Research Article
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Year 2025, Volume: 54 Issue: 6, 2525 - 2542, 30.12.2025
https://doi.org/10.15672/hujms.1726843

Abstract

References

  • [1] C. Su, Y. Hu, Y. Ma and J. Yang, Simulation study and proper orthogonal decomposition analysis of buoyant flame dynamics and heat transfer of wind-aided fires spreading on sloped terrain. Fire 8 (1), 139, 2025.
  • [2] A. T. Murray, L. Carvalho, R. L. Church, C. Jones, D. Roberts, J. Xu, K. Zigner and D. Nash, Coastal vulnerability under extreme weather. Appl. Spatial Anal. Policy 14 (1), 497–523, 2021.
  • [3] D. Shadrin, S. Illarionova, F. Gubanov, K. Evteeva, M. Mironenko, I. Levchunets, R. Belousov and E. Burnaev, Wildfire spreading prediction using multimodal data and deep neural network approach. Sci. Rep. 14 (1), 2606, 2024.
  • [4] B. Chen, W. Cai and A. Garg, Relationship between bioelectricity and soilwater characteristics of biochar-aided plant microbial fuel cell. Acta Geotech. 18 (1), 3529– 3542, 2023.
  • [5] Y. Zhang, H. S. Lim, C. Hu and R. Zhang, Spatiotemporal dynamics of forest fires in the context of climate change: a review. Environ. Sci. Pollut. Res. 31 (1), 2024.
  • [6] D. Smith, T. Abeli, E. B. Bruns, S. E. Dalrymple, J. Foster, T. C. Gilbert, C. J. Hogg, N. A. Lloyd, A. Meyer, A. Moehrenschlager, O. Murrell, J. P. Rodriguez, P. P. Smith, A. Terry and J. G. Ewen, Extinct in the wild: The precarious state of earths most threatened group of species. Science 379 (1), 2023.
  • [7] A. F. Feldman, X. Feng, A. J. Felton, A. G. Konings, A. K. Knapp, J. A. Biederman and B. Poulter, Plant responses to changing rainfall frequency and intensity. Nat. Rev. Earth Environ. 5 (1), 276–294, 2024.
  • [8] M. W. Jones, D. I. Kelley, C. A. Burton, F. D. Giuseppe, M. L. F. Barbosa, E. Brambleby, A. J. Hartley, A. Lombardi, G. Mataveli, J. R. McNorton, F. R. Spuler, J. B.Wessel, J. T. Abatzoglou, L. O. Anderson, N. Andela, S. Archibald, D. Armenteras, E. Burke, R. Carmenta, E. Chuvieco, H. Clarke, S. H. Doerr, P. M. Fernandes, L. Giglio, D. S. Hamilton, S. Hantson, S. Harris, P. Jain, C. A. Kolden, T. Kurvits, S. Lampe, S. Meier, S. New, M. Parrington, M. M. G. Perron, Y. Qu, N. S. Ribeiro, B. H. Saharjo, J. San-Miguel-Ayanz, J. K. Shuman, V. Tanpipat, G. R. van der Werf, S. Veraverbeke and G. Xanthopoulos, State of wildfires 20232024. Earth Syst. Sci. Data 16 (1), 3601–3685, 2024.
  • [9] S. C. Izah, A. O. Iyiola, B. Yarkwan and G. Richard, Impact of air quality as a component of climate change on biodiversity-based ecosystem services. In: Elsevier (Ed.), pp. 123–148, 2023.
  • [10] R. A. Zahra, E. Nurjani and A. B. Sekaranom, The analysis of fire hotspot distribution in Kalimantan and its relationship with ENSO phases. Quaest. Geogr. 42 (1), 75–86, 2023.
  • [11] T. T. Tora, L. T. Andarge, A. T. Abebe, A. U. Utallo, D. T. Meshesha and A. F. Wubie, An expert-based assessment of early warning systems effectiveness in South Ethiopia Regional State. Discov. Sustain. 6 (1), 188, 2025.
