A New Approach of Fuzzy Methods for Evaluating of Hydrological Data

Authors: Nasser Shamskia, Seyyed Habib Rahmati, Hassan Haleh , Seyyedeh Hoda Rahmati

Abstract:

The main criteria of designing in the most hydraulic constructions essentially are based on runoff or discharge of water. Two of those important criteria are runoff and return period. Mostly, these measures are calculated or estimated by stochastic data. Another feature in hydrological data is their impreciseness. Therefore, in order to deal with uncertainty and impreciseness, based on Buckley-s estimation method, a new fuzzy method of evaluating hydrological measures are developed. The method introduces triangular shape fuzzy numbers for different measures in which both of the uncertainty and impreciseness concepts are considered. Besides, since another important consideration in most of the hydrological studies is comparison of a measure during different months or years, a new fuzzy method which is consistent with special form of proposed fuzzy numbers, is also developed. Finally, to illustrate the methods more explicitly, the two algorithms are tested on one simple example and a real case study.

Keywords: Fuzzy Discharge, Fuzzy estimation, Fuzzy ranking method, Hydrological data

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081725

References:

[1] Abolpour, B., Javan, M., Karamouz M.. 2007. Water allocation improvement in river basin using adaptive Neural Fuzzy Reinforcement Learning approach, Applied Soft Computing 7, pp. 265-285.
[2] Agostino, R.B. D and Stephens, M.A., Eds. 1986. Goodness-of-Fit Techniques, Marcel Dekker.
[3] Bankert, R., Hadjimichael, M. and Hansen, B. 2001. Fuzzy logic in Environmental Sciences (http:// www.chebucto.ns.ca/Science/AIMET/fuzzy_environment/.
[4] Bardossy, A., Bronstert, A., and Merz, B. 1995. "1, 2, and 3 Dimensional Modeling of Water Movement in the Unsaturated soil Matrix Using a Fuzzy Approach". Adv. Wat. Resour. 18, pp. 237-251.
[5] Buckley, J.J., Eslami, E., 2003a. Uncertain probabilities I: the discrete case, Soft Computing, 7, pp. 500-505.
[6] Buckley, J.J., Eslami, E., 2003b.Uncertain probabilities II: the continuous case, Soft Computing, 7, pp. 500- 505.
[7] Buckley, J.J., 2005. Fuzzy Statistics: hypothesis testing, Soft Computing 9, pp. 512-518.
[8] Filliben, J.J. 1975. "The Probability Plot Correlation Coefficient Test for Normality," Technometrics, 17, 111.
[9] Fontane, D.G., Timothy, K.G., and Moncado, E., 1997. Planning reservoir operation with imprecise objectives. Journal of water resources planning and management. ASCE, 123, pp. 154-162.
[10] Jacquin, A. and Shawseldin, A. 2006. "Development of Rainfall-Runoff Model Using Takagi-Sugeno, fuzzy inference system". Journal of Hydrology, vol. 329, pp. 154-173.
[11] Kang, M.S., Kang, M.G., Park, S.W., Lee, J. J., Yoo, K.H., 2006. Application of grey model and artificial neural networks to flood forecasting. Journal of the American water resources association, vol. 42, pp. 473- 489.
[12] Khan, E., 1999. Neural fuzzy based intelligent systems and applications, in: Jain, L.C., and Martin, N.M. (Eds.), Fusion of Neural Networks, Fuzzy Sets, and Genetic Algorithms: Industrial Applications. CRC Press, Washington, DC, p. 331.
[13] Lilliefore, H.W. 1967. "On the Kolmogorov−Smirnov Test for Normality with Mean and Variance Unknown," Journal of the American Statistical Association, 62, pp. 399-402.
[14] Mathon, Bree R., Ozbek, Metin M., Pinder, George F., 2008. Transmissivity and storage coefficient estimation by coupling the Cooper-Jacob method and modified fuzzy least-squares regression. Journal of Hydrology vol. 353, pp. 267- 274.
[15] May, D., Sivakumar, M. 2008. Comparison of artificial neural network and regression models in the Prediction of urban storm water quality. Water environment research, vol. 80, pp. 4-9.
[16] Montgomery, D.C. 2001, Introduction to Statistical Quality Control, John Wiley & Sons, New York.
[17] Nayak, P.C., Svdheer, K. p., Ragan, D. M., Ramasaty, K. S., 2004. A neuro-fuzzy computing technique for modeling hydrological time series. Journal of Hydrology, vol. 291, pp. 52-66.
[18] Rahimi Bondarabadi, S., Saghafian, B. Estimating Spatial Distribution of rainfall by Fuzzy Set theory, Iran- Water Resources Research.3, pp. 17-18.
[19] Razavi Toosi, S. L., Samani, J. M. V., Kooreshpazan Dezfuli, A., 2007. Ranking Inter Basin Water Resources Projects Using Fuzzy Multiple Attribute Group Decision Making Method, Iran- Water Resources Research. 3, pp. 12-13.
[20] Ramachandra Rao, A., Srinivas, V.V., 2006.Regionalization of watersheds by fuzzy cluster analysis. Journal of Hydrology 318, pp. 57-79.
[21] Srinivas V.V., Tripathi, Shivam, Ramachandra Rao, A., Govindaraju, Rao S. 2008. Regional flood frequency analysis by combining self-organizing feature map and fuzzy clustering, Journal of Hydrology, 348, pp. 148- 166.
[22] Tayfur, G., Ozdemir, S., Singh, V.P., 2003. Fuzzy logic algorithm for runoff-induced sediment- transport from bare soil surfaces, Advanced in Water Resources 26, 1249-1256.
[23] Viessman Warren J. r., Lewis, Gary L. Introduction to Hydrology 1996, (Fourth edition), Harper Collins Collage Publishers, 551, 48.
[24] Zadeh, L.A., 1965. Fuzzy sets. Information and Control 8(3), pp. 338-353.
[25] Ziaee, H., 1990. The application of statistical concepts in engineering Hydrology. Iranian Jahad Daneshgahi puplisher. 12350.