Abstract
The probable rainfall is an excellent climatic parameter of information since it consists of the highest/lowest expected rainfall for a particular period of the year considering a certain level of probability. This study aims to evaluate traditional PDF performance using different goodness-of-fit tests to establish a criterion for choosing them on a monthly rainfall scale, in Mato Grosso do Sul, Brazil. The Cramer-von Misses (CVM) and Anderson–Darling (AD) tests were the most rigorous in rejecting the hypothesis of PFD suitable for monthly rainfall data, while the Kolmogorov–Smirnov (KS) was the least rigorous. The application of stricter goodness-of-fit tests as the CVM implies the use of up to 60% fewer series compared to the KS test. However, suitable series by the KS test presented erroneous estimates of probable monthly rainfall. The CVM and AD tests indicate the PDF with the best statistical performance (higher precision and accuracy between the observed and estimated frequency by the PDF) in more than 60% of situations. The most suitable PDFs for total monthly rainfall by the goodness-of-fit tests was gamma (12 months of the year). The exponential and Generalized Extreme Values (GEV) can be used for both the dry and rainy periods, respectively. The parameters of PDF are correlated with geographical variables, describing the total monthly rainfall distribution such as, for example, the influence of the South Atlantic Subtropical Anticyclone, the South Atlantic Convergence Zone in the rainy period, and the orographic effect in the dry period.
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Data availability
The datasets generated during and/or analyzed during the current study are available in the Hydroweb repository: www.snirh.gov.br/hidroweb/serieshistoricas. The R script used in the article will be fully available by request, in order to contribute to transparency.
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References
Abreu MC, Cecílio RA, Pruski FF, Rodrigues G, Almeida LT, Zanetti SS (2018) Critérios para escolha de distribuições de probabilidades em estudos de eventos extremos de precipitação. Rev Bras Meteorol 33(4):601–613. https://doi.org/10.1590/0102-7786334004
Abreu MC, Souza A, Lyra GB, Pobocikova I, Cecílio RA (2020a) Analysis of monthly and annual rainfall variability using linear models in the state of Mato Grosso do Sul, Midwest of Brazil. Int J Climatol 41(S1):E2445–E2461. https://doi.org/10.1002/joc.6857
Abreu MC, Souza A, Lins TMP, Oliveira-Júnior JF, Oliveira SS, Fernandes WA, Almeida LT, Torsen E (2020b) Comparison and validation of TRMM satellite precipitation estimates and data observed in Mato Grosso do Sul state, Brazil. Revista Brasileira De Climatologia 27:567–590. https://doi.org/10.5380/abclima.v27i0.68569
Alam MA, Emura K, Farnham C, Yuan J (2018) Best-fit probability distributions and return periods for maximum monthly rainfall in Bangladesh. Climate 6(9):1–16. https://doi.org/10.3390/cli6010009
Alvares CA, Stape JL, Sentelhas PC, Gonçalves JLM, Sparovek G (2013) Köppen’s climate classification map for Brazil. Meteorol Z 22(6):711–728. https://doi.org/10.1127/0941-2948/2013/0507
Armstrong MS, Kiem AS, Vence TR (2020) Comparing instrumental, palaeoclimate, and projected rainfall data: implications for water resources management and hydrological modelling. J Hydrol: Reg Stud 31:100728. https://doi.org/10.1016/j.ejrh.2020.100728
Ávila LF, Mello CR, Viola MR (2009) (2009) Mapeamento da precipitação mínima provável para o sul de Minas Gerais. Rev Bras Eng Agr Amb 13:906–915. https://doi.org/10.1590/S1415-43662009000700013