  • [12] D. Munandar, B. N. Ruchjana, A. S. Abdullah and H. F. Pardede, Integration GSTARIMA with deep neural network to enhance prediction accuracy on rainfall data. Syst. Sci. Control Eng. 12 (1), 2024.
  • [13] H. Pratiwi, N. Imro’ah and N. M. Huda, Forest fire analysis from perspective of spatial-temporal using GSTAR ($p$;$\lambda_1,\lambda_2,\dots,\lambda_p$) model. BAREKENG J. Ilmu Mat. Terap. 19 (1), 1379–1392, 2025.
  • [14] M. Y. Ayyash, N. Miftahul Huda and N. Imroah, The GSTAR (1;1) modelling with three combinations of the grid sizes and spatial weight matrix in forest fires cases. JTAM 9 (1), 134–146, 2025.
  • [15] N. M. Huda and N. Imroah, Determination of the best weight matrix for the GSTAR model in the COVID-19 case on Java Island, Indonesia. Spatial Stat. 54 (1), 100734, 2023.
  • [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. J. Mat. UNAND 14 (1), 31–45, 2025.
  • [17] N. Imro’ah and N. M. Huda, Double intervention analysis on the ARIMA model of COVID-19 cases in Bali. J. Indones. Math. Soc. 31 (1), 1347, 2025.
  • [18] N. M. Huda and N. Imro’ah, Modeling the dynamics of forest fires: A vector autoregressive approach across three fire classifications. JTAM 8 (1), 1157, 2024.
  • [19] U. Mukhaiyar, D. Widyanti and S. Vantika, The time series regression analysis in evaluating the economic impact of COVID-19 cases in Indonesia. Model Assist. Stat. Appl. 16 (1), 197–210, 2021.
  • [20] K. N. Sh, I. Irfani and U. Mukhaiyar, Predicting air pollution levels in Jakarta using vector autoregressive analysis. pp. 14–22, 2023.
  • [21] U. Mukhaiyar, A. W. Mahdiyasa, T. Prastoro, B. C. Suherlan, U. S. Pasaribu and S. W. Indratno, Spatial and time series modelling for the groundwater level of peatlands in Riau and Central Kalimantan, Indonesia. pp. 89–104, 2024.
  • [22] U. Mukhaiyar, A. W. Mahdiyasa, T. Prastoro, U. S. Pasaribu, K. N. Sari, S. W. Indratno, I. Soekarno, D. N. Choesin, I. Ismail, D. Rosleine and D. T. Qoyyimi, The generalized STAR modelling with three-dimensional spatial weight matrix in predicting the Indonesia peatlands water level. Environ. Sci. Eur. 36 (1), 180, 2024.
  • [23] U. Mukhaiyar, A. W. Mahdiyasa, K. N. Sari and N. T. Noviana, The generalized STAR modeling with minimum spanning tree approach of spatial weight matrix. Front. Appl. Math. Stat. 10 (1), 2024.
  • [24] P. E. Pfeifer and S. J. Deutsch, Identification and interpretation of first order spacetime ARMA models. Technometrics 22 (1), 397–408, 1980.
  • [25] A. B. Salsabila, B. N. Ruchjana and A. S. Abdullah, Development of the GSTARIMA(1,1,1) model order for climate data forecasting. Int. J. Data Netw. Sci. 8 (1), 773–788, 2024.
  • [26] D. Munandar, B. N. Ruchjana, A. S. Abdullah and H. F. Pardede, Literature review on integrating GSTARIMA and deep neural networks in machine learning for climate forecasting. Mathematics 11 (1), 2975, 2023.
  • [27] N. H. A. Rahman, S. N. M. Yusof, I. S. C. Ilias, K. Gopal, H. Yaacob and N. M. Sham, Spatio-temporal model to forecast COVID-19 confirmed cases in high-density areas of Malaysia. Malaysian J. Fundam. Appl. Sci. 20 (1), 972–984, 2024.

Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices

Year 2025, Volume: 54 Issue: 6, 2525 - 2542, 30.12.2025
https://doi.org/10.15672/hujms.1726843

Abstract

This study proposes a new approach to spatio-temporal modeling of fire data by utilizing the generalized space-time autoregressive (1;1) model and the construction of spatial weight matrices based on dynamic environmental variables. The data used consisted of the highest confidence level for fire spots in West Kalimantan from April 2020 to September 2023. These fire points were separated into seven grids, each measuring 3 $\times$ 3 degrees. This research analyzes three different types of weight matrices, departing from the typical methods that only employ inverse distance weights. These weight matrices are the inverse distance, the distance relative to the average maximum wind speed, and the distance relative to the average maximum total rainfall. Evaluations using the mean absolute percentage error, the mean square error, and the mean absolute error demonstrate that the weight matrix based on wind speed generates the most accurate model by producing the highest level of precision. A more accurate and adaptable representation of the fire spread process is made possible by incorporating meteorological elements into the spatial structure of the model. It is the primary innovation featured in the model. In an effort to increase the accuracy of forest and land fire predictions in tropical regions such as West Kalimantan, these findings highlight the importance of keeping atmospheric dynamics in mind when performing spatial weighting.

References

  • [1] C. Su, Y. Hu, Y. Ma and J. Yang, Simulation study and proper orthogonal decomposition analysis of buoyant flame dynamics and heat transfer of wind-aided fires spreading on sloped terrain. Fire 8 (1), 139, 2025.
  • [2] A. T. Murray, L. Carvalho, R. L. Church, C. Jones, D. Roberts, J. Xu, K. Zigner and D. Nash, Coastal vulnerability under extreme weather. Appl. Spatial Anal. Policy 14 (1), 497–523, 2021.
  • [3] D. Shadrin, S. Illarionova, F. Gubanov, K. Evteeva, M. Mironenko, I. Levchunets, R. Belousov and E. Burnaev, Wildfire spreading prediction using multimodal data and deep neural network approach. Sci. Rep. 14 (1), 2606, 2024.
  • [4] B. Chen, W. Cai and A. Garg, Relationship between bioelectricity and soilwater characteristics of biochar-aided plant microbial fuel cell. Acta Geotech. 18 (1), 3529– 3542, 2023.
  • [5] Y. Zhang, H. S. Lim, C. Hu and R. Zhang, Spatiotemporal dynamics of forest fires in the context of climate change: a review. Environ. Sci. Pollut. Res. 31 (1), 2024.
  • [6] D. Smith, T. Abeli, E. B. Bruns, S. E. Dalrymple, J. Foster, T. C. Gilbert, C. J. Hogg, N. A. Lloyd, A. Meyer, A. Moehrenschlager, O. Murrell, J. P. Rodriguez, P. P. Smith, A. Terry and J. G. Ewen, Extinct in the wild: The precarious state of earths most threatened group of species. Science 379 (1), 2023.
  • [7] A. F. Feldman, X. Feng, A. J. Felton, A. G. Konings, A. K. Knapp, J. A. Biederman and B. Poulter, Plant responses to changing rainfall frequency and intensity. Nat. Rev. Earth Environ. 5 (1), 276–294, 2024.
  • [8] M. W. Jones, D. I. Kelley, C. A. Burton, F. D. Giuseppe, M. L. F. Barbosa, E. Brambleby, A. J. Hartley, A. Lombardi, G. Mataveli, J. R. McNorton, F. R. Spuler, J. B.Wessel, J. T. Abatzoglou, L. O. Anderson, N. Andela, S. Archibald, D. Armenteras, E. Burke, R. Carmenta, E. Chuvieco, H. Clarke, S. H. Doerr, P. M. Fernandes, L. Giglio, D. S. Hamilton, S. Hantson, S. Harris, P. Jain, C. A. Kolden, T. Kurvits, S. Lampe, S. Meier, S. New, M. Parrington, M. M. G. Perron, Y. Qu, N. S. Ribeiro, B. H. Saharjo, J. San-Miguel-Ayanz, J. K. Shuman, V. Tanpipat, G. R. van der Werf, S. Veraverbeke and G. Xanthopoulos, State of wildfires 20232024. Earth Syst. Sci. Data 16 (1), 3601–3685, 2024.
