Abstract
In this paper, the use of MDNs (Mixture Density Networks) is proposed for deciding rating curves. This method is beneficial especially when a single curve is developed when the relation between stage and discharge exhibits hysteresis. The computational analyses performed for the Han River and Mokkye stations showed that the MDN-based method yields more meaningful results than the conventional least squares approach. Of particular significance was the possible identification of the bi-modal characteristics of rating curves under the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birkhead, A. L. and James, C. S. (1998). “Synthesis of rating curves from local stage and remote discharge monitoring using non-linear Muskingum routing.” Journal of Hydrology, Vol. 205, No. 1–2, pp. 52–65.
Bishop, C. M. (1994). Mixture density networks, Neural Computing Research Group Report: NCRG/94/004, Aston University.
Bishop, C. M. (1995). Neural networks for pattern recognition, Oxford University Press.
Clarke, R. T. (1999). “Uncertainty in the estimation of mean annual flood due to rating-curve identification.” Journal of Hydrology, Vol. 222, No. 1–4, pp. 185–190.
DeGagene, P. J., Douglas, G. G., Hudson, H. R., and Simonovic, S. P. (1996). “A decision support system for the analysis and use of stagedischarge rating curves.” Journal of Hydrology, Vol. 184, No. 3–4, pp. 225–241.
Hangang Flood Control Center (2003). http://www.hrfco.go.kr/YearCD/2003/discharge/index.html.
Haykin, S. (1998). Neural networks: A comprehensive foundation, 2nd Edition, Prentice Hall.
ISO (1983). Measurement of liquid flow in open channels, ISO Standard Handbook 16, International Organization of Standards, Geneva.
Jacobs, R. A., Jordan, M. I., Nowlan, S. J., and Hinton, G. E. (1991). “Adaptive mixtures of local experts.” Neural Computations, Vol. 3, No. 1, pp. 79–87.
Moller, M. (1993). “A scaled conjugate gradient algorithm for fast supervised learning.” Neural Networks, Vol. 6, No. 4, pp. 525–533.
Nabney, I. T. (2001). NETLAB: Algorithms for pattern recognition, Springer.
Perumal, M., Shrestha, K. B., and Chaube, U. C. (2004). “Reproduction of hysteresis in rating curve.” Journal of Hydraulic Engineering, ASCE, Vol. 130, No. 9, pp. 870–878.
Petersen-Øverleir, A. (2004). “Accounting for heteroscedasticity in rating curve estimates.” Journal of Hydrology, Vol. 292, No. 1–4, pp. 173–181.
Rantz, S. E. (1982). Measurement and computation of stream flow, Volume 2, Computation of Discharge, Paper #2175, US Geological Survey Water Supply.
Schittenkopf, C., Dorffner, G., and Dockner, E. J. (1998). Identifying stochastic processes with mixture density networks, Technical Report TR-98-16, Austrian Research Institute for Artificial Intelligence, Vienna.
Singh, V. P. (1992). Elementary hydrology, Prentice-Hall, Inc., Eagle Wood Cliffs, NJ, pp. 406–407.
Supharatid, S. (2003). “Application of a neutral network model in establishing a stage-discharge relationship for a tidal river.” Hydrological Processes, Vol. 17, No. 15, pp. 3085–3099.
Tawfik, M., Ibrahim, A., and Fahmy, H. (1997). “Hysteresis sensitive neural network for modeling rating curves.” Journal of Computing in Civil Engineering, ASCE, Vol. 11, No. 3, pp. 206–211.
Yu, B. (2000). “A systematic over-estimation of flows.” Journal of Hydrology, Vol. 233, No. 1–4, pp. 258–262.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yoo, C., Park, J. A mixture-density-network based approach for finding rating curves: Facing multi-modality and unbalanced data distribution. KSCE J Civ Eng 14, 243–250 (2010). https://doi.org/10.1007/s12205-010-0243-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-010-0243-0