Skip to main content
SpringerLink
Log in

Use of Gene-Expression Programming to Estimate Manning’s Roughness Coefficient for High Gradient Streams

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

Manning’s roughness coefficient (n) has been widely used in the estimation of flood discharges or depths of flow in natural channels. Therefore, the selection of appropriate Manning’s n values is of paramount importance for hydraulic engineers and hydrologists and requires considerable experience, although extensive guidelines are available. Generally, the largest source of error in post-flood estimates (termed indirect measurements) is due to estimates of Manning’s n values, particularly when there has been minimal field verification of flow resistance. This emphasizes the need to improve methods for estimating n values. The objective of this study was to develop a soft computing model in the estimation of the Manning’s n values using 75 discharge measurements on 21 high gradient streams in Colorado, USA. The data are from high gradient (S > 0.002 m/m), cobble- and boulder-bed streams for within bank flows. This study presents Gene-Expression Programming (GEP), an extension of Genetic Programming (GP), as an improved approach to estimate Manning’s roughness coefficient for high gradient streams. This study uses field data and assessed the potential of gene-expression programming (GEP) to estimate Manning’s n values. GEP is a search technique that automatically simplifies genetic programs during an evolutionary processes (or evolves) to obtain the most robust computer program (e.g., simplify mathematical expressions, decision trees, polynomial constructs, and logical expressions). Field measurements collected by Jarrett (J Hydraulic Eng ASCE 110: 1519–1539, 1984) were used to train the GEP network and evolve programs. The developed network and evolved programs were validated by using observations that were not involved in training. GEP and ANN-RBF (artificial neural network-radial basis function) models were found to be substantially more effective (e.g., R2 for testing/validation of GEP and RBF-ANN is 0.745 and 0.65, respectively) than Jarrett’s (J Hydraulic Eng ASCE 110: 1519–1539, 1984) equation (R2 for testing/validation equals 0.58) in predicting the Manning’s n.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Ab Ghani A, Zakaria NA, Chang CK, Ariffin J, Abu Hasan Z, Abdul Ghaffar AB (2007) Revised equations for Manning’s coefficient for sand-bed rivers. Int J River Basin Manag 5(4):329–346

    Google Scholar 

  • American Society of Civil Engineers (ASCE) Task Committee (2000) The ASCE Task Committee on Application of artificial neural networks in hydrology. J Hydrologic Eng 5(2):115–137

    Article  Google Scholar 

  • Azamathulla HM, Ghani AA (2011) Genetic programming for longitudinal dispersion coefficients in streams. Water Resour Manag 25(6):1537–1544

    Article  Google Scholar 

  • Azamathulla HM, Deo MC, Deolalikar PB (2008) Alternative neural networks to estimate the scour below spillways. Adv Eng Softw 39(8):689–698

    Article  Google Scholar 

  • Azamathulla HM, Ghani AA, Zakaria NA, Aytac G (2010) Genetic programming to predict bridge pier scour. J Hydraul Eng ASCE 136(3):165–169

    Article  Google Scholar 

  • Azamathulla HM, Ghani AA, Leow CS, Chang CK, Zakaria NA (2011) Gene-expression programming for the development of a stage-discharge curve of the Pahang River. Water Resour Manag 25(11):2901–2916

    Article  Google Scholar 

  • Azmathulla HM, Deo MC, Deolalikar PB (2005) Neural networks for estimation of scour downstream of ski-jump bucket. J HydraulEng 131(10):898–908

    Article  Google Scholar 

  • Barnes Jr., HH (1967) Roughness characteristics of natural channels. U.S. Geological Survey Water-Supply Paper 1849, p. 213

  • Bathurst JC (1985) Flow resistance estimation in mountain rivers: ASCE. J Hydraul Eng 111:625–641

    Article  Google Scholar 

  • Bray DI (1979) Estimating average velocity in gravel-bed rivers. J Hydraul Div 105:1103–1122

