Development of Stage – Distance – Discharge Relationship and Rating Curve using Least Square Method
Vol. 5 No. 9 (2019): September
Research Articles
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For any river, besides the importance of stage – discharge relationship (rating curve), a stage-discharge- distance relationship is of more significance. The accurate estimation of both relationships along a river reach is considered a key point for various applications of water resources engineering such as operation and management of water resources projects, designing of hydraulic structures, and sediment analysis. In this paper, both relationships were established for the Shatt Al – Hillah river reach by applying multiple linear regression and simple linear regression using least square method for determining regression equations. Twelve gauging stations including three primary and nine secondary stations were considered for this method. Moreover, for evaluating the performance of both regressions, statistical measures such as coefficient of determination, root mean square error, mean square error, and Thiel's factor were used. The study results generally indicate a superior performance of both modeling techniques. MLR model was able to predict and mimic the stage-discharge-distance relationship with a coefficient correlation of about 0.932, while SLR model was able to predict three rating curves for the three primary stations with coefficient correlation of about 0.960, 0.943, and 0.924 respectively.
Othman, N. Y., Abd Saleh, Z., & Omran, Z. A. (2019). Development of Stage – Distance – Discharge Relationship and Rating Curve using Least Square Method. Civil Engineering Journal, 5(9), 1959–1969. https://doi.org/10.28991/cej-2019-03091385
[1] Farkas, George. "Book Review: David A. Freedman (2005). Statistical Models: Theory and Practice. New York: Cambridge University Press.” Sociological Methods & Research 36, no. 1 (August 2007): 138–140. doi:10.1177/0049124106295976.
[2] Cook, R. Dennis, and Sanford Weisberg. "Criticism and Influence Analysis in Regression.” Sociological Methodology 13 (1982): 313. doi:10.2307/270724.
[3] Rencher, Alvin C. and Christensen, William F. "Chapter 10, Multivariate regression – Section 10.1, Introduction", Methods of Multivariate Analysis, Wiley Series in Probability and Statistics, (August 1, 2012) 709 (3rd ed.), John Wiley & Sons. doi:10.1002/9781118391686.ch1.
[4] Li, Mingjun, and Junxing Wang. "An Empirical Comparison of Multiple Linear Regression and Artificial Neural Network for Concrete Dam Deformation Modelling.” Mathematical Problems in Engineering 2019 (April 17, 2019): 1–13. doi:10.1155/2019/7620948.
[5] Zhenquan Li, Qiaoyu Li, Haijun Qiu, Yimin Wang, and Zezhong Zhang. "Application Research of Multiple Linear Regression Analysis in Yellow River Water Diversion of the Lower Reachs.”, Revista de la Facultad de Ingeniería U.C.V. (2017): Vol 32, No14, pp. 925-930.
[6] Sharad Patel, M. K. Hardaha, Mukesh K. Seetpal and K. K. Madankar. "Multiple Linear Regression Model for Stream Flow Estimation of Wainganga River.” American Journal of Water Science and Engineering, (March 1 2016); 2(1): 1-5.
[7] Uma Seeboonruang. "A Multiple Regression Analysis for Predicting Salinity in Shallow Groundwater.” Proceedings of the International MultiConference of Engineers and Computer Scientists Vol II, IMECS 2017, March 15 - 17, 2017, Hong Kong.
[8] Bohla N.S. Ghimire, M. Janga Reddy. "Development of Stage – Discharge Rating Curve In River Using Genetic Algorithms and Model Tree.” International Workshop Advances in Statistical Hydrology, may 23-25, 2010, Taormina, Italy.
[9] Lari A. Knochenmus and Dann K. Yobbi. "Hydrology of Coastal Springs Ground – Water Basin and Adjacent Parts of Pasco, Hernando and Citrus Counties, Florida.” USGS, (2001): Water-Resources Investigations, Report 01-4230. doi:10.3133/wri014230.
[10] Al-Mukhtar, Mustafa, and Fuaad Al-Yaseen. "Modeling Water Quality Parameters Using Data-Driven Models, a Case Study Abu-Ziriq Marsh in South of Iraq.” Hydrology 6, no. 1 (March 17, 2019): 24. doi:10.3390/hydrology6010024.
