Interpolation of Fire Radiative Power Based on GSTAR Model Predictions with Queen Contiguity Weights Using Ordinary Kriging

Gita Fitriyana, Nurfitri Imro'ah, Nur’ainul Miftahul Huda

Abstract


Forest fires are a persistent environmental issue in West Kalimantan, Indonesia, driven by both natural and human factors. Fire Radiative Power (FRP) serves as a vital indicator for assessing wildfire intensity and energy release. This study aims to model and predict the spatial temporal dynamics of FRP using the Generalized Space Time Autoregressive [GSTAR(1;1)] model combined with Ordinary Kriging interpolation.
The dataset covers West Kalimantan from July 2024 to September 2025, comprising four attributes: observation date, longitude, latitude, and FRP value. Data filtering was applied from the national to provincial level, focusing on three regencies Sanggau, Sekadau, and Ketapang across 14 sub-districts represented by a 1.25 × 1.25 grid. The data consisted of 65 weekly observations, with 61 used for training and 4 for testing. The GSTAR(1;1) model with a spatial area-based framework achieved an optimal RMSE of 7.42 and satisfied the white noise assumption, indicating reliable performance. Predictions for October 2025 indicated relatively stable fire intensity, with a slight FRP decrease in Nanga Tayap and Sandai during the final week. Overall, the integrated GSTAR–Kriging framework effectively captured both temporal and spatial variations, supporting improved fire risk assessment and regional decision making for wildfire management in West Kalimantan.

Keywords


Weight; Spatial Temporal; Kriging; Forest Fire.

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References


[1] C. Filizzola et al., “Fire characterization by using an original rst-based approach for fire radiative power (frp) computation,” Fire, vol. 6, no. 2, p. 48, 2023. doi: 10.3390/fire6020048.

[2] G. Fitriyana, N. Imro’ah, N. M. Huda, and Z. Zuleha, “Interpolation of fire radiative power in west kalimantan using ordinary kriging,” Jurnal Teori dan Aplikasi Matematika, vol. 9, no. 4, pp. 1287–1300, 2025. doi: 10.31764/jtam.v9i4.32643.

[3] E. B. Wiggins et al., “High temporal resolution satellite observations of fire radiative power reveal link between fire behavior and aerosol and gas emissions,” Geophysical Research Letters, vol. 47, no. 23, 2020. doi: 10.1029/2020gl090707.

[4] S. S. Kumar, J. Hult, J. Picotte, and B. Peterson, “Potential underestimation of satellite fire radiative power retrievals over gas flares and wildland fires,” Remote Sensing, vol. 12, no. 2, p. 238, 2020.

[5] Z. Dong, C. Zheng, F. Zhao, G. Wang, Y. Tian, and H. Li, “A deep learning framework: Predicting fire radiative power from the combination of polar-orbiting and geostationary satellite data during wildfire spread,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 17, pp. 10 827–10 841, 2024. doi: 10.1109/jstars.2024.3403146.

[6] H. Pratiwi, N. Imro’ah, and N. M. Huda, “Forest fire analysis from perspective of spatial-temporal using gstar (p;λ1, λ2, . . ., λp) model,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 19, no. 2, pp. 1379–1392, 2025. doi: 10.30598/barekengvol19iss2pp1379-1392.

[7] Y. Supriya and T. R. Gadekallu, “Particle swarm-based federated learning approach for early detection of forest fires,” Sustainability, vol. 15, no. 2, p. 964, 2023. doi: 10.3390/su15020964.

[8] R. Alkhatib, W. Sahwan, A. Alkhatieb, and B. Schütt, “A brief review of machine learning algorithms in forest fires science,” Applied Sciences, vol. 13, no. 14, p. 8275, 2023. doi: 10.3390/app13148275.

[9] M. Y. Ayyash, N. M. Huda, and N. Imro’ah, “The gstar (1;1) modelling with three combination of the grid sizes and spatial weight matrix in forest fires cases,” JTAM (Jurnal Teori dan Aplikasi Matematika), vol. 9, no. 1, p. 134, 2025. doi: 10.31764/jtam.v9i1.27543.

[10] X. Lu, M. Salehi, M. Haenggi, E. Hossain, and H. Jiang, “Stochastic geometry analysis of spatial-temporal performance in wireless networks: A tutorial,” IEEE Communications Surveys & Tutorials, vol. 23, no. 4, pp. 2753–2801, 2021. doi: 10.1109/comst.2021.3104581.

[11] S. Y. Chung, S. Venkatramanan, H. E. Elzain, S. Selvam, and M. Prasanna, “Supplement of missing data in groundwater-level variations of peak type using geostatistical methods,” in GIS and Geostatistical Techniques for Groundwater Science. Elsevier, 2019, pp. 33–41. doi: 10.1016/b978-0-12-815413-7.00004-3.

[12] U. Mukhaiyar, N. R. Dianti, E. S. Rezeki, and N. R. Richardo, “Prediksi risiko emisi karbon dioksida melalui pemodelan gstar kriging di wilayah asia,” Journal of Mathematics, Computations and Statistics, vol. 7, no. 2, pp. 396–412, 2024. doi: 10.35580/jmathcos.v7i2.4309.

[13] J. U. Devkota, “Statistical analysis of active fire remote sensing data: Examples from south asia,” Environmental Monitoring and Assessment, vol. 193, no. 9, 2021. doi: 10.1007/s10661-021-09354-x.

