Ajuste de distribuições de probabilidade à precipitação mensal no estado de Pernambuco – Brasil

Autores

DOI:

https://doi.org/10.33448/rsd-v9i11.9894

Palavras-chave:

Precipitação mensal; Pernambuco; Distribuições de probabilidade.

Resumo

Este estudo teve como objetivo identificar modelos de distribuição de probabilidade que melhor se ajustam a dados de precipitação mensal para o estado de Pernambuco – Brasil. Foram analisados os ajustes de seis distribuições de probabilidade de 2 parâmetros: gama (GAM), log normal (LNORM), Weibull (WEI), Pareto Generalizado (PG), Gumbel (GUM) e normal (NORM) para dados de precipitação mensal de 40 estações pluviométricas distribuídas no estado de Pernambuco, no período de 1988 a 2017 (30 anos). O método de Máxima Verossimilhança (ML) foi utilizado para estimar os parâmetros dos modelos e a seleção do modelo baseou-se em uma modificação da estatística de Shapiro-Wilk. Os resultados mostraram que as distribuições de 2 parâmetros são flexíveis o suficiente para descrever dados de precipitação mensal para o estado de Pernambuco e que os modelos log normal, gama, Weibull e PG se ajustaram melhor aos dados. Os modelos Gumbel e normal raramente se ajustaram aos dados independente do mês analisado.

Referências

Aksoy, H. (2000). Use of gamma distribution in hydrological analysis. Turkish Journal of Engineering and Environmental Sciences, 24(6), 419-428.

Ashkar, F., & Aucoin, F. (2012). Choice between competitive pairs of frequency models for use in hydrology: a review and some new results. Hydrological sciences journal, 57(6), 1092-106. https://doi.org/10.1080/02626667.2012.701746

Ashkar, F., & Ba, I. (2017). Selection between the generalized Pareto and kappa distributions in peaks-over-threshold hydrological frequency modelling. Hydrological Sciences Journal, 62(7), 1167-1180. https://doi.org/10.1080/02626667.2017.1302089

Ashkar, F., & Tatsambon, C. N. (2007). Revisiting some estimation methods for the generalized Pareto distribution. Journal of Hydrology, 346(3-4), 136-143.

https://doi.org/10.1016/j.jhydrol.2007.09.007

Ashkar, F., Arsenault, M., & Zoglat, A. (1997). On the discrimination between statistical distributions for hydrological frequency analysis. In The 1997 Annual Conference of the Canadian Society for Civil Engineering. Part 3(of 7), Sherbrooke, Can, 05/27-30/97 (pp. 169-178).

Ashkar, F., Ba, I., & Dieng, B. B. (2019, May). Hydrological Frequency Analysis: Some Results on Discriminating between the Gumbel or Weibull Probability Distributions and Other Competing Models. In World Environmental and Water Resources Congress 2019: Watershed Management, Irrigation and Drainage, and Water Resources Planning and Management (pp. 374-387). Reston, VA: American Society of Civil Engineers.

Bermudez, V.A.B.; Abilgos, A.B.B.; Cuaresma, D.C.N. & Rabajante, J.F (2017). Probability Distribution of Philippine Daily Rainfall Data. Preprints, 2017120150. https://doi.org/10.20944/preprints201712.0150.v1

Bjureland, W., Johansson, F., Sjölander, A., Spross, J., & Larsson, S. (2019). Probability distributions of shotcrete parameters for reliability-based analyses of rock tunnel support. Tunnelling and Underground Space Technology, 87, 15-26.

https://doi.org/10.1016/j.tust.2019.02.002

Bolfarine, H., & Sandoval, M. C. (2001). Introdução à inferência estatística (Vol. 2). São Paulo: SBM.

Brito, S., Marengo, J., & Coutinho, M. (2017). Reduction of vulnerability to disasters: from knowledge to action. Climate change and drought in Brazil (pp. 361-376).São Paulo: Editora RIMA.

Chang, T. P. (2011). Performance comparison of six numerical methods in estimating Weibull parameters for wind energy application. Applied Energy, 88(1), 272-282. https://doi.org/10.1016/j.apenergy.2010.06.018

Cheng, K. S., Chiang, J. L., & Hsu, C. W. (2007). Simulation of probability distributions commonly used in hydrological frequency analysis. Hydrological Processes: An International Journal, 21(1), 51-60. https://doi.org/10.1002/hyp.6176

Elsherpieny, E. A., Muhammed, H. Z., & Radwan, N. U. M. M. (2017). On discriminating between gamma and log-logistic distributions in case of progressive type II censoring. Pakistan Journal of Statistics and Operation Research, 157-183. https://doi.org/10.18187/pjsor.v13i1.1524

Haberlandt, U., & Radtke, I. (2014). Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows. Hydrology and Earth System Sciences 18 (2014), Nr. 1, 18(1), 353-365. http://dx.doi.org/10.5194/hess-18-353-2014

Hussain, Z., Mahmood, Z., & Hayat, Y. (2010). Modeling the daily rainfall amounts of north-west Pakistan for agricultural planning. Sarhad J. Agric, 27(2), 313-321.

