Journal of Mountain Science

, Volume 11, Issue 5, pp 1169–1181 | Cite as

Uncertainty of slope length derived from digital elevation models of the Loess Plateau, China

  • Shi-jie Zhu
  • Guo-an TangEmail author
  • Li-yang Xiong
  • Gang Zhang


Although many studies have investigated slope gradient uncertainty derived from Digital Elevation Models (DEMs), the research concerning slope length uncertainty is far from mature. This discrepancy affects the availability and accuracy of soil erosion as well as hydrological modeling. This study investigates the formation and distribution of existing errors and uncertainties in slope length derivation based on 5-m resolution DEMs of the Loess Plateau in the middle of China. The slope length accuracy in three different landform areas is examined to analyse algorithm effects. The experiments indicate that the accuracy of the flat test area is lower than that of the rougher areas. The value from the specific contributing area (SCA) method is greater than the cumulative slope length (CSL), and the differences between these two methods arise from the shape of the upslope area. The variation of mean slope length derived from various DEM resolutions and landforms. The slope length accuracy decreases with increasing grid size and terrain complexity at the six test sites. A regression model is built to express the relationship of mean slope length with DEM resolution less than 85 m and terrain complexity represented by gully density. The results support the understanding of the slope length accuracy, thereby aiding in the effective evaluation of the modeling effect of surface process.


