New Approach for Stage–Discharge Relationship: Gene-Expression Programming
Publication: Journal of Hydrologic Engineering
Volume 14, Issue 8
Abstract
This study presents gene-expression programming (GEP), which is an extension to genetic programming, as an alternative approach to modeling stage–discharge relationship. The results obtained are compared to more conventional methods, stage rating curve and multiple linear regression techniques. Statistical measures such as average, standard deviation, minimum and maximum values, as well as criteria such as mean square error and determination coefficient, the coefficient of efficiency, and the adjusted coefficient of efficiency are used to measure the performance of the models developed by employing GEP. Also, the explicit formulations of the developed GEP models are presented. Statistics and scatter plots indicate that the proposed equations produce quite satisfactory results and perform superior to conventional models.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers are grateful to the Gaziantep University Research Projects Administration Unit for funding the research reported in this paper.
References
Aytek, A., and Kisi, O. (2008). “A genetic programming approach to suspended sediment modeling.” J. Hydrol., 351, 288–298.
Babovic, V., and Keijzer, M. (2002). “Rainfall-runoff modeling based on genetic programming.” Nord. Hydrol., 33(5), 331–346.
Babovic, V., Keijzer, M., Rodrigez Aguilera, D., and Harrington, J. (2001). “Automatic discovery of settling velocity equations.” D2K Technical Rep. No. 0201-1, Danish Technical Research Council (STVF).
Baiamonte, G., and Ferro, V. (2007). “Simple flume for flow measurement in sloping channel.” J. Irrig. Drain. Eng., 133(1), 71–78.
Bhattacharya, B., and Solomatine, D. P. (2005). “Neural networks and M5 model trees in modeling water level-discharge relationship.” Neurocomputing, 63, 381–396.
Clemmens, A. J., and Wahlin, B. T. (2006). “Accuracy of annual volume from current-meter-based discharges.” J. Hydrol. Eng., 11(5), 489–501.
Cousin, N., and Savic, D. A. (1997). “A rainfall-runoff model using genetic programming, Centre for Systems and Control Engineering.” Rep. No. 97/03, School of Engineering, Univ. of Exeter, Exeter, U.K.
Deka, P., and Chandramouli, V. (2003). “A fuzzy neural network model for deriving the river stage-discharge relationship.” Hydrol. Sci. J., 48(2), 197–209.
Dorado, J., Rabunal, J. R., Pazos, A., Rivero, D., Santos, A., and Puertas, J. (2003). “Prediction and modeling of the rainfall-runoff transformation of a typical urban basin using ANN and GP.” Appl. Artif. Intell., 17, 329–343.
Drecourt, J. P. (1999). “Application of neural networks and genetic programming to rainfall-runoff modeling.” D2K Technical Rep. No. 0699-1-1, Danish Hydraulic Institute, Hørsholm, Denmark.
Ferreira, C. (2001a). “Gene expression programming in problem solving.” 6th Online World Conf. on Soft Computing in Industrial Applications (invited tutorial).
Ferreira, C. (2001b). “Gene expression programming: A new adaptive algorithm for solving problems.” Complex Syst., 13(2), 87–129.
Ferreira, C. (2006). Gene-expression programming: Mathematical modeling by an artificial intelligence, Springer, Berlin.
Fread, D. L. (1973). “A dynamic model of stage-discharge relations affected by changing discharge.” NOAA Techical Memorandom No. NWS HYDRO-16, National Weather Service, Silver Spring, Md.
Fread, D. L. (1975). “Computation of stage-discharge relationships affected by unsteady flow.” Water Resour. Bull., 11(2), 213–228.
Giustolisi, O. (2004). “Using genetic programming to determine Chezy resistance coefficient in corrugated channels.” J. Hydroinform., 6(3), 157–173.
Guven, A., Aytek, A., Yuce, M. I., and Aksoy, H. (2007). “Genetic programming-based empirical model for daily reference evapotranspiration estimation.” CLEAN–Soil, Air, Water J., 36(10–11), 905–912.
