Journal of Mountain Science

, Volume 12, Issue 3, pp 533–548 | Cite as

Probabilistic properties of a curve number: A case study for small Polish and Slovak Carpathian Basins

  • Agnieszka RutkowskaEmail author
  • Silvia Kohnová
  • Kazimierz Banasik
  • Ján Szolgay
  • Beata Karabová


The proper determination of the curve number (CN) in the SCS-CN method reduces errors in predicting runoff volume. In this paper the variability of CN was studied for 5 Slovak and 5 Polish Carpathian catchments. Empirical curve numbers were applied to the distribution fitting. Next, theoretical characteristics of CN were estimated. For 100-CN the Generalized Extreme Value (GEV) distribution was identified as the best fit in most of the catchments. An assessment of the differences between the characteristics estimated from theoretical distributions and the tabulated values of CN was performed. The comparison between the antecedent runoff conditions (ARC) of Hawkins and Hjelmfelt was also completed. The analysis was done for various magnitudes of rainfall. Confidence intervals (CI) were helpful in this evaluation. The studies revealed discordances between the tabulated and estimated CNs. The tabulated CNs were usually lower than estimated values; therefore, an application of the median value and the probabilistic ARC of Hjelmfelt for wet runoff conditions is advisable. For dry conditions the ARC of Hjelmfelt usually better estimated CN than ARC of Hawkins did, but in several catchments neither the ARC of Hawkins nor Hjelmfelt sufficiently depicted the variability in CN.


