Prediction of hotspots pattern in Kalimantan using copula-based quantile regression and probabilistic model: a study of precipitation and dry spells across varied ENSO conditions

Mohamad K. Najib, Sri Nurdiati, Ardhasena Sopaheluwakan
Author affiliations


  • Mohamad K. Najib Division of Computational Mathematics, Department of Mathematics, IPB University, Bogor 16680, Indonesia
  • Sri Nurdiati Division of Computational Mathematics, Department of Mathematics, IPB University, Bogor 16680, Indonesia
  • Ardhasena Sopaheluwakan Center for Applied Climate Services, Agency for Meteorology, Climatology, and Geophysics, Jakarta 10720, Indonesia



Copula-based quantile regression, El Nino-Southern Oscillation (ENSO), hotspots, probabilistic model, rotated copula


Hotspots in Kalimantan are significantly correlated with local and global climatic conditions. These hotspots have been represented in previous explorations using copula-based mean regression technique. However, this study focused on advancing hotspots model through the use of copula-based quantile regression. Probabilistic method was also introduced to depict the characteristics of hotspots in Kalimantan. To achieve this objective, the technique of the inference of functions for margins was applied. Several copula functions, including Gumbel, Clayton, Frank, Joe, Galambos, BB1, BB6, BB7, and BB8, were meticulously chosen. The selection of the most suitable copula was based on the results of the Anderson-Darling and Cramer-von Mises hypothesis tests. The results showed that the combination of quantile and mean regression yielded satisfactory results. Moreover, an uncertainty range was established by assessing the outermost quantile, which aided the assessment of the reliability of estimated hotspots. Probabilistic model introduced a fresh viewpoint to modeling process. Instead of forecasting an exact value, model estimated the probability of hotspots occurrences based on specific climatic conditions. Among the three scenarios examined, precipitation-based model showed an average accuracy of 89.7%, while dry spells-based outperformed the value with a score of 90.3%. After evaluating the results from both regression and probabilistic model, dry spells-based method outperformed precipitation-based. On the other hand, precipitation-based performed better in capturing certain minor details compared to dry spells-based model.


Download data is not yet available.


Abdallah M., Mohammadi B., Modathir M.A., Omer A., Cheraghalizadeh M., Eldow M.E.E., Duan Z., 2022. Reference evapotranspiration estimation in hyper-arid regions via D-vine copula based-quantile regression and comparison with empirical approaches and machine learning models. Journal of Hydrology: Regional Studies, 44. Doi: 10.1016/j.ejrh.2022.101259.

Amini S., Bidaki R.Z., Mirabbasi R., Shafaei M., 2022. Flood risk analysis based on nested copula structure in Armand Basin, Iran. Acta Geophysica, 70(3), 1385-1399. Doi: 10.1007/s11600-022-00766-y.

Amirudin A.A., Salimun E., Tangang F., Juneng L., Zuhairi M., 2020. Differential influences of teleconnections from the Indian and Pacific oceans on rainfall variability in Southeast Asia. Atmosphere, 11(9), 886. Doi: 10.3390/ATMOS11090886.

Anderson T.W., 2011. Anderson-Darling Tests of Goodness-of-Fit. In: International Encyclopedia of Statistical Science. Berlin, Heidelberg: Springer, 52-54. Doi: 10.1007/978-3-642-04898-2_118.

Ardiyani E., Nurdiati S., Sopaheluwakan A., Septiawan P., Najib M.K., 2023. Probabilistic Hotspot Prediction Model Based on Bayesian Inference Using Precipitation, Relative Dry Spells, ENSO and IOD. Atmosphere, 14(2), 286.

Babić S., Ley C., Veredas D., 2019. Comparison and classification of flexible distributions for multivariate skew and heavy-tailed data. Symmetry, 11(10). Doi: 10.3390/sym11101216.

Berg D., 2009. Copula goodness-of-fit testing: An overview and power comparison. European Journal of Finance, 15(7-8), 675-701. Doi: 10.1080/13518470802697428.

Brechmann E.C., 2014. Hierarchical Kendall copulas: Properties and inference. Canadian Journal of Statistics, 42(1), 78-108. Doi: 10.1002/cjs.11204.

