Revisiting the probabilistic definition of drought: strengths, limitations and an agrometeorological adaptation

Abstract

Drought is a slow-moving hazard that occurs in virtually all countries of the world. In the light of this, several indices have been developed to improve the detection of drought's onset, as well as quantifying other features of this phenomenon. The Standardized Precipitation Index (SPI) is often used in order to characterize meteorological droughts. In addition, this index is largely used by Brazilian's agricultural institutions. In order to add important information to the drought literature, this review article described a general definition of drought, evaluated it from a statistical point of view, and also described the SPI strengths and limitations. An adaptation of the SPI that aims to develop a probability-based agricultural drought index was also presented. The results obtained herein, associated with several studies carried out throughout the world, demonstrated that the SPI is not an agricultural index. It is just a mathematical approach developed to transforming skewed distributions into the Gaussian form. If this standardization cannot be achieved, the use of this index becomes meaningless. Therefore, a normality test should be used in establishing a temporal lower limit for the SPI computations. It was also verified that for periods in which the probability associated with the zero precipitation value is close to 0.5, the SPI may erroneously indicate the end of an existing drought (or a decrease in its severity) in the presence of a decrease in the actual evapotranspiration values.Key words: standardized precipitation index, normality, evapotranspiration.Revisão da definição probabilística de seca: qualidades, limitações e adaptação agrometeorológica Resumo A seca é uma adversidade que se desenvolve lentamente ao longo do tempo, ocorrendo em praticamente todos os países do mundo. Consequentemente, diversos índices tem sido desenvolvidos para melhorar a detecção de seu início, bem como para quantificar demais características desse fenômeno. O Índice Padronizado de Precipitação (SPI) é frequentemente empregado na caracterização da seca meteorológica. Em adição, este índice é frequentemente utilizado por instituições agrícolas brasileiras. Objetivando adicionar relevantes informações à literatura relativa à referida adversidade, este trabalho descreveu uma definição geral de seca, avaliou a mesma sob o aspecto estatístico e ressaltou qualidades e limitações do SPI. Apresentou--se também uma adaptação desse modelo matemático que visa ao desenvolvimento de um índice probabilístico de seca agrícola. Os resultados, associados a diversos estudos desenvolvidos nas distintas regiões do Globo, demonstram que o SPI não é um índice de seca agrícola, sendo apenas uma abordagem matemática que visa transformar distribuições assimétricas para a forma Gaussiana. Uma vez que essa padronização não for atingida, o uso deste índice torna-se pouco consistente. Portanto, um teste de normalidade deve ser utilizado no estabelecimento de uma escala temporal mínima para seu cálculo. Verificou-se também que, em período...

Inadequacy of the gamma distribution to calculate the Standardized Precipitation Index

“…After evaluating the results depicted in Figure 1, it becomes worth emphasizing that the analysis of the SPI literature revels that virtually all studies use a single distribution (frequently the 2-parameter gamma) to calculate this drought index (Guttman, 1999;Wu et al, 2007;Lopez-Moreno & Vicente-Serrano, 2008;Blain 2012;Dutra et al, 2013; among many others). In other words, the use of the SPI has been based on the assumption that, for a given location, a single distribution is always capable of fitting the rainfall amounts summed over several timescales.…”

“…The normality tests have revealed that the median of the SPI values calculated from generalized normal distribution fall more often within the [-0.05:+0.05] interval than the median of the SPI values obtained from the other distributions. Naturally, this is an important feature for an index developed to represent floods and drought events in a similar probabilistic fashion (Wu et al, 2007;Blain, 2012).…”

“…It may be regarded as a slow-moving hazard that presents no single or universal definition (Hayes et al, 2011;Lloyde, 2014). However, it is well known that a prolonged and abnormally dry period can severely impact virtually all human and natural processes (Blain, 2012). Accordingly, a great number of drought indices have been proposed to monitor the drought conditions in several parts of the world.…”

“…available soil moisture or natural reservoirs; Dutra et al, 2013). Further information on the advantages and drawbacks of the SPI and its association with the different types of drought can be found in several studies including Fernandes et al (2010) and Blain (2012).…”

“…Thus, the parametric distribution used to calculate this probabilitybased index should also be capable of providing normally distributed SPI series. Further details on the importance of meeting the normality assumption of the SPI series may be found in Wu et al (2007), Blain (2012) and Stagge et al (2015).…”