Curve number Theoretical distribution Antecedent runoff conditions 


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  1. Akaike H (1974) A new look at the statistical model identification IEEE. Transactions on Automatic Control 19(6): 716–723.CrossRefGoogle Scholar
  2. ASCE (2009) Curve Number Hydrology: State of the Practice American Society of Civil Engineers. Reston, USA. p 116.Google Scholar
  3. Arnold JG, Williams JR, Srinivasan R, et al. (1994) SWAT — soil and water assessment tool. USDA, Agricultural Research Service, Grassland, Soil and Water Research Laboratory, 808 East Blackland Road, Temple, TX 76502, revised 10/25/94Google Scholar
  4. Babu PS, Mishra SK (2012) Improved SCS-CN-Inspired Model. Journal of Hydrologic Engineering 17: 1164–1172.CrossRefGoogle Scholar
  5. Baltas EA, Dervos NA, Mimikou MA (2007) Research on the initial abstraction — storage ratio and its effect on hydrograph simulation at a watershed in Greece. Hydrology and Earth System Sciences Discussions 4(4): 2169–2204. DOI: 105194/hessd-4-2169-2007.CrossRefGoogle Scholar
  6. Banasik K, Madeyski M, Więzik B, et al. (1994) Applicability of curve number technique for runoff estimation from small Carpathian watersheds. Proceedings of the International Conference on Developments in Hydrology in Mountainous Areas. Stara Lesna, Slovakia, Sept 12–16, UNESCO IHP-IV Project H-5-6.pp 125–126.Google Scholar
  7. Banasik K, Madeyski M, Mitchell JK, et al. (2005) An investigation of lag times for rainfall-runoff-sediment yield events in small river basins. Hydrological Sciences Journal 50(5): 857–866. DOI: 101623/hysj2005505857CrossRefGoogle Scholar
  8. Banasik K, Byczkowski A (2007) Probable annual floods in a small lowland river estimated with the use of various sets of data. Annals of Warsaw University of Life Sciences-SGGW. Land Reclamation 38: 3–10.Google Scholar
  9. Banasik K, Woodward D (2010) Empirical determination of runoff Curve Number for a small agricultural watershed in Poland. Proceedings of the 2 Joint Federal Interagency Conference “Hydrology and Sedimentation for a Changing Future: Existing and Emerging Issues” Las Vegas, NV, USA, June 27–July 1. p 11.Google Scholar
  10. Banasik K, Rutkowska A, Kohnova S (2014a) Retention and curve number variability in a small agricultural catchment: the probabilistic approach. Water 6(5): 1118–1133.CrossRefGoogle Scholar
  11. Banasik K, Krajewski A, Sikorska A, et al. (2014b) Curve Number estimation for a small urban catchment from recorded rainfall-runoff events. Archives of Environmental Protection 40(3): 75–86. DOI: 10.2478/aep-2014-0032.CrossRefGoogle Scholar
  12. Choi J, Engel BA, Chung HW (2002) Daily streamflow modelling and assessment based on the Curve Number technique. Hydrological Processes 16(16): 3131–3150.CrossRefGoogle Scholar
  13. Chow Ven Te (1964) Handbook of Applied Hydrology: A Compendium of Water-resources Technology. (Section 14 Runoff) McGraw-Hill Handbook Series, New York, USA. p 1468.Google Scholar
  14. Dingman SL (2008) Physical Hydrology (Second edition). Waveland Press, Long Grove, USA. p 395.Google Scholar
  15. DVWK Regeln (1999) Estimation of Design Discharges. Verlag Paul Parey, Hamburg, Germany. p 53. (In German)Google Scholar
  16. Endale DM, Schomberg HH, Fisher DS, et al. (2010) Examination of curve numbers from a small Piedmont catchment under 33 years of no-till crop management. Proceedings of 2nd Joint Federal Interagency Conference, Las Vegas, NV, USA, June 27–July 1. p 8.Google Scholar
  17. Epps TH, Hitchcock DR, Jayakaran AD, et al. (2013) Curve Number derivation for watersheds draining two headwater streams in lower coastal plain South Carolina, USA. JAWRA Journal of the American Water Resources Association 49(6): 1284–1295. DOI: 101111/jawr12084.CrossRefGoogle Scholar
  18. Gao GY, Fu BJ, Lű Y, et al. (2012) Coupling the Modified SCSCN and RUSLE Models to Simulate Hydrological Effects of Restoring Vegetation in the Loess Plateau of China. Hydrology and Earth System Sciences 16: 2347–2364. DOI: 105194/hess-16-2347-2012.CrossRefGoogle Scholar
