Variation and multi-time series prediction of total hardness in groundwater of the Guanzhong Plain (China) using grey Markov model

Abstract

Total hardness (TH) is an important index representing the water suitability for domestic purpose. TH is represented mainly by Ca²⁺ and Mg²⁺ which are essential elements for human bone development. Between 2000 and 2015, the TH values of groundwater in major cities of the Guanzhong Plain varied significantly. The study was carried out to investigate TH variation over 16 years and to examine how effective the grey Markov model was in predicting TH concentrations in time series datasets. The hydrochemical parameters determining TH concentration and their origins were investigated using statistical analysis and geochemical models. The grey Markov model, which is effective in short time series prediction, was used to forecast the multi-time series of TH. The findings demonstrated a prevalence of HCO₃^- and SO₄^2- in the groundwater types combined with calcite precipitation, gypsum, and dolomite dissolution that increased the concentration of Ca²⁺, Mg²⁺, and HCO₃^-, influencing TH variation. The predicted TH values of the eight monitoring wells for the year 2016 were 1213.66, 124.30, 203.66, 103.01, 349.56, 251.23, 453.31, and 471.81 mg/L, respectively. Datasets with low TH variation were more accurately predicted than datasets with high TH variation. This was especially observed on sample B557 where TH concentration in 2010 was 400.33 mg/L and suddenly dropped to 90.1, 82.6, 85.1, 87.6, and 75.1 mg/L in 2011, 2012, 2013, 2014, and 2015, respectively. The study also shows that the Markov chain model can optimize the GM(1,1) model and improve the prediction accuracy significantly. All samples in Weinan City and one sample in Xi'an City showed a significant decrease in TH concentration. Except one sample in Xi'an City, TH concentrations tended to rise in the other cities (Baoji, Xianyang) of the Guanzhong Plain. This study verified the reliability of the grey Markov model in terms of forecasting time series datasets with high variability, and the results can be referential to similar studies in the world.

Keywords: Grey Markov model; Groundwater quality; Guanzhong Plain; Total hardness; Water quality prediction.