Standardized precipitation index based on pearson type III distribution

Abstract

The initial step in calculating the Standardized Precipitation Index (SPI) is to determine a probability density function (pdf) that describes the precipitation series under analysis. Once this pdf is determined, the cumulative probability of an observed precipitation amount is computed. The inverse normal function is then applied to the cumulative probability. The result is the SPI. This article assessed the changes in SPI final values, when computed based on Gamma 2-parameters (Gam) and Pearson Type III (PE3) distributions (SPIGam and SPIPE3, respectively). Monthly rainfall series, available from five weather stations of the State of São Paulo, were chosen for this study. Considering quantitative and qualitative assessments of goodness-of-fit (evaluated at 1-, 3-, and 6-months precipitation totals), the PE3 distribution seems to be a better choice than the Gam distribution, in describing the longterm rainfall series of the State of São Paulo. In addition, it was observed that the number of SPI time series that could be seen as normally distributed was higher when this drought index was computed from the PE3 distribution. Thus, the use of the Pearson type III distribution within the calculation algorithm of the SPI is recommended in the State of São Paulo. Keywords: drought, Gamma distribution, SPI RESUMO: ÍNDICE PADRONIZADO DE PRECIPITAÇÃO BASEADO NA DISTRIBUIÇÃO PEARSON TIPO III O cálculo do Índice Padronizado de Precipitação (IPP) inicia-se com a adoção de uma distribuição paramétrica (dp) utilizada para a estimativa das probabilidades de ocorrência associadas a uma série de precipitação pluvial. Após essa escolha, a probabilidade acumulada de ocorrência de um determinado valor de precipitação é calculada. O IPP é obtido após a aplicação da função normal inversa a essa probabilidade acumulada. O artigo avaliou as alterações nos valores finais do IPP, quando calculado com base nas distribuições Gama com dois parâmetros (Gam) e Pearson tipo III (PE3; IPPGam e IPPPE3, respectivamente). Utilizaram-se dados de precipitação pluvial de cinco localidades do Estado de São Paulo, nas escalas de 1, 3 e 6 meses. Aplicando testes de aderência, tanto qualitativos, quanto quantitativos, verificou-se que as probabilidades associadas às séries utilizadas foram melhores estimadas por meio da PE3. Foi também observado, que o número de séries temporais do IPP que podem ser consideradas normalmente distribuídas, foi maior quando este índice de seca foi calculado com base na PE3. Dessa forma, recomenda-se a adoção da PE3 no cálculo do IPP no Estado de São Paulo. Palavras-Chave: seca, distribuição gama, IPP

Using the normality assumption to calculate probability‐based standardized drought indices: selection criteria with emphases on typical events

“…This study evaluated the same two-parameter distributions considered by Stagge et al (2015) to calculate the SPI (gamma, Gumbel, logistic, log-logistic, lognormal, normal, and Weibull). Although studies such as Blain (2011Blain ( , 2012a recommend the Pearson type III distribution to calculate the SPI in the state of São Paulo, this three-parameter model introduces an additional difficult that was not considered by these two latter studies, i.e. the problem of truncating the distributions at zero (Stagge et al, 2015).…”

Drought Analysis Using the Standardized Precipitation Index (SPI)

“…The distribution most commonly used in calculating the SPI is the gamma distribution (McKee et al 1993;Hayes et al 1999;Guttman 1999;Hayes 2000;Lloyd-Hughes and Saunders 2002;Ceglar and Kajfež-Bogataj 2008). Guttman 1999, Vicente-Serrano andLopez-Moreno (2005) as well as Blain (2011) used Pearson III distribution in their analysis. Guttman (1999) compared the SPI values calculated with different distributions and found that the gamma and Pearson III distributions fitted data the best.…”

Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

“…According to BLAIN (2011BLAIN ( , 2012b, the rainfall monthly series of Ribeirão Preto can be considered as coming from a 2-parameter gamma distribution or a 3-parameter Pearson Type-III distribution (PE3). The cumulative probability [H(PRE)], associated with a given rainfall amount, is obtained from the following mixed distribution (equation 1) where m is the number of zeros observed in a dataset composed by N observations.…”

“…Based on distinct locations of the State of São Paulo, BLAIN (2011) has indicated that the SPI series obtained from the PE3 meets more frequently the normality assumption (intrinsic to the use of this standardized index) than the SPI series obtained from the gamma. Therefore, we estimated the SPI monthly values by using the PE3 distribution (GUTTMAN, 1999, SANTOS et al, 2010, BLAIN, 2011and BLAIN, 2012b.…”