Abstract

The curve number (CN) equation is a semiempirical, event-based model commonly used to estimate rainfall runoff. This model was originally developed in the 1950s to estimate storm runoff from 24-h rainfall events from small catchments. The model consists of two parameters: (1) the curve number (CN), which represents soil type, land use, and land cover; and (2) the initial abstraction (Ia), i.e., the amount of rain that needs to accumulate before storm runoff begins. Despite its narrow-intended use, the CN model is widely used for many applications from engineering design to hydrologic modeling and uses parameter tables and guidelines developed in the mid-20th century. Changes in land management and hydrological science pose questions about the continued relevancy of the model in general and the tabulated parameters specifically. We used Catchment Attributes and Meteorology for Large-Sample Studies (CAMELS), a recently collated data set of watershed characteristics and performed regression analyses on the watershed attributes to determine whether the CN and Ia parameters can better fit a wider range of attributes than can the currently used tables. Our analyses focused on 5–35 year peak runoff events. We considered 333 small to medium watersheds distributed across the contiguous US and more than 40 watershed characteristics. We found that the CN model generally worked best if Ia was much smaller than traditionally assumed. Indeed, Ia=0 generally worked well. We also found that CN-values generally correlated well with climate (elevation, average precipitation) and soil permeability (sand fraction, saturated hydraulic conductivity). Our results suggest that the CN model can work relatively well for engineering purposes in ungauged watersheds and that the expanding stream of remotely sensed geographic data may allow for better CN-values than those from the current tables. We suggest that this study be expanded to include a wider range of watershed and storm characteristics.

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Data Availability Statement

All data used in this paper are open access, and the code we developed for this analysis is available upon request.

Acknowledgments

This work was funded by USDA National Institute of Food and Agriculture (NIFA) grant number 2019-60719-30122. We acknowledge the ASCE Curve Number Hydrology task committee for their support and feedback on this work.