Bagirov AM, Mahmood A, Barton A (2017) Prediction of monthly rainfall in Victoria, Australia: clusterwise linear regression approach. Atmos Res 188:20–29. https://doi.org/10.1016/j.atmosres.2017.01.003
Beskow S, Caldeira TL, de Mello CR, Faria LC, Guedes HAS (2015) Multiparameter probability distributions for heavy rainfall modeling in extreme southern Brazil. J Hydrol: Reg Stud 4:123–133. https://doi.org/10.1016/j.ejrh.2015.06.007
Blain GC, Meschiatti MC (2015) Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index. Rev Bras Eng Agríc Ambient 19(12). https://doi.org/10.1590/1807-1929/agriambi.v19n12p1129-1135
Boretti A, Rosa L (2019) Reassessing the projections of the World Water Development Report. Clean Water 2:15. https://doi.org/10.1038/s41545-019-0039-9
Caldeira TL, Beskow S, Mello CR, Faria LC, Souza MR, Guedes HAS (2015) Modelagem probabilística de eventos de precipitação extrema no estado do Rio Grande do Sul. Rev Bras Eng Agr Amb 19(3):197–203. https://doi.org/10.1590/1807-1929/agriambi.v19n3p197-203
Catalunha MJ, Sediyama GC, Leal BG, Soares CPB, Ribeiro A (2002) Aplicação de cinco funções densidade de probabilidade a séries de precipitação pluvial no Estado de Minas Gerais. Rev Bras Agrometeorol 10(1):153–162
Cavanaugh NR, Gershunov A, Panorska AK, Kozubowski TJ (2015) The probability distribution of intense daily precipitation. Geophys Res Lett 42:1560–1567. https://doi.org/10.1002/2015GL063238
Cesar K, Lima CD, Alves F, De Tocantins UF, Viola MR, Mello CR, Giongo M, Tocantins UF (2016) Distribuição da precipitação mensal, anual e máxima diária anual na bacia hidrográfica do rio Formoso. Tocantins Ambiência 12(1):49–70. https://doi.org/10.5935/ambiencia.2016.01.03
Coelho CAS, Cardoso DHF, Firpo MF (2016) Precipitation diagnostics of an exceptionally dry event in São Paulo, Brazil. Theor Appl Climatol, Theor Appl Climatol 125:769–784. https://doi.org/10.1007/s00704-015-1540-9
Danfa S, Silva AM, Mello CR, Coelho G, Viola MR, Ávila LF (2011) Distribuição espacial de valores prováveis de precipitação pluvial para períodos quinzenais, em Guiné-Bissau. Rev Bras Eng Agr Amb 15(1):67–74. https://doi.org/10.1590/S1415-43662011000100010
Duan J, Sikka AK, Grant GE (1995) A comparison of stochastic models for generating daily precipitation at the H.J. Andrews Experimental Forest. Northwest Sci 69(4):318–329
Elsebaie IH (2012) Developing rainfall intensity–duration–frequency relationship for two regions in Saudi Arabia. J King Saud Univ - Eng Sci 24(2):131–140. https://doi.org/10.1016/j.jksues.2011.06.001
Franco CS, Marques RFPV, Oliveira AS, Oliveira LFC (2014) Distribuição de probabilidades para precipitação máxima diária na Bacia Hidrográfica do Rio Verde, Minas Gerais. Rev Bras Eng Agr Amb 18(7):735–741. https://doi.org/10.1590/S1415-43662014000700010
Ghosh S, Roy MK, Biswas SC (2016a) Determination of the best fit probability distribution for monthly rainfall data in Bangladesh. Am J Math Stat 6(4):170–174. https://doi.org/10.5923/j.ajms.20160604.05
Ghosh S, Vittal H, Sharma T, Karmakar S, Kasiviswanathan KS, Dhanesh Y, Sudheer KP, Gunthe SS (2016b) Indian summer monsoon rainfall: implications of contrasting trends in the spatial variability of means and extremes. PLoS One 27, 11(7):e0158670. https://doi.org/10.1371/journal.pone.0158670
Gois G, Oliveira-Júnior JF, Silva Junior CA, Sobral BS, Terassi PMB, Leonel Junior AHS (2020) Statistical normality and homogeneity of a 71-year rainfall dataset for the state of Rio de Janeiro—Brazil. Theor Appl Climatol 141:1573–1591. https://doi.org/10.1007/s00704-020-03270-9
