Elsevier

Computers & Geosciences

Volume 30, Issues 9–10, November–December 2004, Pages 1043-1053
Computers & Geosciences

Computing the LS factor for the Revised Universal Soil Loss Equation through array-based slope processing of digital elevation data using a C++ executable

https://doi.org/10.1016/j.cageo.2004.08.001Get rights and content

Abstract

Until the mid-1990s, a major limitation of using the Universal Soil Loss Equation and Revised Universal Soil Loss Equation erosion models at regional landscape scales was the difficulty in estimating LS factor (slope length and steepness) values suitable for use in geographic information systems applications. A series of ArcInfo™ Arc Macro Language scripts was subsequently created that enabled the production of either USLE- or RUSLE-based LS factor raster grids using a digital elevation model input data set. These scripts have functioned exceptionally well for both single- and multiple-watershed applications within targeted study areas. However, due to the nature and complexity of flowpath processing necessary to compute cumulative slope length, the scripts have not taken advantage of available computing resources to the extent possible. It was determined that the speed of the computer runs could be significantly increased without sacrificing accuracy in the final results by performing the majority of the elevation data processing in a two-dimensional array framework outside the ArcInfo environment. This paper describes the evolution of a major portion of the original RUSLE-based AML processing code to an array-based executable program using ANSI C++™ software. Examples of the relevant command-line arguments are provided and comparative results from several AML-vs.-executable time trials are also presented. In wide-ranging areas of the United States where it has been tested, the new RUSLE-based executable has produced LS-factor values that mimic those generated by the original AML as well as the RUSLE Handbook estimates. Anticipated uses of the executable program include water quality assessment, landscape ecology, land-use change detection studies, and decision support activities. This research has now given users the option of either running the executable file alone to process a single watershed reporting unit or running a supporting AML shell program that calls upon the executable file as necessary to perform automated processing for a user-specified number of watersheds.

Introduction

For nearly 40 years, the Universal Soil Loss Equation (USLE) model (Wischmeier and Smith, 1978) and its principal derivative, the Revised Universal Soil Loss Equation (RUSLE) model (Renard et al., 1997) have been used throughout the world to estimate average annual soil loss per unit land area resulting from rill and sheet (interrill) erosion. When applying the USLE or RUSLE models, five component factors (R, K, LS, C, and P) are multiplied together to compute the average annual sheet and rill erosion per unit area. Traditionally, the two models have been used mostly for local conservation planning at an individual farmstead scale because the USLE model was originally developed for gently sloping cropland applications. Recent research leading to the RUSLE model has broadened the applicability of the models somewhat to allow limited soil loss estimation for rangeland, forests, disturbed sites, and steeper slopes. It should be noted here that the term soil loss should not be construed to mean that all eroded soil is lost from the spatial land unit being investigated, as it is possible for eroded soil to be subsequently re-deposited downslope on lesser sloping surfaces (Haan et al., 1994). In this sense, USLE and RUSLE are primarily erosion models with some limited linkages to sediment yield models.

It has been demonstrated that increases in slope length and slope steepness can produce higher overland flow velocities and correspondingly higher erosion (Haan et al., 1994). Moreover, gross soil loss is considerably more sensitive to changes in slope steepness than to changes in slope length (McCool et al., 1987). Slope length has been broadly defined as the distance from the point of origin of overland flow to the point where either the slope gradient decreases enough that deposition begins, or the flow is concentrated in a defined channel (Wischmeier and Smith, 1978). The specific effects of topography on soil erosion are estimated by the dimensionless LS factor as the product of the slope length (L) and slope steepness (S) constituents converging onto a point of interest, such as a farm field or a cell on a GIS raster grid.

Until recently, the use of USLE and RUSLE for regional landscape ecology modeling has been limited by an inability to generate reliable estimates of the LS factor. Although the LS factor is usually either estimated or manually calculated from actual field measurements of slope length and steepness for local conservation planning purposes, labor-intensive field measurements are generally not feasible for modeling soil erosion at significantly larger spatial scales. However, newly developed procedures allow users of geographic information system (GIS) technology to generate both USLE- and RUSLE-based raster grids of the LS factor for various site characterization and landscape ecology applications. A thorough review of available GIS-based methods for calculating the LS factor is included in papers by (Dunn and Hickey (1998); Hickey (2000)). Various approaches and algorithms for quantifying slope length are available, including raster grid cumulation, unit stream power theory, contributing area, and network triangulation techniques. There are also several methods for estimating slope steepness including neighborhood, quadratic surface, maximum slope, and maximum downhill slope techniques. The algorithms described in this paper use the raster grid cumulation and maximum downhill slope methods.