References

Addor, N., A. J. Newman, N. Mizukami, and M. P. Clark. 2017. “The CAMELS data set: Catchment attributes and meteorology for large-sample studies.” Hydrol. Earth Syst. Sci. 21 (10): 5293–5313. https://doi.org/10.5194/hess-21-5293-2017.
Ajmal, M., and T. W. Kim. 2015. “Quantifying excess stormwater using SCS-CN–based rainfall runoff models and different curve number determination methods.” J. Irrig. Drain. Eng. 141 (3): 04014058. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000805.
Ajmal, M., M. Waseem, D. Kim, and T. W. Kim. 2020. “A pragmatic slope-adjusted curve number model to reduce uncertainty in predicting flood runoff from steep watersheds.” Water 12 (5): 1469. https://doi.org/10.3390/w12051469.
Alwan, K. K., M. S. A. Al-Kubaisi, and N. Al-Ansari. 2019. “Validity of existing rain water harvesting dams within part of Western Desert, Iraq.” Engineering 11 (12): 806–818. https://doi.org/10.4236/eng.2019.1112055.
Archibald, J. A., B. P. Buchanan, D. R. Fuka, C. B. Georgakakos, S. W. Lyon, and M. T. Walter. 2014. “A simple, regionally parameterized model for predicting nonpoint source areas in the northeastern US.” J. Hydrol.: Reg. Stud. 1 (Jul): 74–91. https://doi.org/10.1016/j.ejrh.2014.06.003.
Arnold, J., et al. 2009. Soil and water assessment tool (SWAT) global applications. Bangkok, Thailand: World Association of Soil and Water Conservation.
Baltas, E. A., N. A. Dervos, and M. A. Mimikou. 2007. “Determination of the SCS initial abstraction ratio in an experimental watershed in Greece.” Hydrol. Earth Syst. Sci. 11 (6): 1825–1829. https://doi.org/10.5194/hess-11-1825-2007.
Belward, A. E., ed. 1996. “The IGBP-DIS global 1 km land cover data set 'DISCover': Proposal and implementation plans.” In Report of the land recover working group of IGBP-DIS. IGBP-DIS Working Paper, No. 13, 63. Stockholm, Sweden: IGBP-DIS.
Berk, M., O. Špačková, and D. Straub. 2017. “Probabilistic design storm method for improved flood estimation in ungauged catchments.” Water Resour. Res. 53 (12): 10701–10722. https://doi.org/10.1002/2017WR020947.
Beven, K. J., and M. J. Kirkby. 1979. “A physically based, variable contributing area model of basin hydrology.” Hydrol. Sci. Bull. 24 (1): 43–69. https://doi.org/10.1080/02626667909491834.
Bondelid, T. R., R. H. McCuen, and T. J. Jackson. 1982. “Sensitivity of SCS models to curve number variation.” J. Am. Water Resour. Assoc. 18 (1): 111–116. https://doi.org/10.1111/j.1752-1688.1982.tb04536.x.
Boughton, W. 1989. “A review of the USDA SCS curve number method.” Soil Res. 27 (3): 511. https://doi.org/10.1071/SR9890511.
Bovee, B. 2004. “An investigation of the SCS runoff equation: Comparing standard and fitted values of the soil retention parameter based on measured rainfall-runoff data.” In Biological and environmental engineering, 40. Ithaca, NY: Cornell Univ.
Breiman, L. 2001. “Random forests.” Mach. Learn. 45 (1): 5–32. https://doi.org/10.1023/A:1010933404324.
Broyden, C. G. 1970. “The convergence of single-rank quasi-Newton methods.” Math. Comput. 24 (110): 365–382. https://doi.org/10.1090/S0025-5718-1970-0279993-0.
Byrd, R. H., P. Lu, J. Nocedal, and C. Zhu. 1995. “A limited memory algorithm for bound constrained optimization.” SIAM J. Sci. Comput. 16 (5): 1190–1208. https://doi.org/10.1137/0916069.
Caletka, M., M. Šulc Michalková, P. Karásek, and P. Fučík. 2020. “Improvement of SCS-CN initial abstraction coefficient in the Czech Republic: A study of five catchments.” Water 12 (7): 1964. https://doi.org/10.3390/w12071964.
Chin, D. A. 2021. “Deficiencies in the curve number method.” J. Irrig. Drain. Eng. 147 (5). 04021008. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
Cleveland, T. G., D. B. Thompson, and X. Fang. 2011. Use of the rational and modified rational method for hydraulic design. Austin, TX: Texas DOT.
Coles, G. S. 2001. An introduction to statistical modeling of extreme values, 208. New York: Springer.
