Abstract
The curve number (CN) rainfall-runoff method is described, with inferred extension to daily time-step models, which are the bases for most total maximum daily load (TMDL) assessments. Although originally developed for engineering design for extreme rainfall events, its flexibility, its basis in soils and land use, and its history of accepted use have encouraged adaptation and adjustment to the continuous daily time-step models needed for TMDL evaluations. The original event-based CN model itself, background assumptions, improvements, problems, and evolved usage are described. Included are the roles of the initial abstraction ratio (), antecedent conditions (ARC), the limits of application with different land types, model sensitivity, effects of land slope, and seasonality. Inconsistencies and recent improvements are stressed, including (1) the adjustment of the abstraction coefficient to 0.05 from the traditional value of 0.20; (2) awareness of the nonapplicability of the CN method in all cases and the preferred use of distributed/weighted runoffs from an array of CN source areas over the use of runoffs from averages CNs; and (3) use of local data and on-site inspections for calibration and perspective. The application of CN-based watershed hydrology models for TMDL studies should be conducted cautiously because it can produce a biased estimation of hydrograph components in certain soils and landscapes. Model parameter calibration in the application of CN method for continuous simulations of TMDLs is strongly suggested.
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Acknowledgments
The authors want to appreciate the help from the USDA Agricultural Research Service (ARS) for sharing data for Hastings, Nebraska, 44002 for 482 events from 1939 to 1967.
References
Arnold, J. G., J. R. Williams, A. D. Nicks, and N. B. Sammons. 1990. SWRRB—A basin scale simulation model for soil and water resources management. College Station, TX: Texas A&M Press.
Arnold, J. G., J. R. Williams, R. Srinivasan, K. W. King, and R. H. Griggs. 1994. SWAT—Soil and water assessment tool. Temple, TX: USDA.
ASCE-ASABE (American Society of Agricultural and Biological Engineers)-NRCS (Natural Resources Conservation Service) Task Group on Curve Number Hydrology. 2017. Report of Task Group on Curve Number Hydrology, Chapters 8 (Land Use and Land Treatment Classes), 9 (Hydrologic Soil Cover Complexes), 10 (Estimation of Direct Runoff from Storm Rainfall), 12 (Hydrologic Effects of Land Use and Treatment), edited by R. H. Hawkins, T. J. Ward, and D. E. Woodward, 115. Reston, VA: ASCE.
Betson, R. P., J. Bales, and H. E. Pratt. 1980. Users guide to TVA-HYSIM. A hydrologic program for quantifying land-use change effects. Cincinnati: USEPA.
Bingner, R. L., and F. D. Theurer. 2011. “Agricultural non-point source pollution model (AnnAGNPS).” http://www.ars.usda.gov/Research/docs.htm?docid=5222.
Bondelid, T. R., R. H. McCuen, and T. J. Jackson. 1982. “Sensitivity of SCS models to curve number variation.” Water Resour. Bull. 18 (1): 111–116. https://doi.org/10.1111/j.1752-1688.1982.tb04536.x.
Borah, D. K. 2010. Hydrologic Modeling Inventory (HMI) Questionnaire. Denver: Texas A&M Univ. and US Bureau of Reclamation.
Borah, D. K., R. Xia, and M. Bera. 2001. “DWSM—A dynamic watershed simulation model for studying agricultural nonpoint-source pollution.” In Proc., 2001 ASAE Annual Int. Meeting. St. Joseph, MI: ASAE.
Carlson, D. H., T. L. Thurlow, and J. R. Wight. 1995. “SPUR-91: Simulation of production and utilization of rangelands.” Chap. 27 in Computer models of watershed hydrology, edited by V. P. Singh, 1021–1068. Littleton, CO: Suspect Water Resources Publications.
Carsel, R. F., C. N. Smith, L. A. Mulkey, J. D. Dean, and P. Jowsie. 1984. User’s manual for the pesticide root zone model (PRZM): Release 1. Athens, GA: USEPA.
Cronshey, R. G., and F. D. Theurer. 1998. “AnnAGNPS-non-point pollutant loading model.” In Vol. 1 of Proc., 1st Interagency Hydrologic Modeling Conf. Subcommittee on Hydrology of the Interagency Committee on Water Data, 9–16. Washington, DC: USDA.
D’Asaro, F., G. Grillone, and R. H. Hawkins. 2014. “Curve number: Empirical evaluation and comparison with curve number handbook tables in Sicily.” J. Hydrol. Eng. 19 (12): 04014035. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000997.
