965; Lyles and Allison, 1981]. Similar data have also been presented by Findlater et al. [1990] and Leys [1991]. All these data are fitted fairly well by a simple exponential curve of the form This paper is not subject to U.S. copyright. Publishedin 1993 by the American Geophysical Union. Paper number 92JD01922. R Q = exp (-af c) where fc is the fraction of soilcover by the nonerodible roughness and a • 4 +- 1 is an empirical constant. The second approach, introduced by Gillette and Stockton [1989] (henceforth called GS) is to quantify the effect of the roughness on the thresholdfriction velocity u,t, through the "threshold friction velocity ratio" R t = U,tS/U,t R. This is the ratio of u, t for a bare soil surface (u, ts) to that with roughness present (U,tR). Like R Q, R t decreases from1 as roughnessis added to an initially bare erodible surface. The use of threshold friction velocity to quantify roughness effects is based on the hypothesis that the main dynamical effect of adding roughness to an erodible surface is to increaseu, t- Its main conceptualadvantageis a relationship to the dynamics of drag partition on a rough surface. The purpose of this paper is to present an analysis of the effect of roughness on the second of these parameters, the threshold friction velocity ratio R t, usinga generaltreatment of drag and drag partition on rough surfaces developed in a previous paper [Raupach, 1992]. We first discuss drag par- tition in section 2. A theoretical prediction for the depen- denceof R t on the amount of roughness present is derived in section 3 and tested against data in section 4. Discussion and conclusions appear sequentially in section 5. It is necessary to quantify the "amount of roughness present." The attenuating effect of roughnesson erosion is closely related to momentum absorption by roughness, which is controlled primarily by the total frontal area (pro- jected area from the mean wind direction) of the roughness elements on unit ground area [Marshall, 1971; Wooding et al., 1973]. Hence the most appropriate measure is the frontal area index or roughnessdensity h defined by A = nbh/S (1) where ground area S is occupied by n roughness elements, each with mean breadth b, mean height h, and mean frontal area bh. A second roughness measure, used agronomically 3023