RAINFALL MODELING USING THE GEOGRAPHICALLY WEIGHTED POISSON REGRESSION METHOD

• Atiek Iriany Department Statistics, Faculty of Mathematics and Science, Brawijaya University, Indonesia
• Wigbertus Ngabu Statistics Study Program, Faculty of Mathematics and Science, San Pedro University, Indonesia
• Danang Ariyanto Department Statistics, Faculty of Mathematics and Science, Brawijaya University, Indonesia
Keywords: GWR, GWPR, Rainfall

Abstract

Rainfall is an important parameter in understanding the climate and environment in the Malang Regency area. This research aims to model the distribution of rainfall in this region using the Geographically Weighted Poisson Regression (GWPR) method. GWPR is a spatial statistical approach that allows us to understand changes in inhomogeneous rainfall patterns throughout the Malang Regency area. Rainfall data collected from weather stations over several years was used in this study. We use GWR to study the relationship between various environmental factors, such as topography, vegetation, and land use, and rainfall distribution in Malang Regency. The results of the GWR analysis provide a deeper understanding of the spatial differences in the influence of these factors on rainfall. By applying GWR, we can find out how certain factors contribute to different rainfall patterns in certain regions. Rainfall modeling using the Geographically Weighted Poisson Regression (GWPR) method combines the power of Poisson regression in analyzing calculated data with the advantages of GWR in modeling spatial variability. GWPR allows us to identify and map rainfall distribution patterns that vary in geographic space. The main advantage of GWPR is its ability to provide local adjustments and capture the spatial variability associated with rainfall distribution. The results of the modeling analysis show that the GWPR is better, marked by the smallest AIC value, namely 336.84, compared to the generalized poisson regression model, namely 337.76.

References

S. Laimeheriwa, E. L. Madubun, and E. D. Rarsina, “Analisis Tren Perubahan Curah Hujan dan Pemetaan Klasifikasi Iklim Schmidt-Ferguson untuk Penentuan Kesesuaian Iklim Tanaman Pala (Myristica fragrans) di Pulau Seram,” Agrologia, vol. 8, no. 2, pp. 71–81, 2020.

E. Sofia and M. Amalia, “Analisis Karakteristik Curah Hujan di Kota Banjarbaru Berdasarkan Data Stasiun Klimatologi Banjarbaru,” J. Teknol. Berkelanjutan, vol. 10, no. 01, pp. 36–41, 2021.

F. Dwirani, “Menentukan stasiun hujan dan curah hujan dengan metode polygon thiessen daerah kabupaten lebak,” J. Lingkung. Dan Sumberd. Alam, vol. 2, no. 2, pp. 139–146, 2019.

C. Xu, Y. Wang, W. Ding, and P. Liu, “Modeling the spatial effects of land-use patterns on traffic safety using geographically weighted Poisson regression,” Networks Spat. Econ., vol. 20, pp. 1015–1028, 2020.

S. Ji, Y. Wang, and Y. Wang, “Geographically weighted poisson regression under linear model of coregionalization assistance: Application to a bicycle crash study,” Accid. Anal. Prev., vol. 159, p. 106230, 2021.

R. L. Wilby, R. J. Abrahart, and C. W. Dawson, “Detection of conceptual model rainfall—runoff processes inside an artificial neural network,” Hydrol. Sci. J., vol. 48, no. 2, pp. 163–181, 2003.

M. Kumari, C. K. Singh, O. Bakimchandra, and A. Basistha, “Geographically weighted regression based quantification of rainfall–topography relationship and rainfall gradient in Central Himalayas,” Int. J. Climatol., vol. 37, no. 3, pp. 1299–1309, 2017.

M. A. Gebremedhin, M. W. Lubczynski, B. H. P. Maathuis, and D. Teka, “Novel approach to integrate daily satellite rainfall with in-situ rainfall, Upper Tekeze Basin, Ethiopia,” Atmos. Res., vol. 248, p. 105135, 2021.

M. Sachdeva, A. S. Fotheringham, Z. Li, and H. Yu, “On the local modeling of count data: multiscale geographically weighted Poisson regression,” Int. J. Geogr. Inf. Sci., pp. 1–24, 2023.