D’Asaro, F., G. Grillone, and R. H. Hawkins. 2018. “Curve number seasonal variation in mid-mediterranean area.” J. Irrig. Drain. Eng. 144 (9): 04018021. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001334.
Foster, G. R., D. C. Yoder, G. A. Weesies, D. K. McCool, K. C. McGregor, and R. A. Binger. 2003. “Revised universal soil loss equation RUSLE2, users guide (Draft).” http://fargo.nserl.purdue.edu/rusle2dataweb.
Garg, V., I. Chaubey, and B. E. Haggard. 2003. “Impact of calibration watershed on runoff model accuracy.” Trans. Am. Soc. Agric. Eng. 46 (5): 1347–1353. https://doi.org/10.13031/2013.15445.
Grabau, M. R., R. H. Hawkins, K. E. VerWiere, and D. C. Slack. 2009. “Variety of antecedent runoff conditions for rainfall-runoff with the curve number method.” In Proc., 2009 Meetings of the Hydrology Section of the Arizona-Nevada Academy of Science, 45–48. Tucson, AZ: Univ. of Arizona.
Green, W. H., and G. Ampt. 1911. “Studies of soil physics, part I. The flow of air and water through soils.” J. Agric. Sci. 4 (1): 1–24. https://doi.org/10.1017/S0021859600001441.
Haith, D. A., R. Mandel, and R. S. Wu. 1992. GWLF: Generalized watershed loading functions. Ithaca, NY: Cornell Univ.
Hawkins, R. H. 1975. “The importance of accurate curve numbers in the estimation of storm runoff.” Water Resour. Bull. 11 (5): 887–890. https://doi.org/10.1111/j.1752-1688.1975.tb01810.x.
Hawkins, R. H. 1978. “Runoff curve number relationships under varying site moisture levels.” Proc. Am. Soc. Civ. Eng. 104 (IR4): 389–398.
Hawkins, R. H. 1980. “Infiltration and curve number: Pragmatic and theoretic relationships.” In Proc., Watershed Management Symp., 925–937. New York: ASCE.
Hawkins, R. H. 1990. “Asymptotic determination of curve numbers from rainfall-runoff data.” In Proc., Symp. Watershed Planning and Analysis in Action, 67–76. New York: ASCE.
Hawkins, R. H. 1993. “Asymptotic determination of curve numbers from data.” J. Irrig. Drain. Div. 119 (2): 334–345. https://doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
Hawkins, R. H., R. Jiang, and D. E. Woodward. 2002a. “Application of the curve number method in watershed hydrology.” In Proc., American Water Resources Annual Meeting. Middleburg, VA: American Water Resources Association.
Hawkins, R. H., and K. E. VerWeire. 2005. “Effects of prior rainfall and storm variables on curve number rainfall-runoff.” In Proc., ASCE Symp. on Watershed Management. Reston, VA: ASCE.
Hawkins, R. H., and T. J. Ward. 2012. “Expected value of event runoff with curve number theory.” In Proc., ASCE Environmental and World Water Congress, 10. Reston, VA: ASCE.CD-ROM.
Hawkins, R. H., T. J. Ward, and D. E. Woodward. 2015. “The complacent-violent runoff behavior: A departure from tradition”. In Proc., ASCE Watershed Management Conf., 12. Reston, VA: ASCE.
Hawkins, R. H., T. J. Ward, D. E. Woodward, and J. A. Van Mullem. 2009. ASCE EWRI task committee report on state of the practice in curve number hydrology, 106. Reston, VA: ASCE.
Hawkins, R. H., T. J. Ward, D. E. Woodward, and J. A. Van Mullem. 2010. “Continuing evolution of the curve number method.” In Proc., (CD-ROM) Joint Federal Interagency Conf., 10. Las Vegas.
Hawkins, R. H., D. E. Woodward, A. T. Hjelmfelt, Jr., J. A. Van Mullem, and Q. D. Quan. 2002b. “Runoff curve number method; examination of the initial abstraction ratio.” In Proc., Federal Interagency Hydrologic Modeling Conf., 12. Las Vegas.
Hawkins, R. H., D. E. Woodward, and R. Jiang. 2001. “Investigation of the runoff curve number abstraction ratio.” In Proc., USDA-NRCS Hydraulic Engineering Workshop, 10. Washington, DC: US Dept. of Agriculture-NRCS (Natural Resources Conservation Service).