  19. Garen D, Moore DS (2005) Curve Number hydrology in water quality modeling: uses, abuses, and future directions. Journal of the American Water Resources Association 41(2): 377–388.CrossRefGoogle Scholar
  20. Geetha K, Mishra SK, Eldho TI, et al. (2007) Modifications to SCS-CN Method for Long-Term Hydrologic Simulation. Journal of Irrigation and Drainage Engineering. ASCE 133(5): 475–486. DOI: 101061/(ASCE)0733-9437(2007).CrossRefGoogle Scholar
  21. Geetha K, Mishra SK, Eldho TI, et al. (2008) SCS-CN-based continuous simulation model for hydrologic forecasting. Water Resources Management 22(2): 165–190.CrossRefGoogle Scholar
  22. Grimaldi S, Petroselli A, Romano N (2013a) Green-Ampt Curve Number mixed procedure as an empirical tool for rainfall-runoff modelling in small and ungauged basins. Hydrological Processes 27: 1253–1264. DOI: 101002/hyp9303.CrossRefGoogle Scholar
  23. Grimaldi S, Petroselli A, Romano N (2013b) Curve-Number/Green-Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis. Hydrological Processes 27: 1265–1275. DOI: 101002/hyp9749.CrossRefGoogle Scholar
  24. Hawkins R (1973) Improved prediction of storm runoff in mountain watersheds. Journal of the Irrigation and Drainage Division 99(4): 519–523.Google Scholar
  25. Hawkins R (1979) Runoff Curve Numbers from Partial Area Watersheds. Journal of the Irrigation and Drainage Division 105(4): 375–389.Google Scholar
  26. Hawkins RH, Hjelmfelt Jr AT, Zevenbergen AW (1985) Runoff probability, relative storm depth, and runoff curve numbers Journal of Irrigation and Drainage Engineering. ASCE 111(4): 330–340.Google Scholar
  27. Hawkins RH (1990) Asymptotic determination of curve numbers from rainfall-runoff data. Symposium Proceedings, Watershed Planning and Analysis in Action, Durango, CO, USA, New York: American Society of Civil Engineers. pp 67–76.Google Scholar
  28. Hawkins RH (1993) Asymptotic determination of Curve Numbers from data. Journal of Irrigation and Drainage Division 119(2): 334–345.CrossRefGoogle Scholar
  29. Hawkins RH, Ward TJ, Woodward DE, et al. (2008) Curve Number Hydrology. Report of ASCE/EWRI Task Committee. p 106.Google Scholar
  30. Hjelmfelt Jr AT, Kramer LA, Burwell RE (1983) Curve Numbers as random variables. Proceedings of the specialized conference on Advances in Irrigation and Drainage: Surviving External Pressures Jackson WY USA. pp 365–370.Google Scholar
  31. Hjelmfelt A (1991) Investigation of Curve Number Procedure. Journal of Hydraulic Engineering 117(6): 725–737.CrossRefGoogle Scholar
  32. Huang MB, Gallichand J, Dong CY, et al. (2007) Use of moisture data and Curve Number method for estimating runoff in the Loess Plateau of China. Hydrological Processes 21: 1471–1481.CrossRefGoogle Scholar
  33. Jain MK, Mishra SK, Babu PS, et al. (2006) Enhanced runoff Curve Number model incorporating storm duration and a nonlinear Ia-S relation. Journal of Hydrologic Engineering 11(6): 631–635.CrossRefGoogle Scholar
  34. Jiang R (2001) Investigation of runoff curve number initial abstraction ratio. MS thesis Tucson: Watershed Management, University of Arizona. p 120.Google Scholar
  35. Krajewski A, Lee H, Hejduk L, et al. (2014) Predicted small catchment responses to heavy rainfalls with SEGMO and two sets of model parameters. Annals of Warsaw University of Life Sciences — SGGW, Poland. Land Reclamation 46(3): 205–220.Google Scholar
  36. Laio F (2004) Cramer-von Mises and Anderson Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resources Research 40(9): W09308. DOI: 101029/2004WR003204.CrossRefGoogle Scholar
  37. Laio F, Baldassare G, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resources Research 45(7): W07416. DOI:101029/2007WR006666.CrossRefGoogle Scholar
  38. Lyon SW, Walter MT, Gerard MP, et al. (2004) Using a topographic index to distribute variable source area runoff predicted with the SCS curve-number equation. Hydrological Processes 18(15): 2757–2771.CrossRefGoogle Scholar