The previous work of Hickey et al. (1994), Hickey (2000)) resulted in the production of ArcInfo™ Arc Macro Language (AML) programs for creating a USLE-based LS factor grid from an input digital elevation model (DEM) data set. Subsequent RUSLE-based amendments were added by Van Remortel et al. (2001) to the USLE-based code and involved the substitution of several recently developed RUSLE algorithms and the modification of a few assumptions in the AML program concerning the treatment of high points, flat areas, slope breaks, and other specific slope criteria. The RUSLE algorithms derived by McCool et al., 1987, McCool et al., 1989 utilized the results of statistical analysis applied over a much broader range of slope configurations, gradients, and cover types than those modeled for USLE, so the new algorithms are generally considered to be more comprehensive than those of the earlier model (Renard et al., 1997).

Detailed descriptions of the computational basis for our particular RUSLE-based approach for generating an LS factor surface are included in Van Remortel et al. (2001), Hickey (2000). Instead of duplicating that background information within this paper, the authors have chosen to focus on the mechanisms involved in extracting key flowpath-based portions of the original AML program and converting the extracted code to run in a more robust ANSI C++™ executable program. Consequently, supporting information from these previous manuscripts has been brought forward only where needed to understand or clarify a step in the program execution. Users will be shown that it is now possible to compute the RUSLE LS factor either by running the new executable file by itself from a command-line prompt to process a single watershed reporting unit, or by running a supporting AML shell program that calls the executable file as necessary to perform iterative processing for a specified group of watersheds. When the supporting AML shell is utilized, the Arc and Grid modules from the ArcInfo™ Workstation Version 8.2 software for PC/Windows platforms (a product of ESRI, Redlands, California, USA) are called upon to perform the analysis.1

Section snippets

Assumptions and pre-processing caveats

The RUSLE algorithm for calculating slope length (i.e., the L constituent of the LS factor) serves to reference the erosion estimate for a horizontally projected slope length (hpsl) to the experimentally measured erosion for a 22.1-m (72.6-foot) reference slope length (rsl), raised to the power of a designated slope-length exponent (m) value that addresses the ratio of rill-to-interrill erosion, or L=(hpsl/rsl)m as set forth in the RUSLE Handbook (McCool et al., 1997; Renard et al., 1997). The

Slope processing methodology

Our LS factor framework and methodology uses DEM data analyzed in accordance with RUSLE criteria and was primarily derived from Version 3 of the RUSLE-based AML code (Van Remortel et al., 2001) that was in turn developed from Version 2 of the USLE-based AML code (Hickey, 2000). Interested users are directed to Bob's Slope Page on the Internet for more information regarding the AML code, executables, and similar code developed for the IDRISI GIS software.2

Results of test runs

Informal time-trial runs comparing results from the original RUSLE-based AML program (Van Remortel et al., 2001) with results from the new C++ executable program were conducted for two distinct study areas. The first study area selected was the 230-km2 Rincon Creek watershed catchment in southeastern Arizona, which utilized 30-m horizontal and 0.01-m vertical resolution derivatives from the US Geological Survey's National Elevation Dataset DEM data. Fig. 2, Fig. 3, Fig. 4, Fig. 5 show graphical

Conclusions and recommendations

A significant drawback of the original AML-driven runs was that the ArcInfo processing was not able to make efficient use of available computer resources. This problem has now been effectively alleviated with the advent of the executable-driven array processing. Much faster run times can be expected as the DEM is loaded into a matrix and run in memory, assuming the dynamic memory limits of the computer are not exceeded. Performance can be expected to diminish somewhat when the computer must

Acknowledgements

The authors gratefully acknowledge Daniel T. Heggem and Ann M. Pitchford, US Environmental Protection Agency, Las Vegas, Nevada, USA, for their unwavering support in the development and technical transfer of the computer programs, without which this work would not have been possible; Timothy G. Wade, US Environmental Protection Agency, Research Triangle Park, North Carolina, USA, for conducting an informal review and computational accuracy checks of the programs; Lee A. Bice, Lockheed Martin

References (13)

  • R. Hickey et al.

    Slope length calculations from a DEM within ARC/INFO GRID

    Computers, Environment, and Urban Systems

    (1994)
  • J.F. O’Callaghan et al.

    The extraction of drainage networks from digital elevation data

    Computer Vision, Graphics, and Image Processing

    (1984)
  • Byers, G.E., Van Remortel, R.D., Miah, M.J., Teberg, J.E., Papp, M.L., Schumacher, B.A., Conkling, B.L., Cassell, D.L.,...
  • M. Dunn et al.

    The effect of slope algorithms on slope estimates within a GIS

    Cartography

    (1998)
  • M. Griffin et al.

    Estimating soil loss on topographically nonuniform field and farm units

    Journal of Soil and Water Conservation

    (1988)
  • C.T. Haan et al.

    Design Hydrology and Sedimentology for Small Catchments

    (1994)
There are more references available in the full text version of this article.

Cited by (114)

View all citing articles on Scopus
View full text