[11] Gore, James A., and James Banning. "Discharge Measurements and Streamflow Analysis.” Methods in Stream Ecology, Volume 1 (2017): 49–70. doi:10.1016/b978-0-12-416558-8.00003-2.
[12] Barbetta, Silvia, Tommaso Moramarco, and Muthiah Perumal. "A Muskingum-Based Methodology for River Discharge Estimation and Rating Curve Development under Significant Lateral Inflow Conditions.” Journal of Hydrology 554 (November 2017): 216–232. doi:10.1016/j.jhydrol.2017.09.022.
[13] Sikorska, Anna E., and Benjamin Renard. "Calibrating a Hydrological Model in Stage Space to Account for Rating Curve Uncertainties: General Framework and Key Challenges.” Advances in Water Resources 105 (July 2017): 51–66. doi:10.1016/j.advwatres.2017.04.011.
[14] Mansanarez, Valentin, Ida K. Westerberg, Steve W. Lyon, and Norris Lam. "Estimating Uncertainties in Hydraulicallymodelled Rating Curves for Discharge Time Series Assessment.” Edited by A. Paquier and N. Rivière. E3S Web of Conferences 40 (2018): 06013. doi:10.1051/e3sconf/20184006013.
[15] Kiang, Julie E., Chris Gazoorian, Hilary McMillan, Gemma Coxon, Jérí´me Le Coz, Ida K. Westerberg, Arnaud Belleville, et al. "A Comparison of Methods for Streamflow Uncertainty Estimation.” Water Resources Research 54, no. 10 (October 2018): 7149–7176. doi:10.1029/2018wr022708.
[16] Sefe, F. T. K. "A Study of the Stage-Discharge Relationship of the Okavaiigo River at Mohembo, Botswana.” Hydrological Sciences Journal 41, no. 1 (February 1996): 97–116. doi:10.1080/02626669609491481.
[17] Schumann, A.H. "Hydrometry”Principles and Practices, Second Edition; R.W. Herschy (Ed.); John Wiley & Sons, Chichester, 1999 Hardcover, VI+376pp., Price £75.00., ISBN 0-471-97350-5.” Journal of Hydrology 222, no. 1–4 (September 1999): 191–192. doi:10.1016/s0022-1694(99)00091-8.
[18] Kennedy, E.J. "Discharge ratings at gaging stations: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3.” US Government Printing Office. (1984): p. 5. doi:10.3133/twri03A10.
[19] BWRD, Babylon Water Resources Department, (2015): "unpublished record".
[20] Muzzammil, Mohammad, Javed Alam, and Mohammad Zakwan. "A Spreadsheet Approach for Prediction of Rating Curve Parameters.” Water Science and Technology Library (2018): 525–533. doi:10.1007/978-981-10-5801-1_36.
[21] Alfa, M.I., D.B. Adie, M.A. Ajibike, and O.J. Mudiare. "Development of Rating Curve for Ofu River at Oforachi Hydrometric Station.” Nigerian Journal of Technological Development 15, no. 1 (March 7, 2018): 14. doi:10.4314/njtd.v15i1.3.
[22] Kavousizadeh, Amirreza, Mahmoud F. Maghrebi, and Arash Ahmadi. "Stage-Discharge Estimation in Compound Open Channels with Composite Roughness.” Hydrology Research 50, no. 3 (March 27, 2019): 809–824. doi:10.2166/nh.2019.021.
[23] Baten, W. D., Edwin Crow, Frances A. Davis, and Margaret W. Maxfield. "Statistical Manual.” Journal of the American Statistical Association 55, no. 292 (December 1960): 787. doi:10.2307/2281634.
[24] Ezekiel, M., and Fox, K. A. "Methods of correlation and regression analysis.” New York, John Wiley & Sons, Inc., (1959): p.543. doi:10.1002/bimj.19610030207.
[25] Tofallis, Chris. "Least Squares Percentage Regression.” SSRN Electronic Journal (2009): 526–534. doi:10.2139/ssrn.1406472.