    Google Scholar 

  • Brownlie WR (1983) Flow depth in sand-bed channels. J Hydraul Eng 109(7):959–990

    Article  Google Scholar 

  • Bruschin J (1985) Discussion on Brownlie (1983): flow depth in sand-bed channels. J Hydraul Eng ASCE 111:736–739

    Article  Google Scholar 

  • Chow VT (1959) Open Channel Hydraulics. McGraw-Hill, New York

    Google Scholar 

  • Costa JE, Jarrett RD (2008) An Evaluation of selected extraordinary floods in the United States reported by the U.S. Geological Survey and implications for future advancement of flood science: U.S. Geological Survey Scientific Investigations Report 2008–5164, 232 p., 1 appendix. [Available only on-line at http://pubs.usgs.gov/sir/2008/5164/pdf/sir20085164.pdf and http://pubs.usgs.gov/sir/2008/5164/pdf/sir20085164_AppendixA.pdf]

  • Dingman SL, Sharma KP (1997) Statistical development and validation of discharge equations for natural channels. J Hydrol 199:13–35

    Article  Google Scholar 

  • Ferreira C (2001a) Gene expression programming in problem solving”, 6th Online World Conference on Soft Computing in Industrial Applications (invited tutorial)

  • Ferreira C (2001b) Gene expression programming: a new adaptive algorithm for solving problems. Complex Systems 13(2):87–129

    Google Scholar 

  • Ferreira C (2006) Gene-expression programming; mathematical modeling by an artificial intelligence. Springer, Berling, Heidelberg, New York

    Google Scholar 

  • Giustolisi O (2004) Using genetic programming to determine Chèzy resistance coefficient in corrugated channels. J Hydroinformatics 6(3):157–173

    Google Scholar 

  • Golubtsov VV (1969) Hydraulic resistance and formula for computing average flow velocity of mountain rivers. Soviet Hydrol 5:500–510

    Google Scholar 

  • Green JC (2006) Effect of macrophyte spatial variability on channel resistance. Adv Water Resour 29:426–438

    Article  Google Scholar 

  • Guven A (2009) Linear genetic programming for time-series modeling of daily flow rate. Earth Syst Sci 118(2):137

    Article  Google Scholar 

  • Guven A, Aytek A (2009) A new approach for stage-discharge relationship: gene-expression programming. J Hydrol Eng ASCE 14(8):812–820

    Article  Google Scholar 

  • Guven A, Talu NE (2010) Gene-expression programming for estimating suspended sediment in Middle Euphrates Basin, Turkey. CLEAN: Soil, Air, Water 38:1159. doi:12

    Article  Google Scholar 

  • Hicks DM, Mason PD (1991) Roughness characteristics of New Zealand rivers. Water Resources Survey, Wellington, p 329

    Google Scholar 

  • Jarrett RD (1984) Hydraulics of high gradient streams. J Hydraul Eng ASCE 110(1):1519–1539

    Google Scholar 

  • Jarrett RD (1987) Peak discharge errors in slope-area computation in mountain streams. J Hydrol 96(1–4):53–67

    Article  Google Scholar 

  • Jarrett RD (1992) Hydraulics of mountain rivers. In: Yen BC (ed) Channel flow resistance—centennial of Manning’s’ formula: international conference for the centennial of Manning’s and Kuichling’s rational formula. Water Resources Publications, Littleton, pp 287–298

    Google Scholar 

  • Jarrett RD (1994) Historic-flood evaluation and research needs in mountainous areas. In: Cotroneo GV, Rumer RR (eds) Hydraulic Engineering--Proceedings of the symposium sponsored by the American Society of Civil Engineers, Buffalo, New York, August 1–5, 1994. American Society of Civil Engineers, New York, pp 875–879