  39. Madeyski M (1980) Transport of suspended load in little river basins. In: Transport and Sedimentation of Solid Particles (Proc IV Int Seminar at Wroclaw-Trzebieszowice, Poland, 25–28 Sept 1980) vol II, ES1-ES8 Wroclaw Agricultural University Press, Wroclaw, Poland. p 124.Google Scholar
  40. Madeyski M, Banasik K (1989) Applicability of the modified universal soil loss equation in small Carpathian watersheds. Catena Supplement 14: 75–80.Google Scholar
  41. Marcinkowski P, Pniewski M, Kardel I, et al. (2013) Modelling of discharge, nitrate and phosphate loads from the Reda catchment to the Puck Lagoon using SWAT. Annals of Warsaw University of Life Sciences — SGGW. Land Reclamation 45(2): 125–141.Google Scholar
  42. McCuen RH (1982) A guide to hydrologic analysis using SCS methods. Prentice-Hall, Inc, Englewood Cliffs, NJ, USA. p 145.Google Scholar
  43. McCuen RH (2002) Approach to Confidence Interval Estimation for Curve Numbers. Journal of Hydrologic Engineering 7: 43–48. DOI: 101061/(ASCE)/1084-0699(2002) 7:1(43).CrossRefGoogle Scholar
  44. McCutcheon SC, Negussie T, Adams MB, et al. (2006) Rainfall-runoff relationship for selected eastern U.S. forested mountain watersheds: testing of the curve number method for flood analysis. Technical Rep, West Virginia Division of Forestry, Charleston, WV, USA. p 270.Google Scholar
  45. Mishra SK, Singh VP, Sansalone JJ, et al. (2003) A modified SCS-CN method: characterization and testing. Water Resources Management 17: 37–68.CrossRefGoogle Scholar
  46. Mishra SK, Singh VP (2004) Long-term hydrological simulation based on the soil conservation service curve number. Hydrological Processes 18(7): 1291–1313.CrossRefGoogle Scholar
  47. Mishra SK, Sahu RK, Eldho TI, et al. (2006a) An improved Ia-S relation incorporating antecedent moisture in SCS-CN methodology. Water Resources Management 20: 643–660.CrossRefGoogle Scholar
  48. Mishra SK, Tyagi JV, Singh VP, et al. (2006b) SCS-CN-based modeling of sediment yield. Journal of Hydrology 324: 301–322.CrossRefGoogle Scholar
  49. Mishra SK, Takara K, Tachikawa Y (2008) NRCS Curve Number — based Hydrologic Regionalization of Nepalese River Basins for Flood Frequency Analysis. Annals of Disaster Prevention Research Institute, Kyoto University, Japan. 51 B: 93–102.Google Scholar
  50. Petroselli A, Grimaldi S, Romano N (2013) Curve-Number/Green-Ampt Mixed Procedure for Net Rainfall Estimation: A Case Study of the Mignone Watershed. IT Proc. Environmental Sciences 19: 113–121. DOI: 101016/jproenv201306013.CrossRefGoogle Scholar
  51. Pilgrim DH, Cordery I (1992) Flood runoff. In: Maidment, DL (ed.), Handbook of Hydrology. McGraw-Hill, New York, USA. pp 9.1–9.224.Google Scholar
  52. Ponce VM, Hawkins RH (1996) Runoff curve number: Has it reached maturity?. Journal of Hydrologic Engineering 1(1): 11–19.CrossRefGoogle Scholar
  53. Price MA (1998) Seasonal variation in runoff curve numbers. MS thesis, University of Arizona (Watershed Management) Tucson, AZ, USA. p 189.Google Scholar
  54. Rallison RE (1980) Origin and evolution of the SCS runoff equation. Proceedings of Symposium on Watershed Management New York, American Society of Civil Engineers.pp 912–924.Google Scholar
  55. Rallison RE, Miller N (1981) Past, present and future SCS runoff procedure. In: Singh VP (ed.), Rainfall-Runoff Relationship. Water Resources Publication, Littleton, Colorado, USA. pp 353–364.Google Scholar
  56. Rawls WJ, Ahuja LR, Brakensiek DL, et al. (1992) Infiltration and soil water movement. Chapter 5. In: Maidment DL (ed.), Handbook of Hydrology. McGraw-Hill, New York, USA. p 1424.Google Scholar
  57. Rietz PD (1999) Effects of land use on runoff curve numbers. MS thesis, University of Arizona (Watershed Management) Tucson, AZ, USA. p 115.Google Scholar
  58. Schneider L, McCuen R (2005) Statistical guidelines for curve number generation. Journal of Irrigation and Drainage Engineering 131(3): 282–290.CrossRefGoogle Scholar
  59. Soulis К, Dercas Н (2007) development of a GIS-based spatially distributed continuous hydrological model and its first application. Water International 32(1): 177–192. DOI: 101080/02508060708691974.CrossRefGoogle Scholar