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.
Duffy, C. J. 2017. “The terrestrial hydrologic cycle: An historical sense of balance.” Wiley Interdiscip. Rev.: Water 4 (Jul): e1216. https://doi.org/10.1002/wat2.1216.
Dunne, T., and R. D. Black. 1970. “An experimental investigation of runoff production in permeable soils.” Water Resour. Res. 6 (2): 478–490. https://doi.org/10.1029/WR006i002p00478.
Falcone, J. A. 2011. GAGES-II: Geospatial attributes of gages for evaluating streamflow Washington, DC: USGS.
Fletcher, R. 1970. “A new approach to variable metric algorithms.” Comput. J. 13 (3): 317–322. https://doi.org/10.1093/comjnl/13.3.317.
Fu, S., G. Zhang, N. Wang, and L. Luo. 2011. “Initial abstraction ratio in the SCS-CN method in the Loess Plateau of China.” Trans. ASABE 54 (1): 163–169. https://doi.org/10.13031/2013.36271.
Garen, D., and D. Moore. 2005. “Curve number hydrology in water quality modeling: Uses, abuses, and future directions.” J. Am. Water Resour. Assoc. 41 (2): 377–388. https://doi.org/10.1111/j.1752-1688.2005.tb03742.x.
Gleeson, T., N. Moosdorf, J. Hartmann, and L. P. H. Van Beek. 2014. “A glimpse beneath earth’s surface: GLobal HYdrogeology MaPS (GLHYMPS) of permeability and porosity.” Geophys. Res. Lett. 41 (11): 3891–3898. https://doi.org/10.1002/2014GL059856.
Goldfarb, D. 1970. “A family of variable-metric methods derived by variational means.” Math. Comput. 24 (109): 23–26. https://doi.org/10.1090/S0025-5718-1970-0258249-6.
Grimaldi, S., A. Petroselli, and F. Serinaldi. 2012. “Design hydrograph estimation in small and ungauged watersheds: Continuous simulation method versus event-based approach.” Hydrol. Processes 26 (20): 3124–3134. https://doi.org/10.1002/hyp.8384.
Guo, J., H. Y. Li, L. R. Leung, S. Guo, P. Liu, and M. Sivapalan. 2014. “Links between flood frequency and annual water balance behaviors: A basis for similarity and regionalization.” Water Resour. Res. 50 (2): 937–953. https://doi.org/10.1002/2013WR014374.
Haith, D. A., and L. L. Shoemaker. 1987. “Generalized watershed loading functions for stream flow nutrients 1.” JAWRA J. Am. Water Resour. Assoc. 23 (3): 471–478. https://doi.org/10.1111/j.1752-1688.1987.tb00825.x.
Hartmann, J., and N. Moosdorf. 2012. “The new global lithological map database GLiM: A representation of rock properties at the earth surface.” Geochem. Geophys. Geosyst. 13 (12): 1–37. https://doi.org/10.1029/2012GC004370.
Hawkins, R. H. 1978. Effects of rainfall intensity on runoff curve numbers. Glendale, AZ: Arizona-Nevada Academy of Science.
Hawkins, R. H. 1981. “Discussion of ‘curve-number procedure as infiltration method’.” J. Hydraulics Div. 107 (2): 256. https://doi.org/10.1061/JYCEAJ.0005623.
Hawkins, R. H. 1993. “Asymptotic determination of runoff curve numbers from data.” J. Irrig. Drain. Eng. 119 (2): 334–345. https://doi.org/10.1061/(asce)0733-9437(1993)119:2(334).
Hawkins, R. H., A. T. Hjelmfelt Jr., and A. W. Zevenbergen. 1985. “Runoff probability, storm depth, and curve numbers.” J. Irrig. Drain. Eng. 111 (4): 330–340. https://doi.org/10.1061/(ASCE)0733-9437(1985)111:4(330).
Hawkins, R. H., F. D. Theurer, and M. Rezaeianzadeh. 2019. “Understanding the basis of the curve number method for watershed models and TMDLs.” J. Hydrol. Eng. 24 (7): 06019003. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001755.
Hawkins, R. H., T. J. Ward, and D. E. Woodward. 2015. “The complacent-violent runoff: A departure from traditional behavior.” In Proc., ASCE-EWRI Watershed Management Symp. Reston VA: ASCE.
Hjelmfelt, A. T., Jr. 1980. “Empirical investigation of curve number technique.” J. Hydraulics Div. 106 (9): 1471–1476. https://doi.org/10.1061/JYCEAJ.0005506.
Horton, R. E. 1940. “An approach toward a physical interpretation of infiltration-capacity.” Soil Sci. Soc. Am. Proc. 5 (399–417): 24. https://doi.org/10.2136/sssaj1941.036159950005000C0075x.