    Google Scholar 

  • Jarrett RD, Petsch HE Jr (1985) Computer Program NCALC user’s manual, Verification of Manning’s roughness coefficient in channels: U.S. Geological Survey Water-Resources Investigations Report 85–4317, p. 27

  • Jiang M, Li L-X (2010) An improved two-point velocity method for estimating the roughness coefficient of natural channels. Physics and Chemistry of the Earth. (in press)

  • Keulegan GH (1938) Laws of turbulent flow in open channels. J Res Natl BurStand 21:707–741

    Article  Google Scholar 

  • Koza JR (1992) Genetic Programming: On the Programming of Computers by means of Natural Selection. The MIT Press, Cambridge

    Google Scholar 

  • Li Z, Zhang J (2001) Calculation of field Manning’s roughness coefficient. Agric Water Manage 49:153–161

    Article  Google Scholar 

  • Limerinos JT (1970) Determination of the Manning Coefficient from measured bed roughness in natural channels: U.S. Geological Survey Professional Paper 1898-B, p. 47

  • Marcus WA, Roberts K, Harvey L, Tackman G (1992) An evaluation of methods for estimating Manning’s n in small mountain streams. Mt Res Dev 12:227–239

    Article  Google Scholar 

  • Maresova I (1994) Evaluating flow resistance using height of roughness protrusions. In: Cotroneo GV, Rumer RR (eds) Hydraulic Engineering--Proceedings of the Symposium sponsored by the American Society of Civil Engineers, Buffalo, New York, August 1–5, 1994. American Society of Civil Engineers, New York, pp 712–716

    Google Scholar 

  • Millar RG, Quick M (1994) Flow resistance of high-gradient gravel channels. In: Cotroneo GV, Rumer RR (eds) 1994 ASCE National Conference on Hydraulic Engineering. American Society of Civil Engineers, Hydraulics Division, New York, pp 717–721

    Google Scholar 

  • Reid DE, Hickin EJ (2008) Flow resistance in steep mountain streams. Earth Surf Process Landf 33:2211–2240

    Article  Google Scholar 

  • Riggs HC (1976) A simplified slope area method for estimating flood discharges in natural channels. J Res U S Geol Surv 4:285–291

    Google Scholar 

  • Teodorescu L, Sherwood D (2008) High Energy Physics event selection with Gene Expression Programming. Comput Phys Commun 178(6):409–419

    Article  Google Scholar 

  • Thompson SM, Campbell PL (1979) Hydraulics of a large channel paved with boulders. J Hydraul Eng ASCE 17:341–354

    Article  Google Scholar 

  • Traore S, Guven A (2012) Regional-specific Numerical Models of Evapotranspiration Using Gene-expression Programming Interface in Sahel. Wat Resou Manag 26(15):4367–4380

    Article  Google Scholar 

  • Wohl EE (1998) Uncertainty in flood estimates associated with roughness coefficient. J Hydraul Eng ASCE 124:219–223

    Article  Google Scholar 

  • Wohl EE (2000) Channel processes. in Mountain Rivers. Water Resources Monograph 14, American Geophysical Union Press, Washington, D.C, pp 63–147

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. River Engineering and Urban Drainage Research Centre (REDAC), Universiti Sains Malaysia, Engineering Campus, Seri Ampangan, 14300, Nibong Tebal, Pulau Pinang, Malaysia

    H. Md. Azamathulla

  2. National Research Program, Paleohydrology and Climate Change, U.S. Geological Survey, P.O. Box 25046, MS412, Lakewood, CO, 80225-0046, USA

    Robert D. Jarrett

Authors
  1. H. Md. Azamathulla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert D. Jarrett
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Md. Azamathulla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Azamathulla, H.M., Jarrett, R.D. Use of Gene-Expression Programming to Estimate Manning’s Roughness Coefficient for High Gradient Streams. Water Resour Manage 27, 715–729 (2013). https://doi.org/10.1007/s11269-012-0211-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11269-012-0211-1

Keywords

Search

Navigation