Predicting Rainfall Using the Principles of Fuzzy Set Theory and Reliability Analysis

Mahbub Hasan, Salam Md. Mahbubush Khan, Chandrasekhar Putcha, Ashraf Al-Hamdan, Chance M. Glenn

College of Engineering, Technology and Physical Sciences, Alabama Agricultural and Mechanical University, Normal, USA.
Department of Civil & Environmental Engineering, University of Alabama, Huntsville, USA.
Department of Civil and Environmental Engineering, California State University, Fullerton, USA.
Department of Civil Engineering, Alabama Agricultural and Mechanical University, Normal, USA.
Department of Mathematics, Alabama Agricultural and Mechanical University, Normal, USA.

DOI: 10.4236/ajcm.2013.34043                

Abstract

The paper presents occurrence of rainfall using principles of fuzzy set theory and principles of reliability analysis. Both the abstract and the rest of the paper are discussed from these two points of view. First, a fuzzy inference model for predicting rainfall using scan data from the USDA Soil Climate Analysis Network Station at Alabama Agricultural and Mechanical University (AAMU) campus for the year 2004 is presented. The model further reflects how an expert would perceive weather conditions and apply this knowledge before inferring a rainfall. Fuzzy variables were selected based on judging patterns in individual monthly graphs for 2003 and 2004 and the influence of different variables that caused rainfall. A decrease in temperature (TP) and an increase in wind speed (WS) when compared between the ith and (i ? 1)th day were found to have a positive relation with a rainfall (RF) occurrence in most cases. Therefore, TP and WS were used in the antecedent part of the production rules to predict rainfall (RF). Results of the model showed better performance when threshold values for 1) Relative Humidity (RH) of ith day; 2) Humidity Increase (HI) between the ith and (i ? 1)th day; and 3) Product (P) of decrease in temperature (TP) and an increase in wind speed (WS) were introduced. The percentage of error was 12.35 when compared the calculated amount of rainfall with actual amount of rainfall. This is followed by prediction of rainfall using principles of reliability analysis. This is done by comparing theoretical probabilities with experimental probabilities for the occurrence of two main events, namely, Relative Humidity (RH) and Humidity Increase (HI) being in between specified threshold values. The experimental values of probability are falling in between μ ? σ and μ + σ for both RH and HI parameters, where μ is the mean value and σ is the standard deviation.

Keywords

Fuzzy Sets; Prediction; Reliability; Rainfall; Water Resources

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	M. Hasan, T. Tsegaye, X. Shi, G. Schaefer and G. Taylor, “Model for Predicting Rainfall by Fuzzy Set Theory Using USDA-SCAN Data,” Agricultural Water Management, Vol. 95, No. 12, 2008, pp. 1350-1360. http://dx.doi.org/10.1016/j.agwat.2008.07.015
[2]	M. Hasan, M. Mizutani, A. Goto and H. Matsui, “A Model for Determination of Intake Flow Size-Development of Optimum Operational Method for Irrigation Using Fuzzy Set Theory (1). System Nogaku,” Journal of Japan Agricultural System Society, Vol. 11, No. 1, 1995, pp. 1-13.
[3]	D. S. Wilks, “Multisite Generalization of a Daily Stochastic Precipitation Generating Models,” Journal of Hydrology, Vol. 210, No. 1-4, 1998, pp. 178-191. http://dx.doi.org/10.1016/S0022-1694(98)00186-3
[4]	L. A. Carrano, B. J. Taylor, E. Y. Robert, L. L. Richard and E. S. Daniel, “Fuzzy Knowledge-Based Modeling and Regression in Abrasive Wood Machining,” Forest Products Journal, Vol. 54, No. 5, 2004, pp. 66-72.
[5]	T. M. Brown-Brandl, D. D. Jones and W. E. Woldt, “Evaluating Modeling Techniques for Livestock Heat Stress Prediction,” Paper No. 034009, 2003 ASAE Annual Meeting, 2003. http://www.frymulti.com/abstract.asp?aid=14084&t=2
[6]	K. W. Wong, P. M. Wong, T. D. Gedeon and C. C. Fung, “Rainfall Prediction Model Using Soft Computing Technique. Soft Computing-A Fusion of Foundations, Methodologies and Applications,” Springer, Berlin/Heidelberg, 2003.
[7]	S. Lee, S. Cho and P. M. Wong, “Rainfall Prediction Using Artificial Neural Networks,” Journal of Geographic Information and Decision Analysis, Vol. 2, No. 2, 1998, pp. 233-242.
[8]	L. M. Pant and G. Ashwagosh, “Fuzzy Rule-Based System for Prediction of Direct Action Avalanches,” Current Science, Vol. 87, No. 1, 2004, pp. 99-104.
[9]	S. Abe and L. Ming-Shong, “Fuzzy Rules Extraction Directly from Numerical Data for Function Approximation,” IEEE Transactions on System, Man and Cybernetics, Vol. 25, No. 1, 1995, pp. 119-129. http://dx.doi.org/10.1109/21.362960
[10]	A. L. Zadeh, “Fuzzy Logic,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
[11]	T. Hasan and S. Zenkai, “A New Modeling Approach for Predicting the Maximum Daily Temperature from a Time Series,” Turkish Journal of Engineering and Environmental Science, Vol. 23, No. 3, 1999, pp. 173-180.
[12]	C. C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller-Part I,” IEEE Transaction of System, Man and Cybernetics, Vol. 20, No. 2, 1990, pp. 404-418. http://dx.doi.org/10.1109/21.52551