  60. Soulis KX, Valiantzas JD, Dercas N, et al. (2009) Analysis of the runoff generation mechanism for the investigation of the SCSCN method applicability to a partial area experimental watershed. Hydrology and Earth System Sciences 13: 605–615.CrossRefGoogle Scholar
  61. Soulis KX, Valiantzas JD (2012) Variation of runoff curve number with rainfall in heterogeneous watersheds: the two-CN system approach. Hydrology and Earth System Sciences 16: 1001–1015. DOI: 105194/hess-16-1001-2012CrossRefGoogle Scholar
  62. Soulis KX, Valiantzas JD (2013) Identification of the SCS-CN parameter spatial distribution using rainfall-runoff data in heterogeneous watersheds. Water Resources Management 27: 1737–1749. DOI: 101007/s11269-012-0082-5.CrossRefGoogle Scholar
  63. Sneller JA (1985) Computation of runoff curve numbers for rangelands from Landsat data. Technical Report HL85-2, US Dept. of Agriculture, Agricultural Research Service, Hydrology Laboratory, Beltsville, Maryland, USA. p 50.Google Scholar
  64. Tedela NM, McCutcheon SC, Rasmussen TC, et al. (2007) Evaluation and Improvements of the Curve Number Method of Hydrological Analysis on Selected Forested Watersheds of Georgia. The University of Georgia. Report submitted to Georgia Water Resources Institute. p 75. Available online at: http://waterusgsgov/wrri/07grants/progress/2007GA143B.pdf (Accessed on 25 October 2013).Google Scholar
  65. Tedela NH, McCutcheon SC, Rasmussen TC, et al. (2012) Runoff Curve Numbers for 10 Small Forested Watersheds in the Mountains of the Eastern United States. Journal of Hydrologic Engineering 17: 1188–1198. DOI: 101061/(ASCE)HE1943-55840000436.CrossRefGoogle Scholar
  66. USDA (2004) Estimation of direct runoff from storm rainfall. National Engineering Handbook, Chapter 10, part 630. USDA Soil Conservation Service, Washington, USA. pp 1–22.Google Scholar
  67. Wischmeier HW, Smith DD (1978) Predicting rainfall erosion losses — a guide to conservation planning. Agriculture Handbook No 573. U.S.Gouvernment Printing Office, Washington, USA. p 66.Google Scholar
  68. Wood MK, Blackburn WH (1984) An evaluation of the hydrologic soil groups used in the SCS runoff method on rangelands. Water Resources Bulletin 20(3): 379–389.CrossRefGoogle Scholar
  69. Woodward DE (1991) Progress report ARS/SCS runoff curve number work group. ASCE Paper 912607 Chicago, IL, USA. pp 10.Google Scholar
  70. Woodward DE, Hawkins RH, Jiang R, et al. (2003) Runoff curve number method: examination of the initial abstraction ratio. In: Bizier P, DeBarry P (eds.), Proceedings of the World Water & Environmental Resources Congress 2003 and Related Symposia, EWRI, ASCE, 23-26 June, 2003, Philadelphia, Pennsylvania, USA. p 10. DOI: 101061/40685(2003)308.Google Scholar
  71. Woodward DE, Scheer CC, Hawkins RH (2006) Curve Number update for runoff calculation. Annals of Warsaw Agricultural University — SGGW. Land Reclamation 37: 33–42.Google Scholar
  72. Woodward DE, Hoeft CC, Hawkins RH, et al. (2010) Discussion of “Modifications to SCS-CN method for long-term hydrologic simulation” by K. Geetha, S. K. Mishra, T. I. Eldho, A. K. Rastogi, and R. P. Pandey. Journal of Irrigation and Drainage Engineering 136(6): 444–446.CrossRefGoogle Scholar
  73. Young DF, Carleton JNC (2006) Implementation of a probabilistic curve number method in the PRZM runoff model. Environmental Modeling and Software 21(8): 1172–1179.CrossRefGoogle Scholar

Copyright information

© Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Agnieszka Rutkowska
    • 1
    Email author
  • Silvia Kohnová
    • 2
  • Kazimierz Banasik
    • 3
  • Ján Szolgay
    • 2
  • Beata Karabová
    • 2
  1. 1.Department of Applied MathematicsUniversity of AgricultureCracowPoland
  2. 2.Department of Land and Water Resources Management, Faculty of Civil EngineeringSlovak University of TechnologyBratislavaSlovak Republic
  3. 3.Department of River Engineering, Sedimentation LabWarsaw University of Life Sciences-SGGWWarsawPoland

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