IBGE (2020). Instituto Brasileiro de Geografia e Estatística. Recuperado de https://www.ibge.gov.br/

Li, Z., Brissette, F., & Chen, J. (2013). Finding the most appropriate precipitation probability distribution for stochastic weather generation and hydrological modelling in Nordic watersheds. Hydrological Processes, 27(25), 3718-3729. https://doi.org/10.1002/hyp.9499

Lundgren, W. J. C., SOUzA, I. D., & NETTO, A. (2015). Uso de distribuições de probabilidades para ajuste aos dados de precipitação mensal do estado de Sergipe. Revista Brasileira de Geografia Física, 8(01), 071-080.

Mazucheli, J., & Emanuelli, I. P. (2019). The Nakagami Distribution Applied in Precipitation Data Analysis. Revista Brasileira de Meteorologia, 34(1), 1-7. https://doi.org/10.1590/0102-77863340011

McKee, T. B., Doesken, N. J., & Kleist, J. (1993, January). The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology (Vol. 17, No. 22, pp. 179-183).

Netto, A. D. O. A., Souza, I. F. D., & Lundgren, W. J. C. (2010). Comparação entre distribuições de probabilidades da precipitação mensal no estado de Pernambuco. Scientia Plena, 6(6).

Papalexiou, S. M., & Koutsoyiannis, D. (2012). Entropy based derivation of probability distributions: A case study to daily rainfall. Advances in Water Resources, 45, 51-57. https://doi.org/10.1016/j.advwatres.2011.11.007

Pearson, K. (1896). VII. Mathematical contributions to the theory of evolution.—III. Regression, heredity, and panmixia. Philosophical Transactions of the Royal Society of London. Series A, containing papers of a mathematical or physical character, (187), 253-318. https://doi.org/10.1098/rsta.1896.0007

Pereira, A. S., Shitsuka, D. M., Parreira, F. J., & Shitsuka, R. (2018). Metodologia da pesquisa científica.[e-book]. Santa Maria. Ed. UAB/NTE/UFSM. Recuperado de https://repositorio.ufsm.br/bitstream/handle/1/15824/Lic_Computacao_Metodologia-pesquisa-Cientifica. pdf.

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Recuperado de https://www.R-project.org/.

Royston, J. P. (1982). Algorithm AS 181: the W test for normality. Journal of the Royal Statistical Society. Series C (Applied Statistics), 31(2), 176-180. https://doi.org/10.2307/2347986

Royston, J. P. (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Journal of the Royal Statistical Society: Series C (Applied Statistics), 31(2), 115-124. https://doi.org/10.2307/2347973

Royston, P. (1995). Remark AS R94: A remark on algorithm AS 181: The W-test for normality. Journal of the Royal Statistical Society. Series C (Applied Statistics), 44(4), 547-551. https://doi.org/10.2307/2986146

Santana, L. I. T., Silva, A. S. A., Menezes, R. S. C., & Stosic, T. (2020). Recurrence quantification analysis of monthly rainfall time series in Pernambuco, Brazil. Research, Society and Development, 9(9). e637997737. https://doi.org/10.33448/rsd-v9i9.7737

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3/4), 591-611. https://doi.org/10.2307/2333709

Sharma, M. A., & Singh, J. B. (2010). Use of probability distribution in rainfall analysis. New York Science Journal, 3(9), 40-49.

Sijbers, J., den Dekker, A. J., Scheunders, P., & Van Dyck, D. (1998). Maximum-likelihood estimation of Rician distribution parameters. IEEE Transactions on Medical Imaging, 17(3), 357-361. https://doi.org/10.1109/42.712125

Silva, A. S. A. da, Menezes, R. S. C., Telesca, L., Stosic, B., & Stosic, T (2020). Fisher Shannon analysis of drought/wetness episodes along a rainfall gradient in Northeast Brazil. International Journal of Climatology, 1-14. https://doi.org/10.1002/joc.6834

Singh, V. P. (1987). On application of the Weibull distribution in hydrology. Water Resources Management, 1(1), 33-43. https://doi.org/10.1007/BF00421796

Stern, R. D., & Coe, R. (1982). The use of rainfall models in agricultural planning. Agricultural Meteorology, 26(1), 35-50. https://doi.org/10.1016/0002-1571(82)90056-5

Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index. Journal of climate, 23(7), 1696-1718. https://doi.org/10.1175/2009JCLI2909.1

Zhu, B., Chen, J., & Chen, H. (2019). Performance of multiple probability distributions in generating daily precipitation for the simulation of hydrological extremes. Stochastic Environmental Research and Risk Assessment, 33(8-9), 1581-1592. https://doi.org/10.1007/s00477-019-01720-z

Downloads

Publicado

22/11/2020

Como Citar

XIMENES, P. de S. M. P. .; SILVA, A. S. A. da; ASHKAR, F.; STOSIC, T. Ajuste de distribuições de probabilidade à precipitação mensal no estado de Pernambuco – Brasil. Research, Society and Development, [S. l.], v. 9, n. 11, p. e4869119894, 2020. DOI: 10.33448/rsd-v9i11.9894. Disponível em: https://rsdjournal.org/index.php/rsd/article/view/9894. Acesso em: 17 jul. 2024.

Edição

Seção

Ciências Exatas e da Terra