N. Peleg, F. Marra, S. Fatichi, A. Paschalis, P. Molnar, and P. Burlando, “Spatial variability of extreme rainfall at radar subpixel scale,” J. Hydrol., vol. 556, pp. 922–933, 2018.

A. Mahama, J. A. Awuni, F. N. Mabe, and S. B. Azumah, “Modelling adoption intensity of improved soybean production technologies in Ghana-a Generalized Poisson approach,” Heliyon, vol. 6, no. 3, 2020.

G. Gao, H. Wang, and M. V Wüthrich, “Boosting Poisson regression models with telematics car driving data,” Mach. Learn., pp. 1–30, 2022.

Y. Asar and A. Genç, “A new two-parameter estimator for the Poisson regression model,” Iran. J. Sci. Technol. Trans. A Sci., vol. 42, pp. 793–803, 2018.

D. Murakami, N. Tsutsumida, T. Yoshida, T. Nakaya, B. Lu, and P. Harris, “Stable geographically weighted poisson regression for count data,” 2021.

D. N. Sari and Q. Aini, “Geographically weighted bivariate zero inflated generalized Poisson regression model and its application,” Heliyon, vol. 7, no. 7, 2021.

D. R. S. Saputro, A. Susanti, and N. B. I. Pratiwi, “The handling of overdispersion on Poisson regression model with the generalized Poisson regression model,” in AIP Conference Proceedings, 2021, vol. 2326, no. 1.

P. G. Hartono, G. M. Tinungki, J. Jakaria, A. B. Hartono, P. G. Hartono, and R. Wijaya, “Overcoming overdispersion on direct mathematics learning model using the quasi poisson regression,” in 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020), 2021, pp. 442–449.

E. H. Payne, M. Gebregziabher, J. W. Hardin, V. Ramakrishnan, and L. E. Egede, “An empirical approach to determine a threshold for assessing overdispersion in Poisson and negative binomial models for count data,” Commun. Stat. Comput., vol. 47, no. 6, pp. 1722–1738, 2018.

W. Ngabu, H. Pramoedyo, R. Fitriani, and A. B. Astuti, “Spatial Modeling of Fixed Effect and Random Effect with Fast Double Bootstrap Approach,” ComTech Comput. Math. Eng. Appl., vol. 14, no. 1, pp. 1–9, 2023.

W. Ngabu, R. Fitriani, H. Pramoedyo, and A. B. Astuti, “CLUSTER FAST DOUBLE BOOTSTRAP APPROACH WITH RANDOM EFFECT SPATIAL MODELING,” BAREKENG J. Ilmu Mat. dan Terap., vol. 17, no. 2, pp. 945–954, 2023.

D. R. S. Saputro, P. Widyaningsih, N. A. Kurdi, and A. Susanti, “Proporsionalitas Autokorelasi Spasial dengan Indeks Global (Indeks Moran) dan Indeks Lokal (Local Indicator of Spatial Association (LISA)),” 2018.

S. Chakraborty and X. Zhang, “A new framework for distance and kernel-based metrics in high dimensions,” Electron. J. Stat., vol. 15, no. 2, pp. 5455–5522, 2021.

M. Hoffmann and F. Noé, “Generating valid Euclidean distance matrices,” arXiv Prepr. arXiv1910.03131, 2019.

A. Iriany, W. Ngabu, D. Arianto, and A. Putra, “CLASSIFICATION OF STUNTING USING GEOGRAPHICALLY WEIGHTED REGRESSION-KRIGING CASE STUDY: STUNTING IN EAST JAVA,” BAREKENG J. Ilmu Mat. dan Terap., vol. 17, no. 1, pp. 495–504, 2023.

J. G. Liao, J. E. Cavanaugh, and T. L. McMurry, “Extending AIC to best subset regression,” Comput. Stat., vol. 33, pp. 787–806, 2018.

H. Pham, “A new criterion for model selection,” Mathematics, vol. 7, no. 12, p. 1215, 2019.

Published
2024-03-01
How to Cite
[1]
A. Iriany, W. Ngabu, and D. Ariyanto, “RAINFALL MODELING USING THE GEOGRAPHICALLY WEIGHTED POISSON REGRESSION METHOD”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0627-0636, Mar. 2024.
Section
Articles