Brechmann E.C., Schepsmeier U., 2013. Modeling dependence with C- and D-vine copulas: The R package CDVine. Journal of Statistical Software, 52(3), 1-27. Doi: 10.18637/jss.v052.i03.

Charizanos G., Demirhan H., 2023. Bayesian prediction of wildfire event probability using normalized difference vegetation index data from an Australian forest. Ecological Informatics, 73. Doi: 10.1016/j.ecoinf.2022.101899.

Coutts A.M., Harris R.J., Phan T., Livesley S.J., Williams N.S.G., Tapper N.J., 2016. Thermal infrared remote sensing of urban heat: Hotspots, vegetation, and an assessment of techniques for use in urban planning. Remote Sensing of Environment, 186, 637-651. Doi: 10.1016/j.rse.2016.09.007.

Danaher P.J., Smith M.S., 2011. Modeling multivariate distributions using copulas: Applications in marketing. Marketing Science, 30(1), 4-21. Doi: 10.1287/mksc.1090.0491.

El Adlouni S., 2018. Quantile regression C-vine copula model for spatial extremes. Natural Hazards, 94(1), 299-317. Doi: 10.1007/s11069-018-3389-6.

Enríquez-de-Salamanca Á., 2020. Contribution to climate change of forest fires in Spain: Emissions and loss of sequestration. Journal of Sustainable Forestry, 39(4), 417-431. Doi: 10.1080/10549811.2019.1673779.

Fanin T., van der Werf G., 2017. Precipitation-fire linkages in Indonesia (1997-2015). Biogeosciences, 14(18), 3995-4008. Doi: 10.5194/bg-14-3995-2017.

Goldstein J.E., 2020. The Volumetric Political Forest: Territory, Satellite Fire Mapping, and Indonesia’s Burning Peatland. Antipode, 52(4), 1060-1082. Doi: 10.1111/anti.12576.

Grari M., Idrissi I., Boukabous M., Moussaoui O., Azizi M., Moussaoui M., 2022. Early wildfire detection using machine learning model deployed in the fog/edge layers of IoT. Indonesian Journal of Electrical Engineering and Computer Science, 27(2), 1062-1073. Doi: 10.11591/ijeecs.v27.i2.pp1062-1073.

Harrison M.E., Page S.E., Limin S.H., 2009. The global impact of Indonesian forest fires. Biologist, 56(3), 156-163.

Herawati N., 2020. The Effectiveness of Quantile Regression in Dealing with Potential Outliers. Barekeng: Jurnal Ilmu Matematika dan Terapan, 14(2), 301-308.

Hoang Q., 2018. Copula Regression and Robustness. Dissertation, Texas Tech University.

Hoeffding W., 1940. Massstabinvariante korrelationstheorie. Schriften des Mathematischen Seminars und des Instituts fu¨r Angewandte Mathematik der Universita¨t Berlin, 5, 179-233.

Horton A.J., Lehtinen J., Kummu M., 2022. Targeted land management strategies could halve peatland fire occurrences in Central Kalimantan, Indonesia. Communications Earth and Environment, 3(1). Doi: 10.1038/s43247-022-00534-2.

Huijnen V., et al., 2016. Fire carbon emissions over maritime southeast Asia in 2015 largest since 1997. Scientific Reports 6. Doi: 10.1038/srep26886.

Iskandar I., Lestrai D.O., Nur M., 2019. Impact of El Niño and El Niño Modoki Events on Indonesian Rainfall. Makara Journal of Science, 23(4), 217-222. Doi: 10.7454/mss.v23i4.11517.

Jim C.Y., 1999. The forest fires in Indonesia 1997-1998: Possible causes and pervasive consequences. Geography, 84(3), 251-260.

Joe H., 1997. Multivariate models and multivariate dependence concepts. London: CRC Press.

Joe H., 2005. Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis, 94(2), 401-419. Doi: 10.1016/j.jmva.2004.06.003.

Joe H., 2014. Dependence modeling with copulas. CRC Press. Doi: 10.1201/b17116.

Khan M.F., et al. 2020. El Niño driven haze over the Southern Malaysian Peninsula and Borneo. Science of the Total Environment, 730. Doi: 10.1016/j.scitotenv.2020.139091.

Koenker R., 2005. Quantile Regression. Cambridge: Cambridge University Press.

