Spatial Interpolation of the Probability of Mercury Threshold Exceedance using Indicator Kriging

Abstract

Indicator Kriging (IK) is a spatial interpolation method used to estimate the probability that a variable exceeds a specified threshold. This study applies IK to assess the probability of mercury (Hg) concentrations exceeding environmental thresholds in river systems across DKI Jakarta. Given the skewed and non-normally distributed nature of mercury data, IK was selected due to its robustness in handling non-parametric data and its sensitivity to extreme values. Mercury concentration measurements were first transformed into binary indicator data based on a predefined threshold. An experimental semivariogram was then computed to analyze the spatial dependence of the indicator values, followed by the fitting of theoretical semivariogram models (Gaussian, Spherical, and Exponential). The best-fitting model was selected using the Leave-One-Out Cross-Validation (LOOCV) approach, with the Spherical model yielding the lowest root mean square error (RMSE). The final probability map generated through IK reveals five unsampled locations with a probability greater than 0.5 of mercury concentration exceeding the threshold: two located along the Ciliwung River and three along the Sunter River. These findings highlight critical zones requiring monitoring and support the use of IK as an effective geostatistical tool for environmental risk assessment of heavy metal contamination in urban river systems.