Comparison of Ordinary Kriging and Cokriging for Spatial Estimation Based on Simulated Data

Siti Mutiah, Muhammad Nur Aldi, Asep Saefuddin, Fitrah Ernawati

Abstract


This study compares the performance of Ordinary Kriging (OK) and Cokriging (CK) methods in spatial estimation based on simulated data. Twelve scenarios are arranged based on a combination of sample size (50, 250, 500) and correlation levels between variables (ρ=0.1, 0.6, 0.9), with each scenario repeated 30 times. Spatial data are generated randomly within the geographical boundaries of Indonesia, variables are generated based on spherical variograms with nugget or sill or  dan range or ,, and model evaluation is carried out using Leave-One-Out Cross Validation (LOOCV) with RMSE and  metrics. The results show that Cokriging consistently produces more accurate estimates than Ordinary Kriging in all scenarios. In the best configuration (CK, n=500), RMSE = 1.04 and  = 0.945 were obtained, while the best performance of OK only reached RMSE = 1.06 and  = 0.873. All levels of correlation in Cokriging showed good performance, especially when the amount of data is sufficient. Therefore, Cokriging is recommended as a superior spatial interpolation method in the context of multivariate and spatial data, especially when relevant secondary information is available.


Keywords


Cokriging; estimation; geostatistical interpolation; ordinary kriging; spatial simulation

Full Text:

PDF

References


[1] N. Cressie. Statistics for Spatial Data. Revised ed. New York: John Wiley & Sons, INC, 1993.

[2] N. Nur Rohma. “Pendugaan Metode Ordinary Kriging”. Jurnal Penelitian Ilmu Sosial dan Eksakta 2.1 (2022), pp. 21–29. DOI: https://doi.org/10.47134/trilogi.v2i1.33.

[3] O. Arnilia, M. N. Aidi, Indahwati, and F. Ernawati. “Prediction of Pneumonia Patient Proportions Using Kriging and Inverse Distance Weighted Methods”. International Journal of Scientific Research in Science, Engineering and Technology 4099 (2023), pp. 391–399. DOI: https://doi.org/10.32628/ijsrset2310257.

[4] S. M. Meliyana R. and A. S. Ahmar. “Analysis of the Distribution of Diarrhea Patients in Bogor Regency Month Using the Ordinary Kriging Method”. ARRUS Journal of Social Sciences and Humanities 3.2 (2023), pp. 156–162. DOI: https://doi.org/10.35877/soshum1727.

[5] D. Ardianti, H. Pramoedyo, and N. Nurjannah. “Distance and Areas Weighting of GWR Kriging for Stunting Cases In East Java”. CAUCHY: Jurnal Matematika Murni dan Aplikasi 6.4 (2021), pp. 212–217. DOI: https://doi.org/10.18860/ca.v6i4.10455.

[6] T. M. Tebeje, B. L. Seifu, K. U. Mare, and Y. S. Asgedom. “Geospatial determinants and spatio-temporal variation of early initiation of breastfeeding and exclusive breastfeeding in Ethiopia from 2011 to 2019, a multiscale geographically weighted regression analysis”. BMC Public Health 24 (2024), p. 2011. DOI: https://doi.org/10.1186/s12889-024-19552-0.

[7] Y. Flores, A. Chaves, and G. Suza. “Prediction of edapho-climatic parameters in the incidence of Campylobacter spp. in northwestern Mexico”. PLOS Global Public Health 2016 (2024), pp. 1–22. DOI: https://doi.org/10.1371/journal.pgph.0002812.

[8] S. Y. Kassie, H. S. Ngusie, A. W. Demsash, and T. D. Alene. “Spatial distribution of short birth interval and associated factors among reproductive age women in Ethiopia: spatial and multilevel analysis of 2019 Ethiopian mini demographic and health survey”. BMC Pregnancy and Childbirth 23.1 (2023), pp. 1–14. DOI: https://doi.org/10.1186/s12884-023-05610-9.

[9] C. Yuan and X. Wang. “Source Apportionment and Health Risk Assessment of Heavy Metals in Soils of Old Industrial Areas — A Case Study of”. International Journal of Environmental Research and Public Health 20.3 (2023), p. 2395. DOI: https://doi.org/10.3390/ijerph20032395.

[10] N. N. Rohma. “Perbandingan Pendugaan Metode Ordinary Kriging Dan Metode Ordinary Kriging Dengan Teknik Jackknife”. MAp (Mathematics Application) Journal 4.2 (2023), pp. 101–111. DOI: https://doi.org/10.15548/map.v4i2.4736.

[11] M. R. N. N. D. Hendra Perdana. “Metode Cokriging Untuk Mengestimasi Kandungan Air Di Kota Pontianak”. Bimaster: Buletin Ilmiah Matematika, Statistika dan Terapannya 8.4 (2019), pp. 933–942. DOI: https://doi.org/10.26418/bbimst.v8i4.36640.

[12] M. A. Lasaiba. “Pengolahan Data Spasial dalam Perencanaan Penggunaan Lahan yang Berkelanjutan”. Geoforum 2.1 (2023), pp. 1–12. DOI: https://doi.org/10.30598/geoforumvol2iss1pp1-12.

[13] H. N. Fajri, R. Johar, and M. Ikhsan. “Peningkatan kemampuan spasial dan self-efficacy siswa melalui model discovery learning berbasis multimedia”. Jurnal Tadris Matematika 9.2 (2016), pp. 180–196.

[14] E. H. Isaaks and R. M. Srivastava. Applied Geostatistics. Vol. 28, no. 01. 1990. DOI: https://doi.org/10.5860/choice.28-0304.

[15] C. D. Rosita. “Kemampuan Penalaran dan Komunikasi Matematis: Apa, Mengapa, dan Bagaimana Ditingkatkan pada Mahasiswa”. Jurnal Euclid 1.1 (2014), pp. 33–46.

[16] T. P. Robinson and G. Metternicht. “Testing the performance of spatial interpolation techniques for mapping soil properties”. Computers and Electronics in Agriculture 50.2 (2006), pp. 97–108. DOI: https://doi.org/10.1016/j.compag.2005.07.003.

[17] P. Goovaerts. Geostatistics for Natural Resources Evaluation. Oxford University Press, 1997.

[18] H. Wackernagel. Multivariate Geostatistics: An Introduction with Applications. New York: Springer, 1995.

[19] H. Purnomo, S. A. Rande, and R. Prastowo. “Pemetaan Spasial Kadar Kobal pada Endapan Laterit dengan Metode Ordinary Cokriging dan Inverse Distance Weighting”. Jurnal Sains Teknologi & Lingkungan 8.1 (2022), pp. 73–86. DOI: https://doi.org/10.29303/jstl.v8i1.317.

[20] C. Maharza and N. F. Rahmah. “Pengaruh Number Of Neighbors Terhadap Perhitungan Ordinary Kriging Dan Cokriging”. Journal.Itny.Ac.Id 2020 (2020), pp. 170–176. URL: https://journal.itny.ac.id/index.php/ReTII/article/view/2011.

[21] A. P. Nugraha, A. Granitio Irwan, and L. Nugraha. “Perbandingan Geostatistik Metode Kriging Dan Co-Kriging Menggunakan Estimasi Point Kriging”. Vol. 2020, pp. 177–181. URL: https://journal.itny.ac.id/index.php/ReTII/.




DOI: https://doi.org/10.18860/cauchy.v10i2.33409

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Siti Mutiah

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Maulana Malik Ibrahim State Islamic University of Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.