Abstract
The Standardized Precipitation Index (SPI) is a worldwide used probability-based drought index. Considering that the two-parameter gamma distribution (gam) is often used to calculate this index, the quality of the fit of this distribution to rainfall series is a key-factor for its performance. Based on the concept of homogeneous regions, the regional frequency analysis (RFA) improves the probabilistic assessment of a variable because it increases the amount of data available for the fitting process. Despite its potential to improve the probabilistic assessment of rainfall data, there is no study verifying if the RFA improves the performance of SPI estimates for describing drought events. Therefore, the goal of this study was to verify whether the RFA can be applied to gam-distributed series, and how this regionalization technique affects the ability of the SPI algorithm to produce normally distributed estimates. This study was based on Monte Carlo experiments, which simulated homogeneous and heterogeneous groups of rainfall series. A normally test specifically designed to assess the normality of SPI frequency distributions was also used. A case study in which the RFA were used to calculate the SPI in the State of São Paulo—Brazil was also carried out. The results indicated that the RFA can be applied to groups of series formed by gam-distributed series. Both Kappa and Wakeby distribution may be used in the RFA calculation algorithm, with the Kappa distribution leading to slightly better results. The RFA improved the ability of the SPI algorithm to produce normally distributed estimates in regional terms.
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Data availability
The free-license software R was used in this study. The rainfall data belongs to the Agronomic Institute (a public research institute) and they are available at http://clima.iac.sp.gov.br.
Code availability
The fundamental steps of the new method proposed in this study are described in the R-code presented in Table S1.
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Acknowledgements
To CNPq for Fellowship for the first author (Process 307616/2019-3).
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CNPq (fellowship for the fourth author—Process 307616/2019–3) and CAPES (scholarship for the first and third authors).
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Conceptualization: Blain G.C. and Sobierajski G.R.; methodology: Blain G.C. and Sobierajski G.R.; investigation: Blain G.C., Sobierajski G.R., Xavier, A.C.F., Martins L.L., Santos Júnior E. P.; writing—original draft: Blain G.C. and Sobierajski G.R.; writing—review and editing: Blain G.C., Sobierajski G.R., Xavier, A.C.F., Martins L.L., Santos Júnior E. P.; supervision: Blain G.C.
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dos Santos Junior, E.P., Xavier, A.C.F., Martins, L.L. et al. Using a regional frequency analysis approach for calculating the Standardized Precipitation Index: an operational approach based on the two-parameter gamma distribution. Theor Appl Climatol 148, 1199–1216 (2022). https://doi.org/10.1007/s00704-022-03989-7
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DOI: https://doi.org/10.1007/s00704-022-03989-7