  • [9] S. C. Izah, A. O. Iyiola, B. Yarkwan and G. Richard, Impact of air quality as a component of climate change on biodiversity-based ecosystem services. In: Elsevier (Ed.), pp. 123–148, 2023.
  • [10] R. A. Zahra, E. Nurjani and A. B. Sekaranom, The analysis of fire hotspot distribution in Kalimantan and its relationship with ENSO phases. Quaest. Geogr. 42 (1), 75–86, 2023.
  • [11] T. T. Tora, L. T. Andarge, A. T. Abebe, A. U. Utallo, D. T. Meshesha and A. F. Wubie, An expert-based assessment of early warning systems effectiveness in South Ethiopia Regional State. Discov. Sustain. 6 (1), 188, 2025.
  • [12] D. Munandar, B. N. Ruchjana, A. S. Abdullah and H. F. Pardede, Integration GSTARIMA with deep neural network to enhance prediction accuracy on rainfall data. Syst. Sci. Control Eng. 12 (1), 2024.
  • [13] H. Pratiwi, N. Imro’ah and N. M. Huda, Forest fire analysis from perspective of spatial-temporal using GSTAR ($p$;$\lambda_1,\lambda_2,\dots,\lambda_p$) model. BAREKENG J. Ilmu Mat. Terap. 19 (1), 1379–1392, 2025.
  • [14] M. Y. Ayyash, N. Miftahul Huda and N. Imroah, The GSTAR (1;1) modelling with three combinations of the grid sizes and spatial weight matrix in forest fires cases. JTAM 9 (1), 134–146, 2025.
  • [15] N. M. Huda and N. Imroah, Determination of the best weight matrix for the GSTAR model in the COVID-19 case on Java Island, Indonesia. Spatial Stat. 54 (1), 100734, 2023.
  • [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. J. Mat. UNAND 14 (1), 31–45, 2025.
  • [17] N. Imro’ah and N. M. Huda, Double intervention analysis on the ARIMA model of COVID-19 cases in Bali. J. Indones. Math. Soc. 31 (1), 1347, 2025.
  • [18] N. M. Huda and N. Imro’ah, Modeling the dynamics of forest fires: A vector autoregressive approach across three fire classifications. JTAM 8 (1), 1157, 2024.
  • [19] U. Mukhaiyar, D. Widyanti and S. Vantika, The time series regression analysis in evaluating the economic impact of COVID-19 cases in Indonesia. Model Assist. Stat. Appl. 16 (1), 197–210, 2021.
  • [20] K. N. Sh, I. Irfani and U. Mukhaiyar, Predicting air pollution levels in Jakarta using vector autoregressive analysis. pp. 14–22, 2023.
  • [21] U. Mukhaiyar, A. W. Mahdiyasa, T. Prastoro, B. C. Suherlan, U. S. Pasaribu and S. W. Indratno, Spatial and time series modelling for the groundwater level of peatlands in Riau and Central Kalimantan, Indonesia. pp. 89–104, 2024.
  • [22] U. Mukhaiyar, A. W. Mahdiyasa, T. Prastoro, U. S. Pasaribu, K. N. Sari, S. W. Indratno, I. Soekarno, D. N. Choesin, I. Ismail, D. Rosleine and D. T. Qoyyimi, The generalized STAR modelling with three-dimensional spatial weight matrix in predicting the Indonesia peatlands water level. Environ. Sci. Eur. 36 (1), 180, 2024.
  • [23] U. Mukhaiyar, A. W. Mahdiyasa, K. N. Sari and N. T. Noviana, The generalized STAR modeling with minimum spanning tree approach of spatial weight matrix. Front. Appl. Math. Stat. 10 (1), 2024.
  • [24] P. E. Pfeifer and S. J. Deutsch, Identification and interpretation of first order spacetime ARMA models. Technometrics 22 (1), 397–408, 1980.
  • [25] A. B. Salsabila, B. N. Ruchjana and A. S. Abdullah, Development of the GSTARIMA(1,1,1) model order for climate data forecasting. Int. J. Data Netw. Sci. 8 (1), 773–788, 2024.
  • [26] D. Munandar, B. N. Ruchjana, A. S. Abdullah and H. F. Pardede, Literature review on integrating GSTARIMA and deep neural networks in machine learning for climate forecasting. Mathematics 11 (1), 2975, 2023.
  • [27] N. H. A. Rahman, S. N. M. Yusof, I. S. C. Ilias, K. Gopal, H. Yaacob and N. M. Sham, Spatio-temporal model to forecast COVID-19 confirmed cases in high-density areas of Malaysia. Malaysian J. Fundam. Appl. Sci. 20 (1), 972–984, 2024.
There are 27 citations in total.

