Optimal Exponent Values of Distance and Elevation Based on Hourly Rainfall Data in the Modified Inverse Distance Method
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 10
Abstract
Obtaining appropriate, applicable exponent values of distance and elevation in the modified inverse distance method for hourly rainfall interpolation is difficult because the range of the exponent values has not yet been established at existing studies. In this research, an attempt is made to find the optimal exponent values in the modified inverse distance method based on hourly rainfall data. For the purpose of this study, 28 rainfall observation stations providing the data were classified into four groups, which are located at the Han River upstream, the Han River downstream, the Geum River upstream, and the Nakdong River midstream areas in South Korea. A total of 44 cases consisting of one base rainfall station and four index rainfall stations were analyzed. The optimal exponent values of distance and elevation were calculated by a simple nonlinear optimization technique of the steepest gradient method using hourly rainfall data observed for 10 years (2004–2013) and validated using another data for three years (2014–2016) on a case basis across different groups. The proposed modified inverse distance method was found to be superior to the conventional inverse distance method. Worth noting is that the root mean squared error values obtained by the method of this study were smaller than those of the conventional methods in all groups even though they were small in size hydrometeorologically. Therefore, the method proposed in this research can be considered more advanced than the conventional method. The optimal exponent values of distance and elevation obtained in this research were 3.463 and , 2.559 and 0.741, 2.877 and , and 3.738 and 2.001, respectively, in the four groups, and the total mean values of the two values were 3.159 and 0.511, respectively. The main factor influencing rainfall between stations when applying the modified inverse distance method with the optimal exponents was found to be the distance, and the altitude is the minor factor.
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Acknowledgments
This work was supported by the National Research Foundation of Korea Grant, funded by the Korean Government (Ministry of Education) [NRF-2017R1D1A3B03035695].
References
Bartier, P. M., and C. P. Keller. 1996. “Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW).” Comput. Geosci. 22 (7): 795–799. https://doi.org/10.1016/0098-3004(96)00021-0.
Chang, C. L., S. L. Lo, and S. L. Yu. 2005. “Applying fuzzy theory and genetic algorithm to interpolate precipitation.” J. Hydrol. 314 (1–4): 92–104. https://doi.org/10.1016/j.jhydrol.2005.03.034.
Chau, K. W. 2007. “A split-step particle swarm optimization algorithm in river stage forecasting.” J. Hydrol. 346 (3–4): 131–135. https://doi.org/10.1016/j.jhydrol.2007.09.004.
Chen, Y. Z., L. He, Y. Guan, H. W. Lu, and J. Li. 2017. “Life cycle assessment of greenhouse gas emissions and water-energy optimization for shale gas supply chain planning based on multi-level approach: Case study in Barnett, Marcellus, Fayetteville, and Haynesville shales.” Energy Convers. Manage. 134 (15): 382–398. https://doi.org/10.1016/j.enconman.2016.12.019.
Cheng, C. T., X. Y. Wu, and K. W. Chau. 2005. “Multiple criteria rainfall-runoff model calibration using a parallel genetic algorithm in a cluster of computer.” Hydrol. Sci. J. 50 (6): 1069–1087. https://doi.org/10.1623/hysj.2005.50.6.1069.
Dean, J. D., and W. M. Snyder. 1977. “Temporally and areally distributed rainfall.” J. Irrig. Drain. Div. 103 (IR2): 65–73.
DeCoursey, D. G., and W. M. Snyder. 1969. “Computer-oriented method of optimizing hydrologic model parameters.” J. Hydrol. 9 (1): 34–56. https://doi.org/10.1016/0022-1694(69)90013-4.
Diskin, M. H., and E. Simon. 1977. “A procedure for the selection of objective functions for hydrologic simulation models.” J. Hydrol. 34 (1–2): 129–149. https://doi.org/10.1016/0022-1694(77)90066-X.
Duan, Q., V. K. Gupta, and S. Sorooshian. 1993. “A shuffled complex evolution approach for effective and efficient global minimization.” J. Optim. Theory Appl. 76 (3): 501–521. https://doi.org/10.1007/BF00939380.
Duan, Q., S. Sorooshian, and V. K. Gupta. 1992. “Effective and efficient global optimization for conceptual rainfall-runoff models.” Water Resour. Res. 28 (4): 1015–1031. https://doi.org/10.1029/91WR02985.
Gelleszun, M., P. Kreye, and G. Meon. 2017. “Representative parameter estimation for hydrological models using a lexicographic calibration strategy.” J. Hydrol. 553 (Oct): 722–734. https://doi.org/10.1016/j.jhydrol.2017.08.015.
Golkhatmi, N. S., S. H. Sanaeinejad, B. Ghahraman, and H. R. Pazhand. 2012. “Extended modified inverse distance method for interpolation rainfall.” Int. J. Eng. Inventions 1 (3): 57–65.
Gottfried, B. S., and J. Weisman. 1973. Introduction to optimization theory. Upper Saddle River, NJ: Prentice-Hall.
Gupta, H. V., S. Sorooshian, and P. O. Yapo. 1998. “Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information.” Water Resour. Res. 34 (4): 751–763. https://doi.org/10.1029/97WR03495.
He, L., Y. Chen, H. Zhao, P. Tian, Y. Xue, and L. Chen. 2018. “Game-based analysis of energy-water nexus for identifying environmental impacts during Shale gas operations under stochastic input.” Sci. Total Environ. 627 (15): 1585–1601.