Junqueira Junior JA, Gomes NM, Mello CR, Silva AM (2007) Precipitação provável para a região de Madre de Deus, Alto Rio Grande: modelos de probabilidades e valores característicos. Ciênc Agrotec 31:842–850. https://doi.org/10.1590/S1413-70542007000300034
Laio F (2004) Cramer–von Mises and Anderson-Darling goodness-of-fit tests for extreme value distributions with unknown parameters. Water Resour Res 40(9):1–10. https://doi.org/10.1029/2004WR003204
Langat PK, Kumar L, Koech R (2019) Identification of the most suitable probability distribution models for maximum, minimum, and mean streamflow. Water 11(4):1–24. https://doi.org/10.3390/w11040734
Lima AO, Lyra GB, Abreu MC, Oliveira-Júnior JF, Zeri M, Cunha-Zeri G (2021) Extreme rainfall events over Rio de Janeiro State, Brazil: characterization using probability distribution functions and clustering analysis. Atmos Res 247:105221. https://doi.org/10.1016/j.atmosres.2020.105221
Lyra GB, Lozada Garcia BI, De Stefano Piedade SM, Sediyama GC, Sentelhas PC (2006) Regiões homogêneas e funções de distribuição de probabilidade da precipitação pluvial no Estado de Táchira, Venezuela. Pesq Agropec Bras 41(2):205–215. https://doi.org/10.1590/S0100-204X2006000200004
Marques RFPV, Mello CR, Silva AM, Franco CS, Oliveira AS (2014) Performance of the probability distribution models applied to heavy rainfall daily events. Ciênc Agrotec 38(4):335–342. https://doi.org/10.1590/S1413-70542014000400003
Masingi VN, Maposa D (2021) Modelling long-term monthly rainfall variability in selected provinces of South Africa: trend and extreme value analysis approaches. Hydrol 8(70):1–27. https://doi.org/10.3390/hydrology8020070
Mello CR, Viola MR, Curi N, Silva AM (2012) Distribuição espacial da precipitação e da erosividade da chuva mensal e anual no estado do espírito santo. Rev Bras Ciênc Solo 36(6):1878–1891. https://doi.org/10.1590/S0100-06832012000600022
Naranjo-Fernández N, Guardiola-Albert C, Aguilera H, Serrano-Hidalgo C, Rodríguez-Rodriguez M, Fernandez-Ayuso A, Ruiz-Bermudo F, Montero-Gonzales E (2020) Relevance of spatio-temporal rainfall variability regarding groundwater management challenges under global change: case study in Doñana (SW Spain). Stoch Environ Res Risk Assess 34:1289–1311. https://doi.org/10.1007/s00477-020-01771-7
Oliveira PTS, Rodrigues DBB, Sobrinho TA, Carvalho DF, Panachuki E (2012) Spatial variability of the rainfall erosive potential in the state of Mato Grosso do Sul, Brazil. Eng Agríc 32(1):69–79. https://doi.org/10.1590/S0100-69162012000100008
Oliveira- Júnior JF, Teodoro PE, Silva Junior CA, Baio FHR, Gava R, Capristo-Silva GF, Gois G, Correia Filho WLF, Lima MG, Santiago DB, Freitas WK, Santos PJ, Costa M (2020) Fire foci related to rainfall and biomes of the state of Mato Grosso do Sul, Brazil. Agric for Meteorol 282:1–13. https://doi.org/10.1016/j.agrformet.2019.107861
Oliveira-Júnior JF, Silva Junior CA, Teodoro PE, Rossi FS, Blanco CJC, Lima M, Gois G, Correia Filho WLF, Barros SD, Santos MHGV (2021) Confronting CHIRPS dataset and in situ stations in the detection of wet and drought conditions in the Brazilian Midwest. Int J Climatol 41:4478–4493. https://doi.org/10.1002/joc.7080
Ozonur D, Pobocikova I, Souza A (2020) Statistical analysis of monthly rainfall in Central West Brazil using probability distributions. Model Earth Syst Environ. https://doi.org/10.1007/s40808-020-00954-z