Details

Primary Language English
Subjects Spatial Statistics
Journal Section Research Article
Authors

Nurfitri Imro'ah 0009-0006-3770-4687

Nur'ainul Miftahul Huda 0000-0002-5506-3215

Hesty Pratiwi 0009-0001-2272-8399

Muhammad Yahya Ayyash 0009-0002-3497-0745

Submission Date June 25, 2025
Acceptance Date November 27, 2025
Early Pub Date December 11, 2025
Publication Date December 30, 2025
Published in Issue Year 2025 Volume: 54 Issue: 6

Cite

APA Imro’ah, N., Miftahul Huda, N., Pratiwi, H., Ayyash, M. Y. (2025). Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices. Hacettepe Journal of Mathematics and Statistics, 54(6), 2525-2542. https://doi.org/10.15672/hujms.1726843
AMA Imro’ah N, Miftahul Huda N, Pratiwi H, Ayyash MY. Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices. Hacettepe Journal of Mathematics and Statistics. December 2025;54(6):2525-2542. doi:10.15672/hujms.1726843
Chicago Imro’ah, Nurfitri, Nur’ainul Miftahul Huda, Hesty Pratiwi, and Muhammad Yahya Ayyash. “Spatio-Temporal Modeling of Fire Hotspots Using GSTAR(1;1) Model With Meteorology Based Weight Matrices”. Hacettepe Journal of Mathematics and Statistics 54, no. 6 (December 2025): 2525-42. https://doi.org/10.15672/hujms.1726843.
EndNote Imro’ah N, Miftahul Huda N, Pratiwi H, Ayyash MY (December 1, 2025) Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices. Hacettepe Journal of Mathematics and Statistics 54 6 2525–2542.
IEEE N. Imro’ah, N. Miftahul Huda, H. Pratiwi, and M. Y. Ayyash, “Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 6, pp. 2525–2542, 2025, doi: 10.15672/hujms.1726843.
ISNAD Imro’ah, Nurfitri et al. “Spatio-Temporal Modeling of Fire Hotspots Using GSTAR(1;1) Model With Meteorology Based Weight Matrices”. Hacettepe Journal of Mathematics and Statistics 54/6 (December2025), 2525-2542. https://doi.org/10.15672/hujms.1726843.
JAMA Imro’ah N, Miftahul Huda N, Pratiwi H, Ayyash MY. Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices. Hacettepe Journal of Mathematics and Statistics. 2025;54:2525–2542.
MLA Imro’ah, Nurfitri et al. “Spatio-Temporal Modeling of Fire Hotspots Using GSTAR(1;1) Model With Meteorology Based Weight Matrices”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 6, 2025, pp. 2525-42, doi:10.15672/hujms.1726843.
Vancouver Imro’ah N, Miftahul Huda N, Pratiwi H, Ayyash MY. Spatio-temporal modeling of fire hotspots using GSTAR(1;1) model with meteorology based weight matrices. Hacettepe Journal of Mathematics and Statistics. 2025;54(6):2525-42.