Huang, M., J. Gallichand, Z. Wang, and M. Goulet. 2006. “A modification to the soil conservation service curve number method for steep slopes in the Loess Plateau of China.” Hydrol. Processes: Int. J. 20 (3): 579–589. https://doi.org/10.1002/hyp.5925.
Jiang, R. 2002. “Investigation of runoff curve number initial abstraction ratio.” M.S. thesis, Renewable Natural Resources Graduate College, Univ. of Arizona.
Johanson, R. C., J. D. Imhoff, and H. H. Davis Jr.1980. Users manual for hydrological simulation program—Fortran (HSPF). Athens, GA: Environmental Research Laboratory.
Knighton, J. O., and M. T. Walter. 2016. “Critical rainfall statistics for predicting watershed flood responses: Rethinking the design storm concept.” Hydrol. Process. 30 (21): 3788–3803. https://doi.org/10.1002/hyp.10888.
Knisel, W. G. 1980. CREAMS: A field scale model for chemicals, runoff, and erosion from agricultural management systems. Washington, DC: USDA.
Krajewski, A., A. E. Sikorska-Senoner, A. Hejduk, and L. Hejduk. 2020. “Variability of the initial abstraction ratio in an urban and an agroforested catchment.” Water 12 (2): 415. https://doi.org/10.3390/w12020415.
Lal, M., S. K. Mishra, A. Pandey, R. P. Pandey, P. K. Meena, A. Chaudhary, R. K. Jha, A. K. Shreevastava, and Y. Kumar. 2017. “Evaluation of the Soil Conservation Service curve number methodology using data from agricultural plots.” Hydrogeol. J. 25 (1): 151. https://doi.org/10.1007/s10040-016-1460-5.
Li, J., M. Thyer, M. Lambert, G. Kuczera, and A. Metcalfe. 2014. “An efficient causative event-based approach for deriving the annual flood frequency distribution.” J. Hydrol. 510 (Mar): 412–423. https://doi.org/10.1016/j.jhydrol.2013.12.035.
Lian, H., et al. 2020. “CN-China: Revised runoff curve number by using rainfall-runoff events data in China.” Water Res. 177 (Jun): 115767. https://doi.org/10.1016/j.watres.2020.115767.
Liaw, A., and M. Wiener. 2002. “Classification and regression by randomForest.” R News 2 (3): 18–22.
Ling, L., and Z. Yusop. 2014. “A micro focus with macro impact: Exploration of initial abstraction coefficient ratio (λ) in soil conservation curve number (CN) methodology.” IOP Conf. Ser.: Earth Environ. Sci. 18 (1): 012121. https://doi.org/10.1088/1755-1315/18/1/012121.
Lloyd-Davies, D. E. 1906. “The elimination of storm water from sewerage systems.” In Vol. 164 of Minutes of the Proc. of the Institution of Civil Engineers, 41–67. London: Thomas Telford.
McCuen, R. H. 2002. “Approach to confidence interval estimation for curve numbers.” J. Hydrol. Eng. 7 (1): 43–48. https://doi.org/10.1061/(ASCE)1084-0699(2002)7:1(43).
Menberu, M. W., A. T. Haghighi, A. K. Ronkanen, J. Kværner, and B. Kløve. 2015. “Runoff curve numbers for peat-dominated watersheds.” J. Hydrol. Eng. 20 (4): 04014058. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001038.
Miller, D. A., and R. A. White. 1998. “A conterminous United States multilayer soil characteristics dataset for regional climate and hydrology modeling.” Earth Interact. 2 (2): 1–26. https://doi.org/10.1175/1087-3562(1998)002%3C0001:ACUSMS%3E2.3.CO;2.
Mishra, S. K., M. K. Jain, R. P. Pandey, and V. P. Singh. 2005. “Catchment area-based evaluation of the AMC-dependent SCS-CN-based rainfall-runoff models.” Hydrol. Process. 19 (14): 2701–2718. https://doi.org/10.1002/hyp.5736.
Mishra, S. K., and V. P. Singh. 2003. Soil conservation service curve number (SCS-CN) methodology. Dordrecht, Netherlands: Kluwer Academic Publishers.
Mishra, S. K., and V. P. Singh. 2004. “Long-term hydrological simulation based on the Soil Conservation Service curve number.” Hydrol. Processes 18 (7): 1291–1313. https://doi.org/10.1002/hyp.1344.
Mockus, V. 1949. “Estimation of total (and peak rates of) surface runoff for individual storms.” In Interim survey report, Grand (Neosho) River watershed, Appendix B: Exhibit. Washington, DC: USDA.