[26] Chiang, Chin Long. "Statistical Methods of Analysis” (October 2003): Page 274, Section 9.7.4 "Interpolation vs. Extrapolation". doi:10.1142/5224.
[27] Hayden, Robert W. "A Review of: ‘Common Errors in Statistics (and How to Avoid Them), Third Edition, by P. I. Good and J. W. Hardin.'” Journal of Biopharmaceutical Statistics 20, no. 1 (December 31, 2009): 190–190. doi:10.1080/10543400903406028.
[28] Nash, J.E., and J.V. Sutcliffe. "River Flow Forecasting through Conceptual Models Part I ” A Discussion of Principles.” Journal of Hydrology 10, no. 3 (April 1970): 282–290. doi:10.1016/0022-1694(70)90255-6.
[2] Cook, R. Dennis, and Sanford Weisberg. "Criticism and Influence Analysis in Regression.” Sociological Methodology 13 (1982): 313. doi:10.2307/270724.
[3] Rencher, Alvin C. and Christensen, William F. "Chapter 10, Multivariate regression – Section 10.1, Introduction", Methods of Multivariate Analysis, Wiley Series in Probability and Statistics, (August 1, 2012) 709 (3rd ed.), John Wiley & Sons. doi:10.1002/9781118391686.ch1.
[4] Li, Mingjun, and Junxing Wang. "An Empirical Comparison of Multiple Linear Regression and Artificial Neural Network for Concrete Dam Deformation Modelling.” Mathematical Problems in Engineering 2019 (April 17, 2019): 1–13. doi:10.1155/2019/7620948.
[5] Zhenquan Li, Qiaoyu Li, Haijun Qiu, Yimin Wang, and Zezhong Zhang. "Application Research of Multiple Linear Regression Analysis in Yellow River Water Diversion of the Lower Reachs.”, Revista de la Facultad de Ingeniería U.C.V. (2017): Vol 32, No14, pp. 925-930.
[6] Sharad Patel, M. K. Hardaha, Mukesh K. Seetpal and K. K. Madankar. "Multiple Linear Regression Model for Stream Flow Estimation of Wainganga River.” American Journal of Water Science and Engineering, (March 1 2016); 2(1): 1-5.
[7] Uma Seeboonruang. "A Multiple Regression Analysis for Predicting Salinity in Shallow Groundwater.” Proceedings of the International MultiConference of Engineers and Computer Scientists Vol II, IMECS 2017, March 15 - 17, 2017, Hong Kong.
[8] Bohla N.S. Ghimire, M. Janga Reddy. "Development of Stage – Discharge Rating Curve In River Using Genetic Algorithms and Model Tree.” International Workshop Advances in Statistical Hydrology, may 23-25, 2010, Taormina, Italy.
[9] Lari A. Knochenmus and Dann K. Yobbi. "Hydrology of Coastal Springs Ground – Water Basin and Adjacent Parts of Pasco, Hernando and Citrus Counties, Florida.” USGS, (2001): Water-Resources Investigations, Report 01-4230. doi:10.3133/wri014230.
[10] Al-Mukhtar, Mustafa, and Fuaad Al-Yaseen. "Modeling Water Quality Parameters Using Data-Driven Models, a Case Study Abu-Ziriq Marsh in South of Iraq.” Hydrology 6, no. 1 (March 17, 2019): 24. doi:10.3390/hydrology6010024.
[11] Gore, James A., and James Banning. "Discharge Measurements and Streamflow Analysis.” Methods in Stream Ecology, Volume 1 (2017): 49–70. doi:10.1016/b978-0-12-416558-8.00003-2.
[12] Barbetta, Silvia, Tommaso Moramarco, and Muthiah Perumal. "A Muskingum-Based Methodology for River Discharge Estimation and Rating Curve Development under Significant Lateral Inflow Conditions.” Journal of Hydrology 554 (November 2017): 216–232. doi:10.1016/j.jhydrol.2017.09.022.
