JTAM (Jurnal Teori dan Aplikasi Matematika)
Vol 10, No 1 (2026): January

Geostatistical Co-Kriging Approach for Estimating Total Coliform Bacteria in the Rivers of DKI Jakarta

Salsabila, Salwa (Unknown)
Sirodj, Dwi Agustin Nuriani (Unknown)



Article Info

Publish Date
02 Jan 2026

Abstract

Spatial statistics and geostatistics are essential for analyzing spatially distributed data, particularly in environmental studies where data gaps are prevalent. However, limited studies have applied multivariate geostatistical approaches, particularly Co-Kriging (CK), to assess microbial contamination in tropical urban river systems, where pollution patterns are highly variable and data gaps are frequent. This study employs CK, a multivariate geostatistical interpolation technique, to estimate Total Coliform Bacteria concentrations in the rivers of DKI Jakarta, Indonesia. Total Coliform Bacteria served as the primary variable, with Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) incorporated as secondary variables. A total of 120 sampling points were analyzed, with data collected by Dinas Lingkungan Hidup DKI Jakarta during the second monitoring period in June 2022. Semivariogram modelling identified the Gaussian model as the best fit, yielding the lowest root mean square error (RMSE) of 11.468, which performed better than both the Spherical and Exponential models. Model performance was further evaluated through Leave-One-Out Cross-Validation (LOOCV), in which one data point was systematically removed and re-estimated in multiple iterations to calculate the residuals and assess model accuracy. The CK analysis was performed using RStudio software. CK predictions closely matched observed concentrations, demonstrating strong model performance. At unsampled locations, the estimated mean Total Coliform Bacteria concentration was 7.711 × 10⁶ MPN/100 ml with a standard deviation of 4.406 × 10⁶ MPN/100 ml. The high variance indicates substantial spatial heterogeneity, likely driven by data outliers, weak spatial autocorrelation in COD, and low correlations between Total Coliform–COD and BOD–COD pairs. These findings highlight the potential of geostatistical CK to provide reliable spatial predictions of microbial contamination in urban river systems, thereby supporting evidence-based water quality monitoring and management in densely populated regions. The insights generated in this study can help environmental authorities in DKI Jakarta optimize monitoring strategies, prioritize pollution hotspot interventions, and strengthen urban river health management to protect public health and guide sustainable urban water governance.

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Journal Info

Abbrev

jtam

Publisher

Subject

Mathematics

Description

Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model ...