Hewlett, J. D., G. B. Cunningham, and C. A. Troendle. 1977. “Predicting storm flow and peak flow from small basins in humid areas by the R-index method.” Water Resour. Bull. 13 (2): 231–254. https://doi.org/10.1111/j.1752-1688.1977.tb02021.x.
Hewlett, J. D., J. C. Forsten, and J. B. Cunningham. 1984. “Additional tests on the effect of rainfall intensity on stormflow and peak flow from wild-land basins.” Water Resour. Res. 20 (7): 985–989. https://doi.org/10.1029/WR020i007p00985.
Hjelmfelt, A. T., Jr., L. A. Kramer, and R. E. Burwell. 1982. “Curve numbers as random variables.” In Rainfall-runoff relationships, edited by V. Singh, 365–370. Littleton, CO: Water Resources Publications.
Hope, A. S. 1980. “Estimation of catchment moisture status for the SCS stormflow model.” M.S. thesis, Dept. of Agricultural Engineering, Univ. of Natal.
Horton, R. E. 1939. “Analysis of runoff plot experiments with varying infiltration capacity.” Trans. Am. Geophys. Union 20 (4): 693–711.
Jiang, R. 2001. “Investigation of runoff curve number initial abstraction ratio.” M.S. thesis, Dept. of School of Natural ResourcesWatershed Management, Univ. of Arizona.
Kim, N., J. W. Lee, J. Lee, and J. E. Lee. 2010. “SWAT application to estimate design runoff curve number for South Korean conditions.” Hydrol. Processes 24 (2): 156–2170.
Knisel, W. G., ed. 1980. CREAMS: A field-scale model for chemical, runoff, and erosion from agricultural management systems. Washington, DC: US Dept. of Agriculture, Science and Education Administration.
Kowalik, T., and A. Wolega. 2015. “CN parameter for small agricultural watersheds using asymptotic functions.” Water 7 (12): 939–955. https://doi.org/10.3390/w7030939.
Leonard, R. A., W. G. Knisel, and D. A. Still. 1987. “GLEAMS: Groundwater loading effects on agricultural management systems.” Trans. ASAE 30 (5): 1403–1418. https://doi.org/10.13031/2013.30578.
Ohio EPA. n.d. Nutrient model development for Upper Salt Creek and Beech Fork: Appendix C. Columbus, OH: Ohio EPA.
Pandit, A., and H. H. Heck. 2008. “Estimations of SCS curve numbers for concrete and asphalt.” ASCE J. Hydrol. Eng. 14 (4): 335–345. https://doi.org/10.1061/(ASCE)1084-0699(2009)14:4(335).
Price, M. A. 1998. “Seasonal variation in runoff curve numbers.” M.S. thesis, Dept. of School of Natural Resources, Univ. of Arizona.
Rossman, L. A. 2010. Storm water management model. User’s manual, version 5.0, 295. Washington, DC: USEPA.
Santhi, C., J. G. Arnold, J. R. Williams, W. A. Dugas, R. Srinivasan, and L. M. Hauck. 2001. “Validation of the SWAT model on a large river basin with point and nonpoint sources.” J. Am. Water Resour. Assoc. 37 (5): 1169–1188. https://doi.org/10.1111/j.1752-1688.2001.tb03630.x.
Saxton, K. E. 1993. “Soil water hydrology and chemical budgets with the enhanced SPAW model.” In Proc., Federal Interagency Workshop Hydrologic Modeling Demands for the 90’s, 9. Ft. Collins, CO.
Schulze, R. E. 1984. Hydrological models for application to small rural catchments in southern Africa: Refinement and development. Pretoria, Republic of South Africa: Water Research Commission.
Sexton, A. M. 2007. “Evaluation of SWAT model applicability for waterbody impairment identification and TMDL analysis.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Maryland.
Shaffer, M. J., A. D. Halvorson, and F. D. Pierce. 1991. “Nitrate leaching and economic analysis package (NLEAP): Model description and application.” In Managing nitrogen for groundwater quality and farm profitability, edited by R. F. Follet, D. R. Keeney, and R. M. Cruse, 285–322. Madison, WI: Soil Science Society of America.
Shoemaker, L., T. Dai, and J. Koenig. 2005. “TMDL model evaluation and research needs.” Accessed February 4, 2018. http://www.epa.gov/ORD/NRMRL/pubs/600r05149/600r05149.pdf.
