A comparative study of total dissolved solids in water estimation models using Gaussian process regression with different kernel functions

Abstract

Total dissolved solids (TDS) concentration, as an essential variable in evaluating the quality of drinking and agricultural water, represents water body salinity. In a river system, high TDS concentration has negative impacts on human health and crops consuming water. Since anions and cations affect the TDS value, identifying a relationship between these variables and TDS can help predict and monitor river quality. This research investigates the Gaussian process regression (GPR) model capabilities as a data-driven model to capture the relationship and estimates the TDS value in the Tajan River watershed in Northern Iran. Monthly anions and cations measured over 16 years including bicarbonate (${\text{HCO}}_{{3}}^{ - }$), carbonate (${\text{CO}}_{{3}}^{{2 - }}$), sulfate (${\text{SO}}_{{4}}^{{2 - }}$), chloride (${\text{Cl}}^{ - }$), calcium (${\text{Ca}}^{{2 + }}$), magnesium (${\text{Mg}}^{{2 + }}$), sodium (${\text{Na}}^{ + }$), and potassium (${\text{K}}^{ + }$) are considered as the predictor variables. Five GPR kernel functions are applied in the modeling, and their efficiency is evaluated using four statistics: the coefficient of determination (R²), Mean absolute error (MAE), Mean squared error (MSE), and Nash–Sutcliffe efficiency (NSE). Also, the performance of the proposed method is assessed by comparing it to the Artificial neural network (ANN) model, as an efficient and popular prediction model. The results reveal that the GPR model with the rational quadratic kernel function performed better in terms of performance criteria (R² = 0.9836).