Newman, A. J., et al. 2015. “Development of a large-sample watershed-scale hydrometeorological data set for the contiguous USA: Data set characteristics and assessment of regional variability in hydrologic model performance.” Hydrol. Earth Syst. Sci. 19 (1): 209–223. https://doi.org/10.5194/hess-19-209-2015.
NRCS (Natural Resources Conservation Services). 2007. Hydrology, national engineering handbook, supplement A, Section 4, Chap. 7. Washington, DC: NRCS.
Ogden, F. L., R. “Pete” Hawkins, M. T. Walter, and D. C. Goodrich. 2017. “Comment on ‘Beyond the SCS-CN method: A theoretical framework for spatially lumped rainfall-runoff response’ by M. S. Bartlett, A. J. Parolari, J. J. McDonnell, and A. Porporato.” Water Resour. Res. 53 (7): 6345–6350. https://doi.org/10.1002/2016WR020176.
Peel, M. C., and T. A. McMahon. 2020. “Historical development of rainfall-runoff modeling.” Wiley Interdiscip. Rev.: Water 7 (5): e1471. https://doi.org/10.1002/wat2.1471.
Ponce, V. M. 1996. “Notes of my conversation with Vic Mockus.” Accessed June 8, 2020. https://ponce.sdsu.edu/mockus_conversation.html.
Ponce, V. M., and R. H. Hawkins. 1996. “Runoff curve number: Has it reached maturity?” J. Hydrol. Eng. 1 (1): 11–19. https://doi.org/10.1061/(ASCE)1084-0699(1996)1:1(11).
Rossman, L. A. 2010. Storm water management model user’s manual, version 5.0, 276. Cincinnati: National Risk Management Research Laboratory, Office of Research and Development, USEPA.
Saadi, M., L. Oudin, and P. Ribstein. 2019. “Random forest ability in regionalizing hourly hydrological model parameters.” Water 11 (8): 1540. https://doi.org/10.3390/w11081540.
Santikari, V. P., and L. C. Murdoch. 2019. “Accounting for spatiotemporal variations of curve number using variable initial abstraction and antecedent moisture.” Water Resour. Manage. 33 (Jan): 641–656. https://doi.org/10.1007/s11269-018-2124-0.
SCS (Soil Conservation Service). 1956. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
SCS (Soil Conservation Service). 1964. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
SCS (Soil Conservation Service). 1971. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
SCS (Soil Conservation Service). 1985. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
SCS (Soil Conservation Service). 1993. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
SCS (Soil Conservation Service). 2004. Hydrology, national engineering handbook, supplement A, Section 4, Chap.10, Soil conservation service. Washington, DC: USDA.
Shannon, R. E., and J. P. Ignizio. 1970. “A heuristic programming algorithm for warehouse location.” AIIE Trans. 2 (4): 334–339. https://doi.org/10.1080/05695557008974773.
Shaw, S. B., and M. T. Walter. 2009. “Formulating storm runoff risk using bivariate frequency analyses of rainfall and antecedent watershed wetness.” Water Resour. Res. 45 (3):W03404. https://doi.org/10.1029/2008WR006900.
Shi, Z. H., L. D. Chen, N. F. Fang, D. F. Qin, and C. F. Cai. 2009. “Research on the SCS-CN initial abstraction ratio using rainfall-runoff event analysis in the Three Gorges Area, China.” Catena 77 (1): 1–7. https://doi.org/10.1016/j.catena.2008.11.006.
Soulis, K. X., and J. D. Valiantzas. 2013. “Identification of the SCS-CN parameter spatial distribution using rainfall-runoff data in heterogeneous watersheds.” Water Resour. Manage. 27 (Apr): 1737–1749. https://doi.org/10.1007/s11269-012-0082-5.
Steenhuis, T. S., M. Winchell, J. Rossing, J. A. Zollweg, and M. F. Walter. 1995. “SCS runoff equation revisited for variable-source runoff areas.” J. Irrig. Drain. Eng. 121 (3): 234–238. https://doi.org/10.1061/(ASCE)0733-9437(1995)121:3(234).
Tyralis, H., G. Papacharalampous, and A. Langousis. 2019. A brief review of random forests for water scientists and practitioners and their recent history in water resources.” Water 11 (5): 910. https://doi.org/10.3390/w11050910.