Huo, J., L. Liu, and Y. Zhang. 2016. “Comparative research of optimization algorithms for parameters calibration of watershed hydrological model.” J. Comput. Methods Sci. Eng. 16 (3): 653–669. https://doi.org/10.3233/JCM-160647.
Kim, C. S., and H. S. Kim. 2006. “Comparison of estimation methods for the missing rainfall data in an urban sub-drainage area.” In Proc., Korean Water Resources Association Conf., 701–705. Seoul, Korea: Korea Water Resources Association.
Kruizinga, S., and G. J. Yperlaan. 1978. “Spatial interpolation of daily totals of rainfall.” J. Hydrol. 36 (1–2): 65–73. https://doi.org/10.1016/0022-1694(78)90037-9.
Legates, D. R., and G. J. McCabe. 1999. “Evaluating the use of ‘goodness-of-fit’ Measures in hydrologic and hydroclimatic model validation.” Water Resour. Res. 35 (1): 233–241. https://doi.org/10.1029/1998WR900018.
Lo, S. S. 1992. Glossary of hydrology. Littleton, CO: Water Resources Publications.
Lu, H. W., J. Li, L. X. Ren, and Y. Z. Chen. 2018. “Optimal groundwater security management policies by control of inexact health risks under dual uncertainty in slope factors.” Chemosphere 198 (May): 161–173. https://doi.org/10.1016/j.chemosphere.2018.01.121.
Madsen, H. 2000. “Automatic calibration of a conceptual rainfall-runoff model using multiple objectives.” J. Hydrol. 235 (3–4): 276–288. https://doi.org/10.1016/S0022-1694(00)00279-1.
Nalder, I. A., and R. W. Wein. 1998. “Spatial interpolation of climatic normals: Test of a new method in the Canadian boreal forest.” Agric. For. Meteorol. 92 (4): 211–225. https://doi.org/10.1016/S0168-1923(98)00102-6.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1996. Numerical recipes. 2nd ed. New York: Cambridge University Press.
Sehitoglu, H. 1983. “Some algorithms for parameter estimation in water resources systems.” Water Resour. Res. 19 (5): 1193–1202. https://doi.org/10.1029/WR019i005p01193.
Shafii, M., and B. A. Tolson. 2015. “Optimizing hydrological consistency by incorporating hydrological signatures into model calibration objectives.” Water Resour. Res. 51 (5): 3796–3814. https://doi.org/10.1002/2014WR016520.
Singh, V. P. 1988. Vol. I of Hydrologic systems rainfall-runoff modeling. Upper Saddle River, NJ: Prentice-Hall.
Singh, V. P. 1989. Vol. II of Hydrologic systems watershed modeling. Upper Saddle River, NJ: Prentice-Hall.
Sorooshian, S. 1980. “Comparison of two direct search algorithms used in calibration of rainfall-runoff models.” In Water related land resource systems, edited by Y. Y. Haimes and J. Kindler, 477–485. New York: Pergamum.
Sorooshian, S., and V. K. Gupta. 1983. “Automatic calibration of conceptual rainfall-runoff models: The question of parameter observability and uniqueness.” Water Resour. Res. 19 (1): 260–268. https://doi.org/10.1029/WR019i001p00260.
Taormina, R., K. W. Chaua, and B. Sivakumar. 2015. “Neural network river forecasting through baseflow separation and binary-coded swarm optimization.” J. Hydrol. 529 (3): 1788–1797. https://doi.org/10.1016/j.jhydrol.2015.08.008.
Tung, Y. K. 1983. “Point rainfall estimation for a mountainous region.” J. Hydraul. Eng. 109 (10): 1386–1393. https://doi.org/10.1061/(ASCE)0733-9429(1983)109:10(1386).
Vrugt, J. A., H. V. Gupta, L. A. Bastidas, W. Bouten, and S. Sorooshian. 2003. “Effective and efficient algorithm for multiobjective optimization of hydrologic models.” Water Resour. Res. 39 (8): 1214. https://doi.org/10.1029/2002WR001746.
Water Management Information System. 2017. “WAMIS, Han River flood control office, ministry of land, infrastructure and transport, Republic of Korea.” Accessed March 1, 2017. http://www.wamis.go.kr/.
Wei, T. C., and J. L. McGuinness. 1973. Reciprocal distance squared method, a computer technique for estimating area precipitation. North Central Region, OH: US Agricultural Research Service.
Williams, B. J., and W. W-G. Yeh. 1983. “Parameter estimation in rainfall-runoff models.” J. Hydrol. 63 (3–4): 373–393. https://doi.org/10.1016/0022-1694(83)90052-5.
Yoo, J. H. 2010. “A certification of linear programming method for estimating missing precipitation values ungauged.” J. Korean Water Resour. Assoc. 43 (3): 257–264. https://doi.org/10.3741/JKWRA.2010.43.3.257.
Yoo, J. H. 2015. “Analysis of modified distance-and-elevation ratio method with different exponents of elevation and distance.” J. Korean Water Resour. Assoc. 48 (5): 357–365. https://doi.org/10.3741/JKWRA.2015.48.5.357.
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Published In
Journal of Hydrologic Engineering
Volume 24 • Issue 10 • October 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 1, 2018
Accepted: Apr 1, 2019
Published online: Jul 17, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 17, 2019
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