Investigating the Impact of Meteorological Drought on Groundwater Dynamics in a Heterogeneous Aquifer System Using Fuzzy Regression: A Case Study in Southeastern Xanthi, NE Greece

This chapter deals with the impact of meteorological drought on groundwater in a heterogeneous aquifer system located in the plain southeast of Xanthi, northeastern Greece, using fuzzy set theory. The research aims to investigate the linear relationship between meteorological drought and groundwater levels of shallow wells, as well as the key role of geology in drought propagation, in terms of time, to groundwater.

The study area is bounded to the east by the Lake Vistonida, to the north by the River Kosynthos, to the west by the settlements of Vafeika and Genisea, and to the south by the hill of Avdira and the settlement of Nea Kessani. It is irrigated by a substantial number of wells (800 or more), predominantly shallow. The area exhibits strong heterogeneity in soil composition, consisting of coarse-grained fluvial deposits in the northwest and fine-grained lake sediments in the southeast.

To achieve the study's objective, fuzzy regression analysis based on Tanaka's approach is implemented. Tanaka's fuzzy linear regression model is reduced to a linear programming problem with inclusion constraints, ensuring that all observed data is included within the produced fuzzy band. The Standardized Reconnaissance Drought Index (RDISt) and Standardized Precipitation Index (SPI) serve as inputs (independent variables) of the multiple fuzzy linear regression model. These drought indices are used to estimate drought intensity and are calculated for several reference periods. Water table serves the dependent variable, recorded by two water table loggers installed in different geological formation areas. The multiple fuzzy linear regression model produces a water table estimate for each time step with intervals of values assigned, each associated with a membership degree (fuzzy output). Hence, each fuzzy water table estimate is a fuzzy number characterized by its left boundary, right boundary, and central value, thus, effectively incorporating inherent uncertainty in estimation of groundwater level. To address potential inconsistencies, a modification of Tanaka's fuzzy linear regression model is suggested. It involves adding constraints to ensure that the central values of the fuzzy outputs are equal to or greater than their corresponding fuzzy semi-widths. In the evaluation process, the chapter employs three suitability measures and a comparison measure for fuzzy numbers. These measures assess the performance of the multiple fuzzy linear regression models and provide insights into the relationship between meteorological drought indices and groundwater levels.

The findings indicate a significant influence of annual meteorological drought on groundwater. Moreover, groundwater that are hosted in fine sediments, best related to annual drought indices, highlighting the crucial role of geology in drought propagation time. Furthermore, the use of RDISt indices enhances the results of multiple fuzzy linear regression models in all cases, confirming the index's suitability for drought intensity estimation in semi-arid regions. The proposed modification to Tanaka's fuzzy linear regression model improves its applicability and reliability in the specific study area, providing insights for groundwater fluctuation.

In summary, the study contributes to understanding the complex interactions between meteorological drought, geology, and groundwater response in the investigated aquifer system.