Koenker R., Hallock K.F., 2001. Quantile regression. Journal of Economic Perspectives, 15(4), 143-156. Doi: 10.1257/jep.15.4.143.

Koh J., Pimont F., Dupuy J.-L., Opitz T., 2023. Spatiotemporal wildfire modeling through point processes with moderate and extreme marks. The Annals of Applied Statistics, 17(1). Doi: 10.1214/22-aoas1642.

Kosmidis I., Karlis D., 2016. Model-based clustering using copulas with applications. Statistics and Computing, 26(5), 1079-1099. Doi: 10.1007/s11222-015-9590-5.

Lee N., Kim J.M., 2021. Dynamic functional connectivity analysis based on time-varying partial correlation with a copula-DCC-GARCH model. Neuroscience Research, 169, 27-39. Doi: 10.1016/j.neures.2020.06.006.

Li H., Huang G., Li Y., Sun J., Gao P., 2021. A c‐vine copula‐based quantile regression method for streamflow forecasting in xiangxi river basin, China. Sustainability (Switzerland), 13(9). Doi: 10.3390/su13094627.

Li Z., Beirlant J., Yang L., 2022. A new class of copula regression models for modelling multivariate heavy-tailed data. Insurance: Mathematics and Economics, 104, 243-261. Doi: 10.1016/j.insmatheco.2022.02.002.

Li Z., Shao Q., Tian Q., Zhang L., 2020. Copula-based drought severity-area-frequency curve and its uncertainty, a case study of Heihe River basin, China. Hydrology Research, 51(5), 867-881. Doi: 10.2166/nh.2020.173.

Liu J., Sirikanchanarak D., Sriboonchitta S., Xie J., 2018. Analysis of Household Consumption Behavior and Indebted Self-Selection Effects: Case Study of Thailand. Mathematical Problems in Engineering 2018. Doi: 10.1155/2018/5486185.

Liu S., Li S., 2022. Multi-model D-vine copula regression model with vine copula-based dependence description. Computers and Chemical Engineering, 161. Doi: 10.1016/j.compchemeng.2022.107788.

Lounela A.K., 2021. Shifting Valuations of Sociality and the Riverine Environment in Central Kalimantan, Indonesia. Anthropological Forum, 31(1), 34-48. Doi: 10.1080/00664677.2021.1875197.

lvadori G., De Michele C., Kottegoda N.T., Rosso R., 2005. Extremes in Nature: An approach using Copulas. Linz, Austria: Springer Science & Business Media.

Ly S., Pho K.H., Ly S., Wong W.K., 2019. Determining distribution for the product of random variables by using copulas. Risks, 7(1), 23. Doi: 10.3390/risks7010023.

Maposa D., Seimela A.M., Sigauke C., Cochran J.J., 2021. Modelling temperature extremes in the Limpopo province: bivariate time-varying threshold excess approach. Natural Hazards, 107(3), 2227-2246. Doi: 10.1007/s11069-021-04608-w.

Marlier M.E., et al., 2019. Fires, Smoke Exposure, and Public Health: An Integrative Framework to Maximize Health Benefits From Peatland Restoration. GeoHealth, 3(7), 178-189. Doi: 10.1029/2019GH000191.

Masseran N., Hussain S.I., 2020. Copula modelling on the dynamic dependence structure of multiple air pollutant variables. Mathematics, 8(11), 1-16. Doi: 10.3390/math8111910.

Medrilzam M., Dargusch P., Herbohn J., Smith C., 2014. The socio-ecological drivers of forest degradation in part of the tropical peatlands of Central Kalimantan, Indonesia. Forestry, 87(2), 335-345. Doi: 10.1093/forestry/cpt033.

Mezbahuddin S., Nikonovas T., Spessa A., Grant R.F., Imron M.A., Doerr S.H., Clay G.D., 2023. Accuracy of tropical peat and non-peat fire forecasts enhanced by simulating hydrology. Scientific Reports, 13(1). Doi: 10.1038/s41598-022-27075-0.

Mirabbasi R., Fakheri-Fard A., Dinpashoh Y., 2012. Bivariate drought frequency analysis using the copula method. Theoretical and Applied Climatology, 108(1-2), 191-206. Doi: 10.1007/s00704-011-0524-7.