Guven, A., and Gunal, M. (2008). “A genetic programming approach for prediction of local scour downstream hydraulic structures.” J. Irrig. Drain. Eng., 132(4), 241–249.
Habib, E. H., and Meselhe, E. A. (2006). “Stage-discharge relations for low-fradient tidal streams using data driven models.” J. Hydraul. Eng., 132(5), 482–492.
Harris, E. L., Babovic, V., and Falconer, R. A. (2003). “Velocity predictions in compound channels with vegetated floodplains using genetic programming.” Intl. J. River Manag., 1(2), 117–123.
Herschy, R. W. (1995). Streamflow measurement, 2nd Ed., E & FN Spon, London.
Jain, K. S. (2008). “Development of integrated discharge and sediment rating relation using a compound neural network.” J. Hydrol. Eng., 13(3), 124–131.
Jain, K. S., and Chalisgaonkar, D. (2000). “Setting up stage-discharge relations using ANN.” J. Hydrol. Eng., 5(4), 428–433.
Koza, J. R. (1992). Genetic programming: On the programming of computers by means of natural selection, MIT Press, Cambridge, Mass.
Legates, D. R., and McCabe, G. J. (1999). “Evaluating the use of ‘goodness-of-fit’ measures in hydrologic and hydroclimatic model validation.” Water Resour. Res., 35(1), 233–241.
Liao, H., and Knight, D. W. (2007). “Analytic stage-discharge formulas for flow in straight prismatic channels.” J. Hydraul. Eng., 133(10), 1111–1122.
Lohani, A. K., Goel, N. K., and Bhatia, K. K. S. (2006). “Takagi-Sugeno fuzzy inference system for modeling stage-discharge relationship.” J. Hydrol., 331, 146–160.
Petersen-Overleir, A. (2006). “Modelling stage-discharge relationships affected by hysteresis using the Jones formula and nonlinear regression.” J. Hydrol. Eng., 51(3), 365–388.
Rabunal, J. R., Puertas, J., Suarez, J., and Rivero, D. (2007). “Determination of the unit hydrograph of a typical urban basin using genetic programming and artificial neural networks.” Hydrolog. Process., 27(4), 476–485.
Savic, A. D., Walters, A. G., and Davidson, J. W. (1999). “A genetic programming approach to rainfall-runoff modeling.” Water Resour. Manage., 13, 219–231.
Schmidt, A. R., and Yen, B. C. (2002). “Stage-discharge ratings revisited.” Hydraulic Measurements and Experimental Methods, Proc., EWRI and IAHR Joint Conf., Proc., Specialty Conf., Estes Park, Colo., T. L. Wahl, C. A. Pugh, K. A. Oberg, and T. B. Vermeyen, eds.
Sudheer, K. P., and Jain, S. K. (2003). “Radial basis function neural network for modeling rating curves.” J. Hydrol. Eng., 8(3), 161–164.
Weisberg, S. (2005). Applied linear regression, 3rd Ed., Wiley, Hoboken, N.J.
Whigham, P. A., and Crapper, P. F. (1999). “Time series modeling using genetic programming: An application to rainfall-runoff models.” Advances in genetic programming, L. Spector, W. B. Langdon, U.-M. O’Reilly, and P. J. Angeline, eds., MIT, Cambridge, Mass., 89–104.
Whigham, P. A., and Crapper, P. F. (2001). “Modeling rainfall-runoff using genetic programming.” Math. Comput. Modell., 33(6–7), 707–721.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Mar 17, 2008
Accepted: Oct 31, 2008
Published online: Feb 12, 2009
Published in print: Aug 2009
ASCE Technical Topics:
- Analysis (by type)
- Business management
- Computer programming
- Computing in civil engineering
- Curvature
- Engineering fundamentals
- Errors (statistics)
- Geometry
- Linear functions
- Management methods
- Mathematical functions
- Mathematics
- Practice and Profession
- Quality control
- Ratings
- Regression analysis
- Statistical analysis (by type)
- Statistics
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.