Viger, R. J. 2014. Preliminary spatial parameters for PRMS based on the geospatial fabric, NLCD 2001 and SSURGO. Washington, DC: USGS.
Viger, R. J., and A. Bock. 2014. GIS features of the geospatial fabric for national hydrologic modeling. Washington, DC: USGS.
Viglione, A., R. Merz, and G. Blöschl. 2009. “On the role of the runoff coefficient in the mapping of rainfall to flood return periods.” Hydrol. Earth Syst. Sci. 13 (5): 577–593. https://doi.org/10.5194/hess-13-577-2009.
Wang, X., J. R. Williams, P. W. Gassman, C. Baffaut, R. C. Izaurralde, J. Jeong, and J. R. Kiniry. 2012. “EPIC and APEX: Model use, calibration, and validation.” Trans. ASABE 55 (4): 1447–1462.
Wang, Z., C. Lai, X. Chen, B. Yang, S. Zhao, and X. Bai. 2015. “Flood hazard risk assessment model based on random forest.” J. Hydrol. 527 (Aug): 1130–1141. https://doi.org/10.1016/j.jhydrol.2015.06.008.
Waterman, B. R., G. Alcantar, S. G. Thomas, and M. F. Kirk. 2022. “Spatiotemporal variation in runoff and baseflow in watersheds located across a regional precipitation gradient.” J. Hydrol.: Reg. Stud. 41 (1): 101071. https://doi.org/10.1016/j.ejrh.2022.101071.
Williams, J. R., and W. V. LaSeur. 1976. “Water yield model using SCS curve numbers.” J. Hydraulics Div. 102 (9): 1241–1253. https://doi.org/10.1061/JYCEAJ.0004609.
Woods, R. A. 2009. “Analytical model of seasonal climate impacts on snow hydrology: Continuous snowpacks.” Adv. Water Resour. 32 (10): 1465–1481. https://doi.org/10.1016/j.advwatres.2009.06.011.
Woodward, D. E., R. H. Hawkins, R. Jiang, A. T. Hjelmfelt Jr., J. A. Van Mullem, and Q. D. Quan. 2003. “Runoff curve number method: Examination of the initial abstraction ratio.” In World water & environmental resources congress 2003, 1–10. Reston, VA: ASCE.
Xia, Y., et al. 2012. “Continental-scale water and energy flux analysis and validation for the North American Land Data Assimilation System project phase 2 (NLDAS-2): 1. Intercomparison and application of model products.” J. Geophys. Res.: Atmos. 117 (D3): 109–136. https://doi.org/10.1029/2011JD016048.
Young, R. A., C. A. Onstad, 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.
Zeng, X. 2001. “Global vegetation root distribution for land modeling.” J. Hydrometeorol. 2 (5): 525–530. https://doi.org/10.1175/1525-7541(2001)002%3C0525:GVRDFL%3E2.0.CO;2.
Zhou, S., and T. Lei. 2011. “Calibration of SCS-CN initial abstraction ratio of a typical small watershed in the Loess hilly-gully region.” Sci. Agric. Sin. 44 (20): 4240–4247.

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Journal of Hydrologic Engineering
Volume 29Issue 6December 2024

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Received: Oct 2, 2023
Accepted: Jun 13, 2024
Published online: Sep 25, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 25, 2025

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Ph.D. Candidate, Dept. of Biological and Environmental Engineering, Cornell Univ., Ithaca, NY 14850 (corresponding author). ORCID: https://orcid.org/0000-0002-1531-7049. Email: [email protected]
Scott Steinschneider, Ph.D., A.M.ASCE [email protected]
Associate Professor, Dept. of Biological and Environmental Engineering, Cornell Univ., Ithaca, NY 14850. Email: [email protected]
Donald E. Woodward, P.E., F.ASCE [email protected]
Retired; formerly, National Hydraulic Engineer, USDA Natural Resources Conservation Service, 415 Russell Ave. #208, Gaithersburg, MD 20877. Email: [email protected]
Richard Hawkins, Ph.D., P.E., F.ASCE [email protected]
Professor, School of Biological Resources and the Environment, Univ. of Arizona, Tucson, AZ 85721. Email: [email protected]
M. Todd Walter, Ph.D., M.ASCE [email protected]
Professor, Dept. of Biological and Environmental Engineering, Cornell Univ., Ithaca, NY 14850. Email: [email protected]

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