Statistical Modeling of Daily Rainfall Using Zero-tweaked Data

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Aneeta Kalor
Rhysa McNeil
Nurin Dureh

Abstract

The significant amount of zero rainfall led to a highly skewed distribution of rainfall, creating challenges in rainfall modeling. This study aims to introduce a zero-tweaking method for handling a large proportion of zero rainfall data and apply it to daily rainfall data collected at four stations in southern Thailand from 2010 to 2022. The fourth root transformation was used to handle the right skew of rainfall. Zero-tweaking techniques were employed, with zeros substituted by normally distributed random numbers that permitted negative values. The patterns and trends in rainfall at each of the four stations were investigated using natural cubic splines. The trend projection analysis for four rainfall stations up to 2030 revealed an increase in rainfall at two stations in the Gulf of Thailand; however, this increase was not statistically significant. However, this study introduced the zero-tweaking method to handle the zero data, which enabled the use of conventional statistical methods and enhanced the model's validity.

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Research Articles

References

Shu, E.G.; Porter, J.R.; Hauer, M.E.; Olascoaga, S.S.; Gourevitch, J.; Wilson, B.; Pope, M.; Vazquez, D.M.; Kearns, E. Integrating climate change induced flood risk into future population projections. Nat. Commun. 2023, 14, 7870. https://doi.org/10.1038/s41467-023-43493-8

Tabari, H. Climate change impact on flood and extreme precipitation increases with water availability, Sci. Rep. 2020, 10(1), 13768. https://doi.org/10.1038/s41598-020-70816-2

Bevacqua, E.; Rakovec, O.; Schumacher, D.L.; Kumar, R.; Thober, S.; Samaniego, L.; Seneviratne, S.I.; Zscheischler, J. Direct and lagged climate change effects intensified the 2022 European drouth. Nat. Geosci. 2024, 17, 1100-1107. https://doi.org/10.1038/s41561-024-01559-2

Cook, B.I.; Mankin, J.S.; Williams, A.P.; Marvel, K.D.; Smerdon, J.E.; Liu, H. Uncertainties, limits, and benefits of climate change mitigation for soil moisture drought in southwestern North America. Earth's Future, 2021, 9(9), e2021EF002014. https://doi.org/10.1029/2021EF002014

Nielsen, M.; Cook, B.I.; Marvel, K.; Ting, M.; Smerdon, J.E. The changing influence of precipitation on soil moisture drought with warming in the Mediterranean and Western North America. Earth's Future, 2024, 12, e2023EF003987. https://doi.org/10.1029/2023EF003987

Ide, T.; Fröhlich, C.; Donges, J.F. The economic, political, and social implications of environmental crises. Bull. Am. Meteorol. Soc. 2020, 101, E364–E367. https://doi.org/10.1175/BAMS-D-19-0257.1

Madolli, M.J.; Gade, S.A.; Gupta, v.; Chakraborty, A.; Cha-um, S.; Datta, A.; Himashu, S.K. A systematic review on rainfall patterns of Thailand: Insights into variability and its relationship with ENSO and IOD. Earth-Sci. Rev. 2025, 264, 105102. https://doi.org/10.1016/j.earscirev.2025.105102

Limsakul, A.; Limjirakan, S.; Sriburi, T. Observed changes in daily rainfall extremes along Thailand’s coastal zone. J. Environ. Res. 2010, 32, 49-68.

Owusu, B.E.; McNeil, N. Statistical modelling of daily rainfall variability patterns in Australia. Pertanika J. Sci. Technol. 2018, 26(2), 691-706.

Vieira, F.M.C.; Machado, J.M.C.; Vismara, E.; Possenti, J.C. Probability distributions of frequency analysis of rainfall at the southwest region of Paraná State, Brazil. Rev. Cienc. Agroveterinarias 2018, 17, 260–266. https://doi.org/10.5965/223811711722018260

Hasan, M.M.; Croke, B.F.W.; Liu, S.; Shimizu, K.; Karim, F. Using mixed probability distribution functions for modelling non-zero sub-daily rainfall in Australia. Geosciences, 2020, 10(2), 43. https://doi.org/10.3390/geosciences10020043

Ximenes, P.; Silva, A.S.A.; Ashkar, F.; Stosic, T. Best-fit probability distribution models for monthly rainfall of Northeastern Brazil. Water Sci. Technol. 2021, 84(6), 1541-1556. https://doi.org/10.2166/wst.2021.304

Sake, R.; Akhtar, P.M. Fitting of modified exponential model between rainfall and ground water levels: A case study. Int. J. Stat. Appl. Math. 2019, 4(4), 1-6.

Afolabi, A.M.; Adesola, O.I. Exponential probability distribution of short-term rainfall intensity. Equity J. Sci. Technol. 2022, 9(2), 18-27.

Olivera, S.; Heard, C. Increases in the extreme rainfall events: using the Weibull distribution. Environmetrics 2018, 30. https://doi.org/10.1002/env.2532

Lambert, D. Zero-inflated Poisson regression, with an application to defects in manufacturing, Technometrics 1992, 3(1), 1-14. https://doi.org/10.2307/1269547

Feng, C.X. A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. Journal of Statistical Distributions and Applications, 2021, 8, https://doi.org/10.1186/s40488–021–00121–4

Dzupire, N.C.; Ngare, P.; Odongo, L.A. A Poisson-gamma model for zero inflated rainfall data. J. Probab. Stat. 2018, 1012647, https://doi.org/10.1155/2018/1012647

Wilks, D.S. Multisite generalization of a daily stochastic precipitation generation model. J. Hydrol. 1998, 210(4), 178-191. https://doi.org/10.1016/S0022-1694(98)00186-3

Kaewprasert, T.; Khamkong, M.; Bookkamana, P.A. A comparison of data transformation methods of generalized exponential distribution and estimation of summer rainfall in Chiang Dao, Chiang Mai. Burapha Sci. J. 2017, 22(3), 385-396.

Wahba, G. Spline models for observational data. CBMS-NSF Regional Conference Series in Applied Mathematics, 1990; pp 1-161. https://doi.org/doi:10.1137/1.9781611970128

Wold, S. Spline functions in data analysis, Technometrics 1974, 16(1), 1-11. http://www.jstor.org/wqazstable/1267485

Wongsai, N.; Wongsai, S.; Huete, A.R. Annual seasonality extraction using the cubic spline function and decadal trend in temporal daytime MODIS LST data. Remote Sens. 2017, 9(12), https://doi.org/10.3390/rs9121254

Lukas, M.A.; de Hoog, F.R.; Anderssen, R.S. Efficient algorithms for robust generalized cross-validation spline smoothing. J. Comput. Appl. Math. 2010, 235(1), 102–107. https://doi.org/10.1016/j.cam.2010.05.016

Venables, W.N.; Ripley, B.D. Modern Applied Statistics with S. Springer, Queensland, 2002. https://doi.org/10.1007/978-0-387-21706-2

Waqas, M.; Humphries, U.W.; Hlaing, P.T. Time series trend analysis and forecasting of climate variability using deep learning in Thailand. Results Eng. 2024, 24, 102997. https://doi.org/10.1016/j.rineng.2024.102997

Lee, T.; Shin, J.Y. Latent negative precipitation for the delineation of a zero‑precipitation area in spatial interpolations. Sci. Rep. 2021, 11(1), 20426. https://doi.org/10.1038/s41598-021-99888-4