Modified Grey Model and its application to groundwater flow analysis with limited hydrogeological data: a case study of the Nubian Sandstone, Kharga Oasis, Egypt

Groundwater flow at Kharga Oasis, located in the western desert of Egypt, was previously analyzed using numerical models; however, the lack of basic data often limits the implementation of these models, as well as introducing a problem for model calibration and validation. The Grey Model (GM) was used to overcome these difficulties of data limitation and uncertainty of hydrogeological conditions. However, no clear theories exist for selecting the number of input model trends and the most suitable values of input parameters. Therefore, in the current study, a modification of the GM is newly proposed and called the Modified Grey Model (MGM) in an attempt to determine a process for selecting the best input models' trends with the appropriate values of input parameters to achieve acceptable fitting to observations. The sensitivity analysis results showed that the MGM produced more stable results than the GM using a wide range of values for input parameters. Moreover, the MGM reduced the calculation time required for fitting the measured piezometric level trends by 99.8 %. Three development scenarios of groundwater withdrawal were proposed that involved either expanding the present extraction rate or redistributing the groundwater withdrawal over the recent working production wells (RWPWs). The results concluded that the groundwater table in the northern part of the oasis could be temporally recovered to an economical piezometric level; however, the table in the southern part is severely decreased. Therefore, new production wells are recommended to be constructed in the southern part far enough from the RWPWs.