[13] Sikorska, Anna E., and Benjamin Renard. "Calibrating a Hydrological Model in Stage Space to Account for Rating Curve Uncertainties: General Framework and Key Challenges.” Advances in Water Resources 105 (July 2017): 51–66. doi:10.1016/j.advwatres.2017.04.011.
[14] Mansanarez, Valentin, Ida K. Westerberg, Steve W. Lyon, and Norris Lam. "Estimating Uncertainties in Hydraulicallymodelled Rating Curves for Discharge Time Series Assessment.” Edited by A. Paquier and N. Rivière. E3S Web of Conferences 40 (2018): 06013. doi:10.1051/e3sconf/20184006013.
[15] Kiang, Julie E., Chris Gazoorian, Hilary McMillan, Gemma Coxon, Jérí´me Le Coz, Ida K. Westerberg, Arnaud Belleville, et al. "A Comparison of Methods for Streamflow Uncertainty Estimation.” Water Resources Research 54, no. 10 (October 2018): 7149–7176. doi:10.1029/2018wr022708.
[16] Sefe, F. T. K. "A Study of the Stage-Discharge Relationship of the Okavaiigo River at Mohembo, Botswana.” Hydrological Sciences Journal 41, no. 1 (February 1996): 97–116. doi:10.1080/02626669609491481.
[17] Schumann, A.H. "Hydrometry”Principles and Practices, Second Edition; R.W. Herschy (Ed.); John Wiley & Sons, Chichester, 1999 Hardcover, VI+376pp., Price £75.00., ISBN 0-471-97350-5.” Journal of Hydrology 222, no. 1–4 (September 1999): 191–192. doi:10.1016/s0022-1694(99)00091-8.
[18] Kennedy, E.J. "Discharge ratings at gaging stations: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3.” US Government Printing Office. (1984): p. 5. doi:10.3133/twri03A10.
[19] BWRD, Babylon Water Resources Department, (2015): "unpublished record".
[20] Muzzammil, Mohammad, Javed Alam, and Mohammad Zakwan. "A Spreadsheet Approach for Prediction of Rating Curve Parameters.” Water Science and Technology Library (2018): 525–533. doi:10.1007/978-981-10-5801-1_36.
[21] Alfa, M.I., D.B. Adie, M.A. Ajibike, and O.J. Mudiare. "Development of Rating Curve for Ofu River at Oforachi Hydrometric Station.” Nigerian Journal of Technological Development 15, no. 1 (March 7, 2018): 14. doi:10.4314/njtd.v15i1.3.
[22] Kavousizadeh, Amirreza, Mahmoud F. Maghrebi, and Arash Ahmadi. "Stage-Discharge Estimation in Compound Open Channels with Composite Roughness.” Hydrology Research 50, no. 3 (March 27, 2019): 809–824. doi:10.2166/nh.2019.021.
[23] Baten, W. D., Edwin Crow, Frances A. Davis, and Margaret W. Maxfield. "Statistical Manual.” Journal of the American Statistical Association 55, no. 292 (December 1960): 787. doi:10.2307/2281634.
[24] Ezekiel, M., and Fox, K. A. "Methods of correlation and regression analysis.” New York, John Wiley & Sons, Inc., (1959): p.543. doi:10.1002/bimj.19610030207.
[25] Tofallis, Chris. "Least Squares Percentage Regression.” SSRN Electronic Journal (2009): 526–534. doi:10.2139/ssrn.1406472.
[26] Chiang, Chin Long. "Statistical Methods of Analysis” (October 2003): Page 274, Section 9.7.4 "Interpolation vs. Extrapolation". doi:10.1142/5224.
[27] Hayden, Robert W. "A Review of: ‘Common Errors in Statistics (and How to Avoid Them), Third Edition, by P. I. Good and J. W. Hardin.'” Journal of Biopharmaceutical Statistics 20, no. 1 (December 31, 2009): 190–190. doi:10.1080/10543400903406028.
[28] Nash, J.E., and J.V. Sutcliffe. "River Flow Forecasting through Conceptual Models Part I ” A Discussion of Principles.” Journal of Hydrology 10, no. 3 (April 1970): 282–290. doi:10.1016/0022-1694(70)90255-6.
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