Stewart, D., E. Canfield, and R. H. Hawkins. 2010. “A comparison of curve number determination methods and uncertainty in hydrologic soil groups from semi-arid watershed data.” In Proc., Arizona Hydrological Society Annual Meeting. Tucson, AZ: Univ. of Arizona.
Stewart, D., E. Canfield, and R. H. Hawkins. 2012. “A comparison of curve number determination methods and uncertainty in hydrologic soil groups from semi-arid watershed data.” J. Hydrol. Eng. 17 (11): 1180–1187. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000452.
Stone, J. J., L. J. Lane, E. D. Shirley, and K. G. Renard. 1986. “A runoff-sediment model for semiarid regions.” In Vol. 2 of Proc., 4th Federal Interagency Sedimentation Conf., 7-75–6-84. Las Vegas.
Stone, J. J., G. B. Paige, and R. H. Hawkins. 2008. “Rainfall intensity dependent infiltration rates on rangeland rainfall simulation plots.” Trans. Am. Soc. Agric. Biol. Eng. 51 (1): 1–9.
Tedela, N. 2009. “Rainfall-runoff relationships for small, mountainous, forested watersheds in the eastern United States.” Ph.D. dissertation, Dept. of Forest Resources, Univ. of Georgia.
Tedela, N., S. McCutcheon, J. Campbell, W. Swank, M. Adams, and T. Rasmussen. 2012. “Curve numbers for nine mountainous eastern United States watersheds: Seasonal variation and forest cutting.” J. Hydrol. Eng. 17 (11): 1188–1198. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000436.
Tetra Tech, Inc. 2011. “User’s guide spreadsheet tool for the estimation of pollutant load (STEPL) Version 4.1.” Accessed December 7, 2018. http://it.tetratech-ffx.com/steplweb/models$docs.htm.
Titmarsh, G. W., D. H. Pilgrim, I. Cordery, and A. A. Hoissein. 1989. “An examination of design flood estimations using the US Soil Conservation Services method.” In Proc., Hydrology and Water Resources Symp., 247–251. Christchurch, NZ.
USDA. 1986. TR-55 urban hydrology for small watersheds, 164. Washington, DC: USDA.
USDA and NRCS (Natural Resource Conservation Service). 2003. “Hydrology.” Part 630 in National engineering handbook. Accessed January 1, 2010. http://www.wcc.nrcs.usda.gov/hydro/hydro-techref-neh-630.html.
USDA and Soil Conservation Service. 1954. “Section 4: Hydrology.” Chaps. 4–10 in National engineering handbook, 400. Washington, DC: USDA.
Williams, J. D., and W. V. LaSeur. 1976. “Water yield model using SCS curve numbers.” J. Hydraul. Div. 102 (HY9): 1241–1253.
Williams, J. R. 1995. “The EPIC model.” Chap. 25 in Computer models of watershed hydrology, edited by V. P. Singh, 909–1000. Highlands Ranch, CO: Water Resources Publications.
Williams, J. R., P. T. Dyke, and C. A. Jones. 1983. “EPIC: A model for assessing the effects of erosion on soil productivity.” In Analysis of ecological systems: State of the art in ecological modeling, edited by W. K. Lauenroth, G. V. Skogerboe, and M. Flug, 553–572. Amsterdam, Netherlands: Elsevier.
Williams, J. R., C. A. Jones, and P. T. Davis. 1984. “Modeling approach to determining the relationship between erosion and soil productivity.” Soil Sci. Soc. Am. J. 48 (4): 800–805. https://doi.org/10.2136/sssaj1984.03615995004800040020x.
Williams, J. R., N. Kannan, X. Wang, C. Santhi, and J. G. Arnold. 2012. “Evolution of the SCS runoff curve number method and its application to continuous runoff simulation.” J. Hydrol. Eng. 17 (11): 1221–1229. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000529.
Woodward, D. E., R. H. Hawkins, J. A. Van Mullem, and A. Plummer. 2010. Curve number completion study. Beltsville, MD: USDA.
Young, R. A., C. A. Onstadt, D. D. Bosch, and W. P. Anderson. 1989. “AGNPS: A nonpoint-source pollution model for evaluating agricultural watersheds.” J. Soil Water Conserv. 44 (2): 168–173.
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Journal of Hydrologic Engineering
Volume 24 • Issue 7 • July 2019
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©2019 American Society of Civil Engineers.
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Received: Oct 4, 2017
Accepted: Sep 20, 2018
Published online: Apr 29, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 29, 2019
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