Mukhopadhyay S., Parzen E., 2020. Nonparametric universal copula modeling. Applied Stochastic Models in Business and Industry, 36(1), 77-94. Doi: 10.1002/asmb.2503.

Nainggolan H.A., Veanti D.P.O., Akbar D., 2020. Utilisation of Nasa - Gfwed and firms satellite data in determining the probability of hotspots using the Fire Weather Index (Fwi) in Ogan Komering Ilir Regency, South Sumatra. International Journal of Remote Sensing and Earth Sciences (IJReSES), 17(1), 85. Doi: 10.30536/j.ijreses.2020.v17.a3202.

Najib M.K., Nurdiati S., Sopaheluwakan A., 2021. Quantifying the joint distribution of drought indicators in Borneo fire-prone area. IOP Conference Series: Earth and Environmental Science, 880(1). Doi: 10.1088/1755-1315/880/1/012002.

Najib M.K., Nurdiati S., Sopaheluwakan A., 2022a. Copula-based joint distribution analysis of the ENSO effect on the drought indicators over Borneo fire-prone areas. Modeling Earth Systems and Environment, 8(2), 2817-2826. Doi: 10.1007/s40808-021-01267-5.

Najib M.K., Nurdiati S., Sopaheluwakan A., 2022b. Multivariate fire risk models using copula regression in Kalimantan, Indonesia. Natural Hazards, 113(2), 1263-1283. Doi: 10.1007/s11069-022-05346-3.

Nelsen R.B., 2006. An Introduction to Copulas. 2nd ed. New York: Springer Science & Business Media.

Nicholls N., 1984. The Southern Oscillation and Indonesian sea surface temperature. Monthly Weather Review, 112(3), 424-432. Doi: 10.1175/1520-0493(1984)112<0424:TSOAIS>2.0.CO;2.

Nikonovas T., Spessa A., Doerr S.H., Clay G.D., Mezbahuddin S., 2022. ProbFire: A probabilistic fire early warning system for Indonesia. Natural Hazards and Earth System Sciences, 22(2), 303-322. Doi: 10.5194/nhess-22-303-2022.

Nurdiati S., et al., 2022a. The impact of El Niño southern oscillation and Indian Ocean Dipole on the burned area in Indonesia. Terrestrial, Atmospheric and Oceanic Sciences, 33(15). Doi: 10.1007/S44195-022-00016-0.

Nurdiati S., Najib M.K., Thalib A.S., 2022b. Joint distribution and coincidence probability of the number of dry days and the total amount of precipitation in southern sumatra fire-prone area. Geographia Technica, 17(2), 107-118. Doi: 10.21163/GT_2022.172.10.

Nurdiati S., Sopaheluwakan A., Septiawan P., 2021. Spatial and temporal analysis of El Niño impact on land and forest fire in Kalimantan and Sumatra. Agromet, 35(1), 1-10. Doi: 10.29244/j.agromet.35.1.1-10.

Nurdiati S., Sopaheluwakan A., Julianto M.T., Septiawan P., Rohimahastuti F., 2022c. Modelling and analysis impact of El Nino and IOD to land and forest fire using polynomial and generalized logistic function: cases study in South Sumatra and Kalimantan, Indonesia. Modeling Earth Systems and Environment, 8(3), 3341-3356. Doi: 10.1007/s40808-021-01303-4.

Page S.E., Hooijer A., 2016. In the line of fire: The peatlands of Southeast Asia. Philosophical Transactions of the Royal Society B: Biological Sciences, 371(1696). Doi: 10.1098/rstb.2015.0176.

Page S.E., Rieley J.O., Banks C.J., 2011. Global and regional importance of the tropical peatland carbon pool. Global Change Biology, 17(2), 798-818. Doi: 10.1111/j.1365-2486.2010.02279.x.

Pambabay-Calero J., Bauz-Olvera S., Nieto-Librero A., Sánchez-García A., Galindo-Villardón P., 2021. Hierarchical modeling for diagnostic test accuracy using multivariate probability distribution functions. Mathematics, 9(11). Doi: 10.3390/math9111310.

Pan S., Joe H., 2022. Predicting times to event based on vine copula models. Computational Statistics and Data Analysis, 175, 107546. Doi: 10.1016/j.csda.2022.107546.

Philander S.G.H., 1983. El Nino southern oscillation phenomena. Nature, 302(5906), 295-301.