Passos MLV, Mendes TJ (2018) Precipitação pluviométrica mensal e anual provável para o município de Turiaçu-MA. Rev Bras Agric Irrigada 12(1):2283–2292. https://doi.org/10.7127/rbai.v12n100672
Sabino M, Souza AP, Uliana EM, Lisboa L, Almeida FT, Zolin CA (2020) Intensity-duration-frequency of maximum rainfall in Mato Grosso State. Rev Ambiente Água 15(1):1–12. https://doi.org/10.4136/ambi-agua.2373
Sampaio SC, Longo AJ, Queiroz MMF, Gomes BM, Vilas Boas MA, Suszek M (2006) Estimativa e distribuição da precipitação mensal provável no Estado do Pará. Acta Sci Hum Soc Sci 28(2):267–272. https://doi.org/10.4025/actascihumansoc.v28i2.169
Santos V, Blanco CJC, Oliveira-Júnior JF (2019) Distribution of rainfall probability in the Tapajos River Basin, Amazonia, Brazil. Re Ambiente Água 14:1–21. https://doi.org/10.4136/ambi-agua.2284
Sen Z, Eljadid AG (1999) Rainfall distribution functions for Libya and Rainfall Prediction. Hydrol Sci J 44:665–680. https://doi.org/10.1080/02626669909492266
Sharma MA, Singh JB (2010) Use of probability distribution in rainfall analysis. New Yourk Sci J 3(9):40–49
Silva DD, Pereira SB, Pruski FF, Filho RRG, Lana ÂMQ, Baena LGN (2003) Equações de intensidade-duração-frequência da precipitação pluvial para o estado de Tocantins. Eng Agric 11(1–4):7–14
Sobral BS, Oliveira-Júnior JF, Alecrim FB, Gois G, Muniz Junior JGR, Terassi PMB, Pereira Junior ER, Lyra GB, Zeri M (2020) PERSIANN-CDR based characterization and trend analysis of annual rainfall in Rio De Janeiro State, Brazil. Atmos Res 238:1–104873. https://doi.org/10.1016/j.atmosres.2020.104873
Soccol OJ, Cardoso CO, Miquelluti DJ (2010) Análise da precipitação mensal provável para o município de Lages, SC. Rev Bras Eng Agr Amb 14(6):569–574. https://doi.org/10.1590/S1415-43662010000600001
Sukrutha A, Dyuthi SR, Desai S (2018) Multimodel response assessment for monthly rainfall distribution in some selected Indian cities using best fit probability as a tool. Appl Water Sci 8:145. https://doi.org/10.1007/s13201-018-0789-4
Svensson C, Hannaford J, Prosdocimi I (2017) Statistical distributions for monthly aggregations of precipitation and streamflow in drought indicator applications. Water Resour Assoc 53:999–1018. https://doi.org/10.1002/2016WR019276
Szyniszewska AM, Waylen PR (2012) Determining the daily rainfall characteristics from the monthly rainfall totals in central and northeastern Thailand. Appl Geogr 35(1–2):377–393. https://doi.org/10.1016/j.apgeog.2012.09.001
Telesca, V., Caniani, D., Calace, S., Marotta, L., and Mancini, I. M. (2017) Daily temperature and precipitation prediction using neuro-fuzzy networks and weather generators. Computational Science and Its Applications – ICCSA 2017, 10409, 441–455. http://doi-org-443.webvpn.fjmu.edu.cn/https://doi.org/10.1007/978-3-319-62407-5_31
Teodoro PE, Oliveira-Júnior JF, Cunha ER, Correa CCG, Torres FE, Bacani VM, Gois G, Ribeiro LP (2015) Cluster analysis applied to the spatial and temporal variability of monthly rainfall in Mato Grosso do Sul State, Brazil. Meteorol Atmos Phys 128:197–209. https://doi.org/10.1007/s00703-015-0408-y
Teodoro PE, Cargnelutti Filho A, Torres FE, Ribeiro LP, Carpisto DP, Guedes CCC, da Cunha ER, Bacani VM (2016) Functions of probability for fitting monthly rainfall in sites of Mato Grosso do Sul state. Biosci J 32(2):319–327. https://doi.org/10.14393/BJ-v32n2a2016-29394
Teodoro PE, Silva Junior CA, Oliveira-Junior JF, Delgado RC, Gois G, Correa CCG, Torres FE (2017) Probable monthly rainfall associated with distinct biomes of Mato Grosso do Sul state. Biosci J 33:747–753. https://doi.org/10.14393/BJ-v33n3-34944