Slope length Uncertainty Digital Elevation Models (DEM) Loess terrain 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Akhtar MK, Corzo GA, van Andel SJ, et al. (2009) River flow forecasting with artificial neural networks using satellite observed precipitation pre-processed with flow length and travel time information: case study of the Ganges river basin. Hydrology and Earth System Sciences 13: 1607–1618. DOI: 10.5194/hess-13-1607-2009CrossRefGoogle Scholar
  2. Cui LZ (2002) The coupling relationship between the sediment yield from rainfall erosion and the topographic feature of the watershed. PhD thesis, Northwest Agriculture and Forest University, China. (In Chinese)Google Scholar
  3. Desmet PJJ, Govers G (1996) A GIS procedure for automatically calculating the USLE LS factor on topographically complex landscape units. Journal of Soil and Water Conservation 51: 427–433. DOI: 10.2489/jswc.63.3.105Google Scholar
  4. Fisher PE, Tate NJ (2006) Causes and consequences of error in digital elevation models. Progress in Physical Geography 30: 467–489. DOI: 10.1191/0309133306pp492raCrossRefGoogle Scholar
  5. Foster GR, Wischmeier WH (1974) Evaluating irregular slopes for soil loss prediction. Transactions of ASAE 17: 305–309.CrossRefGoogle Scholar
  6. Gao J (1997) Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. International Journal of Geographical Information Science 11:199–212. DOI:10.1080/136588197242464CrossRefGoogle Scholar
  7. Gao J (1998) Impact of sampling intervals on the reliability of topographic variables mapped from grid DEMs at a micro scale. International Journal of Geographical Information Systems 12(8): 875–890. DOI: 10.1080/136588198241545CrossRefGoogle Scholar
  8. Hickey RJ (2000) Slope angle and slope length solutions for GIS. Cartography (Canberra) 29(1): 1–8. DOI: 10.1080/00690805.2000.9714334CrossRefGoogle Scholar
  9. Horton RE (1945) Erosional development of streams and their drainage basins. Hydrophysical approach to quantitative morphology Geological Society of America Bulletin: 275–370. DOI: 10.1080/00690805.2000.9714334Google Scholar
  10. Jiang ZS, Zheng FL, Wu M (2005) Prediction Model of Water Erosion on Hillslopes. Journal of Sediment Research 58: 11–17. DOI: 0468-155X(2005) 04-0001-06Google Scholar
  11. Kinnell PIA (2001) Slope Length Factor for Applying the USLEM to Erosion in Grid Cells. Soil & Tillage Research 11–17. DOI: 10.1016/S0167-1987(00)00179-3Google Scholar
  12. Liu M, Tang G, Wang C, et al. (2007) Analysis of the slope uncertainty derived from DEMs. GEO-INFORMATION SCIENCE 9(2): 65–69. DOI: 10.3969/j.issn.1560-8999.2007.02.014Google Scholar
  13. Liu H, Kiesel J, Hormann G, et al. (2011) Effects of DEM Horizontal Resolution and Methods on Calculating the Slope Length Factor in Gently Rolling Landscapes. Catena 87: 368–375. DOI: 10.1016/j.catena.2011.07.003CrossRefGoogle Scholar
  14. Lu H, Gallant J, Prosser IP, et al. (2001) Prediction of Sheet and Rill Erosion over the Australian Continent, Incorporating Monthly Soil Loss Distribution. Canberra. CSIRO Land and Water DOI: 10.1071/SR02157Google Scholar
  15. Lu H, Prosser IP, Moran CJ, et al. (2003) Predicting sheetwash and rill erosion over the Australian continent. Australian Journal of Soil Research 41: 1037–1062. DOI: 10.1071/SR02157CrossRefGoogle Scholar
  16. Lu HX (2008) Modelling terrain complexity. In: Advances in Digital Terrain Analysis. Springer Berlin Heidelberg, Germany. pp 159–176Google Scholar
  17. Moore ID, Burch GJ (1986) Physical basis of the length-slope factor in the Universal Soil Loss Equation. Soil Science Society of America Journal 50: 1294–1298. DOI: 10.2136/sssaj1986.03615995005000050042xCrossRefGoogle Scholar
  18. Moore ID, Wilson JP (1992) Length-slope factors for the Revised Universal Soil Loss Equation: Simplified method of estimation. Journal of Soil and Water Conservation 47: 423–428.Google Scholar
  19. Renard KG, Foster GR, Weesies GA, et al. (1991) RUSLE: Revised universal soil loss equation. Journal of Soil and Water Conservation 46: 30–33.Google Scholar
  20. Renard KG, Foster, GR, Weesies GA, et al. (1997) Predicting soil erosion by Water: A Guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). Agricultural Handbook No.537, United States Department of Agriculture, Washington.Google Scholar
  21. Shi W (2010) Principles of modeling uncertainties in spatial data and spatial analyses. The Chemical Rubber Company Press, Florida, USA. p 412.Google Scholar
  22. Smith DD, Wischmeier WH (1957) Factors affecting sheet and rill erosion. American Geographer Union Trans 38:889–896. DOI: 10.1029/TR038i006p00889CrossRefGoogle Scholar
  23. Song J, Tang G, Wang C, et al. (2006) Edge effect analysis on deriving slope from grid DEM. Bulletin of Soil and Water Conservation 26(3): 82–85.Google Scholar
  24. Strahler AN (1953). Hypsometric (area-altitude) analysis of erosional topograghy. Geological Society of America Bulletin 63:1117–1142. DOI:10.1130/0016-7606(1952)63[1117:HAAOET]2.0. CO;2CrossRefGoogle Scholar
  25. Tang G, Zhao M, Li T, et al. (2003) Modeling slope uncertainty derived from DEMs in Loess Plateau. Acta Geographica Sinica 58(6):824–830.Google Scholar