Pleis J.R., 2018. Mixtures of discrete and continuous variables: Considerations for dimension reduction. Dissertation, University of Pittsburgh.

Salafsky N., 1994. Drought in the rain forest: Effects of the 1991 El Niño-Southern Oscillation event on a rural economy in West Kalimantan, Indonesia. Climatic Change, 27(4), 373-396. Doi: 10.1007/BF01096268.

Salvadori G., De Michele C., 2007. On the Use of Copulas in Hydrology: Theory and Practice. Journal of Hydrologic Engineering, 12(4), 369-380. Doi: 10.1061/(asce)1084-0699(2007)12:4(369).

Sartika Q.R., Widiharih T., Mukid M.A., 2019. Value at Risk in Stock Portfolio using t-Copula: Case study of PT. Indofood Sukses Makmur, Tbk. and Bank Mandiri (Persero), Tbk. Media Statistika, 12(2), 175. Doi: 10.14710/medstat.12.2.175-187.

Schölzel C., Friederichs P., 2008. Multivariate non-normally distributed random variables in climate research - Introduction to the copula approach. Nonlinear Processes in Geophysics, 15(5), 761-772. Doi: 10.5194/npg-15-761-2008.

Shao Y., Feng Z., Sun L., Yang X., Li Y., Xu B., Chen Y., 2022. Mapping China’s Forest Fire Risks with Machine Learning. Forests, 13(6). Doi: 10.3390/f13060856.

Sklar A., 1959. Fonctions de Répartition à n Dimensions et Leurs Marges. Publications de L’Institut de Statistique de L’Université de Paris, 8, 229-231.

Tacconi L., 2016. Preventing fires and haze in Southeast Asia. Nature Climate Change, 6(640-643). Doi: 10.1038/nclimate3008.

Tahroudi M.N., Ramezani Y., de Michele C., Mirabbasi R., 2022. Multivariate analysis of rainfall and its deficiency signatures using vine copulas. International Journal of Climatology, 42(4), 2005-2018. Doi: 10.1002/joc.7349.

Tahroudi M.N., Ramezani Y., De Michele C., Mirabbasi R., 2020. Analyzing the conditional behavior of rainfall deficiency and groundwater level deficiency signatures by using copula functions. Hydrology Research, 51(6), 1332-1348. Doi: 10.2166/nh.2020.036.

Tan S.R., Li C., Yeap X.W., 2022. A time-varying copula approach for constructing a daily financial systemic stress index. North American Journal of Economics and Finance, 63, 101821. Doi: 10.1016/j.najef.2022.101821.

Thevaraja M., Rahman M., 2019. Regression analysis based on Copula theory - by using Gaussian family Copula. International Journal of Statistics and Reliability Engineering, 6(1), 24-28.

Thoha A.S., Istima N., Daulay I.A., Hulu D.L.N., Budi S., Ulfa M., Mardiyadi Z., 2023. Spatial distribution of 2019 forest and land fires in Indonesia. Journal of Physics: Conference Series, 2421(1), 012035. Doi: 10.1088/1742-6596/2421/1/012035.

Tootoonchi F., Sadegh M., Haerter J.O., Räty O., Grabs T., Teutschbein C., 2022. Copulas for hydroclimatic analysis: A practice-oriented overview. Wiley Interdisciplinary Reviews: Water, 9(2). Doi: 10.1002/wat2.1579.

Treppiedi D., Cipolla G., Francipane A., Noto L.V., 2021. Detecting precipitation trend using a multiscale approach based on quantile regression over a Mediterranean area. International Journal of Climatology, 41(13), 5938-5955. Doi: 10.1002/joc.7161.

Vatresia A., Rais R.R., Utama F.P., Oktarianti W., 2022. Mining fire hotspots over Nusa Tenggara and Bali Islands. Indonesian Journal of Forestry Research, 9(1), 73-85. Doi: 10.20886/ijfr.2022.9.1.73-85.




How to Cite

Najib, M. K., Nurdiati, S., & Sopaheluwakan, A. (2023). Prediction of hotspots pattern in Kalimantan using copula-based quantile regression and probabilistic model: a study of precipitation and dry spells across varied ENSO conditions. Vietnam Journal of Earth Sciences.