Torres FE, Cargnelutti Filho A, Teodoro PE, Corrêa CCG, Ribeiro LP, Cunha ER (2016) Dimensionamento amostral para a estimação da média de precipitação pluvial mensal em locais do Estado do Mato Grosso do Sul. Ciênc Rural 46(1):60–69. https://doi.org/10.1590/0103-8478cr20150348
Vaheddoost B, Aksoy H (2017) Structural characteristics of annual precipitation in Lake Urmia basin. Theoret Appl Climatol 128(3–4):919–932. https://doi.org/10.1007/s00704-016-1748-3
Vieira FMC, Machado JMC, Vismara ES, Possenti JC (2018) Probability distributions of frequency analysis of rainfall at the southwest region of Paraná State, Brazil. Rev Ciênc Agrovet 17(2):260–266. https://doi.org/10.5965/223811711722018260
Vieira FR, Thebaldi MS, Silveira BG, Barros Nogueira VH (2020) Probable rainfall of Divinópolis City, Minas Gerais State, Brazil. Rev Engenharia na Agricultura 28:89–99. https://doi.org/10.13083/reveng.v28i.6385
Ximenes PSMP, Silva ASA, Ashkar F, Stosic T (2021) Best-fit probability distribution models for monthly rainfall of Northeastern Brazil. Water Sci Technol 84(6):1541–1556. https://doi.org/10.2166/wst.2021.304
Ye L, Hanson LS, Ding P, Wang D, Vogel RM (2018) The probability distribution of daily precipitation at the point and catchment scales in the United States. Hydrol Earth Syst Sci 22(12):6519–6531. https://doi.org/10.5194/hess-22-6519-2018
Yue S, Hashino M (2007) Probability distribution of annual, seasonal and monthly precipitation in Japan. Hydrol Sci J 52(5):863–877. https://doi.org/10.1623/hysj.52.5.863
Zhang Y, Li Z (2020) Uncertainty analysis of standardized precipitation index due to the effects of probability distributions and parameter errors. Front Earth Sci 8:1–15. https://doi.org/10.3389/feart.2020.00076
Acknowledgements
The authors would like to thank the National Water and Sanitation Agency (ANA), the Federal Rural University of Rio de Janeiro, Federal University of Mato Grosso do Sul, Federal University of Alagoas, Federal University of Viçosa, Federal University of Espirito Santo, University of Žilina, and Water Management Institute of Minas Gerais (IGAM).
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Abreu, M. C.: conceptualization, design of methodology, data acquisition, data analysis, writing and editing, data curation, software. Souza A.: conceptualization, design of methodology, data acquisition, data analysis, writing, review and editing, data curation. Lyra, G. B.: conceptualization, design of methodology, data acquisition, data analysis, writing, review and editing, data curation, software. Oliveira-Junior, J. F.: conceptualization, design of methodology, data acquisition, data analysis, writing, review and editing. Pobocikova, I.: data analysis, writing, review and editing. Almeida, L.T.: data analysis, writing, review and editing and software. Fraga, M. S.: data analysis, writing, review and editing and software. Aristone, F.: data acquisition, data curation, writing, review and editing. Cecílio, R. A.: conceptualization, methodology design, writing, review and editing.
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Abreu, M.C., de Souza, A., Lyra, G.B. et al. Assessment and characterization of the monthly probabilities of rainfall in Midwest Brazil using different goodness-of-fit tests as probability density functions selection criteria. Theor Appl Climatol 151, 491–513 (2023). https://doi.org/10.1007/s00704-022-04286-z
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DOI: https://doi.org/10.1007/s00704-022-04286-z