[14] N. M. Huda, N. Imro’ah, M. Y. Ayyash, and H. Pratiwi, “Forest fires in peatlands analyzed from various perspectives: Spatial, temporal, and spatial-temporal,” JTAM (Jurnal Teori dan Aplikasi Matematika), vol. 9, no. 2, p. 482, 2025. doi: 10.31764/jtam.v9i2.28884.

[15] F. Hestuningtias and M. H. S. Kurniawan, “The implementation of the generalized space-time autoregressive (gstar) model for inflation prediction,” Enthusiastic: International Journal of Applied Statistics and Data Science, pp. 176–188, 2023. doi: 10 . 20885 / enthusiastic.vol3.iss2.art5.

[16] H. Pratiwi, N. Imro’ah, N. M. Huda, and M. Y. Ayyash, “Comparison of weight matrix in hotspot modeling in west kalimantan using the gstar method,” Jurnal Matematika UNAND, vol. 14, no. 1, pp. 31–45, 2025. doi: 10.25077/jmua.14.1.31-45.2025.

[17] Yundari, U. S. Pasaribu, U. Mukhaiyar, and M. N. Heriawan, “Spatial weight determination of gstar(1;1) model by using kernel function,” Journal of Physics: Conference Series, vol. 1028, p. 012 223, 2018. doi: 10.1088/1742-6596/1028/1/012223.

[18] N. M. Huda and N. Imro’ah, “Determination of the best weight matrix for the generalized space time autoregressive (gstar) model in the covid-19 case on java island, indonesia,” Spatial Statistics, vol. 54, p. 100 734, 2023. doi: 10.1016/j.spasta.2023.100734.

[19] Y. Yundari, U. S. Pasaribu, and U. Mukhaiyar, “Error assumptions on generalized star model,” Journal of Mathematical and Fundamental Sciences, vol. 49, no. 2, p. 136, 2017. doi: 10.5614/j.math.fund.sci.2017.49.2.4.

[20] P. Kumar, B. Rao, A. Burman, S. Kumar, and P. Samui, “Spatial variation of permeability and consolidation behaviors of soil using ordinary kriging method,” Groundwater for Sustainable Development, vol. 20, p. 100 856, 2023. doi: 10.1016/j.gsd.2022.100856.

[21] C. Wu, Interpolation: Kriging, 2017. doi: 10.1002/9781118786352.wbieg0996.

[22] J. Böhner and B. Bechtel, “Gis in climatology and meteorology,” in Comprehensive Geographic Information Systems. Elsevier, 2018, pp. 196–235. doi: 10.1016/b978-0-12-409548-9.09633-0.

[23] N. N. Rohma, “Estimation of ordinary kriging method with jackknife technique on rainfall data in malang raya,” International Journal on Information and Communication Technology (IJoICT), vol. 8, no. 2, pp. 22–39, 2022. doi: 10.21108/ijoict.v8i2.678.

[24] M. Khan, M. M. A. Almazah, A. EIlahi, R. Niaz, A. Y. Al-Rezami, and B. Zaman, “Spatial interpolation of water quality index based on ordinary kriging and universal kriging,” Geomatics, Natural Hazards and Risk, vol. 14, no. 1, 2023. doi: 10.1080/19475705.2023.2190853.

[25] T. Gia Pham, M. Kappas, C. Van Huynh, and L. Hoang Khanh Nguyen, “Application of ordinary kriging and regression kriging method for soil properties mapping in hilly region of central vietnam,” ISPRS International Journal of Geo-Information, vol. 8, no. 3, p. 147, 2019. doi: 10.3390/ijgi8030147.

[26] M. Li, S. Shen, V. Barzegar, M. Sadoughi, C. Hu, and S. Laflamme, “Kriging-based reliability analysis considering predictive uncertainty reduction,” Structural and Multidisciplinary Optimization, vol. 63, no. 6, pp. 2721–2737, 2021. doi: 10.1007/s00158-020-02831-w.

[27] A. Setiyoko, T. Basaruddin, and A. M. Arymurthy, “Minimax approach for semivariogram fitting in ordinary kriging,” IEEE Access, vol. 8, pp. 82 054–82 065, 2020. doi: 10.1109/access.2020.2991428.

[28] H. Xia, S. Zha, J. Huang, and J. Liu, “Radio environment map construction by adaptive ordinary kriging algorithm based on affinity propagation clustering,” International Journal of Distributed Sensor Networks, vol. 16, no. 5, p. 155 014 772 092 248, 2020. doi: 10.1177/1550147720922484.

[29] A. H. Wong and T. J. Kwon, “Development and evaluation of geostatistical methods for estimating weather related collisions: A large-scale case study,” Transportation Research Record: Journal of the Transportation Research Board, vol. 2675, no. 11, pp. 828–840, 2021. doi: 10.1177/03611981211020008.

[30] N. S. V. Studio. “Active fires as observed by viirs, 2020.” Accessed on October 31, 2025, NASA Goddard Space Flight Center. https://svs.gsfc.nasa.gov/4899.

[31] U. Mukhaiyar, “The goodness of generalized star in spatial dependency observations modeling,” in AIP Conference Proceedings, AIP Publishing LLC, 2015. doi: 10.1063/1.4936436.

[32] A. Roza, E. S. Violita, and S. Aktivani, “Study of inflation using stationary test with augmented dickey fuller & phillips-peron unit root test (case in bukittinggi city inflation for 2014-2019),” EKSAKTA: Berkala Ilmiah Bidang MIPA, vol. 23, no. 02, pp. 106–116, 2022. doi: 10.24036/eksakta/vol23-iss02/303.




DOI: https://doi.org/10.18860/cauchy.v11i1.37462

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