  26. Tang G, Li F, Liu X, et al. (2008) Research on the slope spectrum of the Loess Plateau. Science in China Series E: Technological Sciences 51: 175–185. DOI: 10.1007/s11431-008-5002-9CrossRefGoogle Scholar
  27. Tarboton D (2003) Terrain Analysis Using Digital Elevation Models in Hydrology. 23rd ESRI International Users Conference, July 7–11, San Diego, California.Google Scholar
  28. Thieken AH, Lucke A, Diekkruger B, et al. (1999) Scaling input data by GIS for hydrological modeling. Hydrological Process 13: 611–630. DOI: 10.1002/(SICI)1099-1085(199903)13:4<611:: AID-HYP758>3.0.CO;2-6CrossRefGoogle Scholar
  29. Tian J, Tang G, Zhou Y, Song X (2013) Spatial variation of gully density in the Loess Plateau. Scientia Geographica Sinica 33(5): 622–628. (In Chinese)Google Scholar
  30. Van Remortel RD, Hamilton ME, Hickey RJ (2001) Estimating the LS factor for RUSLE through iterative slope length processing of digital elevation data. Cartography 30: 27–35. DOI: 10.1080/00690805.2001.9714133.CrossRefGoogle Scholar
  31. Van Remortel RD, Maichle RW, Hickey RJ (2004) Computing the LS factor for the Revised Universal Soil Loss Equation through array-based slope processing of digital elevation data using a C++ executable. Computers & Geosciences 30:1043–1053. DOI: 10.1016/j.cageo.2004.08.001.CrossRefGoogle Scholar
  32. Williams JR, Berndt HD (1977) Determining the universal soil loss equation’s length-slope factor for watersheds Soil Erosion: Prediction and Control. Soil Conservation Society of American 21: 217–225.Google Scholar
  33. Wilson JP, Lam CS, Deng YX (2007) Comparison of the performance of flow-routing algorithms used in GIS-based hydrologic analysis. Hydrological Processes 21:1026–1044. DOI: 10.1002/hyp.6277CrossRefGoogle Scholar
  34. Wilson JP, Repetto PL, Snyder RD (2000) Effect of data source, grid resolution and flow-routing method on computed topographic attributes. In Terrain Analysis: Principles and Applications. John Wiley & Sons, New York, USA. pp 133–161.Google Scholar
  35. Winchell MF, Jackson SH, Wadley AM, et al. (2008) Extension and validation of a geographic information system-based method for calculating the revised universal soil loss equation length-slop factor for erosion risk assessments in large watersheds. Journal of Soil and Water Conservation 63(3): 105–111.CrossRefGoogle Scholar
  36. Wischmeier WH, Smith DD (1965) Predicting Rainfall-erosion Losses from Cropland East of the Rocky Mountains. Agricultural Handbook 282, Agricultural Research Service, United States Department of Agriculture.Google Scholar
  37. Wischmeier WH, Smith DD (1978) Predicting rainfall erosion losses. Agricultural Handbook 537. United States Department of Agriculture, Science and Education Administration.Google Scholar
  38. Wise S (2011) Cross-validation as a means of investigating DEM interpolation error. Computers & Geosciences 37: 978–991. DOI: 10.1016/j.cageo.2010.12.002CrossRefGoogle Scholar
  39. Xiong L, Tang G, Yan S, et al. (2013) Landform-oriented flowrouting algorithm for the dual-structure loess terrain based on digital elevation models. Hydrological Processes. DOI: 10.1002/hyp.9719.Google Scholar
  40. Xiong LY, Tang GA. Yuan BY, et al. (2014a) Geomorphological inheritance for loess landform evolution in a severe soil erosion region of Loess Plateau of China based on digital elevation models. Science China Earth Sciences 57(8): 1944–1952. DOI: 10.1007/s11430-014-4833-4CrossRefGoogle Scholar
  41. Xiong L, Tang G, Li F, et al. (2014b). Modeling the evolution of loess-covered landforms in the Loess Plateau of China using a DEM of underground bedrock surface. Geomorphology 209(0): 18–26. DOI: 10.1016/j.geomorph.2013.12.009CrossRefGoogle Scholar
  42. Young RA, Onstad CA, Bosch DD, et al. (1989) AGNPS: A nonpoint-source pollution model for evaluating agricultural watersheds. Journal of Soil and Water Conservation 44: 168–173.Google Scholar
  43. Zachar D (1982) Soil erosion: development in soil science 10. Elsevier Scientific Publishing Company, New York. p 547.Google Scholar
  44. Zheng F (1989) The critical slope length and slope in rill erosion. Chinese Water and Soil Conservation: 23–24.Google Scholar
  45. Zhou Q, Liu X (2006) Digital Terrain Analysis. Science Press, Beijing, China. p 327. (In Chinese)Google Scholar
  46. Zhou Y, Tang, GA, Yang X, et al. (2010) Positive and negative terrains on northern Shaanxi Loess Plateau. Journal of Geographical Sciences 20(1):64–76. DOI: 10.1007/s11442-010-0064-6CrossRefGoogle Scholar
  47. Zingg AW (1940) Degree and length of land slope as it affects soil loss in runoff. Agricultural Engineering: 59–64.Google Scholar

Copyright information

© Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Shi-jie Zhu
    • 1
    • 2
  • Guo-an Tang
    • 1
    Email author
  • Li-yang Xiong
    • 1
  • Gang Zhang
    • 1
  1. 1.Key Laboratory of Virtual Geographic Environment Ministry of EducationNanjing Normal UniversityNanjingChina
  2. 2.Zhejiang Academy of Surveying & MappingHangzhouChina

Personalised recommendations