Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

Abstract

This paper studies, through the principles of fuzzy set theory, groundwater response to meteorological drought in the case of an aquifer system located in the plains at the southeast of Xanthi, NE Greece. Meteorological drought is expressed through standardized Reconnaissance Drought Index (RDISt) and Standardized Precipitation Index (SPI), which are calculated for various reference periods. These drought indices are considered as independent variables in multiple fuzzy linear regression based on Tanaka's model, while the observed water table regarding two areas is used as a dependent variable. The fuzzy linear regression of Tanaka is characterized by the inclusion constraints where all the observed data must be included in the produced fuzzy band. Hence, each fuzzy output can get an interval of values where a membership degree corresponds to each of them. A modification of the Tanaka model by adding constraints is proposed in order to avoid irrational behavior. The results show that there was a significant influence of the meteorological drought of the previous hydrological year, while geology plays an important role. Furthermore, the use of RDISt improves the results of fuzzy linear regressions in all cases. Two suitability measures and a measure of comparison between fuzzy numbers are used. HIGHLIGHTS The Fuzzy linear regression of Tanaka is applied between meteorological drought indices and groundwater level in an aquifer system of Xanthi plain.; Two suitability measures are used. The first one includes the objective function of Tanaka's model, while the second one is a fuzzified measure.; A ranking measure is used in order to compare the fuzzified measures of suitability.;

Keywords

• fuzzy linear regression
• meteorological drought
• reconnaissance drought index
• standardized precipitation index
• water table
• xanthi plain