Imputing missing data using grey system theory and the biplot method to forecast groundwater levels and yields

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Jelena Ratković
Dušan Polomčić
Zoran Gligorić
Dragoljub Bajić


Groundwater management is one of today’s important tasks. It has become necessary to seek out increasingly reliable methods to conserve groundwater resources. Dependable forecasting of the amounts of groundwater that can be abstracted in a sustainable manner requires longterm monitoring of the groundwater regime (rate of abstraction and groundwater levels). Monitoring of the groundwater source for the town of Bečej, Serbia had been disrupted for multiple years. The objective of the paper is to assess the possibility of reinterpreting the missing data or, in other words, to reconstruct the operation of the groundwater source and its effect on groundwater levels. At the Bečej source, groundwater is withdrawn from three water-bearing strata comprised of fine- to coarse-grained sands. Historic data are used to reconstruct the operation of the Bečej source between 1st of October 1980 to 1st of May 2010. The monitored parameters are total source yield and piezometric head at seven observation wells and 14 pumping wells. A data reconstruction methodology was developed, which included the use of an autoregressive (AR) model, a grey model (GM), and the biplot method. The methodology is applied to fill the data gaps during the considered period. The paper also describes the criteria for evaluating the accuracy of the AR model, GM, and biplot method. The proposed data reconstruction approach yielded satisfactory results and the methodology is deemed useful for the Bečej source data, as well as other historic data not necessarily associated with groundwater sources, but also groundwater control and protection systems, as well as hydrometeorological, hydrological and similar uses.


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