Abstract

Classical linear regression has been used to measure the relationship between rainfall data and altitude in different meteorological stations, in order to evaluate a linear relation. The values of rainfall are supposed as dependent variables and the values of elevation of each station as independent variables. It has long been known that a classical statistical relationship exists between annual rainfall and the station elevation which in many cases is linear as the one examined in this article. However classical linear regression makes rigid assumptions about the statistical properties of the model, accepting the error terms as random variables, and the violation of this assumption could affect the validity of the classical linear regression. Fuzzy regression assumes ambiguous and imprecise parameters and data. For this reason it may be more effective than classical regression. In this paper we evaluate the relationship between annual rainfall data and the elevation of each station in Thessaly’s meteorological stations, using fuzzy linear regression with trapezoidal membership functions. In this possibilistic model the dependent measured elevations are crisp, and the independent observed rainfall values as well as the parameters of the model are fuzzy.

Highlights

  • The scope of constructing in engineering a model is always to attempt to maximize its usefulness

  • In Hydrology, rainfall measurement models have been extensively used in the design process of water resource projects such as hydrological prediction, spillway design, climatic change studies, rainfall and runoff correlation etc

  • Rainfall measurements in a specific area are commonly displayed in the form of time series, where recorded values can be either continuous or discrete

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Summary

Introduction

The scope of constructing in engineering a model is always to attempt to maximize its usefulness. Charfeddine in [19] extended Tanaka’s method for the case of trapezoidal membership functions with crisp measured input and output values. She used a fuzzy level function , with four crisp level functions. Extended the dual simplex method to fuzzy linear programming, with symmetric trapezoidal fuzzy parameters They studied the variation of values to a certain limit, so that the fuzzy optimal solution remains invariant. A possibilistic model (Tzimopoulos et al model) is described, where membership functions are trapezoidal, measured input values are crisp and measured output values are fuzzy triangular [13]. We present one application of the above model, concerning a hydrological problem in the region of Central Thessaly (Greece), where twenty rainfall measurement stations of the region with rainfall data and their elevation have been used

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